The total number of published articles is 42 (download full list, 2019-04-02).

Some publications can be downloaded from this page. Please respect the publishers’ copyrights: Articles may be downloaded for personal use only. Any other use requires prior permission of the author and the publisher. Due to copyright restrictions I cannot provide all publications for download. If you are interested in a copy, please do not hesitate to contact me!

### 2019

- J. G. Brandenburg, A. Zen, D. Alfè, and A. Michaelides, “Interaction between water and carbon nanostructures: how good are current density functional approximations?,” arXiv:1907.09525, 2019.

[BibTeX] [Abstract] [Download PDF]

Few adsorption systems are of more current and future practical and technological interest than those involving water and carbon, specifically graphitic sp$^{2}$ bonded carbon is widely used in water filters and desalinisation membranes. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and non-covalent interactions in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed WaC18), which we separate into a single water molecule interacting with a broad range of carbon structures and the stability of various 3D- and 2D-ice polymorphs. The performance of several semi-local exchange-correlation functionals, non-local (Fock) exchange contributions, and long-range van der Waals (vdW) treatments are tested. We find that modern vdW corrections to DFT significantly improve over their precursors. While the spread in DFT performance is substantial, we achieve excellent agreement with the reference energies with mean unsigned errors ranging from 135 to 12\,meV. Within all functional classes, we can identify the best performing method: Of the functionals tested, the best performing ones are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, as generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, respectively.

`@Article{brandenburg_ref46, author ={J. G. Brandenburg and A. Zen and D. Alf\`{e} and A. Michaelides}, title ={Interaction between water and carbon nanostructures: How good are current density functional approximations?}, journal ={{arXiv:1907.09525}}, year ={2019}, volume = {}, pages ={}, url = {https://arxiv.org/abs/1907.09525}, abstract ={Few adsorption systems are of more current and future practical and technological interest than those involving water and carbon, specifically graphitic sp$^{2}$ bonded carbon is widely used in water filters and desalinisation membranes. However, these systems are notoriously challenging to model, even for electronic structure methods such as density functional theory (DFT), because of the crucial role played by London dispersion forces and non-covalent interactions in general. Recent efforts have established reference quality interactions of several carbon nanostructures interacting with water. Here, we compile a new benchmark set (dubbed WaC18), which we separate into a single water molecule interacting with a broad range of carbon structures and the stability of various 3D- and 2D-ice polymorphs. The performance of several semi-local exchange-correlation functionals, non-local (Fock) exchange contributions, and long-range van der Waals (vdW) treatments are tested. We find that modern vdW corrections to DFT significantly improve over their precursors. While the spread in DFT performance is substantial, we achieve excellent agreement with the reference energies with mean unsigned errors ranging from 135 to 12\,meV. Within all functional classes, we can identify the best performing method: Of the functionals tested, the best performing ones are BLYP-D4, TPSS-D4, rev-vdW-DF2, and PBE0-D4, as generalized gradient approximated (GGA), meta-GGA, vdW-DF, and hybrid DF, respectively. } }`

- L. \. Doná, J. G. Brandenburg, and B. Civalleri, “Extending and assessing composite electronic structure methods to the solid state,” submitted, 2019.

[BibTeX] [Abstract]

A hierarchy of simplified density functional theory (DFT) methods have been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree–Fock (HF-3c), a small basis set hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semi-classical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the {\sc Crystal} code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test band gaps, vibrational frequencies, elastic constants, and dielctric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error (MAE) for cohesive energies and unit cell volumes of molecular crystals of 1.5\,kcal/mol and 2.8\%, respectively. Lattice parameters of inorganic solids deviate by 3\% from the references and vibrational frequencies of $\alpha$-quartz have standard deviations of 10\,cm$^{-1}$. Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with substantial increase in computational efficiency.

`@Article{brandenburg_ref45, author ={L.\ Don\'{a} and J. G. Brandenburg and B. Civalleri}, title ={Extending and assessing composite electronic structure methods to the solid state}, journal ={{submitted}}, year ={2019}, volume = {}, pages ={}, abstract ={A hierarchy of simplified density functional theory (DFT) methods have been recently proposed for the fast electronic structure computation of large systems. The covered methods are a minimal basis set Hartree–Fock (HF-3c), a small basis set hybrid functional (PBEh-3c), and its screened exchange variant (HSE-3c), all augmented with semi-classical correction potentials. Here, we extend their applicability to inorganic covalent and ionic solids as well as layered materials. The new methods have been dubbed HFsol-3c, PBEsol0-3c and HSEsol-3c, respectively, to indicate their parent functional as well as the correction potentials. They have been implemented in the {\sc Crystal} code to enable routine application for molecular as well as solid materials. We validate the new methods on diverse sets of solid state benchmarks that cover more than 90 solids ranging from covalent, ionic, semi-ionic, layered, and molecular crystals. While we focus on structural and energetic properties, we also test band gaps, vibrational frequencies, elastic constants, and dielctric and piezoelectric tensors. HSEsol-3c appears to be most promising with mean absolute error (MAE) for cohesive energies and unit cell volumes of molecular crystals of 1.5\,kcal/mol and 2.8\%, respectively. Lattice parameters of inorganic solids deviate by 3\% from the references and vibrational frequencies of $\alpha$-quartz have standard deviations of 10\,cm$^{-1}$. Overall, this shows an accuracy competitive to converged basis set dispersion corrected DFT with substantial increase in computational efficiency.} }`

- A. Zen, J. G. Brandenburg, A. Michaelides, and D. Alfè, “A new scheme for fixed node diffusion quantum monte carlo with pseudopotentials: improving reproducibility and reducing the trial-wave function bias,” arXiv:1907.04432, 2019.

[BibTeX] [Abstract] [Download PDF]

Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotentials, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences – such as interaction and ionization energies – DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automization of FN-DMC and its much easier application in large systems.

`@Article{brandenburg_ref44, author ={A. Zen and J. G. Brandenburg and A. Michaelides and D. Alf\`{e}}, title ={A new scheme for fixed node diffusion quantum Monte Carlo with pseudopotentials: improving reproducibility and reducing the trial-wave function bias}, journal ={{arXiv:1907.04432}}, year ={2019}, volume = {}, pages ={}, url = {https://arxiv.org/abs/1907.04432}, abstract ={Fixed node diffusion quantum Monte Carlo (FN-DMC) is an increasingly used computational approach for investigating the electronic structure of molecules, solids, and surfaces with controllable accuracy. It stands out among equally accurate electronic structure approaches for its favorable cubic scaling with system size, which often makes FN-DMC the only computationally affordable high-quality method in large condensed phase systems with more than 100 atoms. In such systems FN-DMC deploys pseudopotentials to substantially improve efficiency. In order to deal with non-local terms of pseudopotentials, the FN-DMC algorithm must use an additional approximation, leading to the so-called localization error. However, the two available approximations, the locality approximation (LA) and the T-move approximation (TM), have certain disadvantages and can make DMC calculations difficult to reproduce. Here we introduce a third approach, called the determinant localization approximation (DLA). DLA eliminates reproducibility issues and systematically provides good quality results and stable simulations that are slightly more efficient than LA and TM. When calculating energy differences -- such as interaction and ionization energies -- DLA is also more accurate than the LA and TM approaches. We believe that DLA paves the way to the automization of FN-DMC and its much easier application in large systems.} }`

- R. J. Maurer, C. Freysoldt, A. M. Reilly, J. G. Brandenburg, O. T. Hofmann, T. Bjöorkman, S. Lebègue, and A. Tkatchenko, “Advances in density-functional calculations for materials modeling,” Annu. Rev. Mater. Res., vol. 49, p. 3.1-3.30, 2019. doi:10.1146/annurev-matsci-070218-010143

[BibTeX] [Abstract]

During the past two decades, density-functional (DF) theory has evolved from niche applications to simple solid-state materials, becoming a workhorse method for studying a wide range of phenomena in a variety of system classes throughout physics, chemistry, biology, and materials science. Here, we review the recent advances in DF calculations for materials modeling, giving a classification of modern DF-based methods when viewed from the materials modeling perspective. While the progress has been very substantial, many challenges remain on the way to achieve consensus on a set of universally applicable DF-based methods for materials modeling. Hence, we focus on recent successes and remaining challenges in DF calculations for modeling hard solids, molecular and biological matter, low-dimensional materials, and hybrid organic-inorganic materials.

`@Article{brandenburg_ref43, author ={R. J. Maurer and C. Freysoldt and A. M. Reilly and J. G. Brandenburg and O. T. Hofmann and T. Bj\"{o}orkman and S. Leb\`{e}gue and A. Tkatchenko}, title ={Advances in Density-Functional Calculations for Materials Modeling}, journal ={{Annu. Rev. Mater. Res.}}, year ={2019}, volume = {49}, pages ={3.1-3.30}, doi = {10.1146/annurev-matsci-070218-010143}, abstract ={During the past two decades, density-functional (DF) theory has evolved from niche applications to simple solid-state materials, becoming a workhorse method for studying a wide range of phenomena in a variety of system classes throughout physics, chemistry, biology, and materials science. Here, we review the recent advances in DF calculations for materials modeling, giving a classification of modern DF-based methods when viewed from the materials modeling perspective. While the progress has been very substantial, many challenges remain on the way to achieve consensus on a set of universally applicable DF-based methods for materials modeling. Hence, we focus on recent successes and remaining challenges in DF calculations for modeling hard solids, molecular and biological matter, low-dimensional materials, and hybrid organic-inorganic materials.} }`

- J. G. Brandenburg, A. Zen, M. Fitzner, B. Ramberger, G. Kresse, T. Tsatsoulis, A. Grüneis, A. Michaelides, and D. Alfè, “Physisorption of water on graphene: sub-chemical accuracy from many-body electronic structure methods,” J. Phys. Chem. Lett., vol. 10, pp. 358-368, 2019. doi:10.1021/acs.jpclett.8b03679

[BibTeX] [Abstract] [Download PDF]

Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world’s largest supercomputers. From this effort a consensus on the water–graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.

`@Article{brandenburg_ref42, author ={Jan Gerit Brandenburg and Andrea Zen and Martin Fitzner and Benjamin Ramberger and Georg Kresse and Theodoros Tsatsoulis and Andreas Gr\"{u}neis and Angelos Michaelides and Dario Alf\`{e}}, title ={Physisorption of water on graphene: Sub-chemical accuracy from many-body electronic structure methods}, journal ={{J. Phys. Chem. Lett.}}, year ={2019}, volume = {10}, pages ={358-368}, doi = {10.1021/acs.jpclett.8b03679}, url = {http://arxiv.org/abs/1811.07645}, abstract ={Wet carbon interfaces are ubiquitous in the natural world and exhibit anomalous properties, which could be exploited by emerging technologies. However, progress is limited by lack of understanding at the molecular level. Remarkably, even for the most fundamental system (a single water molecule interacting with graphene), there is no consensus on the nature of the interaction. We tackle this by performing an extensive set of complementary state-of-the-art computer simulations on some of the world’s largest supercomputers. From this effort a consensus on the water–graphene interaction strength has been obtained. Our results have significant impact for the physical understanding, as they indicate that the interaction is weaker than predicted previously. They also pave the way for more accurate and reliable studies of liquid water at carbon interfaces.} }`

### 2018

- C. Adjiman, J. G. Brandenburg, D. Braun, J. Cole, C. Collins, A. I. Cooper, A. Cruz-Cabeza, G. Day, M. Dudek, A. Hare, L. Iuzzolino, D. McKay, J. Mitchell, S. Mohamed, S. Neelamraju, M. Neumann, S. N. Lill, J. Nyman, A. R. Oganov, S. L. Price, A. Pulido, S. Reutzel-Edens, I. Rietveld, M. T. Ruggiero, C. Schoön, S. Tsuzuki, J. van~den~Ende, G. Woollam, and Q. Zhu, “Applications of crystal structure prediction – organic molecular structures: general discussion,” Faraday Discuss., vol. 211, pp. 493-539, 2018. doi:10.1039/C8FD90032A

[BibTeX] [Abstract]

The first page of this article is displayed as the abstract.

`@Article{brandenburg_ref41, author ={C. Adjiman and J. G. Brandenburg and D. Braun and J. Cole and C. Collins and A. I. Cooper and A. Cruz-Cabeza and G. Day and M. Dudek and A. Hare and L. Iuzzolino and D. McKay and J. Mitchell and S. Mohamed and S. Neelamraju and M. Neumann and S. N. Lill and J. Nyman and A. R. Oganov and S. L. Price and A. Pulido and S. Reutzel-Edens and I. Rietveld and M. T. Ruggiero and C. Scho\"{o}n and S. Tsuzuki and J. van~den~Ende and G. Woollam and Qiang Zhu}, title ={Applications of crystal structure prediction - organic molecular structures: general discussion}, journal ={{Faraday Discuss.}}, year ={2018}, volume = {211}, pages ={493-539}, doi = {10.1039/C8FD90032A}, abstract ={The first page of this article is displayed as the abstract.} }`

- M. Addicoat, C. Adjiman, M. Arhangelskis, G. Beran, D. Bowskill, J. G. Brandenburg, D. Braun, V. Burger, J. Cole, A. Cruz-Cabeza, G. Day, V. Deringer, R. Guo, A. Hare, J. Helfferich, J. Hoja, L. Iuzzolino, S. Jobbins, N. Marom, D. McKay, J. Mitchell, S. Mohamed, M. Neumann, S. N. Lill, J. Nyman, A. R. Oganov, P. Piaggi, S. L. Price, S. Reutzel-Edens, I. Rietveld, M. Ruggiero, M. Ryder, G. Sastre, C. Schoön, C. Taylor, A. Tkatchenko, S. Tsuzuki, J. van~den~Ende, S. Woodley, G. Woollam, and Q. Zhu, “Crystal structure evaluation: calculating relative stabilities and other criteria: general discussion,” Faraday Discuss., vol. 211, pp. 325-381, 2018. doi:10.1039/C8FD90031K

[BibTeX] [Abstract]

The first page of this article is displayed as the abstract.

