Block-Localized Density Functional Theory (BLDFT), Diabatic Coupling, and Their Use in Valence Bond Theory for Representing Reactive Potential Energy Surfaces

Abstract

A multistate density functional theory in the framework of the valence bond model is described. The method is based on a block-localized density functional theory (BLDFT) for the construction of valence-bond-like diabatic electronic states and is suitable for the study of electron transfer reactions and for the representation of reactive potential energy surfaces. The method is equivalent to a valence bond theory with the treatment of the localized configurations by using density functional theory (VBDFT). In VBDFT, the electron densities and energies of the valence bond states are determined by BLDFT. A functional estimate of the off-diagonal matrix elements of the VB Hamiltonian is proposed, making use of the overlap integral between Kohn-Sham determinants and the exchangecorrelation functional for the ground state substituted with the transition (exchange) density. In addition, we describe an approximate approach, in which the off-diagonal matrix element is computed by wave function theory using block-localized Kohn-Sham orbitals. The key feature is that the electron density of the adiabatic ground state is not directly computed nor used to obtain the ground-state energy; the energy is determined by diagonalization of the multistate valence bond Hamiltonian. This represents a departure from the standard single-determinant Kohn-Sham density functional theory. The multistate VBDFT method is illustrated by the bond dissociation of and a set of three nucleophilic substitution reactions in the DBH24 database. In the dissociation of , the VBDFT method yields the correct asymptotic behavior as the two protons stretch to infinity, whereas approximate functionals fail badly. For the S N 2 nucleophilic substitution reactions, the hybrid functional B3LYP severely underestimates the barrier heights, while the approximate two-state VBDFT method overcomes the self-interaction error, and overestimates the barrier heights. Inclusion of the ionic state in a three-state model, VBDFT(3), significantly improves the computed barrier heights, which are found to be in accord with accurate results. The BLDFT method is a versatile theory that can be used to analyze conventional DFT results to gain insight into chemical bonding properties, and it is illustrated by examining the intricate energy contributions to the ion-dipole complex stabilization.

Diabatic-At-Construction Method for Diabatic and Adiabatic Ground and Excited States Based on Multistate Density Functional Theory

“…Let n b and μ b denote respectively the number of electrons and basis functions in fragment block b (where n 1 + ⋯+ n M A = n ). We use block-localized Kohn–Sham (BLKS) orbitals; 50 these are linear combinations of the atomic orbital basis functions restricted to a given block. The determinant function for configuration A is $$false|{\mathrm{\Psi }}_{A}false⟩=N_{\mathrm{A}}\hat{A}false\{{\varphi }_1^A\cdots {\varphi }_{M_A}^{A}false\}$$ where  is the antisymmetrizer, N A is a normalization factor, and ${\phi }_m^A$ specifies a product of the BLKS orbitals of block m .…”

“…50 In step 1(b), the singlet (and analogously triplet) CSFs, as given by eqs 2a and 2d–2g, were obtained by diagonalizing the corresponding spincoupled Hamiltonian matrix. These CSFs are not necessarily the diabatic ground and excited states.…”

“…3,56 The use of BLMO or block-localized Kohn−Sham (BLKS) orbitals reduces a large number of valence bond configurations to a manageable number; only those critical to a given system are retained in a way analogous to the spin-coupled valence bond theory. 64,65 This method has been extended to density functional theory, in which case it is called multistate density functional theory (MSDFT), 18,50,51,66,67 and this is the method that is used in the present work.…”

Flickering dipoles in the gas phase: Structures, internal dynamics, and dipole moments of β-naphthol-H2O in its ground and excited electronic states

“…For this reason, a high-level theoretical treatment of the acid-base interaction in the electronic ground state has been made via a block-localized wavefunction energy and dipole decomposition analysis (BLW-ED), 43 which can be performed both using wave functional theory and density functional theory (DFT). 44,45 The BLW-ED method has been applied to a variety of systems, [43][44][45] including Lewis acid-base complexes. 46 The energy decomposition was performed with the BLDFT method using the XMVB program 24 and a modified version of GAMESS.…”

“…46 The energy decomposition was performed with the BLDFT method using the XMVB program 24 and a modified version of GAMESS. 25,45 These calculations, while not yet accounting for the flickering electric field arising from water internal motion, do vastly improve upon the other issues mentioned above. The dipole moment decomposition of cis-2HNA and cis-2HNW is discussed below.…”