Advances in methods and applications of nonadiabatic quantum dynamics simulation of condensed matters

First-principles molecular dynamics simulations, which can reveal the microscopic mechanisms and the macroscopic properties of molecules and condensed systems, have become a significant driving force in the development of physics. In the past decades, the ground state electronic properties of various materials can be accurately described using the firstprinciples method based on the Born-Oppenheimer approximation. However, in nonadiabatic processes, such as the ultrafast excited-state dynamics where laser interacts with molecules and condensed matters, the Born-Oppenheimer approximation evolving nuclear wave function on the ground state potential energy plane is no longer valid because of the nonnegligible nonadiabatic couplings between electrons and nuclei. In order to investigate the novel physical phenomena in nonadiabatic processes, many nonadiabatic molecular dynamics methods have been proposed, for instance, full quantum dynamics and mixed quantum-classical dynamics. When the nuclear quantum effects are trivial, the mixed quantum-classical dynamics is effective, which solves the time-dependent electron Schrodinger equation and describes the motion of the nuclei in the form of Newtonian mechanics. Two methods based on the mixed quantum-classical dynamics, the fewest-switches trajectory surface-hopping method (FSSH) and Ehrenfest dynamics, have accepted much attention since they could be easily implemented and combined with real-time time-dependent density functional theory (rt-TDDFT) for high-precision calculations. The combination of quantum and classical dynamics reduces the computational cost and allows the applications for real materials. At low temperatures, the nuclear quantum effects, including quantum tunneling and zero-point vibrations, cannot be ignored. Ring-polymer molecular dynamics (RPMD) based on the imaginary-time path integral is widely used to consider the nuclear quantum effects, which describes the quantum behavior of atomic nuclei by sampling a larger number of quantum configurations and paths. By combining RPMD and mixed quantum-classical nonadiabatic dynamics, one can describe quantum motions of nuclei and the excited electrons in quantum nonadiabatic dynamics simulations. Here, we summarize the recent progress of the rt-TDDFT methods based on numerical atomic orbital basis and planewave basis set, as well as highly efficient RP-TDAP method combining rt-TDDFT and RPMD towards a quantum description of electronic-nuclear dynamics. Finally, we show several representative applications employing these methods, including high harmonic generation modulated by two-color light, charge density wave dynamics, photocatalytic water decomposition as well as the quantum evolution of nuclear wave packets. These applications are in good agreement with experimental measurements, which demonstrates the reliability of these methods and their advantages in the corresponding research areas. These developments and applications are in a significant step from ground state methods to full quantum simulation of the coupled motion of electrons and nuclei, providing a new perspective for understanding and predicting the quantum interactions and dynamical behavior of condensed materials in the degree of atomic spatial scales and attosecond time scales.