`@Article{brandenburg_ref40, author ={M. Addicoat and C. Adjiman and M. Arhangelskis and G. Beran and D. Bowskill and J. G. Brandenburg and D. Braun and V. Burger and J. Cole and A. Cruz-Cabeza and G. Day and V. Deringer and R. Guo and A. Hare and J. Helfferich and J. Hoja and L. Iuzzolino and S. Jobbins and N. Marom and D. McKay and J. Mitchell and S. Mohamed and M. Neumann and S. N. Lill and J. Nyman and A. R. Oganov and P. Piaggi and S. L. Price and S. Reutzel-Edens and I. Rietveld and M. Ruggiero and M. Ryder and G. Sastre and C. Scho\"{o}n and C. Taylor and A. Tkatchenko and S. Tsuzuki and J. van~den~Ende and S. Woodley and G. Woollam and Qiang Zhu}, title ={Crystal structure evaluation: calculating relative stabilities and other criteria: general discussion}, journal ={{Faraday Discuss.}}, year ={2018}, volume = {211}, pages ={325-381 }, doi = {10.1039/C8FD90031K}, abstract ={The first page of this article is displayed as the abstract.} }`

- M. Addicoat, C. Adjiman, M. Arhangelskis, G. Beran, J. G. Brandenburg, D. Braun, V. Burger, A. Burow, C. Collins, A. Cooper, G. Day, V. Deringer, M. S. Dyer, A. Hare, K. Jelfs, J. Keupp, S. Konstantinopoulos, Y. Li, Y. Ma, N. Marom, D. McKay, C. Mellot-Draznieks, S. Mohamed, M. Neumann, S. N. Lill, J. Nyman, A. R. Oganov, S. L. Price, S. Reutzel-Edens, M. Ruggiero, G. Sastre, R. Schmid, J. Schmidt, C. Schoön, P. Spackman, S. Tsuzuki, S. Woodley, S. Yang, and Q. Zhu, “Structure searching methods: general discussion,” Faraday Discuss., vol. 211, pp. 133-180, 2018. doi:10.1039/C8FD90030B

[BibTeX] [Abstract]

The first page of this article is displayed as the abstract.

`@Article{brandenburg_ref39, author ={M. Addicoat and C. Adjiman and M. Arhangelskis and G. Beran and J. G. Brandenburg and D. Braun and V. Burger and A. Burow and C. Collins and A. Cooper and G. Day and V. Deringer and M. S. Dyer and A. Hare and K. Jelfs and J. Keupp and S. Konstantinopoulos and Y. Li and Y. Ma and N. Marom and D. McKay and C. Mellot-Draznieks and S. Mohamed and M. Neumann and S. N. Lill and J. Nyman and A. R. Oganov and S. L. Price and S. Reutzel-Edens and M. Ruggiero and G. Sastre and R. Schmid and J. Schmidt and C. Scho\"{o}n and P. Spackman and S. Tsuzuki and S. Woodley and S. Yang and Qiang Zhu}, title ={Structure searching methods: general discussion}, journal ={{Faraday Discuss.}}, year ={2018}, volume = {211}, pages ={133-180}, doi = {10.1039/C8FD90030B}, abstract ={The first page of this article is displayed as the abstract.} }`

- G. Sansone, A. J. Karttunen, D. Usvyat, M. Schutz, J. G. Brandenburg, and L. Maschio, “On the exfoliation and anisotropic thermal expansion of black phosphorus,” Chem. commun., vol. 54, pp. 9793-9796, 2018. doi:10.1039/C8CC04855J

[BibTeX] [Abstract]

Black Phosphorus is a bulk solid allotrope of elemental phosphorus{,} that can be seen as an infinite stacking of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [\emph{J. Phys. Chem. Lett.} {\bf 8}{,} 1290 (2017)] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppress London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional{,} we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations{,} however{,} do not support existence of negative thermal expansion in black Phosphorus{,} reported in some theoretical studies.

`@Article{brandenburg_ref38, author ={G. Sansone and A. J. Karttunen and D. Usvyat and M. Schutz and J. G. Brandenburg and L. Maschio}, title ={On the Exfoliation and Anisotropic Thermal Expansion of Black Phosphorus}, journal ={Chem. Commun.}, year ={2018}, volume = {54}, pages ={9793-9796}, doi = {10.1039/C8CC04855J}, abstract ={Black Phosphorus is a bulk solid allotrope of elemental phosphorus{,} that can be seen as an infinite stacking of phosphorene sheets. It is interesting from a technological point of view as well as from an electronic structure perspective due to the importance of electron correlation effects. In a recent paper [\emph{J. Phys. Chem. Lett.} {\bf 8}{,} 1290 (2017)] a highly accurate exfoliation energy has been computed. Building upon these results we carefully benchmark various dispersion-corrected density functional approximations. The choice of the range-separating function that suppress London dispersion at short interatomic distances apparently has a substantial influence on the results. Having chosen the suitable functional{,} we have computed the thermal expansion coefficients of black phosphorous via a quasi-harmonic approximation. The computed coefficients manifest a strong anisotropy between the two in-plane directions. Our calculations{,} however{,} do not support existence of negative thermal expansion in black Phosphorus{,} reported in some theoretical studies.} }`

- L. Wang, G. Kehr, C. G. Daniliuc, M. Brinkkötter, T. Wiegand, A. -L. Wübker, H. Eckert, L. Liu, J. G. Brandenburg, S. Grimme, and G. Erker, “Solid state frustrated lewis pair chemistry,” Chem. Sci., vol. 9, pp. 4859-4865, 2018. doi:10.1039/c8sc01089g

[BibTeX] [Abstract] [Download PDF]

In solution the PCy$_3$/B(C$_6$F$_5$)$_3$ pair is rapidly deactivated by nucleophilic aromatic substitution. In the solid state deactivation is effectively suppressed and the active frustrated phosphane/borane Lewis pair splits dihydrogen or adds to sulfur dioxide. A variety of phosphane/B(C$_6$F$_5$)$_3$ pairs have been used to carry out active FLP reactions in the solid state. The reactions were analyzed by DFT calculations and by solid state NMR spectroscopy. The solid state dihydrogen splitting reaction was also carried out under near to ambient conditions with suspensions of the non-quenched phosphane/borane mixtures in the fluorous liquid perfluoromethylcyclohexane.

`@Article{brandenburg_ref37, author ={L. Wang and G. Kehr and C. G. Daniliuc and M. Brinkk\"otter and T. Wiegand and A.-L. W\"ubker and H. Eckert and L. Liu and J. G. Brandenburg and S. Grimme and G. Erker}, title ={Solid state frustrated Lewis pair chemistry}, journal ={{Chem. Sci.}}, year ={2018}, volume = {9}, pages = {4859-4865}, year = {2018}, url = {../wp-content/papercite-data/pdf/brandenburg_ref37.pdf}, doi ={10.1039/c8sc01089g}, abstract ={In solution the PCy$_3$/B(C$_6$F$_5$)$_3$ pair is rapidly deactivated by nucleophilic aromatic substitution. In the solid state deactivation is effectively suppressed and the active frustrated phosphane/borane Lewis pair splits dihydrogen or adds to sulfur dioxide. A variety of phosphane/B(C$_6$F$_5$)$_3$ pairs have been used to carry out active FLP reactions in the solid state. The reactions were analyzed by DFT calculations and by solid state NMR spectroscopy. The solid state dihydrogen splitting reaction was also carried out under near to ambient conditions with suspensions of the non-quenched phosphane/borane mixtures in the fluorous liquid perfluoromethylcyclohexane.} }`

- E. Caldeweyher and J. G. Brandenburg, “Simplified dft methods for consistent structures and energies of large systems,” J. Phys.: Condens. Matter, vol. 30, p. 213001, 2018. doi:10.1088/1361-648X/aabcfb

[BibTeX] [Abstract]

Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.

`@Article{brandenburg_ref36, author ={E. Caldeweyher and J. G. Brandenburg}, title ={Simplified DFT methods for consistent structures and energies of large systems}, journal ={{J. Phys.: Condens. Matter}}, year ={2018}, volume = {30}, pages = {213001}, doi ={10.1088/1361-648X/aabcfb}, abstract ={Kohn-Sham density functional theory (DFT) is routinely used for the fast electronic structure computation of large systems and will most likely continue to be the method of choice for the generation of reliable geometries in the foreseeable future. Here, we present a hierarchy of simplified DFT methods designed for consistent structures and non-covalent interactions of large systems with particular focus on molecular crystals. The covered methods are a minimal basis set Hartree-Fock (HF-3c), a small basis set screened exchange hybrid functional (HSE-3c), and a generalized gradient approximated functional evaluated in a medium sized basis set (B97-3c), all augmented with semi-classical correction potentials. We give an overview on the methods design, a comprehensive evaluation on established benchmark sets for geometries and lattice energies of molecular crystals, and highlight some realistic applications on large organic crystals with several hundreds of atoms in the primitive unit cell.} }`

- L. Iuzzolino, P. McCabe, S. L. Price, and J. G. Brandenburg, “Crystal structure prediction of flexible pharmaceutical-like molecules: density functional tight-binding as an intermediate optimization method and for free energy estimation,” Faraday Discuss., vol. 211, p. 275–296, 2018. doi:10.1039/C8FD00010G

[BibTeX] [Abstract] [Download PDF]

Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stage of CSP studies uses a relatively simple lattice energy approximation as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries{,} as well as inaccurate lattice-energy rankings{,} and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here{,} we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all inter and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules{,} saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods{,} suggesting it could be extended to even larger and more flexible molecules. On average{,} this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15 ) and experimental conformers (RMSD1) by 4% and 23%{,} respectively. The intermolecular interactions were then further optimised using distributed multipoles{,} derived from the molecular wave-function{,} to accurately describe the electrostatic component of the intermolecular energy. In all cases{,} the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy{,} providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules{,} bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.

`@Article{brandenburg_ref35, author ={L. Iuzzolino and P. McCabe and S. L. Price and J. G. Brandenburg}, title ={Crystal structure prediction of flexible pharmaceutical-like molecules: Density functional tight-binding as an intermediate optimization method and for free energy estimation}, journal ={{Faraday Discuss.}}, year ={2018}, volume = {211}, pages = {275--296}, url = {../wp-content/papercite-data/pdf/brandenburg_ref35.pdf}, doi ={10.1039/C8FD00010G}, abstract ={Successful methodologies for theoretical crystal structure prediction (CSP) on flexible pharmaceutical-like organic molecules explore the lattice energy surface to find a set of plausible crystal structures. The initial search stage of CSP studies uses a relatively simple lattice energy approximation as hundreds of thousands of minima have to be considered. These generated crystal structures often have poor molecular geometries{,} as well as inaccurate lattice-energy rankings{,} and performing reasonably accurate but computationally affordable optimisations of the crystal structures generated in a search would be highly desirable. Here{,} we seek to explore whether semi-empirical quantum-mechanical methods can perform this task. We employed the dispersion-corrected tight-binding Hamiltonian (DFTB3-D3) to relax all inter and intra-molecular degrees of freedom of several thousands of generated crystal structures of five pharmaceutical-like molecules{,} saving a large amount of computational effort compared to earlier studies. The computational cost scales better with molecular size and flexibility than other CSP methods{,} suggesting it could be extended to even larger and more flexible molecules. On average{,} this optimisation improved the average reproduction of the eight experimental crystal structures (RMSD15 ) and experimental conformers (RMSD1) by 4% and 23%{,} respectively. The intermolecular interactions were then further optimised using distributed multipoles{,} derived from the molecular wave-function{,} to accurately describe the electrostatic component of the intermolecular energy. In all cases{,} the experimental crystal structures are close to the top of the lattice energy ranking. Phonon calculations on some of the lowest energy structures were also performed with DFTB3-D3 methods to calculate the vibrational component of the Helmholtz free energy{,} providing further insights into the solid-state behaviour of the target molecules. We conclude that DFTB3-D3 is a cost-effective method for optimising flexible molecules{,} bridging the gap between the approximate methods used in CSP searches for generating crystal structures and more accurate methods required in the final energy ranking.} }`

- J. G. Brandenburg, C. Bannwarth, A. Hansen, and S. Grimme, “B97-3c: a revised low-cost variant of the b97-d density functional method,” J. Chem. Phys., vol. 148, p. 64104, 2018. doi:10.1063/1.5012601

[BibTeX] [Abstract] [Download PDF]

A revised version of the well-established B97-D density functional approximation with general applicability for chemical properties of large systems is proposed. Like B97-D, it is based on Becke’s power-series ansatz from 1997 and is explicitly parametrized by including the standard D3 semi-classical dispersion correction. The orbitals are expanded in a modified valence triple-zeta Gaussian basis set, which is available for all elements up to Rn. Remaining basis set errors are mostly absorbed in the modified B97 parametrization, while an established atom-pairwise short-range potential is applied to correct for the systematically too long bonds of main group elements which are typical for most semi-local density functionals. The new composite scheme (termed B97-3c) completes the hierarchy of “low-cost” electronic structure methods, which are all mainly free of basis set superposition error (BSSE) and account for most interactions in a physically sound and asymptotically correct manner. B97-3c yields excellent molecular and condensed phase geometries, similar to most hybrid functionals evaluated in a larger basis set expansion. Results on the comprehensive GMTKN55 energy database demonstrate its good performance for main group thermochemistry, kinetics, and non-covalent interactions, when compared to functionals of the same class. This also transfers to metal-organic reactions, which is a major area of applicability for semi-local functionals. B97-3c can be routinely applied to hundreds of atoms on a single processor and we suggest it as a robust computational tool, in particular, for more strongly correlated systems where our previously published “3c” schemes might be problematic.

`@article{brandenburg_ref34, author = {J. G. Brandenburg and C. Bannwarth and A. Hansen and S. Grimme}, title = {B97-3c: A revised low-cost variant of the B97-D density functional method}, journal = {{J. Chem. Phys.}}, volume = {148}, pages = {064104}, year = {2018}, doi = {10.1063/1.5012601}, url = {../wp-content/papercite-data/pdf/brandenburg_ref34.pdf}, abstract={A revised version of the well-established B97-D density functional approximation with general applicability for chemical properties of large systems is proposed. Like B97-D, it is based on Becke's power-series ansatz from 1997 and is explicitly parametrized by including the standard D3 semi-classical dispersion correction. The orbitals are expanded in a modified valence triple-zeta Gaussian basis set, which is available for all elements up to Rn. Remaining basis set errors are mostly absorbed in the modified B97 parametrization, while an established atom-pairwise short-range potential is applied to correct for the systematically too long bonds of main group elements which are typical for most semi-local density functionals. The new composite scheme (termed B97-3c) completes the hierarchy of "low-cost" electronic structure methods, which are all mainly free of basis set superposition error (BSSE) and account for most interactions in a physically sound and asymptotically correct manner. B97-3c yields excellent molecular and condensed phase geometries, similar to most hybrid functionals evaluated in a larger basis set expansion. Results on the comprehensive GMTKN55 energy database demonstrate its good performance for main group thermochemistry, kinetics, and non-covalent interactions, when compared to functionals of the same class. This also transfers to metal-organic reactions, which is a major area of applicability for semi-local functionals. B97-3c can be routinely applied to hundreds of atoms on a single processor and we suggest it as a robust computational tool, in particular, for more strongly correlated systems where our previously published "3c" schemes might be problematic. } }`

- M. Mortazavi, J. G. Brandenburg, R. J. Maurer, and A. Tkatchenko, “Structure and stability of molecular crystals with many body dispersion inclusive density functional tight binding,” J. Phys. Chem. Lett., vol. 9, pp. 399-405, 2018. doi:10.1021/acs.jpclett.7b03234

[BibTeX] [Abstract]

Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko−Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction.

