Transition orbital projection approach for excited state tracking

Abstract

Quantitively comparing the features between different electronic excited states (ESs) is a crucial task in both potential energy surface (PES) studies and excited-state fragmentation approaches. However, it is still a challenging problem in regard to the comparison of complex and highly degenerate systems. Herein, we present a transition orbital projection (TOP) method to calculate the similarity of different ESs based on the configuration vectors of two types of transition densities. It fully considers four significant problems, including phase, hole-particle bijectivity, orbital permutation, and sign of configuration coefficients. TOP state-tracking-based excited-state optimization shows high robustness in several high-symmetric systems, which are difficult to describe with traditional state-tracking approaches. The TOP state-tracking method is expected to be widely applied to the PES of photochemical reactions, ES molecular dynamics to track the diabatic states, and fragmentation approaches for local excitation of large systems.