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

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?

Seonghoon Choi, Jiri Vanicek

Diabatization of the molecular Hamiltonian is a standard approach to remove the singularities of nonadiabatic couplings at conical intersections of adiabatic potential energy surfaces. In general, it is impossible to eliminate the nonadiabatic couplings entirely—the resulting “quasidiabatic” states are still coupled by smaller but nonvanishing residual nonadiabatic couplings, which are typically neglected. Here, we propose a general method for assessing the validity of this potentially drastic approximation by comparing quantum dynamics simulated either with or without the residual couplings. To make the numerical errors negligible to the errors due to neglecting the residual couplings, we use the highly accurate and general eighth-order composition of the implicit midpoint method. The usefulness of the proposed method is demonstrated on nonadiabatic simulations in the cubic Jahn–Teller model of nitrogen trioxide and in the induced Renner–Teller model of hydrogen cyanide. We find that, depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can result in wrong dynamics. In contrast, simulations with the exact quasidiabatic Hamiltonian, which contains the residual couplings, always yield accurate results.

2021

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

Seonghoon Choi

Accurate simulations of molecular quantum dynamics are crucial for understanding numerous natural processes and experimental results. Yet, such high-accuracy simulations are challenging even for relatively simple systems where the Born-Oppenheimer approximation is valid. Worse still, due to the ubiquity of conical intersections in molecules, it is often necessary to go beyond this celebrated approximation and employ even more sophisticated methods that can describe nonadiabatic processes involving multiple coupled electronic states.Geometric integrators provide a way to simulate nonadiabatic quantum dynamics with high accuracy while exactly conserving geometric properties, such as norm, energy, symplecticity, and time reversibility. However, the exact conservation of these properties typically leads to a higher computational cost when compared with non-geometric integrators of the same order of accuracy. We remedy this lack of efficiency by employing various composition methods to obtain high-order geometric integrators, competitive in efficiency even with some non-geometric integrators.To overcome the limited applicability of the popular split-operator algorithms, we present geometric integrators that can solve the time-dependent Schroedinger equation efficiently regardless of the form of the Hamiltonian. Employing these integrators, we systematically compare the different representations of the molecular Hamiltonian for their suitability for simulating nonadiabatic dynamics at a conical intersection and find that the rarely used exact quasidiabatic Hamiltonian, which includes the often-neglected residual nonadiabatic couplings, yields the most accurate results. Accordingly, we present a method for quantifying the validity of ignoring these residual couplings and show that depending on the system, initial state, and employed quasidiabatization scheme, neglecting the residual couplings can indeed result in inaccurate dynamics.The computational cost of exact quantum simulations quickly becomes prohibitively high as the system size increases. For high-dimensional simulations, one can either optimize the available basis set, e.g., by employing adaptive phase space grids or, alternatively, employ a more approximate approach, such as mixed quantum-classical Ehrenfest dynamics, that provides a useful qualitative picture. Although Ehrenfest dynamics and exact quantum dynamics simulated on an adaptive grid may appear unrelated, we show that, surprisingly, the high-order geometric integrators for these two problems can, in fact, be obtained by using the same splitting and composition methods.

EPFL2022

High-order geometric integrators for nonadiabatic molecular quantum dynamics and their applications to explore conical intersections

Seonghoon Choi

EPFL2022