`@article{brandenburg_ref33, author = {M. Mortazavi and J. G. Brandenburg and R. J. Maurer and A. Tkatchenko}, title = {Structure and stability of molecular crystals with many body dispersion inclusive density functional tight binding}, journal = {{J. Phys. Chem. Lett.}}, volume = {9}, pages = {399-405}, year = {2018}, doi = {10.1021/acs.jpclett.7b03234}, abstract={Accurate prediction of structure and stability of molecular crystals is crucial in materials science and requires reliable modeling of long-range dispersion interactions. Semiempirical electronic structure methods are computationally more efficient than their ab initio counterparts, allowing structure sampling with significant speedups. We combine the Tkatchenko−Scheffler van der Waals method (TS) and the many-body dispersion method (MBD) with third-order density functional tight-binding (DFTB3) via a charge population-based method. We find an overall good performance for the X23 benchmark database of molecular crystals, despite an underestimation of crystal volume that can be traced to the DFTB parametrization. We achieve accurate lattice energy predictions with DFT+MBD energetics on top of vdW-inclusive DFTB3 structures, resulting in a speedup of up to 3000 times compared with a full DFT treatment. This suggests that vdW-inclusive DFTB3 can serve as a viable structural prescreening tool in crystal structure prediction. } }`

- A. Zen, J. G. Brandenburg, J. Klimeš, A. Tkatchenko, D. Alfè, and A. Michaelides, “Fast and accurate quantum monte-carlo for molecular crystals,” Proc. Natl. Acad. Sci. U.S.A., vol. 115, pp. 1724-1729, 2018. doi:10.1073/pnas.1715434115

[BibTeX] [Abstract] [Download PDF]

Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated \emph{ab initio} electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers sub-chemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high accuracy methods.

`@article{brandenburg_ref32, author = {A. Zen and J. G. Brandenburg and J. Klime\v{s} and A. Tkatchenko and D. Alf\`e and A. Michaelides}, title = {Fast and accurate quantum Monte-Carlo for molecular crystals}, journal = {{Proc. Natl. Acad. Sci. U.S.A.}}, volume = {115}, pages = {1724-1729}, year = {2018}, doi = {10.1073/pnas.1715434115}, url = {../wp-content/papercite-data/pdf/brandenburg_ref32.pdf}, abstract={Computer simulation plays a central role in modern day materials science. The utility of a given computational approach depends largely on the balance it provides between accuracy and computational cost. Molecular crystals are a class of materials of great technological importance which are challenging for even the most sophisticated \emph{ab initio} electronic structure theories to accurately describe. This is partly because they are held together by a balance of weak intermolecular forces but also because the primitive cells of molecular crystals are often substantially larger than those of atomic solids. Here, we demonstrate that diffusion quantum Monte Carlo (DMC) delivers sub-chemical accuracy for a diverse set of molecular crystals at a surprisingly moderate computational cost. As such, we anticipate that DMC can play an important role in understanding and predicting the properties of a large number of molecular crystals, including those built from relatively large molecules which are far beyond reach of other high accuracy methods.} }`

### 2017

- T. Jensen, J. Potticary, L. R. Terry, H. Bruce-Macdonald, J. G. Brandenburg, and S. R. Hall, “Polymorphism in crystals of bis(4-bromophenyl)fumaronitrile through vapour phase growth,” CrystEngComm, vol. 17, pp. 7223-7228, 2017. doi:10.1039/c7ce01543g

[BibTeX] [Abstract]

Polymorphic selectivity within crystals grown via physical vapour transport (PVT) is dependent on the ther modynamic stabilities of differing molecular conformations and the kinetic regime within the growth apparatus. Crystals of bisIJ4-bromophenyl)fumaronitrile have been grown for the first time via this method, with the formation of both the conventional polymorph and a new, unforseen polymorph. Analysis suggests that the conventional form is less thermodynamically stable, with this form crystallising at higher temperature than the newly discovered form due to the release of binding energy of intermolecular interactions during the growth process. Fluorometry reveals the new form to exhibit weaker, red-shifted fluorescence emission owing to greater intermolecular {$\pi$}-{$\pi$} overlap.

`@article{brandenburg_ref31, author = {T. Jensen and J. Potticary and L. R. Terry and H. Bruce-Macdonald and J. G. Brandenburg and S. R. Hall}, title = {Polymorphism in crystals of bis(4-bromophenyl)fumaronitrile through vapour phase growth}, journal = {{CrystEngComm}}, volume = {17}, pages = {7223-7228}, year = {2017}, doi = {10.1039/c7ce01543g}, abstract={Polymorphic selectivity within crystals grown via physical vapour transport (PVT) is dependent on the ther modynamic stabilities of differing molecular conformations and the kinetic regime within the growth apparatus. Crystals of bisIJ4-bromophenyl)fumaronitrile have been grown for the first time via this method, with the formation of both the conventional polymorph and a new, unforseen polymorph. Analysis suggests that the conventional form is less thermodynamically stable, with this form crystallising at higher temperature than the newly discovered form due to the release of binding energy of intermolecular interactions during the growth process. Fluorometry reveals the new form to exhibit weaker, red-shifted fluorescence emission owing to greater intermolecular {$\pi$}-{$\pi$} overlap.} }`

- J. G. Brandenburg, J. Potticary, H. A. Sparkes, S. L. Price, and S. R. Hall, “Thermal expansion of carbamazepine: systematic crystallographic measurements challenge quantum chemical calculations,” J. Phys. Chem. Lett., vol. 8, pp. 4319-4324, 2017. doi:10.1021/acs.jpclett.7b01944

[BibTeX] [Abstract] [Download PDF]

We report systematic temperature-dependent X-ray measurements on the most stable carbamazepine polymorph. This active pharmaceutical ingredient is used to demonstrate how the thermal expansion can probe certain intermolecular interactions resulting in anisotropic expansion behavior. We show that most structural features can be captured by electronic structure calculations at the quasi-harmonic approximation (QHA) provided a dispersion-corrected density functional based method is employed. The impact of thermal expansion on the phonon modes and hence free energy contributions is large enough to impact the relative stability of different polymorphs.

`@article{brandenburg_ref30, author = {J. G. Brandenburg and J. Potticary and H. A. Sparkes and S. L. Price and S. R. Hall}, title = {Thermal expansion of carbamazepine: Systematic crystallographic measurements challenge quantum chemical calculations}, journal = {{J. Phys. Chem. Lett.}}, volume = {8}, pages = {4319-4324}, year = {2017}, doi = {10.1021/acs.jpclett.7b01944}, url = {../wp-content/papercite-data/pdf/brandenburg_ref30.pdf}, abstract={We report systematic temperature-dependent X-ray measurements on the most stable carbamazepine polymorph. This active pharmaceutical ingredient is used to demonstrate how the thermal expansion can probe certain intermolecular interactions resulting in anisotropic expansion behavior. We show that most structural features can be captured by electronic structure calculations at the quasi-harmonic approximation (QHA) provided a dispersion-corrected density functional based method is employed. The impact of thermal expansion on the phonon modes and hence free energy contributions is large enough to impact the relative stability of different polymorphs.} }`

- Y. S. Al-Hamdani, M. Rossi, D. Alfè, T. Tsatsoulis, B. Ramberger, J. G. Brandenburg, A. Zen, G. Kresse, A. Grüneis, A. Tkatchenko, and A. Michaelides, “Properties of the water to boron nitride interaction: from zero to two dimensions with benchmark accuracy,” J. chem. phys., vol. 147, p. 44710, 2017. doi:10.1063/1.4985878

[BibTeX] [Abstract] [Download PDF]

Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation (RPA), and second order M{\o}ller-Plesset (MP2) theory. These explicitly correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is −107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DlFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.

`@article{brandenburg_ref29, title = {Properties of the water to boron nitride interaction: From zero to two dimensions with benchmark accuracy}, journal = {J. Chem. Phys.}, volume = {147}, pages = {044710}, year = {2017}, doi = {10.1063/1.4985878}, url = {../wp-content/papercite-data/pdf/brandenburg_ref29.pdf}, author = {Y. S. Al-Hamdani and M. Rossi and D. Alf\`e and T. Tsatsoulis and B. Ramberger and J. G. Brandenburg and A. Zen and G. Kresse and A. Gr\"uneis and A Tkatchenko and A. Michaelides}, abstract={Molecular adsorption on surfaces plays an important part in catalysis, corrosion, desalination, and various other processes that are relevant to industry and in nature. As a complement to experiments, accurate adsorption energies can be obtained using various sophisticated electronic structure methods that can now be applied to periodic systems. The adsorption energy of water on boron nitride substrates, going from zero to 2-dimensional periodicity, is particularly interesting as it calls for an accurate treatment of polarizable electrostatics and dispersion interactions, as well as posing a practical challenge to experiments and electronic structure methods. Here, we present reference adsorption energies, static polarizabilities, and dynamic polarizabilities, for water on BN substrates of varying size and dimension. Adsorption energies are computed with coupled cluster theory, fixed-node quantum Monte Carlo (FNQMC), the random phase approximation (RPA), and second order M{\o}ller-Plesset (MP2) theory. These explicitly correlated methods are found to agree in molecular as well as periodic systems. The best estimate of the water/h-BN adsorption energy is −107±7 meV from FNQMC. In addition, the water adsorption energy on the BN substrates could be expected to grow monotonically with the size of the substrate due to increased dispersion interactions but interestingly, this is not the case here. This peculiar finding is explained using the static polarizabilities and molecular dispersion coefficients of the systems, as computed from time-dependent density functional theory (DlFT). Dynamic as well as static polarizabilities are found to be highly anisotropic in these systems. In addition, the many-body dispersion method in DFT emerges as a particularly useful estimation of finite size effects for other expensive, many-body wavefunction based methods.} }`

- S. L. Price and J. G. Brandenburg, Molecular crystal structure prediction, Melbourne, Australia: Elsevier, 2017, vol. Non-covalent interactions in quantum chemistry and physics, Eds. G. DiLabio, A. Otero-de-la-Roza, ISBN: 9780128098356.

[BibTeX] [Abstract] [Download PDF]

Organic crystal structure prediction methods (CSP) aim to predict the crystal structure from the molecular diagram, for use in the design of new functional organic materials. CSP can help avoid the synthesis of molecules which will not give crystals with the desired physical property. However, CSP is mostly applied to determine the risk of polymorphism for molecules, such as pharmaceuticals, to aid the design of the crystallization processes used in their manufacture. CSP can complement experimental solid form screening in helping find and characterize the polymorphs of a given molecule. Most CSP methods are based on the assumption that the observed crystal structures are the most stable, or that they lie within the small energy range for thermodynamically plausible polymorphs. Thus, the generation of possible crystal structures and their energy ranking is required during the prediction. This usually provides a severe test of the model for the relative thermal stability of the computer-generated crystals. Thus, CSP has been used as a test of models for the intermolecular forces between small molecules whose solid state properties are mostly of academic significance. Interest in the organic solid state has grown, with both an increasing desire to use computers to design materials and crystallization processes, and improved experimental characterization techniques providing evidence for the inadequacies of the idealized models currently used in simulaton. Hence, there is a significant complementarity between theory and experiment that stems from finding what range of types of crystal packing and properties may be engineered.

`@book{brandenburg_ref28, title = {Molecular crystal structure prediction}, publisher = {Elsevier}, address = {Melbourne, Australia}, volume = {Non-covalent interactions in quantum chemistry and physics, Eds. G. DiLabio, A. Otero-de-la-Roza, ISBN: 9780128098356}, year = {2017}, url = {https://www.elsevier.com/books/non-covalent-interactions-in-quantum-chemistry-and-physics/otero-de-la-roza/978-0-12-809835-6}, note = {ISBN: 9780128098356}, author = {S. L. Price and J. G. Brandenburg}, abstract={Organic crystal structure prediction methods (CSP) aim to predict the crystal structure from the molecular diagram, for use in the design of new functional organic materials. CSP can help avoid the synthesis of molecules which will not give crystals with the desired physical property. However, CSP is mostly applied to determine the risk of polymorphism for molecules, such as pharmaceuticals, to aid the design of the crystallization processes used in their manufacture. CSP can complement experimental solid form screening in helping find and characterize the polymorphs of a given molecule. Most CSP methods are based on the assumption that the observed crystal structures are the most stable, or that they lie within the small energy range for thermodynamically plausible polymorphs. Thus, the generation of possible crystal structures and their energy ranking is required during the prediction. This usually provides a severe test of the model for the relative thermal stability of the computer-generated crystals. Thus, CSP has been used as a test of models for the intermolecular forces between small molecules whose solid state properties are mostly of academic significance. Interest in the organic solid state has grown, with both an increasing desire to use computers to design materials and crystallization processes, and improved experimental characterization techniques providing evidence for the inadequacies of the idealized models currently used in simulaton. Hence, there is a significant complementarity between theory and experiment that stems from finding what range of types of crystal packing and properties may be engineered.} }`

- H. Buchholz, R. K. Hylton, J. G. Brandenburg, A. Seidel-Morgenstern, H. Lorenz, M. Stein, R. Hylton, and S. L. Price, “The thermochemistry of racemic and enantiopure molecular crystals for predicting enantiomer separation,” Cryst. growth. des., vol. 8, pp. 4319-4324, 2017. doi:10.1021/acs.cgd.7b00582

[BibTeX] [Abstract] [Download PDF]

The separation of an enantiomer from a racemic mixture is of primary relevance to the pharmaceutical industry. The thermochemical properties of organic enantiopure and racemate crystals can be exploited to design an enantioselective crystallization process. The thermodynamic difference between the two crystal forms is accessible by two cycles which give the eutectic composition in solution. The ‘sublimation cycle’ requires calculating the lattice energy and phonon frequencies of the crystal structures. Experimental results from heat capacity and other thermodynamic measurements of enantiopure and racemic crystals are compared with a variety of molecular and crystal structure-based calculations. This is done for three prototypes of pharmaceutical-like molecules with different degrees of molecular flexibility. Differences in crystal packing result in varying temperature-dependent heat capacities and affect the sublimation thermodynamics, relative solubility and eutectic composition. Many simplifying assumptions about the thermodynamics and solubilities of the racemic and enantiopure crystals are critically evaluated. We show that calculations and experimental information using the sublimation cycle can guide the design of processes to resolve enantiomers by crystallization.

