Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency.
Surface hopping, electron translation factors, electron rotation factors, momentum conservation, and size consistency.
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DOI：
10.1063/5.0160965
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发表时间：
2023-08
期刊：
影响因子：
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通讯作者：
V. Athavale;Xuezhi Bian;Z. Tao;Yanze Wu;T. Qiu;J. Rawlinson;R. Littlejohn;Joseph E. Subotnik
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文献类型：
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作者：
V. Athavale;Xuezhi Bian;Z. Tao;Yanze Wu;T. Qiu;J. Rawlinson;R. Littlejohn;Joseph E. Subotnik
对于没有自旋轨道耦合的系统，（i）核加电子线动量和（ii）核加轨道电子角动量是好的量子数。因此，当一个分子系统经历非绝热跃迁时，总的线动量或角动量应该没有变化。现在，标准的表面跳跃算法忽略了电子动量，并间接地将核自由度的动量等同于总动量。然而，即使这样的简化，该算法仍然不保存无论是核的线性或核的角动量。在这里，我们展示了解决这些故障的一种方法是修饰导数耦合（即，跳跃方向）以两种方式：（i）我们不允许通过在平移基础上工作来改变核线性动量;（这是众所周知的，并导致电子平移因子）和（ii）我们不允许通过在围绕质心旋转的基础上工作来改变核角动量[这不是众所周知的，并导致一种新颖的，下面我们将其称为电子旋转因子的导数耦合的旋转可移除分量，参见。当量（96）]。目前的研究结果应该是有帮助的，在短期内解释表面跳跃计算单重态系统（无自旋），然后开发新的表面跳跃算法在长期的系统，其中不能忽略的电子轨道和/或自旋角动量。
For a system without spin-orbit coupling, the (i) nuclear plus electronic linear momentum and (ii) nuclear plus orbital electronic angular momentum are good quantum numbers. Thus, when a molecular system undergoes a nonadiabatic transition, there should be no change in the total linear or angular momentum. Now, the standard surface hopping algorithm ignores the electronic momentum and indirectly equates the momentum of the nuclear degrees of freedom to the total momentum. However, even with this simplification, the algorithm still does not conserve either the nuclear linear or the nuclear angular momenta. Here, we show that one way to address these failures is to dress the derivative couplings (i.e., the hopping directions) in two ways: (i) we disallow changes in the nuclear linear momentum by working in a translating basis (which is well known and leads to electron translation factors) and (ii) we disallow changes in the nuclear angular momentum by working in a basis that rotates around the center of mass [which is not well-known and leads to a novel, rotationally removable component of the derivative coupling that we will call electron rotation factors below, cf. Eq. (96)]. The present findings should be helpful in the short term as far as interpreting surface hopping calculations for singlet systems (without spin) and then developing the new surface hopping algorithm in the long term for systems where one cannot ignore the electronic orbital and/or spin angular momentum.