Spin‐restricted ensemble‐referenced Kohn–Sham method: basic principles and application to strongly correlated ground and excited states of molecules

Abstract

Ensemble density functional theory (DFT) is a novel theoretical approach that is capable of exact treatment of non-dynamic electron correlation in the ground and excited states of many-body fermionic systems. In contrast to ordinary DFT, ensemble DFT has not found so far a way to the repertoire of methods of modern computational chemistry, probably owing to the lack of practically affordable implementations of the theory. The spin-restricted ensemble-referenced Kohn-Sham (REKS) method represents perhaps the first computational scheme that makes ensemble DFT calculations feasible. The REKS method is based on the rigorous ensemble representation of the energy and the density of a strongly correlated system and provides for an accurate and consistent description of molecular systems the electronic structure of which is dominated by the non-dynamic correlation. This includes the ground and excited states of molecules undergoing bond breaking/bond formation, the low-spin states of biradicals and polyradicals, symmetry forbidden chemical reactions and avoided crossings of potential energy surfaces, real intersections between the energy surfaces of the ground and excited states (conical intersections), and many more. The REKS method can be employed in connection with any local, semi-local and hybrid (global and range-separated) functional and affords calculations of large and very large molecular systems at a moderate mean-field cost.

A QTAIM and stress tensor investigation of the torsion path of a light-driven fluorene molecular rotary motor

“…The description of certain types of excited states is further improved by considering coupling between the states described by eqs. and , which leads to the state‐interaction SA‐REKS (SI‐SA‐REKS) methodology …”

Surface Hopping Dynamics with DFT Excited States

“…3 has two main features which dominate the topography and the dynamics in the S 1 state: (a) there is an S 1 minimum near θ ¼ 90 and φ ¼ 60 and (b) there is a conical intersection at θ ¼ 90 and φ ¼ 110 . Among all tested methods, the only ones able to reproduce both features are the DFT-MRCI [102] and REKS [91,99,101], which makes clear the importance of having a multiconfigurational description of the ground state. TDDFT-UBS, which is usually considered a good alternative for qualitatively recovering nondynamic electron correlation near a degeneracy [71], can describe reasonably well the Spurious minima were also observed in TDDFT and TDA with B3LYP [121,122].…”

“…The development of a density functional theory including nondynamic (or "strong") electron correlation -which Becke designated as the "last frontier" in DFT [97] -has been pursued by many groups following different approaches. Among these approaches, we may cite the use of restricted open-shell ground-state representations [98], configuration ensembles with fractional occupations [91,[99][100][101], configuration interaction [102,103], multiconfigurational DFT [104], hybrid multiconfiguration/(TD)DFT [105,106], and spin-unrestricted broken-symmetry (UBS) [107] approaches. Unfortunately, analytical energy gradients are not available for most of these methods, which rules out their use in surface hopping dynamics.…”

Next‐generation quantum theory of atoms in molecules for the photochemical ring‐opening reactions of oxirane

“…Quantum chemical calculations were carried out using the state‐interaction state‐averaged spin‐restricted ensemble‐referenced Kohn‐Sham (SI‐SA‐REKS, or SSR) method . The SSR method enables one to describe electron correlation effects arising in due to multireference character of the ground and excited electronic states through the use of ensemble density functional theory .…”