Choi Seonghoon, Vaníček Jiří
Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.
J Chem Phys. 2020 Dec 7;153(21):211101. doi: 10.1063/5.0033410.
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.
选择合适的分子哈密顿量表示形式是锥形交叉点附近非绝热量子动力学模拟所面临的挑战之一。绝热表示、精确准绝热表示和严格 diabatic 表示是彼此精确且酉的变换，而近似准绝热哈密顿量忽略了精确准绝热哈密顿量中的残余非绝热耦合。由于能够精确定义这四种不同表示形式的系统具有特殊性，并且需要一种极其精确的数值算法来避免将数值误差与由于哈密顿量不同形式导致的误差相混淆，因此对这四种不同表示形式进行严格的数值比较是困难的。利用二次 Jahn - Teller 模型和高阶几何积分器，我们能够进行这种比较，并发现只有很少使用的精确准绝热哈密顿量能产生与严格 diabatic 哈密顿量的基准结果几乎相同的结果，而严格 diabatic 哈密顿量通常是不可得的。在这个 Jahn - Teller 模型中且使用相同的傅里叶网格，常用的近似准绝热哈密顿量导致不准确的波包动力学，而绝热基下的哈密顿量是最不准确的，这是由于锥形交叉点处的奇异非绝热耦合所致。
