Register      Login
Australian Journal of Chemistry Australian Journal of Chemistry Society
An international journal for chemical science
RESEARCH ARTICLE

A Trip to the Density Functional Theory Zoo: Warnings and Recommendations for the User*

Lars Goerigk A B and Nisha Mehta A
+ Author Affiliations
- Author Affiliations

A School of Chemistry, The University of Melbourne, Parkville, Vic. 3010, Australia.

B Corresponding author. Email: lars.goerigk@unimelb.edu.au

Australian Journal of Chemistry 72(8) 563-573 https://doi.org/10.1071/CH19023
Submitted: 17 January 2019  Accepted: 9 February 2019   Published: 1 March 2019

Abstract

This account is written for general users of density functional theory (DFT) methods as well as experimental researchers who are new to the field and would like to conduct such calculations. Its main emphasis lies on how to find a way through the confusing ‘zoo’ of DFT by addressing common misconceptions and highlighting those modern methods that should ideally be used in calculations of energetic properties and geometries. A particular focus is on highly popular methods and the important fact that popularity does not imply accuracy. In this context, we present a new analysis of the openly available data published in Swart and co-workers’ famous annual ‘DFT poll’ (http://www.marcelswart.eu/dft-poll/) to demonstrate the existing communication gap between the DFT user and developer communities. We show that despite considerable methodological advances in the field, the perception of some parts of the user community regarding their favourite approaches has changed little. It is hoped that this account makes a contribution towards changing this status and that users are inspired to adjust their current computational protocols to accommodate strategies that are based on proven robustness, accuracy, and efficiency rather than popularity.


References

[1]  W. Kohn, L. J. Sham, Phys. Rev. 1965, 140, A1133.
         | Crossref | GoogleScholarGoogle Scholar |

[2]  D. C. Langreth, J. P. Perdew, Phys. Rev. B Condens. Matter 1980, 21, 5469.
         | Crossref | GoogleScholarGoogle Scholar |

[3]  D. C. Langreth, M. J. Mehl, Phys. Rev. B Condens. Matter 1983, 28, 1809.
         | Crossref | GoogleScholarGoogle Scholar |

[4]  J. P. Perdew, Phys. Rev. B Condens. Matter 1986, 33, 8822.
         | Crossref | GoogleScholarGoogle Scholar | 9938299PubMed |

[5]  J. P. Perdew, Phys. Rev. B Condens. Matter 1986, 34, 7406.
         | Crossref | GoogleScholarGoogle Scholar | 9949100PubMed |

[6]  A. D. Becke, J. Chem. Phys. 1986, 84, 4524.
         | Crossref | GoogleScholarGoogle Scholar |

[7]  A. D. Becke, Phys. Rev. A 1988, 38, 3098.
         | Crossref | GoogleScholarGoogle Scholar |

[8]  C. Lee, W. Yang, R. G. Parr, Phys. Rev. B Condens. Matter 1988, 37, 785.
         | Crossref | GoogleScholarGoogle Scholar | 9944570PubMed |

[9]  B. Miehlich, A. Savin, H. Stoll, H. Preuss, Chem. Phys. Lett. 1989, 157, 200.
         | Crossref | GoogleScholarGoogle Scholar |

[10]  J. P. Perdew, in Proceedings of the 21st Annual International Symposium on the Electronic Structure of Solids (Eds P. Ziesche, H. Eschrig) 1991, p. 11 (Akademie Verlag: Berlin).

