Perspective: Chemical Information Encoded in Electron Density

doi:10.3866/PKU.WHXB201801261

Abstract

Abstract:

In this perspective, we review the chemical information encoded in electron density and other ingredients used in semilocal functionals. This information is usually looked at from the functional point of view: the exchange density or the enhancement factor are discussed in terms of the reduced density gradient. However, what parts of a molecule do these 3D functions represent? We look at these quantities in real space, aiming to understand the electronic structure information they encode and provide an insight from the quantum chemical topology (QCT). Generalized gradient approximations (GGAs) provide information about the presence of chemical interactions, whereas meta-GGAs can differentiate between the different bonding types. By merging these two techniques, we show new insight into the failures of semilocal functionals owing to three main errors: fractional charges, fractional spins, and non-covalent interactions. We build on simple models. We also analyze the delocalization error in hydrogen chains, showing the ability of QCT to reveal the delocalization error introduced by semilocal functionals. Then, we show how the analysis of localization can help understand the fractional spin error in alkali atoms, and how it can be used to correct it. Finally, we show that the poor description of GGAs of isodesmic reactions in alkanes is due to 1, 3-interactions.

Key words: DFT, Semi-local functional, Electron density, Quantum chemical topology

Julia CONTRERAS-GARCíA,Weitao YANG. Perspective: Chemical Information Encoded in Electron Density[J]. Acta Phys. -Chim. Sin. 2018, 34(6), 567-580. doi: 10.3866/PKU.WHXB201801261

