Abstract
The utilization of first principles calculation, also known as ab initio calculation, has emerged as an indispensable tool for comprehending the fundamental properties of atomic and electronic systems. The present study focuses on investigating first principles free energy calculation methods in aqueous solutions and employing the non-adiabatic dynamics method to analyze gravitational molecules. In this thesis, we commence by presenting a comprehensive overview of electronic structure calculations and ab initio molecular dynamics (AIMD) simulations.
Subsequently, we delve into the examination of redox ow batteries, solvation free energy calculation methods, and a two-phase thermodynamic model. Notably, all these investigations involve the calculation of free energy using the AIMD technique. In the final chapter, we expand our purview to encompass the realm of cosmology. Specially, we employ the non-adiabatic dynamics method to analyze the properties of gravitational molecules, specially binary black holes with axion clouds. This extension of our research not only contributes valuable insights into free energy calculation methods for chemical and electrochemical processes but also oers a fresh perspective on comprehending black holes and dark matter.