Long-range correlations in density functional theory

Accurate and low-cost reproduction of electron correlations remains one of the most difficult problems in chemical physics. Enormous progress has been made in dealing with short-range correlations. But long-range correlations remain challenging, despite contributing to a range of important quantum chemical problems including dispersion forces [1-2], strong correlations [3-4] and charge transfer excitations [5]. This talk will discuss the origins of key types of long-range correlations in density functional theory, and consider physical, chemical and mathematical perspectives on the problem. It will discuss some low-cost solutions to difficult problems in the field, introduced by the author and others, and will highlight some of the challenges that lie ahead. It will stress the importance of the universal functional in devising new approximations, and how ensembles and the fluctuation-dissipation theorem help, even in “mundane” cases. [6]

[1] “London dispersion forces in molecules, solids and nano-structures: …”, J. Ángyán, J. Dobson, G. Jansen, T. Gould, Royal Society of Chemistry (2020)

[2] M. Kim, W. J. Kim, T. Gould, E. K. Lee, S. Lebègue, H. Kim, J. Am. Chem. Soc. 142, 2346–2354 (2020)

[3] T. Gould and S. Pittalis, Phys. Rev. Lett. 123, 016401 (2019).

[4] T. Gould and S. Vuckovic, J. Chem. Phys. 151, 184101 (2019)

[5] T. Gould, L. Kronik, and S. Pittalis, J. Chem. Phys. 148, 174101 (2018)

[6] T. Gould, G. Stefanucci, and S. Pittalis, Phys. Rev. Lett. 125, 233001 (2020)