Estimating the Derivative Coupling Vector Using Gradients

The difference gradient and derivative coupling vectors span the branching planes of conical intersections between electronic states. While gradients are commonly available in many electronic structure methods, the derivative coupling vectors are not always implemented and ready for use in characterizing conical intersections. This Letter shows how the derivative coupling vectors can be computed to high accuracy (direction and magnitude) using energy and gradient information. The new method is based on the combination of a linear-coupling two-state Hamiltonian and a finite-difference Davidson approach for computing the branching plane. Benchmark cases are provided showing these vectors can be efficiently computed near conical intersections.