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分子的几何相位效应，也称为分子 AB 效应，源于对势能面锥形交叉结构的研究. 在核构型空间环绕锥形交叉点时，绝热的电子波函数会获得 $\pi$ 的相位，导致其符号反转；而核的波函数也需相应的改变符号，保持总波函数的单值性. 该相位与锥形交叉结构拓扑相关，只有合适地引入分子几何相位才能在绝热表象下准确地描述量子体系的动力学行为. 在透热表象下，可以隐式地处理几何相位效应以及核-电子的非绝热耦合问题. 本文基于几何相位的量子动力学方法，设计了一种可以直接提取分子动力学中几何相位的方法. 该相位不同于由锥形交叉拓扑结构导致的量子化的 $\pi$ 相位，它是连续变化的. 它是量子体系在投影希尔伯特空间演化时，几何相位的一种规范不变的表示. 当前的研究为探索分子几何相位及其效应开辟了一个新视角，并有望为实验研究分子动力学中的几何相位提供一个可能的观测量.The geometric phase effect of molecules, also known as the molecular Aharonov-Bohm effect, arises from the study of the conical intersections of potential energy surfaces. When encircling a conical intersection in the nuclear configuration space, the adiabatic electronic wave function acquires a $\pi$ phase, leading to a change in sign. Consequently, the nuclear wave function must also change its sign to preserve the single-valueless of the total wave function. This phase is topologically related to the conical intersection structure. Only by appropriately introducing the molecular geometric phase can the quantum dynamical behavior in the adiabatic representation be accurately described. In the diabatic representation, the geometric phase effects and the non-adiabatic couplings between nuclei and electrons can be implicitly handled.
In this paper, based on the quantum kinematic approach to the geometric phase, a method for directly extracting the geometric phase in molecular dynamics is proposed. To demonstrate the unique features of this method, the $E \otimes e$ Jahn-Teller model, which is a standard model incorporating a conical intersection, is employed. This model comprises two diabatic electronic states coupled with two vibrational modes. The initial wave function is designed in such a way that it can circumnavigate the conical intersection in an almost adiabatic manner within approximately 2.4 ms. Subsequently, the quantum kinematic approach to the geometric phase is utilized to extract the geometric phase during the evolution. In contrast to the typical topological effect of a quantized geometric phase of $\pi$, this extracted geometric phase in this case varies in a continuous manner. It is a representation-independent and a gauge-invariant formulation of the geometric phase when a quantum system performs a path in its projected Hilbert space. This research offers a new perspective for exploring molecular geometric phases and the geometric phase effects. It may also provide a possible observable for experimental studies on geometric phases in molecular dynamics.-
Keywords:
- geometric phase /
- molecular dynamics /
- conical intersection /
- AB effect
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