[11]  J. P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 1996, 77, 3865.
         | Crossref | GoogleScholarGoogle Scholar | 10062328PubMed |

[12]  A. D. Becke, J. Chem. Phys. 1993, 98, 1372.
         | Crossref | GoogleScholarGoogle Scholar |

[13]  A. D. Becke, J. Chem. Phys. 1993, 98, 5648.
         | Crossref | GoogleScholarGoogle Scholar |

[14]  H. Kruse, L. Goerigk, S. J. Grimme, J. Org. Chem. 2012, 77, 10824.
         | Crossref | GoogleScholarGoogle Scholar | 23153035PubMed |

[15]  P. Hohenberg, W. Kohn, Phys. Rev. B 1964, 136, 864.
         | Crossref | GoogleScholarGoogle Scholar |

[16]  J. P. Perdew, K. Schmidt, AIP Conf. Proc. 2001, 577, 1.
         | Crossref | GoogleScholarGoogle Scholar |

[17]  A. Szabo, N. S. Ostlund, Modern Quantum Chemistry: Introduction to Advanced Electronic Structure Theory 1989 (McGraw-Hill: New York, NY).

[18]  See pp. 254–255 in: F. Jensen Introduction to Computational Chemistry, 3rd edn 2017 (Wiley: Chichester).

[19]  W. Koch, M. C. Holthausen, A Chemist’s Guide to Density Functional Theory, 2nd edn 2001 (Wiley-VCH: New York, NY).

[20]  P.-F. Loos, P. M. W. Gill, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2016, 6, 410.
         | Crossref | GoogleScholarGoogle Scholar |

[21]  J. C. Slater, Phys. Rev. 1951, 81, 385.
         | Crossref | GoogleScholarGoogle Scholar |

[22]  S. J. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 1980, 58, 1200.
         | Crossref | GoogleScholarGoogle Scholar |

[23]  J. P. Perdew, Y. Wang, Phys. Rev. B Condens. Matter 1992, 45, 13244.
         | Crossref | GoogleScholarGoogle Scholar | 10001404PubMed |

[24]  S. Grimme, J. Comput. Chem. 2006, 27, 1787.
         | Crossref | GoogleScholarGoogle Scholar | 16955487PubMed |

[25]  R. Peverati, D. G. Truhlar, J. Chem. Theory Comput. 2012, 8, 2310.
         | Crossref | GoogleScholarGoogle Scholar | 26588964PubMed |

[26]  J. Tao, J. P. Perdew, V. N. Staroverov, G. E. Scuseria, Phys. Rev. Lett. 2003, 91, 146401.
         | Crossref | GoogleScholarGoogle Scholar | 14611541PubMed |

[27]  Y. Zhao, D. G. Truhlar, J. Chem. Phys. 2006, 125, 194101.
         | Crossref | GoogleScholarGoogle Scholar | 17129083PubMed |

[28]  M. Ernzerhof, G. E. Scuseria, J. Chem. Phys. 1999, 110, 5029.
         | Crossref | GoogleScholarGoogle Scholar |

[29]  C. Adamo, V. Barone, J. Chem. Phys. 1999, 110, 6158.
         | Crossref | GoogleScholarGoogle Scholar |

[30]  P. J. Stephens, F. J. Devlin, C. F. Chabalowski, M. J. Frisch, J. Phys. Chem. 1994, 98, 11623.
         | Crossref | GoogleScholarGoogle Scholar |

[31]  Y. Zhao, D. G. Truhlar, Theor. Chem. Acc. 2008, 120, 215.
         | Crossref | GoogleScholarGoogle Scholar |

[32]  S. Grimme, J. Chem. Phys. 2006, 124, 034108.
         | Crossref | GoogleScholarGoogle Scholar | 16438568PubMed |

[33]  L. Goerigk, S. Grimme, J. Chem. Theory Comput. 2011, 7, 291.
         | Crossref | GoogleScholarGoogle Scholar | 26596152PubMed |

[34]  S. Kozuch, D. Gruzman, J. M. L. Martin, J. Phys. Chem. C 2010, 114, 20801.
         | Crossref | GoogleScholarGoogle Scholar |

[35]  S. Kozuch, J. M. L. Martin, Phys. Chem. Chem. Phys. 2011, 13, 20104.
         | Crossref | GoogleScholarGoogle Scholar | 21993810PubMed |

[36]  S. Kozuch, J. M. L. Martin, J. Comput. Chem. 2013, 34, 2327.
         | Crossref | GoogleScholarGoogle Scholar | 23983204PubMed |

