Analytic Gradients and Derivative Couplings for Configuration Interaction with All Single Excitations and One Double Excitation -- En Route to Nonadiabatic Dynamics

TL;DR

This paper develops analytic gradients and derivative couplings for the CIS-1D method, enabling efficient nonadiabatic dynamics simulations by including key double excitations on top of Hartree-Fock reference.

Contribution

It introduces stable, efficient equations for gradients and couplings in CIS-1D, a multireference method with all singles and one double excitation, implemented in Q-Chem.

Findings

Equations are numerically stable and require similar integrals as standard CIS.

Differentiation of frontier orbitals is computationally minimal.

Implementation facilitates understanding of photochemical $S_{0}$-$S_{1}$ crossings.

Abstract

We present analytic gradients and derivative couplings for the simplest possible multireference configuration interaction method, CIS-1D, an electronic structure ansatz that includes all single excitations and one lone double excitation on top of a Hartree-Fock reference state. We show that the resulting equations are numerically stable and require the evaluation of a similar number of integrals as compared to standard CIS theory; one can easily differentiate the required frontier orbitals ($\mathtt{h}$ and $\mathtt{l}$) with minimal cost. The resulting algorithm has been implemented within the Q-Chem electronic structure package and should be immediately useful for understanding photochemistry with $S_{0}$-$S_{1}$ crossings.