Development Of Theoretical Methods For Non-adiabatic Molecular Dynamics In Periodic Solid-state Materials

The excited states and carrier dynamics in photovoltaic materials,solid-state lightemitting diodes,photocatalytic materials,and field-effect transistors are important fundamental physical processes,and understanding these processes plays a key role in material design and improving device performance.These excited state dynamic evolution processes are non-adiabatic,so the Born-Oppenheimer approximation is no longer applicable and the non-adiabatic dynamics need to be used for simulation.Among them,the trajectory-surface hopping method has become a mainstream method in the study of non-adiabatic dynamics because of its simple algorithm and easy combination with the first-principles calculation software,and it can well meet the detailed balance conditions and give a clear physical insight.However,for periodic solid-state systems containing a large number of atoms,the degrees of freedom of the electrons and nuclei are extremely large,and their quasi-continuous energy levels form energy bands,so the non-adiabatic dynamic process is much more complicated than those in the molecular systems,which makes the application of this method in periodic solid-state materials still challenging.In this thesis,we developed a novel surface hopping approach particularly suitable for the simulation of non-adiabatic processes in periodic solid systems based on the linear vibronic coupling(LVC)model,and we applied this new method to study the relaxation dynamics of photo-excited carriers in the one-dimensional periodic carbon chain.The main work of the thesis is as follows:(1)The Kohn-Sham states at the equilibrium position are used as the diabatic representation in this method,the single-electron Hamiltonian in any normal coordinate is constructed by using the linear vibronic coupling model,and the Hamiltonian is diagonalized to obtain the adiabatic potential energy surface and adiabatic wave function.The parameters of the LVC model,including the electron,phonon energy,and electron-phonon coupling strength,are calculated using density-functional theory and density-functional perturbation theory and then interpolated in fine sampling points of the Brillouin zone with maximally localized Wannier functions to get the LVC model of a Born-von Kármán supercell with arbitrary size.With Wannier interpolation,the description of the degrees of freedom of electron and lattice vibration in the nonadiabatic dynamics process is more complete and includes more comprehensive nonradiative relaxation pathways,which leads to more accurate results.(2)We presented the fewest switches surface hopping(FSSH)approach based on the LVC model in this thesis,and derived the probability of electron hopping between different potential energy surfaces and the Langevin equation of nucleus normal coordinates on different adiabatic potential energy surfaces.Since the electronic structure calculation based on the first principle is not required for each step in the dynamic process,which makes this scheme has high computational efficiency,and can be used for performing massive,large-scale,long-time simulations of excited-state dynamics in periodic systems.In addition,the non-adiabatic coupling term in this approach can be solved analytically,without the use of classical path approximation,and the feedback effect of electronic transitions on the nucleus is considered.(3)We employed this approach to study the relaxation process of photo-excited carriers in a one-dimensional periodic carbon chain.The non-adiabatic dynamics simulation was carried out with the fewest switches surface hopping method,and the time-dependent distribution of photo-excited electrons and holes in each energy band and adiabatic potential energy surface,as well as the phonon energy and temperature of different normal modes change with time were obtained in reciprocal space.By analyzing the time-dependent changes of phonon energy in different modes,we found that the long-wave longitudinal optical phonons mode plays a major role in the electron and hole relaxation process.By interpolating the electron Hamiltonian and lattice vibration in the reciprocal space with different sampling points,we found that more sampling points in the reciprocal space lead to more relaxation paths for hot electrons and holes,and the relaxation process is faster.Therefore,the completeness of the Hilbert space and the lattice vibration degrees of freedom is of great significance to the accuracy of the non-adiabatic dynamics simulation in periodic systems.The relaxation times of photo-excited electrons and holes in an infinitely extended periodic carbon chain were obtained using the extrapolating method by fitting the variation of the carrier relaxation time with the number of sampling points in the reciprocal space with a stretched-compressed exponential function.(4)The populations of electron and hole evolution over time obtained by nonadiabatic dynamics simulation can be used to simulate ultrafast time-resolved spectroscopy,which need to accurately calculate the band structure and optical properties,and the quasiparticle effect and exciton effect need to be considered in optical properties calculation.The initial excited states of the photo-excited electrons and holes in the non-adiabatic molecular dynamics simulation are chosen according to a Gaussian-shaped Franck-Condon window,which also requires an accurate calculation of the energy band structure and the transition dipole moments among different electronic states.These problems are studied in Chapter 5,and we use the firstprinciples calculation to study the optical properties of ZnGeP2 crystal,including the influence of different exchange-correlation functionals and approximation methods on the energy band structure,and the influence of quasiparticle effect and exciton effect on the linear and nonlinear optical properties.It is found that the band gap and optical properties calculated by mBJ functional can reach the level of hybrid functional and GW approximation,and the calculation cost is much smaller,therefore,the mBJ functional can be used as a better choice for calculating the parameters of LVC model.