Culpitt Tanner, Peters Laurens D M, Tellgren Erik I, Helgaker Trygve
Hylleraas Centre for Quantum Molecular Sciences, Department of Chemistry, University of Oslo, P.O. Box 1033 Blindern, N-0315 Oslo, Norway.
J Chem Phys. 2022 Jan 28;156(4):044121. doi: 10.1063/5.0079304.
The diagonal nonadiabatic term arising from the Born-Oppenheimer wave function ansatz contains contributions from a vector and scalar potential. The former is provably zero when the wave function can be taken to be real valued, and the latter, known as the diagonal Born-Oppenheimer correction (DBOC), is typically small in magnitude. Therefore, unless high accuracy is sought, the diagonal nonadiabatic term is usually neglected when calculating molecular properties. In the presence of a magnetic field, the wave function is generally complex, and the geometric vector potential gives rise to a screening force that is qualitatively important for molecular dynamics. This screening force is written in terms of the Berry curvature and is added to the bare Lorentz force acting on the nuclei in the presence of the field. In this work, we derive analytic expressions for the Berry curvature and DBOC using both first- and second-quantization formalisms for the case of generalized and restricted Hartree-Fock theories in a uniform magnetic field. The Berry curvature and DBOC are calculated as a function of the magnetic field strength and the bond distance for the ground-state singlets of H, LiH, BH, and CH. We also examine the stability and time-reversal symmetry of the underlying self-consistent field solutions. The character of the DBOC and Berry curvature is found to depend on the magnetic field and varies between molecules. We also identify instances of broken time-reversal symmetry for the dissociation curves of BH and CH.
由玻恩-奥本海默波函数假设产生的对角非绝热项包含矢量势和标量势的贡献。当波函数可被视为实值时，前者可证明为零，而后者，即所谓的对角玻恩-奥本海默修正（DBOC），其大小通常较小。因此，除非追求高精度，在计算分子性质时通常会忽略对角非绝热项。在存在磁场的情况下，波函数通常是复数形式，几何矢量势会产生一种屏蔽力，这对分子动力学在定性上很重要。这种屏蔽力用贝里曲率表示，并添加到在场存在时作用于原子核的裸洛伦兹力上。在这项工作中，我们针对均匀磁场中广义和受限哈特里-福克理论的情况，使用一阶和二阶量子化形式推导了贝里曲率和DBOC的解析表达式。计算了H、LiH、BH和CH基态单线态的贝里曲率和DBOC作为磁场强度和键长的函数。我们还研究了基础自洽场解的稳定性和时间反演对称性。发现DBOC和贝里曲率的特性取决于磁场，并且在不同分子之间有所变化。我们还确定了BH和CH解离曲线的时间反演对称性破缺的情况。