`@article{brandenburg_ref27, title = {The thermochemistry of racemic and enantiopure molecular crystals for predicting enantiomer separation}, journal = {Cryst. Growth. Des.}, volume = {8}, pages = {4319-4324}, year = {2017}, doi = {10.1021/acs.cgd.7b00582}, url = {../wp-content/papercite-data/pdf/brandenburg_ref27.pdf}, author = {H. Buchholz and R. K. Hylton and J. G. Brandenburg and A. Seidel-Morgenstern and H. Lorenz and M. Stein and R. Hylton and S. L. Price,}, abstract={The separation of an enantiomer from a racemic mixture is of primary relevance to the pharmaceutical industry. The thermochemical properties of organic enantiopure and racemate crystals can be exploited to design an enantioselective crystallization process. The thermodynamic difference between the two crystal forms is accessible by two cycles which give the eutectic composition in solution. The 'sublimation cycle' requires calculating the lattice energy and phonon frequencies of the crystal structures. Experimental results from heat capacity and other thermodynamic measurements of enantiopure and racemic crystals are compared with a variety of molecular and crystal structure-based calculations. This is done for three prototypes of pharmaceutical-like molecules with different degrees of molecular flexibility. Differences in crystal packing result in varying temperature-dependent heat capacities and affect the sublimation thermodynamics, relative solubility and eutectic composition. Many simplifying assumptions about the thermodynamics and solubilities of the racemic and enantiopure crystals are critically evaluated. We show that calculations and experimental information using the sublimation cycle can guide the design of processes to resolve enantiomers by crystallization.} }`

- L. Liu, J. G. Brandenburg, and S. Grimme, “On the hydrogen activation by frustrated lewis pairs in solid state: benchmark studies and theoretical insights,” Phil. trans. a., vol. 375, p. 20170006, 2017. doi:10.1098/rsta.2017.0006

[BibTeX] [Abstract]

Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs which have been experimentally investigated and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-GGA TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce reaction electronic energies. Computed Gibbs free energies for dihydrogen activation are around zero or strongly exergonic for experimentally reactive FLP while they are largely positive for inactive ones indicating the predictive quality of our theoretical treatment. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid state FLPs.

`@article{brandenburg_ref26, title = {On the hydrogen activation by frustrated Lewis pairs in solid state: Benchmark studies and theoretical insights}, journal = {Phil. Trans. A.}, volume = {375}, pages = {20170006}, year = {2017}, doi = {10.1098/rsta.2017.0006}, author = {L. Liu and J. G. Brandenburg and S. Grimme}, abstract={Recently, the concept of small molecule activation by frustrated Lewis pairs (FLPs) has been expanded to the solid state showing a variety of interesting reactivities. Therefore, there is a need to establish a computational protocol to investigate such systems theoretically. In the present study, we selected several FLPs which have been experimentally investigated and applied multiple levels of theory, ranging from a semi-empirical tight-binding Hamiltonian to dispersion corrected hybrid density functionals. Their performance is benchmarked for the computation of crystal geometries, thermostatistical contributions, and reaction energies. We show that the computationally efficient HF-3c method gives accurate crystal structures and is numerically stable and sufficiently fast for routine applications. This method also gives reliable values for the thermostatistical contributions to Gibbs free energies. The meta-GGA TPSS-D3 evaluated in a projector augmented plane wave basis set is able to produce reaction electronic energies. Computed Gibbs free energies for dihydrogen activation are around zero or strongly exergonic for experimentally reactive FLP while they are largely positive for inactive ones indicating the predictive quality of our theoretical treatment. The established protocol is intended to support experimental studies and to predict new reactions in the emerging field of solid state FLPs.} }`

- S. A. Katsyuba, M. V. Vener, E. E. Zvereva, and J. G. Brandenburg, “The role of london dispersion interactions in strong and moderate intermolecular hydrogen bonds in the crystal and in the gas phase,” Chem. phys. lett., vol. 672, pp. 124-127, 2017. doi:10.1016/j.cplett.2017.01.070

[BibTeX] [Abstract] [Download PDF]

Two variants of density functional theory computations have been applied to characterization of hydrogen bonds of the 1-(2-hydroxylethyl)-3-methylimidazolium acetate ([C2OHmim][OAc]), i.e. with and without inclusion of dispersion interactions. A comparison of the results demonstrates that London dispersion interactions have very little impact on the energetical, geometrical, infrared spectroscopic and electron density parameters of charge-assisted intermolecular hydrogen bonds functioning both in the crystal of the [C2OHmim][OAc] and in the isolated [C2OHmim]+ [OAc]− ion pairs.

`@article{brandenburg_ref25, title = {The role of London dispersion interactions in strong and moderate intermolecular hydrogen bonds in the crystal and in the gas phase}, journal = {Chem. Phys. Lett.}, volume = {672}, pages = {124-127}, year = {2017}, doi = {10.1016/j.cplett.2017.01.070}, url = {../wp-content/papercite-data/pdf/brandenburg_ref25.pdf}, author = {Sergey A. Katsyuba and Mikhail V. Vener and Elena E. Zvereva and J. G. Brandenburg}, abstract={Two variants of density functional theory computations have been applied to characterization of hydrogen bonds of the 1-(2-hydroxylethyl)-3-methylimidazolium acetate ([C2OHmim][OAc]), i.e. with and without inclusion of dispersion interactions. A comparison of the results demonstrates that London dispersion interactions have very little impact on the energetical, geometrical, infrared spectroscopic and electron density parameters of charge-assisted intermolecular hydrogen bonds functioning both in the crystal of the [C2OHmim][OAc] and in the isolated [C2OHmim]+ [OAc]− ion pairs.} }`

### 2016

- J. Chen, A. Zen, J. G. Brandenburg, D. Alfé, and A. Michaelides, “Evidence for stable square ice from quantum monte-carlo,” Phys. Rev. B, vol. 94, p. 220102, 2016. doi:10.1103/PhysRevB.94.220102

[BibTeX] [Abstract] [Download PDF]

Recent experiments on ice formed by water under nanoconfinement provide evidence for a two-dimensional (2D) ‘square ice’ phase. However, the interpretation of the experiments has been questioned and the stability of square ice has become a matter of debate. Partially this is because the simulation approaches employed so far (force fields and density functional theory) struggle to accurately describe the very small energy differences between the relevant phases. Here we report a study of 2D ice using an accurate wave-function based electronic structure approach, namely Diffusion Monte Carlo (DMC). We find that at relatively high pressure square ice is indeed the lowest enthalpy phase examined, supporting the initial experimental claim. Moreover, at lower pressures a ‘pentagonal ice’ phase (not yet observed experimentally) has the lowest enthalpy, and at ambient pressure the ‘pentagonal ice’ phase is degenerate with a ‘hexagonal ice’ phase. Our DMC results also allow us to evaluate the accuracy of various density functional theory exchange correlation functionals and force field models, and in doing so we extend the understanding of how such methodologies perform to challenging 2D structures presenting dangling hydrogen bonds.

`@article {brandenburg_ref24, author = {J. Chen and A. Zen and J. G. Brandenburg and D. Alfé and A. Michaelides}, title = {Evidence for stable square ice from quantum Monte-Carlo}, journal = {{Phys. Rev. B}}, volume = {94}, pages = {220102}, year = {2016}, doi = {10.1103/PhysRevB.94.220102}, url = {../wp-content/papercite-data/pdf/brandenburg_ref24.pdf}, abstract = {Recent experiments on ice formed by water under nanoconfinement provide evidence for a two-dimensional (2D) 'square ice' phase. However, the interpretation of the experiments has been questioned and the stability of square ice has become a matter of debate. Partially this is because the simulation approaches employed so far (force fields and density functional theory) struggle to accurately describe the very small energy differences between the relevant phases. Here we report a study of 2D ice using an accurate wave-function based electronic structure approach, namely Diffusion Monte Carlo (DMC). We find that at relatively high pressure square ice is indeed the lowest enthalpy phase examined, supporting the initial experimental claim. Moreover, at lower pressures a 'pentagonal ice' phase (not yet observed experimentally) has the lowest enthalpy, and at ambient pressure the 'pentagonal ice' phase is degenerate with a 'hexagonal ice' phase. Our DMC results also allow us to evaluate the accuracy of various density functional theory exchange correlation functionals and force field models, and in doing so we extend the understanding of how such methodologies perform to challenging 2D structures presenting dangling hydrogen bonds.} }`

- J. G. Brandenburg, J. E. Bates, J. Sun, and J. P. Perdew, “Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction,” Phys. Rev. B, vol. 94, p. 115144, 2016. doi:10.1103/PhysRevB.94.115144

[BibTeX] [Abstract] [Download PDF]

The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGAs), and it includes some medium-range correlation effects. Long-range London dispersion interactions are still missing, but they can be accounted for via an appropriate correction scheme. In this study, we combine SCAN with an efficient London dispersion correction and show that lattice energies of simple organic crystals can be improved with the applied correction by 50%. The London-dispersion corrected SCAN meta-GGA outperforms all other tested London-dispersion corrected meta-GGAs for molecular geometries. Our method yields mean absolute deviations (MADs) for main group bond lengths that are consistently below 1 pm, rotational constants with MADs of 0.2%, and noncovalent distances with MADs below 1%. For a large database of general main group thermochemistry and kinetics (∼800 chemical species), one of the lowest weighted mean absolute deviations for long-range corrected meta-GGA functionals is achieved. Noncovalent interactions are of average quality, and hydrogen bonded systems in particular seem to suffer from overestimated polarization related to the self-interaction error of SCAN. We also discuss some consequences of numerical sensitivity encountered for meta-GGAs.

`@article {brandenburg_ref23, author = {J. G. Brandenburg and J. E. Bates and J. Sun and J. P. Perdew}, title = {Benchmark tests of a strongly constrained semilocal functional with a long-range dispersion correction }, journal = {{Phys. Rev. B}}, volume = {94}, pages = {115144}, year = {2016}, doi = {10.1103/PhysRevB.94.115144}, url = {../wp-content/papercite-data/pdf/brandenburg_ref23.pdf}, abstract = {The strongly constrained and appropriately normed (SCAN) semilocal density functional [J. Sun, A. Ruzsinszky, and J. P. Perdew, Phys. Rev. Lett. 115, 036402 (2015)] obeys all 17 known exact constraints for meta-generalized-gradient approximations (meta-GGAs), and it includes some medium-range correlation effects. Long-range London dispersion interactions are still missing, but they can be accounted for via an appropriate correction scheme. In this study, we combine SCAN with an efficient London dispersion correction and show that lattice energies of simple organic crystals can be improved with the applied correction by 50%. The London-dispersion corrected SCAN meta-GGA outperforms all other tested London-dispersion corrected meta-GGAs for molecular geometries. Our method yields mean absolute deviations (MADs) for main group bond lengths that are consistently below 1 pm, rotational constants with MADs of 0.2%, and noncovalent distances with MADs below 1%. For a large database of general main group thermochemistry and kinetics (∼800 chemical species), one of the lowest weighted mean absolute deviations for long-range corrected meta-GGA functionals is achieved. Noncovalent interactions are of average quality, and hydrogen bonded systems in particular seem to suffer from overestimated polarization related to the self-interaction error of SCAN. We also discuss some consequences of numerical sensitivity encountered for meta-GGAs.} }`

- M. Cutini, B. Civalleri, M. Corno, R. Orlando, J. G. Brandenburg, L. Maschio, and P. Ugliengoa, “Assessment of different quantum mechanical methods for the prediction of structure and cohesive energy of molecular crystals,” J. Chem. Theory Comput., vol. 12, pp. 3340-3352, 2016. doi:10.1021/acs.jctc.6b00304

[BibTeX] [Abstract]

A comparative assessment of the accuracy of different quantum mechanical methods for evaluating the structure and the cohesive energy of molecular crystals is presented. In particular, we evaluate the performance of the semiempirical HF-3c method in comparison with the B3LYP-D* and the Local MP2 (LMP2) methods by means of a fully periodic approach. Three benchmark sets have been investigated: X23, G60, and the new K7; for a total of 82 molecular crystals. The original HF-3c method performs well but shows a tendency at overbinding molecular crystals, in particular for weakly bounded systems. For the X23 set, the mean absolute error for the cohesive energies computed with the HF-3c method is comparable to the LMP2 one. A refinement of the HF-3c has been attempted by tuning the dispersion term in the HF-3c energy. While the performance on cohesive energy prediction slightly worsens, optimized unit cell volumes are in excellent agreement with experiment. Overall, the B3LYP-D* method combined with a TZP basis set gives the best results. For cost-effective calculations on molecular crystals, we propose to compute cohesive energies at the B3LYP-D*/TZP level of theory on the dispersion-scaled HF-3c optimized geometries (i.e., B3LYP-D*/TZP//HF-3c(0.27) also dubbed as SP-B3LYP-D*). Besides, for further benchmarking on molecular crystals, we propose to combine the three test sets in a new one denoted as MC82.

`@article {brandenburg_ref22, author = {M. Cutini and B. Civalleri and M. Corno and R. Orlando and J. G. Brandenburg and L. Maschio and P. Ugliengoa}, title = {Assessment of different quantum mechanical methods for the prediction of structure and cohesive energy of molecular crystals}, journal = {{J. Chem. Theory Comput.}}, volume = {12}, pages = {3340-3352}, year = {2016}, doi = {10.1021/acs.jctc.6b00304}, abstract = {A comparative assessment of the accuracy of different quantum mechanical methods for evaluating the structure and the cohesive energy of molecular crystals is presented. In particular, we evaluate the performance of the semiempirical HF-3c method in comparison with the B3LYP-D* and the Local MP2 (LMP2) methods by means of a fully periodic approach. Three benchmark sets have been investigated: X23, G60, and the new K7; for a total of 82 molecular crystals. The original HF-3c method performs well but shows a tendency at overbinding molecular crystals, in particular for weakly bounded systems. For the X23 set, the mean absolute error for the cohesive energies computed with the HF-3c method is comparable to the LMP2 one. A refinement of the HF-3c has been attempted by tuning the dispersion term in the HF-3c energy. While the performance on cohesive energy prediction slightly worsens, optimized unit cell volumes are in excellent agreement with experiment. Overall, the B3LYP-D* method combined with a TZP basis set gives the best results. For cost-effective calculations on molecular crystals, we propose to compute cohesive energies at the B3LYP-D*/TZP level of theory on the dispersion-scaled HF-3c optimized geometries (i.e., B3LYP-D*/TZP//HF-3c(0.27) also dubbed as SP-B3LYP-D*). Besides, for further benchmarking on molecular crystals, we propose to combine the three test sets in a new one denoted as MC82.} }`

- J. G. Brandenburg, E. Caldeweyher, and S. Grimme, “Screened exchange hybrid density functional for accurate and efficient structures and interaction energies,” Phys. Chem. Chem. Phys., vol. 18, pp. 15519-15523, 2016. doi:10.1039/C6CP01697A

[BibTeX] [Abstract] [Download PDF]

We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50\% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.

