Block-Localized Wavefunction (BLW) Method at the Density Functional Theory (DFT) Level

Abstract

The block-localized wavefunction (BLW) approach is an ab initio valence bond (VB) method incorporating the efficiency of molecular orbital (MO) theory. It can generate the wavefunction for a resonance structure or diabatic state self-consistently by partitioning the overall electrons and primitive orbitals into several subgroups and expanding each block-localized molecular orbital in only one subspace. Although block-localized molecular orbitals in the same subspace are constrained to be orthogonal (a feature of MO theory), orbitals between different subspaces are generally nonorthogonal (a feature of VB theory). The BLW method is particularly useful in the quantification of the electron delocalization (resonance) effect within a molecule and the charge-transfer effect between molecules. In this paper, we extend the BLW method to the density functional theory (DFT) level and implement the BLW-DFT method to the quantum mechanical software GAMESS. Test applications to the pi conjugation in the planar allyl radical and ions with the basis sets of 6-31G(d), 6-31+G(d), 6-311+G(d,p), and cc-pVTZ show that the basis set dependency is insignificant. In addition, the BLW-DFT method can also be used to elucidate the nature of intermolecular interactions. Examples of pi-cation interactions and solute-solvent interactions will be presented and discussed. By expressing each diabatic state with one BLW, the BLW method can be further used to study chemical reactions and electron-transfer processes whose potential energy surfaces are typically described by two or more diabatic states.

A comparison of approaches to estimate the resonance energy

“…In the BLW approach, the delocalisation energy is thus calculated. Of course other methods like DFT could be used as well for BLW, instead of HartreeFock [14,15]. In any case, the hypothetical molecules are only accessible computationally by restricting the variational space in which the wave function is expanded or by the use of fixed (non-optimised) orbitals.…”

What governs nitrogen configuration in substituted aminophosphines?

“…The higher the separation (bifurcation) value, the higher the expected degree of delocalization of electron pairing between these domains. [56] The geometric and energetic effects of p-electron delocalization are measured using the block-localized wavefunction (BLW) approach of Mo et al [57,58] BLW is a molecular orbital-based procedure for obtaining valence bond quantities that represents a unique approach for probing electron delocalization in chemical systems. It allows for the localization of electrons in specific regions of the molecular system, which may, for example, include 2p electrons in a C --C bond, or an electron lone pair.…”

Advanced Potential Energy Surfaces for Molecular Simulation

“…Several popular categories of EDA methods include symmetry-adapted perturbation theory (SAPT) [152][153][154] , and variational methods that originate from the Kituara-Morokuma EDA formalism 149,[155][156][157][158][159][160] , including the absolutely localized molecular orbital (ALMO)-EDA developed by Head-Gordon and co-workers. [161][162][163] In recently submitted work, we have used the second generation of (ALMO)-EDA [164][165][166] , combined with the high quality ωB97X-V density functional 128 , to compare against the energy decomposition of terms in the AMOEBA potential for the water dimer and various simple ionwater dimers 76 , an example of which is shown in Figure 6.…”