标题： 时变核-电子轨道哈特里-福克理论在强均匀磁场中 显示英文标题

标题： Time-Dependent Nuclear-Electronic Orbital Hartree-Fock Theory in a Strong Uniform Magnetic Field

摘要： 玻恩-奥本海默（BO）近似在存在强磁场的情况下不如在无场情况下准确。 这是由于电子结构对磁场的复杂且不可预测的响应，特别是在混合区域$B \approx B_0 = 2.35 \times 10^5\,$T。 因此，探索磁场中的非BO方法是有益的。 在本工作中，采用核-电子轨道（NEO）方法研究强磁场中存在的质子振动激发能。 NEO广义哈特里-福克理论和时间依赖哈特里-福克理论被推导并实现，考虑了在磁场中分子系统非微扰处理所导致的所有项。 将固定重核的HCN和FHF$^-$的NEO结果与二次特征值问题（QEP）进行比较。 每种分子由于氢而具有三种半经典模式——两种在无场情况下简并的进动模式和一种伸缩模式。 发现NEO-TDHF模型表现良好——特别是它能够自动捕捉电子对核的屏蔽效应，这些效应通过进动模式的能量差异来量化。 显示英文摘要

摘要： The Born-Oppenheimer (BO) approximation is less accurate in the presence of a strong magnetic field than in the absence of a field. This is due to the complicated and unpredictable response of electronic structure to the field, especially in the mixed regime $B \approx B_0 = 2.35 \times 10^5\,$T. Therefore, it is desirable to explore non-BO methods in magnetic fields. In this work, the nuclear-electronic orbital (NEO) method is employed to study protonic vibrational excitation energies in the presence of a strong magnetic field. NEO Generalized Hartree-Fock theory and time-dependent Hartree-Fock theory are derived and implemented, accounting for all terms that result as a consequence of the nonperturbative treatment of molecular systems in a magnetic field. The NEO results for HCN and FHF$^-$ with clamped heavy nuclei are compared against the quadratic eigenvalue problem (QEP). Each molecule has three semi-classical modes owing to the hydrogen - two precession modes that are degenerate in the absence of a field and one stretching mode. The NEO-TDHF model is found to perform well - in particular it automatically captures the screening effects of the electrons on the nuclei, which are quantified through the difference in energy of the precession modes.