[37]  J.-D. Chai, M. Head-Gordon, J. Chem. Phys. 2009, 131, 174105.
         | Crossref | GoogleScholarGoogle Scholar | 19894996PubMed |

[38]  N. Mardirossian, M. Head-Gordon, J. Chem. Phys. 2018, 148, 241736.
         | Crossref | GoogleScholarGoogle Scholar | 29960332PubMed |

[39]  L. Goerigk, S. Grimme, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2014, 4, 576.
         | Crossref | GoogleScholarGoogle Scholar |

[40]  N. Mehta, M. Casanova-Páez, L. Goerigk, Phys. Chem. Chem. Phys. 2018, 20, 23175.
         | Crossref | GoogleScholarGoogle Scholar | 30062343PubMed |

[41]  R. M. Irelan, T. M. Henderson, G. E. Scuseria, J. Chem. Phys. 2011, 135, 094105.
         | Crossref | GoogleScholarGoogle Scholar | 21913751PubMed |

[42]  H. Eshuis, F. Furche, J. Phys. Chem. Lett. 2011, 2, 983.
         | Crossref | GoogleScholarGoogle Scholar |

[43]  A. J. Garza, I. W. Bulik, A. G. S. Alencar, J. Sun, J. P. Perdew, G. E. Scuseria, Mol. Phys. 2016, 114, 997.
         | Crossref | GoogleScholarGoogle Scholar |

[44]  S. Grimme, M. Steinmetz, Phys. Chem. Chem. Phys. 2016, 18, 20926.
         | Crossref | GoogleScholarGoogle Scholar | 26695184PubMed |

[45]  P. D. Mezei, G. I. Csonka, A. Ruzsinszky, M. Kállay, J. Chem. Theory Comput. 2015, 11, 4615.
         | Crossref | GoogleScholarGoogle Scholar | 26574252PubMed |

[46]  P. D. Mezei, G. I. Csonka, A. Ruzsinszky, M. Kállay, J. Chem. Theory Comput. 2017, 13, 796.
         | Crossref | GoogleScholarGoogle Scholar | 28052197PubMed |

[47]  J. Almlöf, Chem. Phys. Lett. 1991, 181, 319.
         | Crossref | GoogleScholarGoogle Scholar |

[48]  Y. S. Jung, R. C. Lochan, A. D. Dutoi, M. Head-Gordon, J. Chem. Phys. 2004, 121, 9793.
         | Crossref | GoogleScholarGoogle Scholar |

[49]  O. Vahtras, J. Almlöf, M. W. Feyereisen, Chem. Phys. Lett. 1993, 213, 514.
         | Crossref | GoogleScholarGoogle Scholar |

[50]  K. Raghavachari, A. Saha, Chem. Rev. 2015, 115, 5643.
         | Crossref | GoogleScholarGoogle Scholar | 25849163PubMed |

[51]  A. Karton, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2016, 6, 292.
         | Crossref | GoogleScholarGoogle Scholar |

[52]  L. A. Curtiss, K. Raghavachari, G. W. Trucks, J. A. Pople, J. Chem. Phys. 1991, 94, 7221.
         | Crossref | GoogleScholarGoogle Scholar |

[53]  L. A. Curtiss, K. Raghavachari, P. C. Redfern, J. A. Pople, J. Chem. Phys. 1997, 106, 1063.
         | Crossref | GoogleScholarGoogle Scholar |

[54]  L. A. Curtiss, K. Raghavachari, P. C. Redfern, V. Rassolov, J. A. Pople, J. Chem. Phys. 1998, 109, 7764.
         | Crossref | GoogleScholarGoogle Scholar |

[55]  L. A. Curtiss, P. C. Redfern, K. Raghavachari, J. Chem. Phys. 2005, 123, 124107.
         | Crossref | GoogleScholarGoogle Scholar | 16392475PubMed |

[56]  L. Goerigk, S. Grimme, Phys. Chem. Chem. Phys. 2011, 13, 6670.
         | Crossref | GoogleScholarGoogle Scholar | 21384027PubMed |