`@article {brandenburg_ref21, author = {J. G. Brandenburg and E. Caldeweyher and S. Grimme}, title = {Screened exchange hybrid density functional for accurate and efficient structures and interaction energies}, journal = {{Phys. Chem. Chem. Phys.}}, volume = {18}, pages = {15519-15523}, year = {2016}, doi = {10.1039/C6CP01697A}, url = {../wp-content/papercite-data/pdf/brandenburg_ref21.pdf}, abstract = {We extend the recently introduced PBEh-3c global hybrid density functional [S. Grimme et al., J. Chem. Phys., 2015, 143, 054107] by a screened Fock exchange variant based on the Henderson-Janesko-Scuseria exchange hole model. While the excellent performance of the global hybrid is maintained for small covalently bound molecules, its performance for computed condensed phase mass densities is further improved. Most importantly, a speed up of 30 to 50\% can be achieved and especially for small orbital energy gap cases, the method is numerically much more robust. The latter point is important for many applications, e.g., for metal-organic frameworks, organic semiconductors, or protein structures. This enables an accurate density functional based electronic structure calculation of a full DNA helix structure on a single core desktop computer which is presented as an example in addition to comprehensive benchmark results.} }`

- J. G. Brandenburg and S. Grimme, “Organic crystal polymorphism: a benchmark for dispersion corrected mean field electronic structure methods,” Acta Cryst. B, vol. 72, pp. 502-513, 2016. doi:10.1107/S2052520616007885

[BibTeX] [Abstract] [Download PDF]

We analyze the energy landscape of the 6th crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pair-wise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler TS method, and the density dependent dispersion correction dDsC. Recent methodological progress includes higher order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many body dispersion MBD, and the nonlocal van der Waals density functional vdW-DF2. The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.

`@article {brandenburg_ref20, author = {J. G. Brandenburg and S. Grimme}, title = {Organic crystal polymorphism: A benchmark for dispersion corrected mean field electronic structure methods}, journal = {{Acta Cryst. B}}, volume = {72}, pages = {502-513}, year = {2016}, doi = {10.1107/S2052520616007885}, url = {../wp-content/papercite-data/pdf/brandenburg_ref20.pdf}, abstract = {We analyze the energy landscape of the 6th crystal structure prediction blind test targets with various first principles and semi-empirical quantum chemical methodologies. A new benchmark set of 59 crystal structures (termed POLY59) for testing quantum chemical methods based on the blind test target crystals is presented. We focus on different means to include London dispersion interactions within the density functional theory (DFT) framework. We show the impact of pair-wise dispersion corrections like the semi-empirical D2 scheme, the Tkatchenko-Scheffler TS method, and the density dependent dispersion correction dDsC. Recent methodological progress includes higher order contributions in both the many-body and multipole expansions. We use the D3 correction with Axilrod-Teller-Muto type three-body contribution, the TS based many body dispersion MBD, and the nonlocal van der Waals density functional vdW-DF2. The density functionals with D3 and MBD correction provide an energy ranking of the blind test polymorphs in excellent agreement with the experimentally found structures. As computationally less demanding method, we test our recently presented minimal basis Hartree-Fock method (HF-3c) and a density functional tight-binding Hamiltonian (DFTB). Considering the speed-up of three to four orders of magnitudes, the energy ranking provided by the low-cost methods is very reasonable. We compare the computed geometries with the corresponding X-ray data where TPSS-D3 performs best. The importance of zero-point vibrational energy and thermal effects on crystal densities is highlighted.} }`

- A. M. Reilly, R. I. Cooper, C. S. Adjiman, S. Bhattacharya, D. A. Boese, J. G. Brandenburg, P. J. Bygrave, R. Bylsma, J. E. Campbell, R. Car, D. H. Case, R. Chadha, J. C. Cole, K. Cosburn, H. M. Cuppen, F. Curtis, G. M. Day, R. A. {DiStasio Jr}, A. Dzyabchenko, B. P. van Eijck, D. M. Elking, J. A. van den Ende, J. C. Facelli, M. B. Ferraro, L. Fusti-Molnar, C. Gatsiou, T. S. Gee, R. de Gelder, L. M. Ghiringhelli, H. Goto, S. Grimme, R. Guo, D. W. M. Hofmann, J. Hoja, R. K. Hylton, L. Iuzzolino, W. Jankiewicz, D. T. de Jong, J. Kendrick, N. J. J. de Klerk, H. Ko, L. N. Kuleshova, X. Li, S. Lohani, F. J. J. Leusen, A. M. Lund, J. Lv, Y. Ma, N. Marom, A. E. Masunov, P. McCabe, D. P. McMahon, H. Meekes, M. P. Metz, A. J. Misquitta, S. Mohamed, B. Monserrat, R. J. Needs, M. A. Neumann, J. Nyman, S. Obata, H. Oberhofer, A. R. Oganov, A. M. Orendt, G. I. Pagola, C. C. Pantelides, C. J. Pickard, R. Podeszwa, L. S. Price, S. L. Price, A. Pulido, M. G. Read, K. Reuter, E. Schneider, C. Schober, G. P. Shields, P. Singh, I. J. Sugden, K. Szalewicz, C. R. Taylor, A. Tkatchenko, M. E. Tuckerman, F. Vacarro, M. Vasileiadis, A. Vázquez-Mayagoitia, L. Vogt, Y. Wang, R. E. Watson, G. A. de Wijs, J. Yang, Q. Zhu, and C. R. Groom, “Report on the sixth blind test of organic crystal-structure prediction methods,” Acta Cryst. B, vol. 72, pp. 439-459, 2016. doi:10.1107/S2052520616007447

[BibTeX] [Abstract] [Download PDF]

The sixth blind test of organic crystal-structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal, and a bulky flexible molecule. This blind test has seen substantial growth in the number of submissions, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and “best practices” forperforming CSP calculations. All of the targets, apart from a single potentially disordered Z = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.

`@article {brandenburg_ref19, author = {Reilly, Anthony M. and Cooper, Richard I. and Adjiman, Claire S. and Bhattacharya, Saswata and Boese, A. Daniel and Brandenburg, Jan Gerit and Bygrave, Peter J. and Bylsma, Rita and Campbell, Josh E. and Car, Roberto and Case, David H. and Chadha, Renu and Cole, Jason C. and Cosburn, Katherine and Cuppen, Herma M. and Curtis, Farren and Day, Graeme M. and {DiStasio Jr}, Robert A. and Dzyabchenko, Alexander and van Eijck, Bouke P. and Elking, Dennis M. and van den Ende, Joost A. and Facelli, Julio C. and Ferraro, Marta B. and Fusti-Molnar, Laszlo and Gatsiou, Christina-Anna and Gee, Thomas S. and de Gelder, R{\'e}ne and Ghiringhelli, Luca M. and Goto, Hitoshi and Grimme, Stefan and Guo, Rui and Hofmann, Detlef W.M. and Hoja, Johannes and Hylton, Rebecca K. and Iuzzolino, Luca and Jankiewicz, Wojciech and de Jong, Dani{\"e}l T. and Kendrick, John and de Klerk, Niek J.J. and Ko, Hsin-Yu and Kuleshova, Liudmila N. and Li, Xiayue and Lohani, Sanjaya and Leusen, Frank J.J. and Lund, Albert M. and Lv, Jian and Ma, Yanming and Marom, Noa and Masunov, Art{\"e}m E. and McCabe, Patrick and McMahon, David P. and Meekes, Hugo and Metz, Michael P. and Misquitta, Alston J. and Mohamed, Sharmarke and Monserrat, Bartomeu and Needs, Richard J. and Neumann, Marcus A. and Nyman, Jonas and Obata, Shigeaki and Oberhofer, Harald and Oganov, Artem R. and Orendt, Anita M. and Pagola, Gabriel I. and Pantelides, Constantinos C. and Pickard, Chris J. and Podeszwa, Rafa\l{} and Price, Louise S. and Price, Sarah L. and Pulido, Angeles and Read, Murray G. and Reuter, Karsten and Schneider, Elia and Schober, Christoph and Shields, Gregory P. and Singh, Pawanpreet and Sugden, Isaac J. and Szalewicz, Krzysztof and Taylor, Christopher R. and Tkatchenko, Alexandre and Tuckerman, Mark E. and Vacarro, Francesca and Vasileiadis, Manolis and V{\'a}zquez-Mayagoitia, Alvaro and Vogt, Leslie and Wang, Yanchao and Watson, Rona E. and de Wijs, Gilles A. and Yang, Jack and Zhu, Qiang and Groom, Colin R.}, title = {Report on the sixth blind test of organic crystal-structure prediction methods}, journal = {{Acta Cryst. B}}, volume = {72}, pages = {439-459}, year = {2016}, doi = {10.1107/S2052520616007447}, url = {../wp-content/papercite-data/pdf/brandenburg_ref19.pdf}, abstract = {The sixth blind test of organic crystal-structure prediction (CSP) methods has been held, with five target systems: a small nearly rigid molecule, a polymorphic former drug candidate, a chloride salt hydrate, a co-crystal, and a bulky flexible molecule. This blind test has seen substantial growth in the number of submissions, with the broad range of prediction methods giving a unique insight into the state of the art in the field. Significant progress has been seen in treating flexible molecules, usage of hierarchical approaches to ranking structures, the application of density-functional approximations, and the establishment of new workflows and “best practices” forperforming CSP calculations. All of the targets, apart from a single potentially disordered Z = 2 polymorph of the drug candidate, were predicted by at least one submission. Despite many remaining challenges, it is clear that CSP methods are becoming more applicable to a wider range of real systems, including salts, hydrates and larger flexible molecules. The results also highlight the potential for CSP calculations to complement and augment experimental studies of organic solid forms.} }`

- S. Grimme, A. Hansen, J. G. Brandenburg, and C. Bannwarth, “Dispersion-corrected mean-field electronic structure methods,” Chem. Rev., vol. 116, pp. 5105-5154, 2016. doi:10.1021/acs.chemrev.5b00533

[BibTeX] [Abstract] [Download PDF]

Mean-field electronic structure methods like Hartree−Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlations (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes were classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energy with a typical relative error of 5\%. For many chemical problems, this accuracy is higher compared to the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).

`@article {brandenburg_ref18, author = {S. Grimme and A. Hansen and J. G. Brandenburg and C. Bannwarth}, title = {Dispersion-corrected mean-field electronic structure methods}, journal = {{Chem. Rev.}}, volume = {116}, pages = {5105-5154}, year = {2016}, doi = {10.1021/acs.chemrev.5b00533}, url = {../wp-content/papercite-data/pdf/brandenburg_ref18.pdf}, abstract = {Mean-field electronic structure methods like Hartree−Fock, semilocal density functional approximations, or semiempirical molecular orbital (MO) theories do not account for long-range electron correlations (London dispersion interaction). Inclusion of these effects is mandatory for realistic calculations on large or condensed chemical systems and for various intramolecular phenomena (thermochemistry). This Review describes the recent developments (including some historical aspects) of dispersion corrections with an emphasis on methods that can be employed routinely with reasonable accuracy in large-scale applications. The most prominent correction schemes were classified into three groups: (i) nonlocal, density-based functionals, (ii) semiclassical C6-based, and (iii) one-electron effective potentials. The properties as well as pros and cons of these methods are critically discussed, and typical examples and benchmarks on molecular complexes and crystals are provided. Although there are some areas for further improvement (robustness, many-body and short-range effects), the situation regarding the overall accuracy is clear. Various approaches yield long-range dispersion energy with a typical relative error of 5\%. For many chemical problems, this accuracy is higher compared to the underlying mean-field method (i.e., a typical semilocal (hybrid) functional like B3LYP).} }`

- R. Sure, J. G. Brandenburg, and S. Grimme, “Small atomic orbital basis set first-principles quantum chemical methods for large molecular and periodic systems,” ChemistryOpen, vol. 5, pp. 94-109, 2016. doi:10.1002/open.201500192

[BibTeX] [Abstract] [Download PDF]

In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.

`@article {brandenburg_ref17, author = {R. Sure and J. G. Brandenburg and S. Grimme}, title = {Small atomic orbital basis set first-principles quantum chemical methods for large molecular and periodic systems}, journal = {{ChemistryOpen}}, volume = {5}, pages = {94-109}, year = {2016}, doi = {10.1002/open.201500192}, url = {../wp-content/papercite-data/pdf/brandenburg_ref17.pdf}, abstract = {In quantum chemical computations the combination of Hartree-Fock or a density functional theory (DFT) approximation with relatively small atomic orbital basis sets of double-zeta quality is still widely used, for example, in the popular B3LYP/6-31G* approach. In this Review, we critically analyze the two main sources of error in such computations, that is, the basis set superposition error on the one hand and the missing London dispersion interactions on the other. We review various strategies to correct those errors and present exemplary calculations on mainly noncovalently bound systems of widely varying size. Energies and geometries of small dimers, large supramolecular complexes, and molecular crystals are covered. We conclude that it is not justified to rely on fortunate error compensation, as the main inconsistencies can be cured by modern correction schemes which clearly outperform the plain mean-field methods.} }`

### 2015

- N. Struch, J. G. Brandenburg, G. Schnakenburg, N. Wagner, J. Beck, S. Grimme, and A. Lützen, “A case study of mechanical strain in supramolecular complexes to manipulate the spin state of iron(II) centres,” Eur. J. Inorg. Chem., vol. 33, p. 5503–5510, 2015. doi:10.1002/ejic.201501057

[BibTeX] [Abstract]

Two novel supramolecular meso-helicates have been synthesized and characterized by single-crystal X-ray diffraction, variable-temperature magnetic susceptibility measurements, NMR and UV/Vis spectroscopy, mass spectrometry and density functional theory (DFT) simulations. Both compounds show a considerably high stabilization of the high-spin state of the metal centres compared with other compounds with similar types of ligands. Whereas the pyridyl complex [Fe$_2$L$^2_3$] {[L\(^2\) = $N,N’$-bis(pyridin-2-ylmethylene)benzene-1,3-diamine]} exhibits the beginning of a spin transition at around 350 K, the imidazolyl complex [Fe$_2$L$^1_3$] [L$^1$ = $N,N’$-bis(1H-imidazol-4-ylmethylene)benzene-1,3-diamine] still exhibits a high-spin configuration at 20 K. We applied DFT to characterize the molecular as well as solid states of both compounds. Although the low-spin state of both systems is stabilized by crystal packing, an additional stabilization of the high-spin state is induced by intramolecular interactions. This effect can be ascribed to mechanical strain in the backbone of the ligands hailing from very short CH-$\pi$ interactions and being similar in effect to sterically demanding methyl groups.

