AI 中文总结
研究核运动诱导的与核速度相关相位对电子原子轨道的影响，采用厄伦费斯特拉格朗日方法和紧束缚方法确定运动方程与振动响应，通过测试校正发现与从头算计算高度吻合，为相关研究提供了新方法和贡献。
AI 中文摘要
核运动在电子原子轨道中诱导出与核速度相关的相位（也称为电子平移因子），它会修改由局域原子轨道构建的有效哈密顿量。本文采用厄伦费斯特拉格朗日方法处理局域原子轨道（LCAO）和紧束缚方法，在核速度的任意阶次下，在线性响应形式体系中确定运动方程和振动响应，重点关注对玻恩有效电荷和力常数矩阵的紧束缚评估。相互作用非局域部分中与核速度相关的类皮尔斯相位的出现恢复了频率相关振动响应的全电子和规则。在紧束缚模型中，这些校正从定性角度显著改变了振动响应，还为捕获诸如振动圆二色性等现象提供了所需贡献。我们在金属能隙石墨烯的紧束缚模型以及拓扑时间反演对称性破缺的霍尔丹模型中测试了这些校正，发现与从头算计算结果高度吻合。
英文摘要
The nuclear motion induces in the electronic atomic orbitals a nuclear-velocity-dependent phase (also known as electron-translation factor), which modifies the effective Hamiltonians constructed from localised atomic orbitals. In this work, using an Ehrenfest Lagrangian approach for the localised atomic orbitals (LCAO) and tight-binding methods, we determine, at any order in the nuclear velocity, the equations of motion and the vibrational responses within a linear response formalism, focusing on the tight-binding assessment of the Born effective charges and the force-constant matrix. The appearance of nuclear-velocity-dependent Peierls-like phases in the non-local part of the interactions restores the all-electron sum rules for frequency-dependent vibrational responses. In tight-binding models these corrections crucially modify the vibrational response from a qualitative point of view, also yielding contributions required to capture phenomena such as vibrational circular dichroism. We test these corrections in the tight-binding model for metallic gapped graphene - finding excellent agreement with \textit{ab initio} calculations - and for the topological time-reversal symmetry breaking Haldane model.
