A Dynamically Weighted Constrained Complete Active Space Ansatz for Constructing Multiple Potential Energy Surfaces Within the Anderson-Holstein Model

Abstract

We derive and implement the necessary equations for solving a dynamically weighted, state-averaged constrained CASSCF(2,2) wavefunction describing a molecule on a metal surface. We show that a partial constraint is far more robust than a full constraint. We further calculate the system-bath electronic couplings that arise because, near a metal, there is a continuum (rather than discrete) number of electronic states. This approach should be very useful for simulating heterogeneous electron transfer going forward.

Nonadiabatic Potential Energy Surfaces for a Molecule on a Surface as Found by Constrained Complete Active Space Theory

“…Our experience above will lead us to the concept of a constrained CASSCF (cCASSCF) optimization procedure, whereby we insist that the molecular population in the active space (spanned by active orbitals { t , u }) always has magnitude equal to unity: ∑ μ ∈ impurity ⟨ t | d μ † d μ | t ⟩ + ⟨ u | d μ † d μ | u ⟩ = 1 This approach helps with the intruder state problem, but excited states can still be discontinuous far away from the crossing regime. Dynamically weighted state-averaged constrained CASSCF (DW-SA-cCASSCF). Our best overall candidate for exploring excited state dynamics at an interface, with accurate electronic energies and smooth surfaces, combines both the dynamical weighting and the impurity constraint to definitively solve the intruder state problem for the AH model. For a complete description of the relevant theory and all of the relevant equations needed to define and implement these methods, please see ref .…”

“…This conclusion leads to the constraint in eq . In ref , we derive in detail the necessary equations that must be implemented in order to solve CASSCF­(2,2) with such a constraint. In short, one can integrate a standard CASSCF routine within a Lagrange multiplier self-consistent loop.…”

“…Note that these raw diabats are not calculated from an adiabatic-to-diabatic transformation. The parameter set is mω 2 For a complete description of the relevant theory and all of the relevant equations needed to define and implement these methods, please see ref 71.…”