Generalization of Block-Localized Wave Function for Constrained Optimization of Excited Determinants

Abstract

The block-localized wave function method is useful to provide insights on chemical bonding and intermolecular interactions through energy decomposition analysis. The method relies on block localization of molecular orbitals (MOs) by constraining the orbitals to basis functions within given blocks. Here, a generalized block-localized orbital (GBLO) method is described to allow both physically localized and delocalized MOs to be constrained in orbital-block definitions. Consequently, GBLO optimization can be conveniently tailored by imposing specific constraints. The GBLO method is illustrated by three examples: (1) constrained polarization response orbitals through dipole and quadrupole perturbation in a water dimer complex, (2) the ground and first excited-state potential energy curves of ethene about its C–C bond rotation, and (3) excitation energies of double electron excited states. Multistate density functional theory is used to determine the energies of the adiabatic ground and excited states using a minimal active space (MAS) comprising specifically charge-constrained and excited determinant configurations that are variationally optimized by the GBLO method. We find that the GBLO expansion that includes delocalized MOs in configurational blocks significantly reduces computational errors in comparison with physical block localization, and the computed ground- and excited-state energies are in good accordance with experiments and results obtained from multireference configuration interaction calculations.

Minimal Active Space for Diradicals Using Multistate Density Functional Theory

“…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 ].…”

Self-Adaptive Real-Time Time-Dependent Density Functional Theory for Core Excitations

“…In particular, full spin adaptation can be achieved within the framework of multi-state DFT [2][3][4][5] . Yet, such one-by-one calculations of core excited states may not always be possible due to the non-Aufbau nature, given the availability of many algorithms [6][7][8][9][10][11][12][13][14][15][16] . In contrast, TDDFT can access all core excited states in one shot, by either diagonalization as in linear response (LR) TDDFT [17][18][19][20][21][22][23][24][25][26][27][28][29] or spectral analysis of the time signal generated by real-time (rt) TDDFT [30][31][32][33][34][35][36][37][38] .…”

A Critical Look at Linus Pauling’s Influence on the Understanding of Chemical Bonding

“…However, it is fair to say that problems like the homolytic bond breaking of electron-pair bonds are more easily dealt with using VB calculations, which remains an important approach in the toolbox of quantum chemical methods [ 99 , 100 , 101 , 102 , 103 , 104 , 126 , 127 ]. The VB and MO methods have been compared and discussed in several papers, which shed further light on the two approaches [ 128 , 129 , 130 , 131 , 132 , 133 , 134 ].…”