Abstract
A recently developed valence-bond-based multireference density functional theory, named λ-DFVB, is revisited in this paper. λ-DFVB remedies the double-counting error of electron correlation by decomposing the electron–electron interactions into the wave function term and density functional term with a variable parameter λ. The λ value is defined as a function of the free valence index in our previous scheme, denoted as λ-DFVB(K) in this paper. Here we revisit the λ-DFVB method and present a new scheme based on natural orbital occupation numbers (NOONs) for parameter λ, named λ-DFVB(IS), to simplify the process of λ-DFVB calculation. In λ-DFVB(IS), the parameter λ is defined as a function of NOONs, which are straightforwardly determined from the many-electron wave function of the molecule. Furthermore, λ-DFVB(IS) does not involve further self-consistent field calculation after performing the valence bond self-consistent field (VBSCF) calculation, and thus, the computational effort in λ-DFVB(IS) is approximately the same as the VBSCF method, greatly reduced from λ-DFVB(K). The performance of λ-DFVB(IS) was investigated on a broader range of molecular properties, including equilibrium bond lengths and dissociation energies, atomization energies, atomic excitation energies, and chemical reaction barriers. The computational results show that λ-DFVB(IS) is more robust without losing accuracy and comparable in accuracy to high-level multireference wave function methods, such as CASPT2.
Highlights
The electronic structure calculations of strongly correlated systems, which cannot be well described by a single configuration space function, are still challenging in the methodology development of electronic structure theory
In order to validate the use of ND in measuring the static correlation, Figure 1 shows the plots of the correlation entropy S2 = −∑ln(ni/2), which is widely used for i diagnosing the extent of the multireference character versus the free valence index K (a) and the number of effectively unpaired electrons, the ND index, (b) for the transition states in the DBH24 datasets computed by valence bond self-consistent field (VBSCF)
Different from the previous work, λ-density functional valence bond (λ-DFVB)(K), where parameter λ was determined by the free valence of a molecule, in this paper, we present a simplified definition for parameter λ
Summary
The electronic structure calculations of strongly correlated systems, which cannot be well described by a single configuration space function, are still challenging in the methodology development of electronic structure theory. In valence bond (VB) theory, the valence bond self-consistent field (VBSCF) [2,3], which is a multiconfigurational self-consistent field (MCSCF) analog with atomic orbitals (AOs), covers the static correlation by expressing the many-electron wave function of the molecule as a linear combination of VB structures. To cover dynamic correlations within the CASSCF scheme, post-CASSCF methods are required, such as the complete active space second-order perturbation theory (CASPT2) [4] and multireference configuration interaction (MRCI) [5]. Their analogs are present in VB theory, valence bond configuration interaction (VBCI) [6,7], and valence bond perturbation theory (VBPT2) [8,9], respectively. The computational costs of both methods are still expensive, compared to their MO analogs
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