CONSIDERATION ON THE DEFINITION OF MOLECULAR SYMMETRY COORDINATES, CALCULATION OF PHYSICALLY MEANINGFUL FORCE-CONSTANTS, AND THE USE OF APPROPRIATE FORMULAS IN NORMAL-COORDINATE ANALYSES OF RING MOLECULES - A CASE-STUDY ON THE INPLANE FORCE-FIELD OF BENZENE

The way of defining molecular symmetry coordinates and the physical me aning of calculated force constants in normal coordinate analyses of r ing molecules are discussed. Formulae for normal coordinate analyses, starting from force constants obtained by ab initio molecular orbital calculations or those determined empirically, are reviewed in the form applicable even to the cases where molecular symmetry coordinates are not orthogonal to the redundant coordinates. An appropriate procedure is suggested for normal coordinate analyses of ring molecules startin g from empirically determined force constants. By taking the case of t he in-plane force field of benzene calculated at the CCD (coupled clus ter with double excitations) level with the 6-31G basis set as an exa mple, it is shown that values of force constants in the local coordina te system (F-R) and those in the molecular symmetry coordinate system (F-S) strongly depend on the way of defining molecular symmetry coordi nates. It is demonstrated that physically meaningful force constants a re obtained only when the definition of molecular symmetry coordinates correctly reflects the source of the potential energy gained by the d isplacements along the defined coordinates.