Time-frequency Analysis Of Molecular Vibration Based On First-principles Molecular Dynamics Simulation

The energy transfer and dissipation in molecules are closely related to the coupling between vibration modes.Experimentally,two-dimensional infrared spectroscopy is often used to study the vibrational relaxation dynamics of molecules.However,since the current experimental results cannot exclude the effects of Fermi resonance and overtone vibration,it is difficult to establish the energy relaxation pathways of fundamental frequency vibration through experiments.The emergence of the first principles molecular dynamics simulation and the development of time-frequency analysis methods have provided possibilities for solving this problem.Within the framework of density functional theory,the first principles molecular dynamics can accurately simulate the fundamental frequency vibration behavior of single molecule when the temperature is close to 0 K.The quantitative analysis of its fundamental frequency vibration can be achieved by combining atomic trajectories and appropriate time-frequency analysis methods.Compared with Fourier transform and short-time Fourier transform,continuous wavelet transform is more suitable for multi-resolution time-frequency analysis of molecular fundamental frequency vibration.When the complex Morlet wavelet function is used as the basis function for continuous wavelet transform,two parameters,namely bandwidth and center frequency,need to be selected.However,there is currently no clear method for selecting the optimal parameters.Therefore,based on the essence of complex Morlet wavelet transform,the selection method of optimal bandwidth and center frequency is proposed.Theoretically,when the bandwidth and center frequency selected by this method are used for time-frequency analysis,the results can meet the requirement of frequency resolution and the limit of edge effect.In this work,the fundamental frequency vibration behaviors of single water molecule and single benzene molecule at ultra-low temperature(0.16 K)were simulated by using first-principles molecular dynamics in the microcanonical ensemble,and the time-frequency analysis of atomic trajectories was carried out based on the complex Morlet wavelet transform.The time-frequency analysis results of the fundamental frequency vibrations of water and benzene molecule indicate that there is a complex energy relaxation process between different vibration modes of the molecules.For the water molecule,during the entire simulation process,the fundamental frequency vibrations are mainly dominated by O-H bending vibration(1560.6 cm-1),which is accompanied by slight O-H stretching vibration.And the O-H stretching vibration is mainly expressed as the O-H symmetric stretching vibration(3711.1 cm-1),the O-H asymmetric stretching vibration(3819.3 cm-1)does not appear in the initial vibration process.The fundamental frequency vibrations of water molecule not only have uphill energy relaxation(O-H bending vibration excites O-H stretching vibration),but also have downhill energy relaxation(O-H symmetric stretching vibration excites O-H bending vibration).For the benzene molecule,during the entire simulation process,C-C bending vibrations with a vibration mode of v16(392.9 cm-1)have the highest intensity and is therefore most likely to be excited by other vibration modes.The intensity variation of C-C stretching vibration with a vibration mode of v8(1631.9 cm-1)is the most stable,making it difficult to excite or be excited by other vibration modes.The intensity of the C-H stretching vibration with a vibration mode of v2(3128.0 cm-1)gradually decreases,making it most likely to excite other vibration modes in the benzene molecule.This work not only presents a simple and reliable method for selecting the optimal parameters of complex Morlet wavelet transform,but also reveals the energy relaxation path of the fundamental frequency vibration of single water molecule and single benzene molecule based on this method,which is helpful to understand the fundamental frequency vibration behavior of single molecule.