论文标题
哪种形式的分子哈密顿量最适合在圆锥形交叉点模拟非绝热量子动力学？
Which form of the molecular Hamiltonian is the most suitable for simulating the nonadiabatic quantum dynamics at a conical intersection?
论文作者
论文摘要
选择分子哈密顿量的适当表示是模拟圆锥形交集周围非绝热量子动力学所面临的挑战之一。绝热，确切的准绝热和严格的绝热表示是彼此的确切和单一的变换，而近似近似糖的哈密顿量却忽略了确切的准绝热哈密顿量中残留的非绝热耦合。由于可以精确定义四个表示的系统的特殊性质，并且需要具有非常精确的数值算法的必要性，因此很难对四个不同表示形式进行严格的数值比较，从而避免了由于汉密尔顿的不同形式而将数值错误与错误混合在一起。使用二次Jahn-Teller模型和高阶几何积分器，我们能够进行此比较，并发现只有很少使用的精确的准绝热汉密尔顿人才能与严格的绝型糖尿病哈密顿量的基准结果产生几乎相同的结果，这在总体上是不可用的。在这个Jahn-Teller模型和相同的傅立叶网格中，通常使用的近似糖绝热的哈密顿量导致了波袋动力学不准确，而在绝热基础上，哈密顿量是最不准确的，由于圆锥形交叉口处的奇异非耐绝热耦合。
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.