`@article {brandenburg_ref16, author = {Struch, Niklas and Brandenburg, Jan Gerit and Schnakenburg, Gregor and Wagner, Norbert and Beck, Johannes and Grimme, Stefan and L\"{u}tzen, Arne}, title = {A case study of mechanical strain in supramolecular complexes to manipulate the spin state of iron({II}) centres}, journal = {{Eur. J. Inorg. Chem.}}, volume = {33}, doi = {10.1002/ejic.201501057}, pages = {5503--5510}, year = {2015}, abstract = {Two novel supramolecular meso-helicates have been synthesized and characterized by single-crystal X-ray diffraction, variable-temperature magnetic susceptibility measurements, NMR and UV/Vis spectroscopy, mass spectrometry and density functional theory (DFT) simulations. Both compounds show a considerably high stabilization of the high-spin state of the metal centres compared with other compounds with similar types of ligands. Whereas the pyridyl complex [Fe$_2$L$^2_3$] {[L\(^2\) = $N,N'$-bis(pyridin-2-ylmethylene)benzene-1,3-diamine]} exhibits the beginning of a spin transition at around 350 K, the imidazolyl complex [Fe$_2$L$^1_3$] [L$^1$ = $N,N'$-bis(1H-imidazol-4-ylmethylene)benzene-1,3-diamine] still exhibits a high-spin configuration at 20 K. We applied DFT to characterize the molecular as well as solid states of both compounds. Although the low-spin state of both systems is stabilized by crystal packing, an additional stabilization of the high-spin state is induced by intramolecular interactions. This effect can be ascribed to mechanical strain in the backbone of the ligands hailing from very short CH-$\pi$ interactions and being similar in effect to sterically demanding methyl groups.} }`

- S. A. Katsyuba, M. V. Vener, E. E. Zvereva, Z. Fei, R. Scopelliti, J. G. Brandenburg, S. Siankevich, and P. J. Dyson, “Quantification of conventional and nonconventional charge-assisted hydrogen bonds in the condensed and gas phases,” J. Phys. Chem. Lett., vol. 6, pp. 4431-4436, 2015. doi:10.1021/acs.jpclett.5b02175

[BibTeX] [Abstract]

Charge-assisted hydrogen bonds (CAHBs) play critical roles in many systems from biology through to materials. In none of these areas has the role and function of CAHBs been explored satisfactorily because of the lack of data on the energy of CAHBs in the condensed phases. We have, for the first time, quantified three types of CAHBs in both the condensed and gas phases for 1-(2′-hydroxylethyl)-3-methylimidazolium acetate ([C2OHmim][OAc]). The energy of conventional OH···[OAc]- CAHBs is ∼10 kcal/mol, whereas nonconventional C(sp2)H···[OAc] and C(sp3)H···[OAc] CAHBs are weaker by ∼5−7 kcal/mol. In the gas phase, the strength of the nonconventional CAHBs is doubled, whereas the conventional CAHBs are strengthened by <20%. The influence of cooperativity effects on the ability of the [OAc] anion to deprotonate the imidazolium cation is evaluated. The ability to quantify CAHBs in the condensed phase on the basis of easier accessible gas-phase estimates is highlighted.

`@article{brandenburg_ref15, author = {Sergey A. Katsyuba and Mikhail V. Vener and Elena E. Zvereva and Zhaofu Fei and Rosario Scopelliti and Jan Gerit Brandenburg and Sviatlana Siankevich and Paul J. Dyson}, title = {Quantification of conventional and nonconventional charge-assisted hydrogen bonds in the condensed and gas phases}, journal = {{J. Phys. Chem. Lett.}}, volume = {6}, pages = {4431-4436}, year = {2015}, doi = {10.1021/acs.jpclett.5b02175}, abstract = {Charge-assisted hydrogen bonds (CAHBs) play critical roles in many systems from biology through to materials. In none of these areas has the role and function of CAHBs been explored satisfactorily because of the lack of data on the energy of CAHBs in the condensed phases. We have, for the first time, quantified three types of CAHBs in both the condensed and gas phases for 1-(2′-hydroxylethyl)-3-methylimidazolium acetate ([C2OHmim][OAc]). The energy of conventional OH···[OAc]- CAHBs is ∼10 kcal/mol, whereas nonconventional C(sp2)H···[OAc] and C(sp3)H···[OAc] CAHBs are weaker by ∼5−7 kcal/mol. In the gas phase, the strength of the nonconventional CAHBs is doubled, whereas the conventional CAHBs are strengthened by <20%. The influence of cooperativity effects on the ability of the [OAc] anion to deprotonate the imidazolium cation is evaluated. The ability to quantify CAHBs in the condensed phase on the basis of easier accessible gas-phase estimates is highlighted.} }`

- S. Grimme, J. G. Brandenburg, C. Bannwarth, and A. Hansen, "Consistent structures and interactions by density functional theory with small atomic orbital basis sets," J. Chem. Phys., vol. 143, p. 54107, 2015. doi:10.1063/1.4927476

[BibTeX] [Abstract] [Download PDF]

A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust “high-speed” computational tool in theoretical chemistry and physics.

`@article{brandenburg_ref14, author = {S. Grimme and J. G. Brandenburg and C. Bannwarth and A. Hansen}, title = {Consistent structures and interactions by density functional theory with small atomic orbital basis sets}, journal = {{J. Chem. Phys.}}, year = {2015}, volume = {143}, pages = {054107}, doi = {10.1063/1.4927476}, url = {../wp-content/papercite-data/pdf/brandenburg_ref14.pdf}, abstract = {A density functional theory (DFT) based composite electronic structure approach is proposed to efficiently compute structures and interaction energies in large chemical systems. It is based on the well-known and numerically robust Perdew-Burke-Ernzerhoff (PBE) generalized-gradient-approximation in a modified global hybrid functional with a relatively large amount of non-local Fock-exchange. The orbitals are expanded in Ahlrichs-type valence-double zeta atomic orbital (AO) Gaussian basis sets, which are available for many elements. In order to correct for the basis set superposition error (BSSE) and to account for the important long-range London dispersion effects, our well-established atom-pairwise potentials are used. In the design of the new method, particular attention has been paid to an accurate description of structural parameters in various covalent and non-covalent bonding situations as well as in periodic systems. Together with the recently proposed three-fold corrected (3c) Hartree-Fock method, the new composite scheme (termed PBEh-3c) represents the next member in a hierarchy of “low-cost” electronic structure approaches. They are mainly free of BSSE and account for most interactions in a physically sound and asymptotically correct manner. PBEh-3c yields good results for thermochemical properties in the huge GMTKN30 energy database. Furthermore, the method shows excellent performance for non-covalent interaction energies in small and large complexes. For evaluating its performance on equilibrium structures, a new compilation of standard test sets is suggested. These consist of small (light) molecules, partially flexible, medium-sized organic molecules, molecules comprising heavy main group elements, larger systems with long bonds, 3d-transition metal systems, non-covalently bound complexes (S22 and S66×8 sets), and peptide conformations. For these sets, overall deviations from accurate reference data are smaller than for various other tested DFT methods and reach that of triple-zeta AO basis set second-order perturbation theory (MP2/TZ) level at a tiny fraction of computational effort. Periodic calculations conducted for molecular crystals to test structures (including cell volumes) and sublimation enthalpies indicate very good accuracy competitive to computationally more involved plane-wave based calculations. PBEh-3c can be applied routinely to several hundreds of atoms on a single processor and it is suggested as a robust “high-speed” computational tool in theoretical chemistry and physics.} }`

- J. G. Brandenburg, "Development and application of electronic structure methods for noncovalent interactions in organic solids," Rheinische Friedrich-Wilhelms-Universität Bonn, vol. Dissertation URN: nbn:de:hbz:5n-40608, 2015.

[BibTeX] [Abstract] [Download PDF]

This thesis reports on multilevel electronic structure approaches for the description of noncovalent interactions. They play an important role in various areas of chemistry and physics, ranging from bio-molecular applications to organic semi-conductors. The main focus lies on the cost-effective yet reasonably accurate description of noncovalently bound solids in the framework of organic crystal structure prediction (CSP). In principle, high-level quantum chemical wavefunction theory methods can seamlessly describe all of the local and nonlocal interactions but are computationally too demanding for large organic complexes, specifically for molecular crystals of larger molecules. London dispersion inclusive density functional theory (DFT-D) is state-of-the-art in molecular gas phase applications. However, its absolute accuracy for lattice energies and crystal geometries was still uncertain. The good performance of DFT-D on standard and newly compiled benchmark sets is shown to be close (or within) the chemical accuracy of 1 kcal/mol. Exact exchange and three-body dispersion overall improve the performance, e.g., the mean absolute relative deviation of the hybrid functional PBE0-D3atm from the reference lattice energies of the X23 and ICE10 sets is 6.6\% and 6.1\%, respectively. Because the references are typically experimental sublimation energies and X-ray geometries at finite temperature, a correct treatment of zero-point and thermodynamic effects is mandatory.When compared to the experimental unit-cells, which are corrected for zero-point and thermal effects, the DFT-D unit cell volumes are accurate within 1–3%. Thus, DFT-D in principle is applicable to CSP, but the computational demands to sample a huge number of polymorphs, are too high. In the second part of this thesis, alternative low-cost methods are developed, extended to periodic boundary conditions, and evaluated on standard benchmarks. Two approaches, namely the London dispersion corrected density functional tight-binding (DFTB3-D3) and the corrected small basis set Hartree-Fock (HF-3c) are especially promising. The empiricism of HF-3c is comparable to modern density functionals (nine global parameters) while the tight binding Hamiltonian relies on element-specific parametrized pair potentials. Both schemes are shown to accurately model both solid- and gas phase inter- and intramolecular noncovalent interactions. The mean absolute deviation for interaction (lattice) energies are typically 1-3 kcal/mol (5–20\%), that is, only about two times larger than those for DFT-D. At the same time, a speed-up of two to three orders of magnitude can be achieved. HF-3c yields very reasonable unit cell volumes (mass densities) within 3-5\% error, while DFTB3-D3 yields larger errors up to 15\%. However, the deviations of thermodynamic corrections to sublimation energies between the DFTB3-D3 and DFT-D level is below 0.5 kcal/mol and the tight binding model can be ideally used in a multilevel approach. One can, for instance, combine the thermal corrections of DFTB3-D3 with the electronic energy from DFT-D or use the computationally cheaper method to screen a huge number of possible conformations. The presented methods can be routinely applied to molecular crystals as demonstrated in the last part of the thesis. The correct description of a variety of crystal packing effects is presented. Specifically, the change of the molecular conformer of ethyl acetate, the stacking of $\pi$-systems, the spin state of iron spin-crossover compounds, and the bond isomerization of certain zirconium complexes are computed in agreement with corresponding experiments.

`@article{brandenburg_ref13, author = {J. G. Brandenburg}, title = {Development and application of electronic structure methods for noncovalent interactions in organic solids}, journal = {{Rheinische Friedrich-Wilhelms-Universit\"at Bonn}}, year = {2015}, volume = {Dissertation URN: nbn:de:hbz:5n-40608}, url = {http://hss.ulb.uni-bonn.de/2015/4060/4060.htm}, abstract = {This thesis reports on multilevel electronic structure approaches for the description of noncovalent interactions. They play an important role in various areas of chemistry and physics, ranging from bio-molecular applications to organic semi-conductors. The main focus lies on the cost-effective yet reasonably accurate description of noncovalently bound solids in the framework of organic crystal structure prediction (CSP). In principle, high-level quantum chemical wavefunction theory methods can seamlessly describe all of the local and nonlocal interactions but are computationally too demanding for large organic complexes, specifically for molecular crystals of larger molecules. London dispersion inclusive density functional theory (DFT-D) is state-of-the-art in molecular gas phase applications. However, its absolute accuracy for lattice energies and crystal geometries was still uncertain. The good performance of DFT-D on standard and newly compiled benchmark sets is shown to be close (or within) the chemical accuracy of 1 kcal/mol. Exact exchange and three-body dispersion overall improve the performance, e.g., the mean absolute relative deviation of the hybrid functional PBE0-D3atm from the reference lattice energies of the X23 and ICE10 sets is 6.6\% and 6.1\%, respectively. Because the references are typically experimental sublimation energies and X-ray geometries at finite temperature, a correct treatment of zero-point and thermodynamic effects is mandatory.When compared to the experimental unit-cells, which are corrected for zero-point and thermal effects, the DFT-D unit cell volumes are accurate within 1--3%. Thus, DFT-D in principle is applicable to CSP, but the computational demands to sample a huge number of polymorphs, are too high. In the second part of this thesis, alternative low-cost methods are developed, extended to periodic boundary conditions, and evaluated on standard benchmarks. Two approaches, namely the London dispersion corrected density functional tight-binding (DFTB3-D3) and the corrected small basis set Hartree-Fock (HF-3c) are especially promising. The empiricism of HF-3c is comparable to modern density functionals (nine global parameters) while the tight binding Hamiltonian relies on element-specific parametrized pair potentials. Both schemes are shown to accurately model both solid- and gas phase inter- and intramolecular noncovalent interactions. The mean absolute deviation for interaction (lattice) energies are typically 1-3 kcal/mol (5--20\%), that is, only about two times larger than those for DFT-D. At the same time, a speed-up of two to three orders of magnitude can be achieved. HF-3c yields very reasonable unit cell volumes (mass densities) within 3-5\% error, while DFTB3-D3 yields larger errors up to 15\%. However, the deviations of thermodynamic corrections to sublimation energies between the DFTB3-D3 and DFT-D level is below 0.5 kcal/mol and the tight binding model can be ideally used in a multilevel approach. One can, for instance, combine the thermal corrections of DFTB3-D3 with the electronic energy from DFT-D or use the computationally cheaper method to screen a huge number of possible conformations. The presented methods can be routinely applied to molecular crystals as demonstrated in the last part of the thesis. The correct description of a variety of crystal packing effects is presented. Specifically, the change of the molecular conformer of ethyl acetate, the stacking of $\pi$-systems, the spin state of iron spin-crossover compounds, and the bond isomerization of certain zirconium complexes are computed in agreement with corresponding experiments.} }`

- J. G. Brandenburg, T. Maas, and S. Grimme, "Benchmarking dft and semiempirical methods on structures and lattice energies for ten ice polymorphs," J. Chem. Phys., vol. 142, p. 124104, 2015. doi:10.1063/1.4916070

[BibTeX] [Abstract] [Download PDF]

Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm$^3$ and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3$^{atm}$ gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7\% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1\%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3\%.

`@article{brandenburg_ref12, author = {J. G. Brandenburg and T. Maas and S. Grimme}, title = {Benchmarking DFT and semiempirical methods on structures and lattice energies for ten ice polymorphs}, journal = {{J. Chem. Phys.}}, year = {2015}, volume = {142}, pages = {124104}, doi = {10.1063/1.4916070}, url = {../wp-content/papercite-data/pdf/brandenburg_ref12.pdf}, abstract = {Water in different phases under various external conditions is very important in bio-chemical systems and for material science at surfaces. Density functional theory methods and approximations thereof have to be tested system specifically to benchmark their accuracy regarding computed structures and interaction energies. In this study, we present and test a set of ten ice polymorphs in comparison to experimental data with mass densities ranging from 0.9 to 1.5 g/cm$^3$ and including explicit corrections for zero-point vibrational and thermal effects. London dispersion inclusive density functionals at the generalized gradient approximation (GGA), meta-GGA, and hybrid level as well as alternative low-cost molecular orbital methods are considered. The widely used functional of Perdew, Burke and Ernzerhof (PBE) systematically overbinds and overall provides inconsistent results. All other tested methods yield reasonable to very good accuracy. BLYP-D3$^{atm}$ gives excellent results with mean absolute errors for the lattice energy below 1 kcal/mol (7\% relative deviation). The corresponding optimized structures are very accurate with mean absolute relative deviations (MARDs) from the reference unit cell volume below 1\%. The impact of Axilrod-Teller-Muto (atm) type three-body dispersion and of non-local Fock exchange is small but on average their inclusion improves the results. While the density functional tight-binding model DFTB3-D3 performs well for low density phases, it does not yield good high density structures. As low-cost alternative for structure related problems, we recommend the recently introduced minimal basis Hartree-Fock method HF-3c with a MARD of about 3\%.} }`

### 2014

- J. G. Brandenburg, M. Hochheim, T. Bredow, and S. Grimme, "Low-cost quantum chemical methods for non-covalent interactions," J. Phys. Chem. Lett., vol. 5, p. 4275–4284, 2014. doi:10.1021/jz5021313

[BibTeX] [Abstract] [Download PDF]

The efficient and reasonably accurate description of non-covalent interactions is important for various areas of chemistry, ranging from supramolecular host−guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster “low-cost” methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular- orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree−Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10-30\%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.

