Bian Xuezhi, Qiu Tian, Chen Junhan, Subotnik Joseph E
Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, USA.
J Chem Phys. 2022 Jun 21;156(23):234107. doi: 10.1063/5.0093092.
We show that the Berry force as computed by an approximate, mean-field electronic structure can be meaningful if properly interpreted. In particular, for a model Hamiltonian representing a molecular system with an even number of electrons interacting via a two-body (Hubbard) interaction and a spin-orbit coupling, we show that a meaningful nonzero Berry force emerges whenever there is spin unrestriction-even though the Hamiltonian is real-valued and formally the on-diagonal single-surface Berry force must be zero. Moreover, if properly applied, this mean-field Berry force yields roughly the correct asymptotic motion for scattering through an avoided crossing. That being said, within the context of a ground-state calculation, several nuances do arise as far interpreting the Berry force correctly, and as a practical matter, the Berry force diverges near the Coulson-Fischer point (which can lead to numerical instabilities). We do not address magnetic fields here.
我们表明，通过近似的平均场电子结构计算出的贝里力，如果解释得当，可能是有意义的。具体而言，对于一个表示分子系统的模型哈密顿量，该系统具有偶数个通过两体（哈伯德）相互作用和自旋 - 轨道耦合相互作用的电子，我们表明，只要存在自旋非限制，就会出现有意义的非零贝里力——尽管哈密顿量是实值的，并且形式上对角单表面贝里力必须为零。此外，如果应用得当，这种平均场贝里力对于通过避免交叉的散射会产生大致正确的渐近运动。话虽如此，在基态计算的背景下，在正确解释贝里力方面确实会出现一些细微差别，并且实际上，贝里力在库尔森 - 费舍尔点附近会发散（这可能导致数值不稳定性）。我们在此不讨论磁场。