References

1	Perdew J. P. ; Schmidt K. AIP Conference Proceedings 2001, 577, 1.
2	Popelier P. L. A. Quantum Chemical Topology in "The Chemical Bond Ⅱ: 100 Years Old and Getting Stronger"; Mingos, D., Michael P.., Eds. Springer: Cham, Switzerland 2016.
3	Bader R. F. W. Atoms in Molecules: A Quantum Theory Oxford Science Publications: Oxford, UK 1990.
4	Matta C. F. ; Boyd R. J. An Introduction to the Quantum Theory of Atoms in Molecules Wiley-VCH Verlag GmbH & Co.: Hoboken, NJ, US 2007.
5	Becke A. D. ; Edgecombe K. E. J. Chem. Phys. 1990, 92, 5397.
6	Silvi B. ; Savin A. Nature 1994, 371, 683.
7	Savin A. ; Nesper R. ; Wengert S. ; F?ssler T. F. Angew. Chem. Int. Ed. 1997, 36, 1808.
8	Schmider H. L. ; Becke A. D. J. Mol. Struct. Theochem. 2000, 527, 51.
9	Schmider H. L. ; Becke A. D. J. Chem. Phys. 2002, 116, 3184.
10	Hohenberg P. ; Kohn W. Phys. Rev B 1964, 136, 864.
11	Spackman M. ; Maslen E. J. Phys. Chem. 1986, 90, 2020.
12	Gunnarsson O. ; Lunqvist B. I. Phys. Rev. B 1976, 13, 4274.
13	Becke A. D. Phys. Rev. A. 1988, 38, 3098.
14	Perdew J. P. ; Wang Y. Phys. Rev. B 1992, 45, 13244.
15	Lee C. ; Yang W. ; Parr R. G. Phys. Rev. B. 1988, 37, 785.
16	Sahni V. ; Gruenebaum J. ; Perdew J. P. Phys. Rev. B. 1982, 26, 4371.
17	Pearson E. W. ; Gordon R. G. J. Chem. Phys 1985, 82, 881.
18	Perdew J. P. ; Burke K. ; Ernzerhof M. Phys. Rev. Lett. 1996, 77, 3865.
19	Zupan A. ; Perdew J. P. ; Burke K. ; Causá M. Int. J. Quantum Chem. 1997, 61, 835.
20	Zupan A. ; Burke K. ; Ernzerhof M. ; Perdew J. P. J. Chem. Phys. 1997, 106, 10184.
21	Tognetti V. ; Cortona P. ; Adamo C. J. Chem. Phys. 2008, 128, 034101.
22	Boto R. A. ; Contreras-García J. ; Tierny J. ; Piquemal J. P. Mol. Phys. 2015, 114, 1.
23	Johnson E. R. ; Keinan S. ; Mori-Sánchez P. ; Contreras-García J. ; Cohen A. J. ; Yang W. J. Am. Chem. Soc. 2010, 132, 6498.
24	Lane J. R. ; Contreras-García J. ; Piquemal J. P. ; Miller B. J. ; Kjaergaard H. G. J. Chem. Theory Comp. 2013, 9, 3263.
25	del Campo J. M. ; Gázquez J. L. ; Alvarez-Mendez R. J. ; Vela A. Int. J. Quantum Chem. 2012, 112, 3594.
26	Boto R. A. ; Piquemal J. P. ; Contreras-García J. Theor. Chem. Acc. 2017, 136, 139.
27	Arfken G. Mathematical Methods for Physicists Academic Press: Orlando, FL, USA 1985.
28	Bader R. F. W. ; Essén H. J. Chem. Phys. 1984, 80, 1943.
29	Slater J. C. J. Chem. Phys. 1933, 1, 687.
30	Silvi B. J. Phys. Chem. A. 2003, 107, 3081.
31	Kohout M. ; Pernal K. ; Wagner F. R. ; Grin Y. Theor. Chem. Acc. 2005, 113, 287.
32	Becke A. D. J. Chem. Phys. 2000, 112, 4020.
33	Contreras-García J. ; Recio J. M. Theor. Chem. Acc. 2011, 128, 411.
34	Contreras-García J. ; Martin Pendás A. ; Silvi B. ; Recio J. M. Phys. Chem. B 2009, 113, 1068.
35	Kohout M. ; Savin A. Int. J. Quantum Chem. 1996, 60, 875.
36	Sun J. ; Perdew J. P. ; Ruzsinszky A. Proc. Natl. Acad. Sci. USA 2015, 112, 685.
37	Philipsen P. H. T. ; Baerends E. J. Phys. Rev. B 1996, 54, 5326.
38	Sun J. ; Xiao B. ; Fang Y. ; Haunschild R. ; Hao P. ; Ruzsinszky A. ; Csonka G. I. ; Scuseria E. ; Perdew J. P. Phys. Rev. Lett. 2013, 111, 106401.
39	Zhao Y. ; Truhlar D. G. J. Chem. Phys. 2006, 125, 194101.
40	Sun J. ; Haunschild R. ; Xiao B. ; Bulik I. W. ; Scuseria G. E. ; Perdew J. P. J. Chem. Phys. 2013, 138, 044113.
41	Tao J. ; Perdew J. P. ; Starorerov V. N. ; Scuseria G. E. Phys. Rev. Lett. 2003, 91, 146401.
42	Johnson E. R. ; Becke A. D. ; Sherrill C. D. ; DiLabio G. A. J. Chem. Phys. 2009, 131, 034111.
43	Sun J. ; Remsing R. C. ; Zhang Y. ; Sun Z. ; Ruzsinszky A. ; Peng H. ; Yang Z. ; Paul A. ; Waghmare U. ; Wu X. ; et al Nat. Chem. 2016, 8, 831.
44	Car R. Nat. Chem. 2016, 8, 820.
45	Cohen A. J. ; Mori-Sánchez P. ; Yang W. Science 2008, 321, 792.
46	Mori-Sánchez P. ; Cohen A. J. ; Yang W. Phys. Rev. Lett. 2008, 100, 146401.