`@article{brandenburg_ref11, author = {J. G. Brandenburg and M. Hochheim and T. Bredow and S. Grimme}, title = {Low-Cost quantum chemical methods for non-covalent interactions}, journal = {{J. Phys. Chem. Lett.}}, year = {2014}, volume = {5}, pages = {4275--4284}, doi = {10.1021/jz5021313}, url = {../wp-content/papercite-data/pdf/brandenburg_ref11.pdf}, abstract = {The efficient and reasonably accurate description of non-covalent interactions is important for various areas of chemistry, ranging from supramolecular host−guest complexes and biomolecular applications to the challenging task of crystal structure prediction. While London dispersion inclusive density functional theory (DFT-D) can be applied, faster “low-cost” methods are required for large-scale applications. In this Perspective, we present the state-of-the-art of minimal basis set, semiempirical molecular- orbital-based methods. Various levels of approximations are discussed based either on canonical Hartree−Fock or on semilocal density functionals. The performance for intermolecular interactions is examined on various small to large molecular complexes and organic solids covering many different chemical groups and interaction types. We put the accuracy of low-cost methods into perspective by comparing with first-principle density functional theory results. The mean unsigned deviations of binding energies from reference data are typically 10-30\%, which is only two times larger than those of DFT-D. In particular, for neutral or moderately polar systems, many of the tested methods perform very well, while at the same time, computational savings of up to 2 orders of magnitude can be achieved.} }`

- J. G. Brandenburg, G. Bender, J. Ren, A. Hansen, S. Grimme, H. Eckert, C. G. Daniliuc, G. Kehr, and G. Erker, "Crystal packing induced carbon-carbon double-triple bond isomerization in a zirconocene complex," Organometallics, vol. 33, p. 5358–5364, 2014. doi:10.1021/om500678p

[BibTeX] [Abstract]

We present a combined theoretical and experimental analysis of the carbon-carbon bond character in two prototypical zirconocene complexes. The two cyclic seven-membered ring zirconium compounds 2a and 2b differ by the substitution of a tert-butyl by a trimethylsilyl group. Due to the coordination of the π-system to the metal atom, a formally forbidden ($\eta^2$-allenyl)/enamido-Zr to ($\eta^2$-alkyne)/$\kappa$N- imine-Zr complex isomerization is feasible. State-of-the-art dispersion-corrected density functional theory (DFT-D3) is used in both the solid and condensed phase to examine and quantify the experimental structures (X-ray diffraction) and $^{13}$C NMR magnetic shielding. The complementary investigations demonstrate the importance of nonlocal London dispersion interactions. Both X-ray structures agree excellently with the results of the solid-state DFT-D3 calculations. Interestingly, 2b exhibits a mixed allene-alkyne form in the solid state, while its gas phase structure has a strong allene character. The substitution leading to 2a prevents this isomerization in the solid state by the intramolecular stabilization of the allene structure. NMR solid and liquid phase measurements confirm the theoretically proposed transition. By combining the experimental and theoretical information, the rather unusual triple/single to double/double-bond transition is attributed to an intermolecular London dispersion induced crystal packing effect.

`@article{brandenburg_ref10, author = {J. G. Brandenburg and G. Bender and J. Ren and A. Hansen and S. Grimme and H. Eckert and C. G. Daniliuc and G. Kehr and G. Erker}, title = {Crystal packing induced carbon-carbon double-triple bond isomerization in a zirconocene complex}, journal = {{Organometallics}}, year = {2014}, volume = {33}, pages = {5358--5364}, doi = {10.1021/om500678p}, abstract = {We present a combined theoretical and experimental analysis of the carbon-carbon bond character in two prototypical zirconocene complexes. The two cyclic seven-membered ring zirconium compounds 2a and 2b differ by the substitution of a tert-butyl by a trimethylsilyl group. Due to the coordination of the π-system to the metal atom, a formally forbidden ($\eta^2$-allenyl)/enamido-Zr to ($\eta^2$-alkyne)/$\kappa$N- imine-Zr complex isomerization is feasible. State-of-the-art dispersion-corrected density functional theory (DFT-D3) is used in both the solid and condensed phase to examine and quantify the experimental structures (X-ray diffraction) and $^{13}$C NMR magnetic shielding. The complementary investigations demonstrate the importance of nonlocal London dispersion interactions. Both X-ray structures agree excellently with the results of the solid-state DFT-D3 calculations. Interestingly, 2b exhibits a mixed allene-alkyne form in the solid state, while its gas phase structure has a strong allene character. The substitution leading to 2a prevents this isomerization in the solid state by the intramolecular stabilization of the allene structure. NMR solid and liquid phase measurements confirm the theoretically proposed transition. By combining the experimental and theoretical information, the rather unusual triple/single to double/double-bond transition is attributed to an intermolecular London dispersion induced crystal packing effect.} }`

- D. Schweinfurth, S. Demeshko, S. Hohloch, M. Steinmetz, J. G. Brandenburg, S. Dechert, F. Meyer, S. Grimme, and B. Sarkar, "Spin crossover in Fe(II) and Co(II) complexes with the same click-derived tripodal ligand," Inorg. Chem., vol. 53, p. 8203–8212, 2014. doi:10.1021/ic500264k

[BibTeX] [Abstract]

The complexes [Fe(tbta)2](BF4)2·2EtOH (1), [Fe(tbta)2](BF4)2·2CH3CN (2), [Fe(tbta) 2](BF4)2·2CHCl3 (3), and [Fe(tbta)2](BF4)2 (4) were synthesized from the respective metal salts and the click-derived tripodal ligand tris[(1-benzyl- 1H-1,2,3-triazol-4-yl)methyl]amine (tbta). Structural characterization of these complexes (at 100 or 133 K) revealed Fe-N bond lengths for the solvent containing compounds 1−3 that are typical of a high spin (HS) Fe(II) complex. In contrast, the solvent-free compound 4 show Fe−N bond lengths that are characteristic of a low spin (LS) Fe(II) state. The Fe center in all complexes is bound to two triazole and one amine N atom from each tbta ligand, with the third triazole arm remaining uncoordinated. The benzyl substituents of the uncoordinated triazole arms and the triazole rings engage in strong intermolecular and intramolecular noncovalent interactions. These interactions are missing in the solvent containing molecules 1, 2, and 3, where the solvent molecules occupy positions that hinder these noncovalent interactions. The solvent-free complex (4) displays spin crossover (SCO) with a spin transition temperature T1/2 near room temperature, as revealed by superconducting quantum interference device (SQUID) magnetometric and Moössbauer spectroscopic measurements. The complexes 1, 2, and 3 remain HS throughout the investigated temperature range. Different torsion angles at the metal centers, which are influenced by the noncovalent interactions, are likely responsible for the differences in the magnetic behavior of these complexes. The corresponding solvent-free Co(II) complex (6) is also LS at lower temperatures and displays SCO with a temperature T1/2 near room temperature. Theoretical calculations at molecular and periodic DFT-D3 levels for 1−4 qualitatively reproduce the experimental findings, and corroborate the importance of intermolecular and intramolecular noncovalent interactions for the magnetic properties of these complexes. The present work thus represents rare examples of SCO complexes where the use of identical ligand sets produces SCO in Fe(II) as well as Co(II) complexes.

`@article{brandenburg_ref09, author = {D. Schweinfurth and S. Demeshko and S. Hohloch and M. Steinmetz and J. G. Brandenburg and S. Dechert and F. Meyer and S. Grimme and B. Sarkar}, title = {Spin crossover in {Fe(II)} and {Co(II)} complexes with the same click-derived tripodal ligand}, journal = {{Inorg. Chem.}}, year = {2014}, volume = {53}, pages = {8203--8212}, doi = {10.1021/ic500264k}, abstract = {The complexes [Fe(tbta)2](BF4)2·2EtOH (1), [Fe(tbta)2](BF4)2·2CH3CN (2), [Fe(tbta) 2](BF4)2·2CHCl3 (3), and [Fe(tbta)2](BF4)2 (4) were synthesized from the respective metal salts and the click-derived tripodal ligand tris[(1-benzyl- 1H-1,2,3-triazol-4-yl)methyl]amine (tbta). Structural characterization of these complexes (at 100 or 133 K) revealed Fe-N bond lengths for the solvent containing compounds 1−3 that are typical of a high spin (HS) Fe(II) complex. In contrast, the solvent-free compound 4 show Fe−N bond lengths that are characteristic of a low spin (LS) Fe(II) state. The Fe center in all complexes is bound to two triazole and one amine N atom from each tbta ligand, with the third triazole arm remaining uncoordinated. The benzyl substituents of the uncoordinated triazole arms and the triazole rings engage in strong intermolecular and intramolecular noncovalent interactions. These interactions are missing in the solvent containing molecules 1, 2, and 3, where the solvent molecules occupy positions that hinder these noncovalent interactions. The solvent-free complex (4) displays spin crossover (SCO) with a spin transition temperature T1/2 near room temperature, as revealed by superconducting quantum interference device (SQUID) magnetometric and Mo\"{o}ssbauer spectroscopic measurements. The complexes 1, 2, and 3 remain HS throughout the investigated temperature range. Different torsion angles at the metal centers, which are influenced by the noncovalent interactions, are likely responsible for the differences in the magnetic behavior of these complexes. The corresponding solvent-free Co(II) complex (6) is also LS at lower temperatures and displays SCO with a temperature T1/2 near room temperature. Theoretical calculations at molecular and periodic DFT-D3 levels for 1−4 qualitatively reproduce the experimental findings, and corroborate the importance of intermolecular and intramolecular noncovalent interactions for the magnetic properties of these complexes. The present work thus represents rare examples of SCO complexes where the use of identical ligand sets produces SCO in Fe(II) as well as Co(II) complexes.} }`

- F. Malberg, J. G. Brandenburg, W. Reckien, O. Hollóczki, S. Grimme, and B. Kirchner, "Substitution effect and effect of axle's flexibility at (pseudo-) rotaxanes," Beilstein J. Org. Chem., vol. 10, p. 1299–1307, 2014. doi:10.3762/bjoc.10.131

[BibTeX] [Abstract] [Download PDF]

This study investigates the effect of substitution with different functional groups and of molecular flexibility by changing within the axle from a single C-C bond to a double C–C bond. Therefore, we present static quantum chemical calculations at the dispersion-corrected density functional level (DFT-D3) for several Leigh-type rotaxanes. The calculated crystal structure is in close agreement with the experimental X-ray data. Compared to a stiffer axle, a more flexible one results in a stronger binding by 1-3 kcal/mol. Alterations of the binding energy in the range of 5 kcal/mol could be achieved by substitution with different functional groups. The hydrogen bond geometry between the isophtalic unit and the carbonyl oxygen atoms of the axle exhibited distances in the range of 2.1 to 2.4 \AA\ for six contact points, which shows that not solely but to a large amount the circumstances in the investigated rotaxanes are governed by hydrogen bonding. Moreover, the complex with the more flexible axle is usually more unsymmetrical than the one with the stiff axle. The opposite is observed for the experimentally investigated axle with the four phenyl stoppers. Furthermore, we considered an implicit continuum solvation model and found that the complex binding is weakened by approximately 10 kcal/mol, and hydrogen bonds are slightly shortened (by up to 0.2 \AA).

`@article{brandenburg_ref08, author = {F. Malberg and J. G. Brandenburg and W. Reckien and O. Holl\'{o}czki and S. Grimme and B. Kirchner}, title = {Substitution effect and effect of axle's flexibility at (pseudo-) rotaxanes}, journal = {{Beilstein J. Org. Chem.}}, year = {2014}, volume = {10}, pages = {1299--1307}, doi = {10.3762/bjoc.10.131}, url = {../wp-content/papercite-data/pdf/brandenburg_ref08.pdf}, abstract = {This study investigates the effect of substitution with different functional groups and of molecular flexibility by changing within the axle from a single C-C bond to a double C--C bond. Therefore, we present static quantum chemical calculations at the dispersion-corrected density functional level (DFT-D3) for several Leigh-type rotaxanes. The calculated crystal structure is in close agreement with the experimental X-ray data. Compared to a stiffer axle, a more flexible one results in a stronger binding by 1-3 kcal/mol. Alterations of the binding energy in the range of 5 kcal/mol could be achieved by substitution with different functional groups. The hydrogen bond geometry between the isophtalic unit and the carbonyl oxygen atoms of the axle exhibited distances in the range of 2.1 to 2.4 \AA\ for six contact points, which shows that not solely but to a large amount the circumstances in the investigated rotaxanes are governed by hydrogen bonding. Moreover, the complex with the more flexible axle is usually more unsymmetrical than the one with the stiff axle. The opposite is observed for the experimentally investigated axle with the four phenyl stoppers. Furthermore, we considered an implicit continuum solvation model and found that the complex binding is weakened by approximately 10 kcal/mol, and hydrogen bonds are slightly shortened (by up to 0.2 \AA).} }`

- J. G. Brandenburg and S. Grimme, "Accurate modeling of organic molecular crystals by dispersion-corrected density functional tight-binding (DFTB)," J. Phys. Chem. Lett., vol. 5, p. 1785–1789, 2014. doi:10.1021/jz500755u

[BibTeX] [Abstract] [Download PDF]

The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20\%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of $<$0.5 kcal/mol compared to DFT-D are obtained.

