MATHEMATICAL SCIENCES

The research on non-adiabatic total quantization method has been progressed


In the process of using molecular dynamics simulations to calculate substances such as molecules and solid materials, the commonly used method is based on the Born-Oppenheimer approximation adiabatic kinetics method, that is, the electron and the nucleus are treated separately, and the electron is always in the ground state of the nuclear configuration determined for adiabatic evolution. This is the mainstream molecular simulation method since 1927 when Born and Oppenheimer developed the theory of quantum dynamics after adiabatic approximation. In recent years, some hybrid quantum-classical kinetic methods that take into account the quantum evolution of electrons but are still based on the classical point particle approximation of atomic nuclei have been developed. Of the two dominant approaches, the former cannot describe non-adiabatic phenomena, while the latter ignores the quantum effects of atomic nuclei. In this regard, the material system is accurately described by directly solving the time-containing Schrödinger equation of the “nucleus-electron” coupling wave function (i.e., the total quantum wave function). Subject to the huge amount of computation brought about by the “dimensional disaster” of the quantum mechanical wave function, the current direct solution method can only be applied to small systems with several atoms, and cannot do first-principles calculations for real material systems. There are a few approximation methods for full quantum dynamics (considering the quantum evolution of electrons and atomic nuclei) in the literature, but due to the large amount of calculation, it is limited by model systems or small systems, and it is difficult to combine with commonly used first-principles calculation methods to describe the dynamic characteristics of specific materials. Therefore, it is particularly important to propose a computational method that can simulate the full quantum effect of real materials with controllable calculation quantity in the field of condensed matter physics.

Meng Sheng, researcher of the State Key Laboratory of Surface Physics of the Institute of Physics, Chinese Academy of Sciences/Beijing National Research Center for Condensed Matter Physics, supervised doctoral student Zhao Ruji and doctoral student You Peiwei, and made important progress in non-adiabatic total quantum dynamics methods. In this study, a non-adiabatic kinetic method (RPMD-IB) based on pathway integral molecular dynamics is proposed, which can simultaneously describe the nuclear quantum effect and electron transition effect of condensed matter matter. This method combines path-integral molecular dynamics with Ehrenfest’s theorem, which can accurately describe the nuclear quantum effect of the nucleus during motion (i.e., the nucleus is no longer regarded as a classical point particle and the path integral is used to represent the nuclear wave function), and can also describe the excitation of electrons between different energy levels during motion (i.e., non-adiabatic effect). This method can be combined with TDAP, the first-principle excited state dynamics simulation software developed by our research group, to simulate the non-adiabatic dynamics process in real material systems with more than hundreds of atoms in protocells.

After comparing the new method with the strict quantum packet kinetic solution, and comparing it with other non-adiabatic kinetic methods in the field, it is found that the electron transition probability obtained by the new method is closer to the quantum distribution of the nucleus and the result of the strict solution of quantum mechanics, indicating that the new method has higher accuracy. It is found that the quantum effect of atomic nuclei has an important influence on the electron excitation process, which is an important embodiment of the full quantum effect of condensed matter. The new method is applied to first-principles computational simulation, and the proton transfer rate caused by photoexcitation in the water dimer H2O-H2O+ is consistent with the experimental results. The study shows the accuracy of the new method and discovers that the new method can be used to simulate the full quantum dynamics process of real materials containing quantum effects of atomic nuclei and non-adiabatic effects.

The research was recently published in Physical Review Letters. The research work is supported by the National Key Research and Development Program of China, the National Natural Science Foundation of China, and the Chinese Academy of Sciences. (Source: Institute of Physics, Chinese Academy of Sciences)

Related paper information:https://doi.org/10.1103/PhysRevLett.130.166401

Figure 1. Illustration of several non-adiabatic pathway integration molecular dynamics methods. (a)RPMD-CA, (b) RPMD-BA, (c) RPMD-IB。

Figure 2. Results of the newly developed RPMD-IB method in a two-level model. (a) Potential energy surface (black line) and non-adiabatic coupling (green line) in the two-level model. (b) The number of electrons occupied at high energy levels over time in different methods. The dashed line is a strict solution to quantum mechanics.

Figure 3. Under the RPMD-IB method, the distribution of path integration “beads” at different moments is compared with the probability distribution of nuclear wave packets in a two-level system.

Figure 4. Comparison of the RPMD-IB method with the traditional Ehrenfest average field method to simulate the proton transfer process in H2O-H2O+. (a) Changes in the position of protons in water dimers over time, and (b) comparison of spatial structures of water dimers at different times.

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