[57]  Y. Zhao, B. J. Lynch, D. G. Truhlar, Phys. Chem. Chem. Phys. 2005, 7, 43.
         | Crossref | GoogleScholarGoogle Scholar |

[58]  Y. Zhao, N. González-García, D. G. Truhlar, J. Phys. Chem. A 2005, 109, 2012.
         | Crossref | GoogleScholarGoogle Scholar | 16833536PubMed |

[59]  P. Jurečka, J. Sponer, J. Cerny, P. Hobza, Phys. Chem. Chem. Phys. 2006, 8, 1985.
         | Crossref | GoogleScholarGoogle Scholar | 16633685PubMed |

[60]  J. Rezáč, K. E. Riley, P. Hobza, J. Chem. Theory Comput. 2011, 7, 2427.
         | Crossref | GoogleScholarGoogle Scholar | 21836824PubMed |

[61]  A. Karton, A. Tarnopolsky, J. F. Lamere, G. C. Schatz, J. M. L. Martin, J. Phys. Chem. A 2008, 112, 12868.
         | Crossref | GoogleScholarGoogle Scholar | 18714947PubMed |

[62]  D. Gruzman, A. Karton, J. M. L. Martin, J. Phys. Chem. A 2009, 113, 11974.
         | Crossref | GoogleScholarGoogle Scholar | 19795892PubMed |

[63]  A. Karton, S. Daon, J. M. L. Martin, B. Ruscic, Chem. Phys. Lett. 2011, 510, 165.
         | Crossref | GoogleScholarGoogle Scholar |

[64]  S. Grimme, M. Steinmetz, M. Korth, J. Org. Chem. 2007, 72, 2118.
         | Crossref | GoogleScholarGoogle Scholar | 17286442PubMed |

[65]  M. Korth, S. Grimme, J. Chem. Theory Comput. 2009, 5, 993.
         | Crossref | GoogleScholarGoogle Scholar | 26609608PubMed |

[66]  K. Raghavachari, G. W. Trucks, J. A. Pople, M. Head-Gordon, Chem. Phys. Lett. 1989, 157, 479.
         | Crossref | GoogleScholarGoogle Scholar |

[67]  D. Beckett, T. J. El-Baba, D. E. Clemmer, K. Raghavachari, J. Chem. Theory Comput. 2018, 14, 5406.
         | Crossref | GoogleScholarGoogle Scholar | 30192543PubMed |

[68]  L. Goerigk, A. Hansen, C. Bauer, S. Ehrlich, A. Najibi, S. Grimme, Phys. Chem. Chem. Phys. 2017, 19, 32184.
         | Crossref | GoogleScholarGoogle Scholar | 29110012PubMed |

[69]  H. S. Yu, X. He, S. L. Li, D. G. Truhlar, Chem. Sci. 2016, 7, 5032.
         | Crossref | GoogleScholarGoogle Scholar | 30155154PubMed |

[70]  L. Goerigk, S. Grimme, J. Chem. Theory Comput. 2010, 6, 107.
         | Crossref | GoogleScholarGoogle Scholar | 26614324PubMed |

[71]  N. Mardirossian, M. Head-Gordon, Mol. Phys. 2017, 115, 2315.
         | Crossref | GoogleScholarGoogle Scholar |

[72]  B. Chan, J. Chem. Theory Comput. 2018, 14, 4254.
         | Crossref | GoogleScholarGoogle Scholar | 30004698PubMed |

[73]  Web of Science Core Collection, see http://www.webofscience.com

[74]  A. Najibi, L. Goerigk, J. Chem. Theory Comput. 2018, 14, 5725.
         | Crossref | GoogleScholarGoogle Scholar | 30299953PubMed |

[75]  T. Gould, Phys. Chem. Chem. Phys. 2018, 20, 27735.
         | Crossref | GoogleScholarGoogle Scholar | 30387792PubMed |

[76]  S. Kristyán, P. Pulay, Chem. Phys. Lett. 1994, 229, 175.
         | Crossref | GoogleScholarGoogle Scholar |

