Canonicalensemble stateaveraged complete active space selfconsistent field (SACASSCF) strategy for problems with more diabatic than adiabatic states: Chargebond resonance in monomethine cyanines
Abstract
This paper reviews basic results from a theory of the a priori classical probabilities (weights) in stateaveraged complete active space selfconsistent field (SACASSCF) models. It addresses how the classical probabilities limit the invariance of the selfconsistency condition to transformations of the complete active space configuration interaction (CASCI) problem. Such transformations are of interest for choosing representations of the SACASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SACASSCF can be selfconsistently transformed only within degenerate subspaces of the CASCI ensemble density matrix. For uniformly distributed (“microcanonical”) SACASSCF ensembles, selfconsistency is invariant to any unitary CASCI transformation that acts locally on the ensemble support. Most SACASSCF applications in current literature are microcanonical. A problem with microcanonical SACASSCF models for problems with “more diabatic than adiabatic” states is described. The problem is that not all diabatic energies and couplings are selfconsistently resolvable. A canonicalensemble SACASSCF strategy is proposed to solve the problem. For canonicalensemble SACASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CASCI Hamiltonian and a Lagrange multiplier acting as an inverse “temperature,” unrelated to the physical temperature. Like the convergence criterion for microcanonicalensemble SACASSCF, the equilibration condition formore »
 Authors:
 School of Mathematics and Physics, The University of Queensland, Brisbane QLD 4072 (Australia)
 Publication Date:
 OSTI Identifier:
 22416042
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 142; Journal Issue: 4; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; CHEMICAL BONDS; CONFIGURATION INTERACTION; CONVERGENCE; COVALENCE; CYANIDES; DENSITY MATRIX; ELECTRONIC STRUCTURE; HAMILTONIANS; HYDROCARBONS; PHOTONS; RESONANCE; SELFCONSISTENT FIELD; TRANSFORMATIONS; VALENCE
Citation Formats
Olsen, Seth, Email: seth.olsen@uq.edu.au. Canonicalensemble stateaveraged complete active space selfconsistent field (SACASSCF) strategy for problems with more diabatic than adiabatic states: Chargebond resonance in monomethine cyanines. United States: N. p., 2015.
Web. doi:10.1063/1.4904298.
Olsen, Seth, Email: seth.olsen@uq.edu.au. Canonicalensemble stateaveraged complete active space selfconsistent field (SACASSCF) strategy for problems with more diabatic than adiabatic states: Chargebond resonance in monomethine cyanines. United States. doi:10.1063/1.4904298.
Olsen, Seth, Email: seth.olsen@uq.edu.au. 2015.
"Canonicalensemble stateaveraged complete active space selfconsistent field (SACASSCF) strategy for problems with more diabatic than adiabatic states: Chargebond resonance in monomethine cyanines". United States.
doi:10.1063/1.4904298.
@article{osti_22416042,
title = {Canonicalensemble stateaveraged complete active space selfconsistent field (SACASSCF) strategy for problems with more diabatic than adiabatic states: Chargebond resonance in monomethine cyanines},
author = {Olsen, Seth, Email: seth.olsen@uq.edu.au},
abstractNote = {This paper reviews basic results from a theory of the a priori classical probabilities (weights) in stateaveraged complete active space selfconsistent field (SACASSCF) models. It addresses how the classical probabilities limit the invariance of the selfconsistency condition to transformations of the complete active space configuration interaction (CASCI) problem. Such transformations are of interest for choosing representations of the SACASSCF solution that are diabatic with respect to some interaction. I achieve the known result that a SACASSCF can be selfconsistently transformed only within degenerate subspaces of the CASCI ensemble density matrix. For uniformly distributed (“microcanonical”) SACASSCF ensembles, selfconsistency is invariant to any unitary CASCI transformation that acts locally on the ensemble support. Most SACASSCF applications in current literature are microcanonical. A problem with microcanonical SACASSCF models for problems with “more diabatic than adiabatic” states is described. The problem is that not all diabatic energies and couplings are selfconsistently resolvable. A canonicalensemble SACASSCF strategy is proposed to solve the problem. For canonicalensemble SACASSCF, the equilibrated ensemble is a Boltzmann density matrix parametrized by its own CASCI Hamiltonian and a Lagrange multiplier acting as an inverse “temperature,” unrelated to the physical temperature. Like the convergence criterion for microcanonicalensemble SACASSCF, the equilibration condition for canonicalensemble SACASSCF is invariant to transformations that act locally on the ensemble CASCI density matrix. The advantage of a canonicalensemble description is that more adiabatic states can be included in the support of the ensemble without running into convergence problems. The constraint on the dimensionality of the problem is relieved by the introduction of an energy constraint. The method is illustrated with a complete active space valencebond (CASVB) analysis of the charge/bond resonance electronic structure of a monomethine cyanine: Michler’s hydrol blue. The diabatic CASVB representation is shown to vary weakly for “temperatures” corresponding to visible photon energies. Canonicalensemble SACASSCF enables the resolution of energies and couplings for all covalent and ionic CASVB structures contributing to the SACASSCF ensemble. The CASVB solution describes resonance of charge and bondlocalized electronic structures interacting via bridge resonance superexchange. The resonance couplings can be separated into channels associated with either covalent charge delocalization or chemical bonding interactions, with the latter significantly stronger than the former.},
doi = {10.1063/1.4904298},
journal = {Journal of Chemical Physics},
number = 4,
volume = 142,
place = {United States},
year = 2015,
month = 1
}

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