Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?

Abstract

Choosing an appropriate representation of the molecular Hamiltonian is one of the challenges faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact and unitary transforms of each other, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings in the exact quasidiabatic Hamiltonian. A rigorous numerical comparison of the four different representations is difficult because of the exceptional nature of systems where the four representations can be defined exactly and the necessity of an exceedingly accurate numerical algorithm that avoids mixing numerical errors with errors due to the different forms of the Hamiltonian. Using the quadratic Jahn-Teller model and high-order geometric integrators, we are able to perform this comparison and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results to the benchmark results of the strictly diabatic Hamiltonian, which is not available in general. In this Jahn-Teller model and with the same Fourier grid, the commonly employed approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the Hamiltonian in the adiabatic basis was the least accurate, due to the singular nonadiabatic couplings at the conical intersection.

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

“…S2 of the supplementary material and in Ref. 43). Although the nonseparable form of this Hamiltonian complicates the time propagation, there exist efficient geometric integrators, such as the high-order compositions of the implicit midpoint method, that are applicable even to such Hamiltonians.…”

“…The results obtained with the exact quasidiabatic Hamiltonian serve as the exact benchmark as long as the numerical errors are negligible. 43 Therefore, for a valid comparison, one needs a time propagation scheme that can treat even the nonseparable exact quasidiabatic Hamiltonian and that ensures negligible numerical errors (in comparison to the errors due to neglecting the residual couplings). This consideration led us to choose the optimal eighth-order 44 composition [45][46][47][48] of the implicit midpoint method, 47,49,50 which satisfies both requirements and, moreover, preserves exactly geometric properties of the exact solution.…”