[77]  J. Pérez-Jordá, A. D. Becke, Chem. Phys. Lett. 1995, 233, 134.
         | Crossref | GoogleScholarGoogle Scholar |

[78]  P. Hobza, J. Sponer, T. Reschel, J. Comput. Chem. 1995, 16, 1315.
         | Crossref | GoogleScholarGoogle Scholar |

[79]  J. Sponer, J. Leszczynski, P. Hobza, J. Comput. Chem. 1996, 17, 841.
         | Crossref | GoogleScholarGoogle Scholar |

[80]  S. Grimme, A. Hansen, J. G. Brandenburg, C. Bannwarth, Chem. Rev. 2016, 116, 5105.
         | Crossref | GoogleScholarGoogle Scholar | 27077966PubMed |

[81]  S. Grimme, J. Antony, S. Ehrlich, H. Krieg, J. Chem. Phys. 2010, 132, 154104.
         | Crossref | GoogleScholarGoogle Scholar | 20423165PubMed |

[82]  A. Tkatchenko, R. A. DiStasio, R. Car, M. Scheffler, Phys. Rev. Lett. 2012, 108, 236402.
         | Crossref | GoogleScholarGoogle Scholar | 23003978PubMed |

[83]  A. Ambrosetti, A. M. Reilly, R. A. DiStasio, A. Tkatchenko, J. Chem. Phys. 2014, 140, 18A508.
         | Crossref | GoogleScholarGoogle Scholar | 24832316PubMed |

[84]  S. Grimme, J. Comput. Chem. 2004, 25, 1463.
         | Crossref | GoogleScholarGoogle Scholar | 15224390PubMed |

[85]  S. Grimme, S. Ehrlich, L. Goerigk, J. Comput. Chem. 2011, 32, 1456.
         | Crossref | GoogleScholarGoogle Scholar | 21370243PubMed |

[86]  H. Schröder, A. Creon, T. Schwabe, J. Chem. Theory Comput. 2015, 11, 3163.
         | Crossref | GoogleScholarGoogle Scholar | 26575753PubMed |

[87]  E. Caldeweyher, C. Bannwarth, S. Grimme, J. Chem. Phys. 2017, 147, 034112.
         | Crossref | GoogleScholarGoogle Scholar | 28734285PubMed |

[88]  E. Caldeweyher, S. Ehlert, A. Hansen, H. Neugebauer, S. Spicher, C. Bannwarth, S. Grimme, ChemRxiv 2018,
         | Crossref | GoogleScholarGoogle Scholar |

[89]  A. D. Becke, E. R. Johnson, J. Chem. Phys. 2005, 123, 154101.
         | Crossref | GoogleScholarGoogle Scholar | 16252936PubMed |

[90]  E. R. Johnson, A. D. Becke, J. Chem. Phys. 2006, 124, 174104.
         | Crossref | GoogleScholarGoogle Scholar | 16689564PubMed |

[91]  A. D. Becke, E. R. Johnson, J. Chem. Phys. 2007, 127, 154108.
         | Crossref | GoogleScholarGoogle Scholar | 17949133PubMed |

[92]  A. Tkatchenko, M. Scheffler, Phys. Rev. Lett. 2009, 102, 073005.
         | Crossref | GoogleScholarGoogle Scholar | 19257665PubMed |

[93]  S. N. Steinmann, C. Corminboeuf, J. Chem. Theory Comput. 2010, 6, 1990.
         | Crossref | GoogleScholarGoogle Scholar | 26615928PubMed |

[94]  S. N. Steinmann, C. Corminboeuf, J. Chem. Phys. 2011, 134, 044117.
         | Crossref | GoogleScholarGoogle Scholar | 21280697PubMed |

[95]  J. Hepburn, G. Scoles, R. Penco, Chem. Phys. Lett. 1975, 36, 451.
         | Crossref | GoogleScholarGoogle Scholar |

[96]  R. Ahlrichs, R. Penco, G. Scoles, Chem. Phys. 1977, 19, 119.
         | Crossref | GoogleScholarGoogle Scholar |

[97]  C&En Year in Review 2016, see: http://yearinreview.cenmag.org/lookback-at-2006/post-1576.

