A biorthonormal formalism for nonadiabatic coupled cluster dynamics

TL;DR

This paper extends coupled cluster theory to a biorthonormal formalism for nonadiabatic molecular dynamics, enabling more efficient computation of nonadiabatic couplings without full-CI normalization.

Contribution

It introduces a biorthonormal formalism for coupled cluster methods applied to nonadiabatic dynamics, allowing invariant and efficient calculation of couplings.

Findings

Formalism is invariant under electronic basis transformations.

Nonadiabatic coupling elements can be expressed with biorthonormal wave functions.

Normalization factors scale more favorably than full-CI calculations.

Abstract

In coupled cluster methods, the electronic states are biorthonormal in the sense that the left states are orthonormal to the right states. Here we present an extension of this formalism to a left and right total molecular wave function. Starting from left and right Born-Huang expansions, we derive projected Schr\"odinger equations for the left and right nuclear wave functions. Observables may be extracted from the resulting wave function pair using standard expressions. The formalism is shown to be invariant under electronic basis transformations, such as normalization of the electronic states. Consequently, the nonadiabatic coupling elements can be expressed with biorthonormal wave functions. Calculating normalization factors that scale as full-CI is therefore not necessary, contrary to claims in the literature. For nuclear dynamics, we therefore need expressions for the vector and scalar couplings in the biorthonormal formalism. We derive these expressions using a Lagrangian formalism.