Density functional theory with fractional orbital occupations

TL;DR

This paper introduces a modified density functional theory with fractional orbital occupations that better captures static correlation in many-electron systems, improving results for multi-reference cases and large acenes.

Contribution

It proposes a DFT approach with fractional occupations that enhances modeling of static correlation, applicable to complex molecules like acenes.

Findings

Improved accuracy for multi-reference systems like dissociation of H2 and N2.

Good agreement of singlet-triplet gaps with experimental data.

Large acenes exhibit polyradical singlet ground states.

Abstract

In contrast to the original Kohn-Sham (KS) formalism, we propose a density functional theory (DFT) with fractional orbital occupations for the study of ground states of many-electron systems, wherein strong static correlation is shown to be described. Even at the simplest level represented by the local density approximation (LDA), our resulting DFT-LDA is shown to improve upon KS-LDA for multi-reference systems, such as dissociation of H2 and N2, and twisted ethylene, while performing similarly to KS-LDA for single-reference systems, such as reaction energies and equilibrium geometries. Because of its computational efficiency (similar to KS-LDA), this DFT-LDA is applied to the study of the singlet-triplet energy gaps (ST gaps) of acenes, which are "challenging problems" for conventional electronic structure methods due to the presence of strong static correlation effects. Our calculated ST gaps are in good agreement with the existing experimental and high-level ab initio data. The ST gaps are shown to decrease monotonically with the increase of chain length, and become vanishingly small (within 0.1 kcal/mol) in the limit of an infinitely large polyacene. In addition, based on our calculated active orbital occupation numbers, the ground states for large acenes are shown to be polyradical singlets.