Theoretical approach to classical reduced mass vector in the many-body problem and its application to vibrations of water

Abstract Reduced mass value and vector are well known for two-body problem; the study of many-body problems and their applications (such as vibrational spectroscopy) is one of the important physical problems. Vibrational spectroscopy provides a powerful tool to perceive the molecular structures and atom motions of molecules. The water molecule is a three-body system stretching vibration that has been previously quantized, showing the infrared (IR) absorption spectrum based on Morse potential. In this work, the molecule was studied in classical and quantum mechanics to determine its absorption intensity. The results show molecular atomic motions and changes in dipole and reduced mass vector. A Morse-like model for bending was predicted based on the spectroscopic vibration frequency and intensity, defining the bending potential depth of 93.5 kJ/mol.