λ-Density Functional Valence Bond: A Valence Bond-Based Multiconfigurational Density Functional Theory With a Single Variable Hybrid Parameter

Abstract

A new valence bond (VB)-based multireference density functional theory (MRDFT) method, named λ-DFVB, is presented in this paper. The method follows the idea of the hybrid multireference density functional method theory proposed by Sharkas et al. ( 2012 ). λ-DFVB combines the valence bond self-consistent field (VBSCF) method with Kohn–Sham density functional theory (KS-DFT) by decomposing the electron–electron interactions with a hybrid parameter λ. Different from the Toulouse's scheme, the hybrid parameter λ in λ-DFVB is variable, defined as a function of a multireference character of a molecular system. Furthermore, the E C correlation energy of a leading determinant is introduced to ensure size consistency at the dissociation limit. Satisfactory results of test calculations, including potential energy surfaces, bond dissociation energies, reaction barriers, and singlet–triplet energy gaps, show the potential capability of λ-DFVB for molecular systems with strong correlation.

A Valence-Bond-Based Multiconfigurational Density Functional Theory: The λ-DFVB Method Revisited

“…The value of K ranges from 0 to 1, as F A is identical to V A in the dissociation limit. Equation ( 7) can be implemented by a modified VBSCF route [42]. To this end, the structure coefficients {C K } and orbitals {φ i } are optimized by minimizing…”

“…In a similar fashion, the strategy of hybrid VB theory with DFT has been implemented, such as VBDFT(s) [35][36][37][38], VB-DFT [39], and DFVB [40][41][42]. Recently, a newly developed MRDFT scheme based on the valence bond wave function, namely the λ-density functional valence bond (λ-DFVB) method [42], was presented. This method is inspired by the MC1H approximation proposed by Sharkas et al [22].…”

“…To describe the extent of the multireference character, the molecular free valence index K is used in λ-DFVB, and the functional form of λ is taken tentatively as λ = K 1/4 . The molecular free valence index K is defined by the total atomic free valences and the bond orders of the molecule, expressed in terms of the overlap and spin density matrices [42].…”

Incorporating dynamic correlation into the variational determination method of the second‐order reduced density matrix in the doubly occupied configuration interaction space

“…[42] using a hybrid scheme, hereafter denoted as v2RDM‐DOCI‐ λ PDFT, given by the following equation where the E X and E C functionals are the exchange and correlation terms, respectively. [ 43 ] The hybrid parameter, λ ∈ [0, 1], balances the contributions of the v2RDM‐DOCI and PDFT schemes according to the nature of the system described. Equation ) constitutes an improvement of the treatment represented by Equation ) and can be particularly recommended when very strongly correlated systems are considered.…”

“…where the E X and E C functionals are the exchange and correlation terms, respectively. [43] The hybrid parameter, λ ∈ [0, 1], balances the contributions of the v2RDM-DOCI and PDFT schemes according to the nature of the system described. Equation (10) constitutes an improvement of the treatment represented by Equation ( 8) and can be particularly recommended when very strongly correlated systems are considered.…”