热力学性质中的几何相位效应及在虚时间多电子态路径积分 formulation 中的影响
Geometric Phase Effect in Thermodynamic Properties and in the Imaginary-Time Multi-Electronic-State Path Integral Formulation
AI总结：
本文探讨几何相位对热力学性质的影响，提出多电子态路径积分方法自然捕捉几何相位效应，通过构建几何签名矩阵和 winding-number 引起的相位因子，量化其对热力学性质的影响。
摘要：
几何相位（GP）是源于锥形交点（CIs）的基本量子效应，对振动能级有深远影响。基于Born-Oppenheimer近似的标准虚时间路径积分分子动力学（PIMD）不考虑GP，可能导致低温热力学性质的显著误差。本文表明，虚时间多电子态路径积分（MES-PI）方法通过统计加权重叠矩阵的电子迹自然捕捉GP效应。这一关键能力已在基础工作中通过基准MES-PIMD模拟隐含体现。为隔离拓扑效应与其他非绝热效应，我们引入几何签名矩阵（用于CI）和由 winding-number 引起的相位因子，构建了一个非正式的GP排除MES-PI方法。将此非正式基线与严格MES-PI方法对比，可以无歧义地量化GP对热力学性质的影响。虽然在仅考虑基态电子态时存在更简单的近似方法，但MES-PIMD是适用于真实复杂系统最通用和准确的方法，其中CI缝的位置和拓扑结构通常事先未知。
英文摘要：
The geometric phase (GP) is a fundamental quantum effect arising from conical intersections (CIs), with profound consequences for vibronic energy levels. Standard imaginary-time path integral molecular dynamics (PIMD) based on the Born-Oppenheimer approximation does not account for the GP, potentially leading to significant errors in low-temperature thermodynamic properties. In this Perspective, we demonstrate that the multi-electronic-state path integral (MES-PI) formulation in imaginary time (developed in J. Chem. Phys. 2018, 148, 102319) naturally captures the GP effect through the electronic trace of the product of statistically weighted overlap matrices between successive imaginary-time slices. This crucial capability was already implicit in the benchmark MES-PIMD simulations in that foundational work. To isolate this topological effect from other nonadiabatic effects, we introduce a geometric signature matrix (for the CI) and a winding-number-induced phase factor, constructing an ad hoc GP-excluded MES-PI method. Comparing this ad hoc baseline against the rigorous MES-PI approach allows us to unambiguously quantify the impact of the GP on thermodynamic properties. While simpler approximations exist when only the ground electronic-state is considered, MES-PIMD is the most general and accurate approach applicable to real complex systems where the location and topology of CI seams are often not known a priori.
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