[98]  M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, et al., Gaussian 16 2016 (Gaussian, Inc.: Wallingford, CT).

[99]  L. Goerigk, in Non-Covalent Interactions in Quantum Chemistry and Physics (Eds A. Otero de la Roza, G. A. DiLabio) 2017, pp 195–219 (Elsevier: Amsterdam).

[100]  L. Goerigk, J. Phys. Chem. Lett. 2015, 6, 3891.
         | Crossref | GoogleScholarGoogle Scholar | 26722889PubMed |

[101]  M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, B. I. Lundqvist, Phys. Rev. Lett. 2004, 92, 246401.
         | Crossref | GoogleScholarGoogle Scholar | 15245113PubMed |

[102]  O. A. Vydrov, T. Van Voorhis, Phys. Rev. Lett. 2009, 103, 063004.
         | Crossref | GoogleScholarGoogle Scholar | 19792562PubMed |

[103]  K. Lee, E. D. Murray, L. Kong, B. I. Lundqvist, D. C. Langreth, Phys. Rev. B Condens. Matter Mater. Phys. 2010, 82, 081101.
         | Crossref | GoogleScholarGoogle Scholar |

[104]  O. A. Vydrov, T. J. Van Voorhis, Chem. Phys. 2010, 133, 244103.
         | Crossref | GoogleScholarGoogle Scholar |

[105]  W. Hujo, S. Grimme, J. Chem. Theory Comput. 2011, 7, 3866.
         | Crossref | GoogleScholarGoogle Scholar | 26598333PubMed |

[106]  N. Mardirossian, M. Head-Gordon, Phys. Chem. Chem. Phys. 2014, 16, 9904.
         | Crossref | GoogleScholarGoogle Scholar | 24430168PubMed |

[107]  N. Mardirossian, M. Head-Gordon, J. Chem. Phys. 2015, 142, 074111.
         | Crossref | GoogleScholarGoogle Scholar | 25702006PubMed |

[108]  N. Mardirossian, M. Head-Gordon, J. Chem. Phys. 2016, 144, 214110.
         | Crossref | GoogleScholarGoogle Scholar | 27276948PubMed |

[109]  F. Neese, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 73.
         | Crossref | GoogleScholarGoogle Scholar |

[110]  J. M. Turney, A. C. Simmonett, R. M. Parrish, E. G. Hohenstein, F. A. Evangelista, J. T. Fermann, B. J. Mintz, L. A. Burns, J. J. Wilke, M. L. Abrams, N. J. Russ, M. L. Leininger, C. L. Janssen, E. T. Seidl, W. D. Allen, H. F. Schaefer, R. A. King, E. F. Valeev, C. D. Sherrill, T. D. Crawford, Wiley Interdiscip. Rev. Comput. Mol. Sci. 2012, 2, 556.
         | Crossref | GoogleScholarGoogle Scholar |

[111]  Y. Shao, Z. Gan, E. Epifanovsky, A. T. Gilbert, M. Wormit, J. Kussmann, A. W. Lange, A. Behn, J. Deng, X. Feng, et al. Mol. Phys. 2015, 113, 184.
         | Crossref | GoogleScholarGoogle Scholar |

[112]  J. Lehtola, M. Hakala, A. Sakko, K. Hämäläinen, J. Comput. Chem. 2012, 33, 1572.
         | Crossref | GoogleScholarGoogle Scholar | 22528614PubMed |

[113]  O. A. von Lilienfeld, I. Tavernelli, U. Rothlisberger, D. Sebastiani, Phys. Rev. Lett. 2004, 93, 153004.
         | Crossref | GoogleScholarGoogle Scholar | 15524874PubMed |

[114]  G. A. DiLabio, Chem. Phys. Lett. 2008, 455, 348.
         | Crossref | GoogleScholarGoogle Scholar |

