Berry Phase Effects of Nuclei in Chemical Reaction Dynamics

In calculations on quantum state-resolved dynamics of a chemical reaction, reactants are usually prepared in separated eigenstates of individual fragments, and their direct-product is then evolved in time. In this work, we focus on the essence in separating them and the Berry phase effects of the nuclear wave function. By the present theory, mechanism of inter/intramolecular energy redistribution is also proposed to deeply understand reactive dynamics with multirovibrational states. To demonstrate the phase transition of the nuclear wave function, two three-dimensional (3D) models reductively describing the molecular reaction are developed to simulate transport of the system along a closed path in a parameter space represented of inter/intramolecular energy transfers. Employing these 3D models, extensive multiconfigurational time-dependent Hartree (MCTDH) calculations are performed to solve the time-dependent nuclear Schr{ö}dinger equation at various initial conditions. Moreover, 98D multilayer MCTDH (ML-MCTDH) calculations are launched to demonstrate the transition of Berry phase. These calculations clearly indicate that the wave function can change sign allowing quantum interference in the parameter space. Discussions on the separation of the reactants are made, while perspectives on the Berry phase effects predicted by the present work are given from the viewpoint of differential geometry. As a conclusion remark, the Berry phase effects on molecular dynamics are also thoroughly compared with those on electronic properties (see, for example, {\it Rev. Mod. Phys.} {\bf 82} (2010), 1959) and mode/bond-specific reactivity (see, for example, {\it Nat. Chem.} {\bf 14} (2022), 545).