Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

Molecular vibrational constants of some simple polyatomic molecules : Valence force constants and compliance constants of some halogenated methanes, silanes and germanes

The valence force constants and compliance constants of twenty-six halogenated methanes, silanes and germanes of symmetry C_3v and C_2v are reported. Correlations have been found between the primary force constants and the nature of the central atom and of the halogen, and the number of attached halogen atoms. Relationships have also been confirmed between the force and compliance constants and the bond lengths and strengths.     

Compliant fields for molecular interactions: Water dimer and formic acid dimer

The redundancy-free internal valence compliance constants of open-chain water dimer and formic acid cyclic dimer have been determined by the combined use of the CNDO /Force method and the compliance constant formalism. The final compliant fields of these dimers have been refined with the help of experimental frequency data.