[115]  E. Torres, G. A. DiLabio, J. Phys. Chem. Lett. 2012, 3, 1738.
         | Crossref | GoogleScholarGoogle Scholar | 26291852PubMed |

[116]  T. Starkloff, J. D. Joannopoulos, Phys. Rev. B 1977, 16, 5212.
         | Crossref | GoogleScholarGoogle Scholar |

[117]  L. Goerigk, J. Chem. Theory Comput. 2014, 10, 968.
         | Crossref | GoogleScholarGoogle Scholar | 26580176PubMed |

[118]  A. Otero-de-la-Roza, G. A. DiLabio, J. Chem. Theory Comput. 2017, 13, 3505.
         | Crossref | GoogleScholarGoogle Scholar | 28636358PubMed |

[119]  V. K. Prasad, A. Otero-de-la Roza, G. A. DiLabio, J. Chem. Theory Comput. 2018, 14, 726.
         | Crossref | GoogleScholarGoogle Scholar | 29262249PubMed |

[120]  D. N. Tahchieva, D. Bakowies, R. Ramakrishnan, O. A. von Lilienfeld, J. Chem. Theory Comput. 2018, 14, 4806.
         | Crossref | GoogleScholarGoogle Scholar | 30011363PubMed |

[121]  A. Karton, J. M. L. Martin, J. Chem. Phys. 2012, 136, 124114.
         | Crossref | GoogleScholarGoogle Scholar | 22462842PubMed |

[122]  Y. Zhao, N. E. Schultz, D. G. Truhlar, J. Chem. Theory Comput. 2006, 2, 364.
         | Crossref | GoogleScholarGoogle Scholar | 26626525PubMed |

[123]  R. Peverati, D. G. Truhlar, Philos. Trans. R. Soc. A 2014, 372, 20120476.
         | Crossref | GoogleScholarGoogle Scholar |

[124]  L. Goerigk, H. Kruse, S. Grimme, ChemPhysChem 2011, 12, 3421.
         | Crossref | GoogleScholarGoogle Scholar | 22113958PubMed |

[125]  N. Mardirossian, M. Head-Gordon, J. Chem. Theory Comput. 2016, 12, 4303.
         | Crossref | GoogleScholarGoogle Scholar | 27537680PubMed |

[126]  H. S. Yu, X. He, D. G. Truhlar, J. Chem. Theory Comput. 2016, 12, 1280.
         | Crossref | GoogleScholarGoogle Scholar | 26722866PubMed |

[127]  S. Grimme, P. R. Schreiner, Angew. Chem. Int. Ed. 2011, 50, 12639.
         | Crossref | GoogleScholarGoogle Scholar |

[128]  S. Grimme, R. Huenerbein, S. Ehrlich, ChemPhysChem 2011, 12, 1258.
         | Crossref | GoogleScholarGoogle Scholar | 21445954PubMed |

[129]  J. P. Wagner, P. R. Schreiner, Angew. Chem. Int. Ed. 2015, 54, 12274.
         | Crossref | GoogleScholarGoogle Scholar |

[130]  S. Rösel, H. Quanz, C. Logemann, J. Becker, E. Mossou, L. Cañadillas-Delgado, E. Caldeweyher, S. Grimme, P. R. Schreiner, J. Am. Chem. Soc. 2017, 139, 7428.
         | Crossref | GoogleScholarGoogle Scholar | 28502175PubMed |

[131]  J. R. Reimers, D. Panduwinata, J. Visser, Y. Chin, C. Tang, L. Goerigk, M. J. Ford, M. Sintic, T.-J. Sum, M. J. J. Coenen, B. L. M. Hendriksen, J. A. A. W. Elemans, N. S. Hush, M. J. Crossley, Proc. Natl. Acad. Sci. USA 2015, 112, E6101.
         | Crossref | GoogleScholarGoogle Scholar | 26512115PubMed |

