How important are the residual nonadiabatic couplings for an accurate simulation of nonadiabatic quantum dynamics in a quasidiabatic representation?

Abstract

Quasidiabatization of the molecular Hamiltonian is a standard approach to remove the singularity of nonadiabatic couplings at a conical intersection of adiabatic potential energy surfaces. Typically, the residual nonadiabatic couplings between quasidiabatic states are simply neglected. Here, we investigate the validity of this potentially drastic approximation by comparing the quantum dynamics simulated either with or without these couplings. By comparing the two simulations in the same quasidiabatic representation, we entirely avoid errors due to the transformation between representations. To eliminate grid and time discretization errors even in simulations with the nonseparable quasidiabatic Hamiltonian, we use the highly accurate and general eighth-order composition of the implicit midpoint method. To show that the importance of the residual couplings can depend on the employed quasidiabatization scheme, we compare the first-and second-order regular diabatizations applied to the cubic E ⊗e Jahn-Teller model, whose parameters were chosen so that the magnitudes of the residual couplings differed by a factor of 200. As a consequence, neglecting the residual couplings in the first-order scheme results in very unreliable dynamics, while it has almost no effect in the second-order scheme. In contrast, the simulation with the exact quasidiabatic Hamiltonian is accurate regardless of the quasidiabatization scheme.