`@article{brandenburg_ref07, author = {J. G. Brandenburg and S. Grimme}, title = {Accurate modeling of organic molecular crystals by dispersion-corrected density functional tight-binding {(DFTB)}}, journal = {{J. Phys. Chem. Lett.}}, year = {2014}, volume = {5}, pages = {1785--1789}, doi = {10.1021/jz500755u}, url = {../wp-content/papercite-data/pdf/brandenburg_ref07.pdf}, abstract = {The ambitious goal of organic crystal structure prediction challenges theoretical methods regarding their accuracy and efficiency. Dispersion-corrected density functional theory (DFT-D) in principle is applicable, but the computational demands, for example, to compute a huge number of polymorphs, are too high. Here, we demonstrate that this task can be carried out by a dispersion-corrected density functional tight binding (DFTB) method. The semiempirical Hamiltonian with the D3 correction can accurately and efficiently model both solid- and gas-phase inter- and intramolecular interactions at a speed up of 2 orders of magnitude compared to DFT-D. The mean absolute deviations for interaction (lattice) energies for various databases are typically 2-3 kcal/mol (10-20\%), that is, only about two times larger than those for DFT-D. For zero-point phonon energies, small deviations of $<$0.5 kcal/mol compared to DFT-D are obtained. } }`

- J. G. Brandenburg and S. Grimme, "Dispersion corrected hartree-fock and density functional theory for organic crystal structure prediction," Top. Curr. Chem., vol. 345, p. 1–23, 2014. doi:10.1007/128_2013_488

[BibTeX] [Abstract]

We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they strongly suffer from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method, which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs excellently for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.

`@article{brandenburg_ref06, author = {J. G. Brandenburg and S. Grimme}, title = {Dispersion corrected Hartree-Fock and density functional theory for organic crystal structure prediction}, journal = {{Top. Curr. Chem.}}, year = {2014}, volume = {345}, pages = {1--23}, doi = {10.1007/128_2013_488}, abstract = {We present and evaluate dispersion corrected Hartree-Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they strongly suffer from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method, which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs excellently for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.} }`

### 2013

- J. G. Brandenburg and S. Grimme, "A dispersion-corrected density functional theory case study on ethyl acetate conformers, dimer, and molecular crystal," Theo. Chem. Acc., vol. 132, p. 1399, 2013. doi:10.1007/s00214-013-1399-8

[BibTeX] [Abstract]

We present a dispersion-corrected density functional theory case study on recently reported apparently difficult systems (Boese et al. in Chem Phys Chem 14:799, 2013). The relative stability of the trans, gauche, and cis conformers of ethyl acetate, the dissociation energy of the (trans–trans) dimer, and the structure and electronic lattice energy of the corresponding molecular crystal are calculated. We utilize the generalized gradient approximation density functionals PBE and BLYP, the hybrid functional B3LYP, and the double-hybrid functional B2PLYP. It is shown that all semilocal density functionals must be corrected for missing long-range electron correlation, a.k.a. London dispersion interaction. The performance of the ab initio dispersion correction DFT-D3 is excellent and significantly improves the results compared to the uncorrected functionals and compared to the older more empirical DFT-D2 correction. The three-body dispersion contribution to the lattice energy is 7 %, while its impact on the crystal geometry and the conformer energies is negligible. A nonlocal correction approach termed DFT-NL is also tested and shows good performance comparable to the DFT-D3 results. Overall, it is shown that dispersion-corrected density functional theory can accurately describe the properties of ethyl acetate in various states ranging from single-molecule conformers to the infinite periodic molecular crystal.

`@article{brandenburg_ref05, author = {J. G. Brandenburg and S. Grimme}, title = {A dispersion-corrected density functional theory case study on ethyl acetate conformers, dimer, and molecular crystal}, journal = {{Theo. Chem. Acc.}}, year = {2013}, volume = {132}, pages = {1399}, doi = {10.1007/s00214-013-1399-8}, abstract = {We present a dispersion-corrected density functional theory case study on recently reported apparently difficult systems (Boese et al. in Chem Phys Chem 14:799, 2013). The relative stability of the trans, gauche, and cis conformers of ethyl acetate, the dissociation energy of the (trans–trans) dimer, and the structure and electronic lattice energy of the corresponding molecular crystal are calculated. We utilize the generalized gradient approximation density functionals PBE and BLYP, the hybrid functional B3LYP, and the double-hybrid functional B2PLYP. It is shown that all semilocal density functionals must be corrected for missing long-range electron correlation, a.k.a. London dispersion interaction. The performance of the ab initio dispersion correction DFT-D3 is excellent and significantly improves the results compared to the uncorrected functionals and compared to the older more empirical DFT-D2 correction. The three-body dispersion contribution to the lattice energy is 7 %, while its impact on the crystal geometry and the conformer energies is negligible. A nonlocal correction approach termed DFT-NL is also tested and shows good performance comparable to the DFT-D3 results. Overall, it is shown that dispersion-corrected density functional theory can accurately describe the properties of ethyl acetate in various states ranging from single-molecule conformers to the infinite periodic molecular crystal.} }`

- J. G. Brandenburg, M. Alessio, B. Civalleri, M. F. Peintinger, T. Bredow, and S. Grimme, "Geometrical correction for the inter-and intramolecular basis set superposition error in periodic density functional theory calculations," J. Phys. Chem. A, vol. 117, p. 9282–9292, 2013. doi:10.1021/jp406658y

[BibTeX] [Abstract] [Download PDF]

We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys−Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13\% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 \AA and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.

`@article{brandenburg_ref04, author = {J. G. Brandenburg and M. Alessio and B. Civalleri and M. F. Peintinger and T. Bredow and S. Grimme}, title = {Geometrical correction for the inter-and intramolecular basis set superposition error in periodic density functional theory calculations}, journal = {{J. Phys. Chem. A}}, year = {2013}, volume = {117}, pages = {9282--9292}, doi = {10.1021/jp406658y}, url = {../wp-content/papercite-data/pdf/brandenburg_ref04.pdf}, abstract = {We extend the previously developed geometrical correction for the inter- and intramolecular basis set superposition error (gCP) to periodic density functional theory (DFT) calculations. We report gCP results compared to those from the standard Boys−Bernardi counterpoise correction scheme and large basis set calculations. The applicability of the method to molecular crystals as the main target is tested for the benchmark set X23. It consists of 23 noncovalently bound crystals as introduced by Johnson et al. (J. Chem. Phys. 2012, 137, 054103) and refined by Tkatchenko et al. (J. Chem. Phys. 2013, 139, 024705). In order to accurately describe long-range electron correlation effects, we use the standard atom-pairwise dispersion correction scheme DFT-D3. We show that a combination of DFT energies with small atom-centered basis sets, the D3 dispersion correction, and the gCP correction can accurately describe van der Waals and hydrogen-bonded crystals. Mean absolute deviations of the X23 sublimation energies can be reduced by more than 70% and 80% for the standard functionals PBE and B3LYP, respectively, to small residual mean absolute deviations of about 2 kcal/mol (corresponding to 13\% of the average sublimation energy). As a further test, we compute the interlayer interaction of graphite for varying distances and obtain a good equilibrium distance and interaction energy of 6.75 \AA and -43.0 meV/atom at the PBE-D3-gCP/SVP level. We fit the gCP scheme for a recently developed pob-TZVP solid-state basis set and obtain reasonable results for the X23 benchmark set and the potential energy curve for water adsorption on a nickel (110) surface.} }`

- B. -H. Xu, K. Bussmann, R. Fröhlich, C. G. Daniliuc, J. G. Brandenburg, S. Grimme, G. Kehr, and G. Erker, "An enamine/HB(C$_6$F$_5$)$_2$ adduct as a dormant state in frustrated lewis pair chemistry," Organometallics, vol. 32, p. 6745–6725, 2013. doi:10.1021/om4004225

[BibTeX] [Abstract]

The enamine piperidinocyclopentene reacts with HB(C6F5)2 by formation of the C-Lewis base/B-Lewis acid adduct 10. It shows a zwitterionic iminium ion/hydridoborate structure. However, this adduct formation is apparently reversible and may generate the “invisible” frustrated Lewis pair 11 as a reactive intermediate by hydroboration of the enamine CC bond in an equilibrium situation at room temperature. Consequently, the FLP 11 was trapped by typical FLP reactions, namely by the reaction with dihydrogen to give the ammonium/hydridoborate 12, the acetylene deprotonation products 13 and 14, and simple borane adducts with pyridine (15) and with an isonitrile (17). The products 10 and 12−15 and the isonitrile adduct 17 were characterized by X-ray diffraction. A DFT study determined the thermodynamic features of the 10 ⇄ 11 equilibrium and of a previously discussed reference system (18 ⇄ 19) derived by reacting piperidinocyclohexene with HB(C6F5)2.

`@article{brandenburg_ref03, author = {B.-H. Xu and K. Bussmann and R. Fr\"ohlich and C. G. Daniliuc and J. G. Brandenburg and S. Grimme and G. Kehr and G. Erker}, title = {An enamine/{HB}({C}$_6${F}$_5$)$_2$ adduct as a dormant state in frustrated Lewis pair chemistry}, journal = {{Organometallics}}, year = {2013}, volume = {32}, pages = {6745--6725}, doi = {10.1021/om4004225}, abstract = {The enamine piperidinocyclopentene reacts with HB(C6F5)2 by formation of the C-Lewis base/B-Lewis acid adduct 10. It shows a zwitterionic iminium ion/hydridoborate structure. However, this adduct formation is apparently reversible and may generate the “invisible” frustrated Lewis pair 11 as a reactive intermediate by hydroboration of the enamine CC bond in an equilibrium situation at room temperature. Consequently, the FLP 11 was trapped by typical FLP reactions, namely by the reaction with dihydrogen to give the ammonium/hydridoborate 12, the acetylene deprotonation products 13 and 14, and simple borane adducts with pyridine (15) and with an isonitrile (17). The products 10 and 12−15 and the isonitrile adduct 17 were characterized by X-ray diffraction. A DFT study determined the thermodynamic features of the 10 ⇄ 11 equilibrium and of a previously discussed reference system (18 ⇄ 19) derived by reacting piperidinocyclohexene with HB(C6F5)2.} }`

- J. G. Brandenburg, S. Grimme, P. G. Jones, G. Markopoulos, H. Hopf, M. K. Cyranski, and D. Kuck, "Unidirectional molecular stacking of tribenzotriquinacenes in the solid state: a combined x-ray and theoretical study," Chem. Eur. J., vol. 19, p. 9930–9938, 2013. doi:10.1002/chem.201300761

[BibTeX] [Abstract]

A combined X-ray diffraction and theoretical study of the solid-state molecular and crystal structures of tribenzotriquinacene (TBTQ, 2) and its centro-methyl derivative (3) is presented. The molecular structure of the parent hydrocarbon displays C3v symmetry and the three indane wings adopt mutually orthogonal orientations, similar to the case in its previously reported methyl derivative (3). Also similarly to the latter structure, the bowl-shaped molecules of compound 2 form infinite molecular stacks with perfectly axial, face-to-back (convex–con-cave) packing and with parallel and unidirectional orientation of the stacks. The experimentally determined intra-stack molecular distance is 4.75 \AA for compound 2 and 5.95 \AA for compound 3. Whereas the molecules of compound 2 show a slight alternating rotation ($\pm$6$^{\circ}$) about the common axis of each stack, those of compound 3 show perfect translational symmetry within the stacks. We used dispersion-corrected density functional theory to compute the crystal structures of tribenzotriquinacenes 2 and 3. The London dispersion correction was crucial for obtaining an accurate description of the crystallization of both analyzed systems and the calculated results agreed excellently with the experimental measurements. We also obtained reasonable sublimation energies for both compounds. In addition, the geometries and dimerization energies of oligomeric stacks of compound 2 were computed and showed smooth convergence to the properties of the infinite polymeric stack.

`@article{brandenburg_ref02, author = {J. G. Brandenburg and S. Grimme and P. G. Jones and G. Markopoulos and H. Hopf and M. K. Cyranski and D. Kuck}, title = {Unidirectional molecular stacking of tribenzotriquinacenes in the solid state: A combined x-ray and theoretical study}, journal = {{Chem. Eur. J.}}, year = {2013}, volume = {19}, pages = {9930--9938}, doi = {10.1002/chem.201300761}, abstract = {A combined X-ray diffraction and theoretical study of the solid-state molecular and crystal structures of tribenzotriquinacene (TBTQ, 2) and its centro-methyl derivative (3) is presented. The molecular structure of the parent hydrocarbon displays C3v symmetry and the three indane wings adopt mutually orthogonal orientations, similar to the case in its previously reported methyl derivative (3). Also similarly to the latter structure, the bowl-shaped molecules of compound 2 form infinite molecular stacks with perfectly axial, face-to-back (convex–con-cave) packing and with parallel and unidirectional orientation of the stacks. The experimentally determined intra-stack molecular distance is 4.75 \AA for compound 2 and 5.95 \AA for compound 3. Whereas the molecules of compound 2 show a slight alternating rotation ($\pm$6$^{\circ}$) about the common axis of each stack, those of compound 3 show perfect translational symmetry within the stacks. We used dispersion-corrected density functional theory to compute the crystal structures of tribenzotriquinacenes 2 and 3. The London dispersion correction was crucial for obtaining an accurate description of the crystallization of both analyzed systems and the calculated results agreed excellently with the experimental measurements. We also obtained reasonable sublimation energies for both compounds. In addition, the geometries and dimerization energies of oligomeric stacks of compound 2 were computed and showed smooth convergence to the properties of the infinite polymeric stack.} }`

- J. G. Brandenburg and B. V. Fine, "Dimensionality of spin modulations in $1/8$-doped lanthanum cuprates from the perspective of nqr and $\mu$sr experiments," J. Supercond. Nov. Magn., vol. 26, p. 2621, 2013. doi:10.1007/s10948-013-2147-y

[BibTeX] [Abstract]

We investigate the dimensionality of inhomogeneous spin modulation patterns in the cuprate family of high-temperature superconductors with particular focus on 1/8-doped lanthanum cuprates. We compare one-dimensional stripe modulation pattern with two-dimensional checkerboard of spin vortices in the context of nuclear quadrupole resonance (NQR) and muon spin rotation ($\mu$SR) experiments. In addition, we also consider the third pattern, a two-dimensional superposition of spin spirals. Overall, we have found that none of the above patterns leads to a consistent interpretation of the two types of experiments considered. This, in particular, implies that the spin vortex checkerboard cannot be ruled out on the basis of available NQR/$\mu$SR experimental results.

`@article{brandenburg_ref01, author = {J. G. Brandenburg and B. V. Fine}, title = {Dimensionality of spin modulations in {$1/8$}-doped lanthanum cuprates from the perspective of NQR and {$\mu$}SR experiments}, journal = {{J. Supercond. Nov. Magn.}}, year = {2013}, volume = {26}, pages = {2621}, doi = {10.1007/s10948-013-2147-y}, abstract = {We investigate the dimensionality of inhomogeneous spin modulation patterns in the cuprate family of high-temperature superconductors with particular focus on 1/8-doped lanthanum cuprates. We compare one-dimensional stripe modulation pattern with two-dimensional checkerboard of spin vortices in the context of nuclear quadrupole resonance (NQR) and muon spin rotation ($\mu$SR) experiments. In addition, we also consider the third pattern, a two-dimensional superposition of spin spirals. Overall, we have found that none of the above patterns leads to a consistent interpretation of the two types of experiments considered. This, in particular, implies that the spin vortex checkerboard cannot be ruled out on the basis of available NQR/$\mu$SR experimental results.} }`