Nuclear-Wavefunction Geometric Phase Verified by Variable Separation for a 96D + 2D Molecule–Surface Model with Nozzle and Surface Parameters

It has been well-known that the geometric phase of the electronic wavefunction is due to separation of electrons and nuclei. The associated geometric phase effects were considered in quantum molecular dynamics by adding a vector potential, called the Berry connection, into the nuclear Hamiltonian operator (e.g., Science, 309 (2005), 1227; 362 (2018), 1289; and 368 (2020), 767). This work shifts the focus to the geometric phase of the nuclear wavefunction by separating the degrees of freedom (DOFs) and then revisits the geometric phase effects resulting from varying environmental parameters around a critical point. For numerical demonstrations, a 96D molecule–surface interaction model is developed to simulate transport of the system in a 2D parameter space encoding the nozzle and surface conditions. Based on the present 96D + 2D model, the multilayer multiconfigurational time-dependent Hartree (ML-MCTDH) calculations predict that the geometric phase of the nuclear wavefunction acquires a jump of π at the critical point, making it change sign. These results indicate the existence of an alternative quantum interference when environmental parameters are varying during the molecular process. Discussion of the geometric phase effects in nuclear motions is also given.