47	Cohen A. J. ; Mori-Sánchez P. ; Yang W. Phys. Rev. B 2008, 77, 115123.
48	Cohen A. J. ; Mori-Sánchez P. ; Yang W. J. Chem. Phys. 2008, 129, 121104.
49	Becke A. D. J. Chem. Phys. 1993, 98, 5648.
50	Perdew J. P. ; Parr R. G. ; Levy M. ; Balduz J. L. Phys. Rev. Lett. 1982, 49, 1691.
51	Geerlings P. ; De Proft F. ; Langenaeker W. Chem. Rev. 2003, 103, 1793.
52	Cohen A. J. ; Mori-Sánchez P. ; Yang W. J. Chem. Phys. 2007, 126, 191109.
53	Yanai T. ; Tew D. P. ; Handy N. C. Chem. Phys. Lett. 2004, 393, 51.
54	Zheng X. ; Liu M. ; Johnson E. R. ; Contreras-García J. ; Yang W. J. Chem. Phys. 2012, 137, 214106.
55	Yang W. ; Zhang Y. ; Ayers P. W. Phys. Rev. Lett. 2000, 84, 5172.
56	Perdew J. P. ; Ruzsinszky A. ; Constantin L. A. ; Sun J. ; Csonka G. I. J. Chem. Theory Comput. 2009, 5, 902.
57	Ruzsinszky A. ; Perdew J. P. ; Csonka G. I. J. Phys. Chem. A 2005, 109, 11006.
58	Mori-Sánchez P. ; Cohen A. J. ; Yang W. Phys. Rev. Lett. 2009, 102, 066403.
59	Cuevas-Saavedra R. ; Chakraborty D. ; Rabi S. ; Cardenas C. ; Ayers P. W. J. Chem. Theory Comp 2012, 8, 4081.
60	Yang D. X. ; Patel A. H. G. ; Miranda-Quintana R. A. ; Heidar-Zadeh F. ; González-Espinoza C. E. ; Ayers P. W. J. Chem. Phys. 2016, 145, 031102.
61	Becke A. D. J. Chem. Phys. 2003, 119, 2972.
62	Becke A. D. J. Chem. Phys. 2005, 122, 064101.
63	Dickson R. M. ; Becke A. D. J. Chem. Phys. 2005, 123, 111101.
64	Johnson E. R. ; Contreras-García J. J. Chem. Phys. Commun. 2011, 135, 081103.
65	Shi Z. ; Boyd R. J. J. Chem. Phys. 1988, 88, 4375.
66	Krukau A. V. ; Scuseria G. E. ; Perdew J. P. ; Savin A. J. Chem. Phys. 2008, 129, 124103.
67	Johnson E. R. ; Mori-Sánchez P. ; Cohen A. J. ; Yang W. J. Chem. Phys. 2008, 129, 204112.
68	Armstrong A. ; Boto R. A. ; Dingwall P. ; Contreras-García J. ; Harvey M. J. ; Mason N. ; Rzepa H. R. Chem. Sci. 2014, 5, 2057.
69	Wodrich M. D. ; Corminboeuf C. ; Schleyer P. v. R. Org. Lett. 2006, 8, 3631.
70	Wodrich M. D. ; Wannere C. S. ; Mo Y. ; Jarowski P. D. ; Houk K. N. ; Schleyer P. v. R. Chem. Eur. J. 2007, 13, 7731.
71	Song J. W. ; Tsuneda T. ; Sato T. ; Hirao K. Org. Lett. 2010, 12, 1440.
72	Grimme S. Org. Lett. 2010, 12, 4670.
73	Steinmann S. N. ; Wodrich M. D. ; Corminboeuf C. Theor. Chem. Acta 2010, 127, 429.
74	Perdew J. P. ; Burke K. ; Ernzerhof M. Phys. Rev. Lett. 1996, 77, 3865.
75	Perdew J. P. ; Ruzsinszky A. ; Csonka G. I. ; Vydrov O. A. ; Scuseria G. E. ; Constantin L. A. ; Zhou X. ; Burke K. Phys. Rev. Lett. 2008, 100, 136406.
76	Grimme S. Angew. Chem. Int. Ed. 2006, 45, 4460.
77	Grimme S. ; Steinmetz M. ; Korth M. J. Org. Chem. 2007, 72, 2118.
78	Karton A. ; Gruzman D. ; Martin J. M. L. J. Phys. Chem. 2009, 113, 8434.
79	Shamov G. A. ; Budzelaar H. M. ; Schreckenbach G. J. Chem. Theory Comput. 2010, 6, 477.
80	Csonka G. I. ; Ruzsinszky A. ; Perdew J. P. ; Grimme S. J. Chem. Theory Comput. 2008, 4, 888.
81	Brittain D. R. B. ; Lin C. Y. ; Gilbert A. T. B. ; Izgorodina E. I. ; Gill P. M. W. ; Coote M. L. Phys. Chem. Chem. Phys. 2009, 11, 1138.
82	Becke A. D. ; Dickson R. M. J. Chem. Phys. 1990, 92, 3610.
83	Curtiss L. A. ; Redfern P. C. ; Raghavachari K. ; Pople J. A. J. Chem. Phys. 2001, 114, 108.
84	Johnson E. R. ; Contreras-García J. ; Yang W. J. Chem. Theor. Comp. 2012, 8, 2626.
85	Grimme S. J. Comput. Chem. 2006, 27, 1787.
86	Frisch M. J. ; Trucks G. W. ; Schlegel H. B. ; Scuseria G. E. ; Robb M. A. ; Cheeseman J. R. ; Scalmani G. ; Barone V. ; Mennucci B. ; Petersson G. A. ; et al Gaussian 09 Revision B. 01; Gaussian, Inc.: Wallingford, CT, USA 2010.
87	Contreras-García J. ; Johnson E. R. ; Keinan S. ; Chaudret R. ; Piquemal J. P. ; Beratan D. N. ; Yang W. J. Chem. Theory Comput. 2011, 7, 625.

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