[132]  A. Karton, L. Goerigk, J. Comput. Chem. 2015, 36, 622.
         | Crossref | GoogleScholarGoogle Scholar | 25649643PubMed |

[133]  L. Goerigk, R. Sharma, Can. J. Chem. 2016, 94, 1133.
         | Crossref | GoogleScholarGoogle Scholar |

[134]  L. Goerigk, J. R. Reimers, J. Chem. Theory Comput. 2013, 9, 3240.
         | Crossref | GoogleScholarGoogle Scholar | 26583999PubMed |

[135]  L. Goerigk, C. A. Collyer, J. R. Reimers, J. Phys. Chem. B 2014, 118, 14612.
         | Crossref | GoogleScholarGoogle Scholar | 25410613PubMed |

[136]  Y. Zhang, W. Yang, Phys. Rev. Lett. 1998, 80, 890.
         | Crossref | GoogleScholarGoogle Scholar |

[137]  J. Sun, A. Ruzsinszky, J. P. Perdew, Phys. Rev. Lett. 2015, 115, 036402.
         | Crossref | GoogleScholarGoogle Scholar | 26230809PubMed |

[138]  J. G. Brandenburg, J. E. Bates, J. Sun, J. P. Perdew, Phys. Rev. B 2016, 94, 115144.
         | Crossref | GoogleScholarGoogle Scholar |

[139]  F. Yu, J. Chem. Theory Comput. 2014, 10, 4400.
         | Crossref | GoogleScholarGoogle Scholar | 26588137PubMed |

[140]  E. Brémond, I. Ciofini, J. C. Sancho-Garcia, C. Adamo, Acc. Chem. Res. 2016, 49, 1503.
         | Crossref | GoogleScholarGoogle Scholar | 27494122PubMed |

[141]  Y.-S. Lin, G.-D. Li, S.-P. Mao, J.-D. Chai, J. Chem. Theory Comput. 2013, 9, 263.
         | Crossref | GoogleScholarGoogle Scholar | 26589028PubMed |

[142]  Y. Zhao, D. G. Truhlar, J. Phys. Chem. A 2005, 109, 5656.
         | Crossref | GoogleScholarGoogle Scholar | 16833898PubMed |

[143]  http://www.marcelswart.eu/dft-poll/.

[144]  F. Neese, T. Schwabe, S. J. Grimme, Chem. Phys. 2007, 126, 124115.
         | Crossref | GoogleScholarGoogle Scholar |

[145]  P. Kraus, I. Frank, J. Phys. Chem. A 2018, 122, 4894.
         | Crossref | GoogleScholarGoogle Scholar | 29750513PubMed |

[146]  W. J. Hehre, R. Ditchfield, J. A. Pople, J. Chem. Phys. 1972, 56, 2257.
         | Crossref | GoogleScholarGoogle Scholar |

[147]  M. Kolar, T. Kubar, P. Hobza, J. Phys. Chem. B 2011, 115, 8038.
         | Crossref | GoogleScholarGoogle Scholar | 21574645PubMed |

[148]  S. Grimme, M. Steinmetz, Phys. Chem. Chem. Phys. 2013, 15, 16031.
         | Crossref | GoogleScholarGoogle Scholar | 23963317PubMed |

[149]  H. Kruse, S. Grimme, J. Chem. Phys. 2012, 136, 154101.
         | Crossref | GoogleScholarGoogle Scholar | 22519309PubMed |

[150]  J. Witte, J. B. Neaton, M. Head-Gordon, J. Chem. Phys. 2017, 146, 234105.
         | Crossref | GoogleScholarGoogle Scholar | 28641421PubMed |

[151]  S. Grimme, J. G. Brandenburg, C. Bannwarth, A. Hansen, J. Chem. Phys. 2015, 143, 054107.
         | Crossref | GoogleScholarGoogle Scholar | 26254642PubMed |

[152]  J. G. Brandenburg, C. Bannwarth, A. Hansen, S. Grimme, J. Chem. Phys. 2018, 148, 064104.
         | Crossref | GoogleScholarGoogle Scholar | 29448802PubMed |