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

Choosing a suitable representation of the molecular Hamiltonian is a challenge faced by simulations of the nonadiabatic quantum dynamics around a conical intersection. The adiabatic, exact quasidiabatic, and strictly diabatic representations are exact, whereas the approximate quasidiabatic Hamiltonian ignores the residual nonadiabatic couplings. A rigorous numerical comparison of these four representations is difficult due to the exceptional nature of systems where these can be defined exactly and the necessity of an accurate algorithm that avoids mixing numerical errors with errors due to the different representations. We are able to perform this comparison [1] using the quadratic Jahn-Teller model and high-order geometric integrators [2,3] and find that only the rarely employed exact quasidiabatic Hamiltonian yields nearly identical results as the strictly diabatic Hamiltonian, which is unavailable in general. In this model and with the same grid, the approximate quasidiabatic Hamiltonian led to inaccurate wavepacket dynamics, while the adiabatic Hamiltonian was the least accurate due to the singular nonadiabatic couplings.

[1] S. Choi and J. Vanicek, arXiv:2010.08214.
[2] S. Choi and J. Vanicek, J. Chem. Phys. (2019).
[3] J. Roulet, S. Choi, and J. Vanicek, J. Chem. Phys. (2019).