On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods.
On the inclusion of the diagonal Born-Oppenheimer correction in surface hopping methods.
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关于在表面跳跃方法中包含对角玻恩-奥本海默校正。
DOI：
10.1063/1.4945817
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
A. Izmaylov
中科院分区：
文献类型：
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作者：
Rami Gherib;L. Ye;I. G. Ryabinkin;A. Izmaylov
对角Born-Oppenheimer修正(DBOC)源于绝热表示中的对角二阶导数耦合项，当相邻的Born-Oppenheimer(BO)势能面(PESS)之间的间隙闭合时，DBOC可以有任意大的量级。然而，在模拟非绝热动力学的混合量子经典方法(如最少开关表面跳跃(FSSH)方法)中，DBOC通常被忽略。在FSSH方法中，直接将DBOC加到BO PESS中，FSSH+D，对于包含圆锥形相交的模型，已经被证明导致了更差的数值结果。相空间表面跳跃(PSSH)是DBOC夹杂的更复杂的变种，比FSSH+D更成功，但在没有锥形相交的模型问题上。这项工作全面评估了DBOC在两个电子态问题的非绝热动力学中的作用，以及FSSH、FSSH+D和PSSH方法在各种一维和二维模型中的性能。我们的结果表明，当同时满足两个条件时，DBOC的加入可以提高表面跳跃模拟的精度：(1)原子核的动能低于DBOC；(2)PESS的非绝热耦合不强。在DBOC的能量尺度变得非常高甚至发散的情况下，DBOC的包含是有害的，因为在这些区域，PES也是非常强耦合的。在这种情况下，真正的量子形式论在很大程度上依赖于对角和非对角非绝热耦合之间的相互作用，而表面跳跃方法将对角项随机地视为PESS和非对角项。
The diagonal Born-Oppenheimer correction (DBOC) stems from the diagonal second derivative coupling term in the adiabatic representation, and it can have an arbitrary large magnitude when a gap between neighbouring Born-Oppenheimer (BO) potential energy surfaces (PESs) is closing. Nevertheless, DBOC is typically neglected in mixed quantum-classical methods of simulating nonadiabaticdynamics (e.g., fewest-switch surface hopping (FSSH) method). A straightforward addition of DBOC to BO PESs in the FSSH method, FSSH+D, has been shown to lead to numerically much inferior results for models containing conical intersections. More sophisticated variation of the DBOC inclusion, phase-space surface-hopping (PSSH) was more successful than FSSH+D but on model problems without conical intersections. This work comprehensively assesses the role of DBOC in nonadiabaticdynamics of two electronic state problems and the performance of FSSH, FSSH+D, and PSSH methods in variety of one- and two-dimensional models. Our results show that the inclusion of DBOC can enhance the accuracy of surface hopping simulations when two conditions are simultaneously satisfied: (1) nuclei have kinetic energy lower than DBOC and (2) PESs are not strongly nonadiabatically coupled. The inclusion of DBOC is detrimental in situations where its energy scale becomes very high or even diverges, because in these regions PESs are also very strongly coupled. In this case, the true quantum formalism heavily relies on an interplay between diagonal and off-diagonal nonadiabatic couplings while surface hopping approaches treat diagonal terms as PESs and off-diagonal ones stochastically.