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. 2021 Sep 28;155(12):124104. doi: 10.1063/5.0061878.
Ehrenfest dynamics is a useful approximation for ab initio mixed quantum-classical molecular dynamics that can treat electronically nonadiabatic effects. Although a severe approximation to the exact solution of the molecular time-dependent Schrödinger equation, Ehrenfest dynamics is symplectic, is time-reversible, and conserves exactly the total molecular energy as well as the norm of the electronic wavefunction. Here, we surpass apparent complications due to the coupling of classical nuclear and quantum electronic motions and present efficient geometric integrators for "representation-free" Ehrenfest dynamics, which do not rely on a diabatic or adiabatic representation of electronic states and are of arbitrary even orders of accuracy in the time step. These numerical integrators, obtained by symmetrically composing the second-order splitting method and exactly solving the kinetic and potential propagation steps, are norm-conserving, symplectic, and time-reversible regardless of the time step used. Using a nonadiabatic simulation in the region of a conical intersection as an example, we demonstrate that these integrators preserve the geometric properties exactly and, if highly accurate solutions are desired, can be even more efficient than the most popular non-geometric integrators.
埃伦费斯特动力学是一种用于从头算混合量子-经典分子动力学的有用近似方法，它可以处理电子非绝热效应。尽管它是对分子含时薛定谔方程精确解的一种严格近似，但埃伦费斯特动力学是辛的、时间可逆的，并且能精确守恒分子总能量以及电子波函数的范数。在此，我们克服了由于经典核运动和量子电子运动耦合而产生的明显复杂性，并提出了用于“无表象”埃伦费斯特动力学的高效几何积分器，该积分器不依赖于电子态的非绝热或绝热表象，并且在时间步长上具有任意偶数阶精度。这些数值积分器通过对称组合二阶分裂方法并精确求解动力学和势传播步骤得到，无论使用何种时间步长，它们都是范数守恒的、辛的且时间可逆的。以锥形交叉区域的非绝热模拟为例，我们证明这些积分器能精确保持几何性质，并且如果需要高精度解，它们甚至比最流行的非几何积分器更高效。
