Knowledge Bank

Wilson's FG Matrix $Method1$ appears to undergo a natural evolution into a comprehensive Integral Group Theoretical Method capable of providing unique force constants in molecules as a consequence of the recognition accorded to the fundamental role of Kinetic $Constants2$ in molecular vibrations. Besides the usual Raman-infrared spectral frequencies, the Integral Group Theoretical Method utilises two additional sets of equations herein called Static Symmetry Equations and Dynamical Symmetry Equations based on extensive studies relating to Kinetic constants in molecules. The Static Symmetry Equations enable us to eliminate the redundant force constants while the Dynamical Symmetry Equations are useful to reduce the number of independent force constants to just the number of spectral frequencies, paving the way for unique solution of the problem. The unique force constants lead, in turn, to unique values for other molecular constants, viz., Mean Amplitudes, Coriolis Coupling Constants and Centrifugal Distortion Constants with due regard to the experimental values concerned. This method of arriving at unique molecular constants, beginning from our studies relating to $XY3$ molecules, has been extended to a large number of molecules with interesting results thanks to the contributions of all our colleagues in this regard. Results relating to some molecules will be presented here. In addition, an interesting feature relating to the nature of molecular forces as revealed by the Static Symmetry Equations will also be discussed.