Diabatic States at Construction (DAC) through Generalized Singular Value Decomposition

Abstract

A procedure, called generalized diabatic-at-construction (GDAC), is presented to transform adiabatic potential energy surfaces into a diabatic representation by generalized singular value decomposition. First, we use a set of localized, valence bond-like configuration state functions, called DAC, as the basis states. Then, the adiabatic ground and relevant excited states are determined using multistate density functional theory (MSDFT). GDAC differs in the opposite direction from traditional approaches based on adiabatic-to-diabatic transformation with certain property restraints. The method is illustrated with applications to a model first-order bond dissociation reaction of CH 3 OCH 2 Cl polarized by a solvent molecule, the ground-and first-excited-state potential energy surfaces near the minimum conical intersection for the ammonia dimer photodissociation, and the multiple avoided curve crossings in the dissociation of lithium hydride. The GDAC diabatization method may be useful for defining charge-localized states in studies of electron transfer and proton-coupled electron transfer reactions in proteins.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

“…The matrix element of the Hamiltonian matrix functional of the multistate density in the subspace spanned by N states, ℛ N ℋ, is given by [ 18 , 20 , 23 ] where the terms on the right-hand side of the equation are, respectively, the kinetic energy, Coulomb (Hartree) and exchange energy, the external potential energy, and the exchange-correlation energy for the interactions between states A and B . If , Equation (1) is equivalent to KS-DFT for the density represented by the determinant .…”

“…Previous studies show that MSDFT can be a practical procedure to treat the ground and excited states on an equal footing [ 18 , 19 , 20 , 21 , 22 ]. Our goal is to use a minimal number of charge, spin or excitation-localized configurations, having valence-bond-like characters to represent charge transfer (CT) and excited configurations of molecular complexes [ 23 , 24 , 25 , 26 , 27 ]. A convenient approximation, in the spirit of configuration interaction (CI) in WFT, is to optimize the individual basis states in the active space that is sufficient to treat a given problem.…”

“…A convenient approximation, in the spirit of configuration interaction (CI) in WFT, is to optimize the individual basis states in the active space that is sufficient to treat a given problem. Such a constrained KS-DFT optimization can be accomplished by fragment block-localization or by targeted orbital optimization techniques [ 20 , 23 , 24 ]. Consequently, orbitals in different determinant functions are nonorthogonal.…”

“…Consequently, orbitals in different determinant functions are nonorthogonal. Since these Slater determinants are used to represent the multistate density for the real interacting system, this procedure is called nonorthogonal state interaction (NOSI) [ 23 , 24 , 25 , 26 ] to distinguish it from a nonorthogonal configuration interaction (NOCI) in which the dynamic correlation is absent [ 21 , 22 ]. Formally, the multistate matrix density corresponds to that derived from the corresponding contracted states of the full configuration interaction (FCI) wave function through singular value decomposition [ 20 ].…”

“…NOSI may be considered as one variant of the dynamic-then-static ansatz described by Liu and coworkers [ 28 ]. Moreover, diabatic states can be constructed within MSDFT framework [ 23 , 29 , 30 ].…”