Variational fractional-spin density-functional theory for diradicals

Abstract

Accurate computation of singlet-triplet energy gaps of diradicals remains a challenging problem in density-functional theory (DFT). In this work, we propose a variational extension of our previous work [D. H. Ess, E. R. Johnson, X. Q. Hu, and W. T. Yang, J. Phys. Chem. A 115, 76 (2011)], which applied fractional-spin density-functional theory (FS-DFT) to diradicals. The original FS-DFT approach assumed equal spin-orbital occupancies of 0.5 α-spin and 0.5 β-spin for the two degenerate, or nearly degenerate, frontier orbitals. In contrast, the variational approach (VFS-DFT) optimizes the total energy of a singlet diradical with respect to the frontier-orbital occupation numbers, based on a full configuration-interaction picture. It is found that the optimal occupation numbers are exactly 0.5 α-spin and 0.5 β-spin for diradicals such as O(2), where the frontier orbitals belong to the same multidimensional irreducible representation, and VFS-DFT reduces to FS-DFT for these cases. However, for diradicals where the frontier orbitals do not belong to the same irreducible representation, the optimal occupation numbers can vary between 0 and 1. Furthermore, analysis of CH(2) by VFS-DFT and FS-DFT captures the (1)A(1) and (1)B(1) states, respectively. Finally, because of the static correlation error in commonly used density functional approximations, both VFS-DFT and FS-DFT calculations significantly overestimate the singlet-triplet energy gaps for disjoint diradicals, such as cyclobutadiene, in which the frontier orbitals are confined to separate atomic centers.

Theory and practice of uncommon molecular electronic configurations

“…In terms of computations, relatively ‘cheap’ methods such as unrestricted or broken symmetry formalisms suffer from a number of serious drawbacks, while rigorous methods—configuration interaction (CI), multiconfigurational self‐consistent field (MCSCF), complete active space (CAS), multireference and spin‐flip equation‐of‐motion coupled clusters (MR‐CC and SF‐EOM‐CC)—are generally not feasible for systems large enough to be practically valuable. A number of promising accurate AND affordable methods to treat strongly correlated systems, including Quantum Monte Carlo with the Jastrow ansatz, DFT with fractional occupations, delta self‐consistent field (∆SCF) approximation in DFT, fractional‐spin DFT, density matrix renormalization group (DMRG) theory, constraint‐pairing mean‐field theory, particle–particle random phase approximation—have been in development in recent years . Despite these challenges, a range of species have already been extensively studied and characterized with either an open‐shell singlet ground state, or nearly degenerate singlet and triplet states.…”

Density Functional Model for Nondynamic and Strong Correlation

“…For comparison, we recite the B13 method, perhaps the only general-purpose DFT functional designed for dynamic, nondynamic, and strong correlations. It adds the following correlation energy to the full exact exchange: 13…”

“…It would dissociate a bond properly, but has the problem of double-counting some of the correlation. Functionals of variable occupation numbers of the KS orbitals have been suggested as a partial remedy 5,12,13 . Related to the latter approach, the density matrix functional theory (DMFT) has been pursued [14][15][16] .…”

Perspective: Fifty years of density-functional theory in chemical physics

“…202. Fractional occupancies 202,203 are implicated in this and other avoided-crossing problems. 204 It is not possible to represent the D 4h density of the open-shell square H 4 structure, or structures near it, without fractional occupancies.…”