具備正確漸近性質的密度泛函評定，以及在TMA-H+-H2O例子上的正交模式分析改進

Abstract

This thesis primarily consists of two parts. In the first one, we benchmarked the performance of the functionals in density functional theory which have the asymptotically correct behavior. We compare the performance of the two different asymptotically corrected schemes, the long-range corrected (LC) hybrid scheme and the asymptotically corrected (AC) model potential scheme, in a wide range of applications. These schemes aim at producing the correct asymptotic behavior, which is known to be important to the Rydberg excitations and the frontier orbital energies of molecules. Based on our investigation, we found that the LC hybrid scheme outperforms the AC model potential scheme almost on all the properties studied, and we conclude that the LC hybrid scheme provides a promising direction for the future development of new exchange-correlation functionals. Besides, in the process of the benchmark, I established a molecular database ``IP131 full set', which consists of 131 experimental geometries of atoms and molecules, and their reference values of 131 experimental vertical ionization energies, 131 CCSD(T) calculated vertical electron affinities, 131 CCSD(T) calculated fundamental gaps and 113 CCSD(T) calculated atomization energies. The IP131 full set can be used in the benchmarks for other Ab Initio calculation methods, or in the parameter fitting in the development of density functionals in the future. In the second part, we adopted the Schrodinger equation numerical solutions to improve the applicability of the normal mode analysis in the case of TMA-H+-H2O, for the motivation that the theoretical simulated infrared spectrum of TMA-H+-H2O given by the normal mode analysis is far from the experiment results. Normal mode analysis is a convenient and widely adopted method that people usually use it to analyse the vibrational motions of multi-body mechanical systems, both classical and quantum. However, normal mode analysis is a approximate method and its assumptions, which make the analysis procedures simple and systematically solvable, also make the normal mode analysis not applicable to some vibrational motions in some mechanical systems. Our main modification method in this work is to regard the vibrational normal modes as some low dimensional quantum systems and adopt the Schrodinger equation numerical solutions in these quantum systems to replace the results from the normal mode analysis. By doing so, we can not only get a closer result to the experimental infrared spectrum, but also have a deeper understanding of the capability and applicability of normal mode analysis. Once in the future we encounter same problems when using the normal mode analysis in different systems, we may again adopt the procedures developed here to make it better.