A Least-squares Fitting Based On Monte Carlo Random Walk And Calculation On The Dynamic Parameters For The Ground States Of Some Molecules

As one of the fundamental contents of atomic and molecular physics, the study of energy level structure and dynamics of atoms and molecules is constrained by the accuracy of experiments.Fortunately, in recent years, advances of the experimental techniques such as the high-resolution electron spectroscopy, laser spectroscopy, synchrotron radiation and particle detection improved the experimental accuracy, and new theoretical and computational methods as well as the develop-pment of large-capacity ultra-high-speed computer promoted the study at the same time. In this paper, we use the existing information of the atoms and molecules, such as the exact energy levels determined by the spectroscopy and the theoretical calculated Franck-Condon factor, or the wave function of ground state calculated by the commercial quantum chemistry software, to fit and calculate the scattering intensity distribution, squared form factor and Compton profile, the specific contents are as follows:1. A least-squares fitting method based on Monte Carlo random walk model is introduced. This method utilizes existing knowledge about the excitation of diatomic molecules, which greatly reduces the number of undetermined parameters in the fitting process, and uses Monte Carlo random walk model to obtain the search method of the minimum value of the whole domain variance. These attempts greatly improve the fitting speed and produce credible results. As an example, we use the MATLAB program based on the fitting method to calculate the optical oscillator strength spectrum of hydrogen molecule. The result is in good agreement with the theoretical and experimental results of other works, which also proved the credibility of the method;2. The wave function of the ground state of atoms and molecules is calculated by Gaussian 03,the wave function is then used to calculate the elastic squared form factor and the Compton profile in this work. Using this method, we calculated the squared form factor of He and C2H2 as well as the Compton Profile of propane using the Mathematica program written by us. The squared form factor is in good agreement with the theoretical and experimental results of other works, and the deviation between the calculated Compton profile and experimental results is less than 1%, which verified validity of the calculation method and the credibility of the program.