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

TL;DR

This study compares different molecular Hamiltonian representations for simulating nonadiabatic quantum dynamics at conical intersections, finding the exact quasidiabatic form most accurate in a Jahn-Teller model.

Contribution

The paper provides a rigorous numerical comparison of adiabatic, exact quasidiabatic, approximate quasidiabatic, and strictly diabatic Hamiltonians using high-order integrators.

Findings

Exact quasidiabatic Hamiltonian closely matches the strictly diabatic benchmark.

Approximate quasidiabatic Hamiltonian yields inaccurate wavepacket dynamics.

Adiabatic basis Hamiltonian is the least accurate due to singular couplings.

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.