Knowledge Bank

The normal coordinate transformation L may be factored into a matrix PA, where P is completely determined by the kinetic energy matrix G, and A is an orthonormal matrix. Hence A may be visualized as a rotation in $n(n-1)/2$ - space, n being the order of the secular equation: It can be determined only by study of isotopic molecules or by the imposition of special restrictions on the potential function. The consideration of all such rotations is a convenient way of considering all possible sets of force constants, bond-moment parameters, etc. In the simple case $n=2$, graphical representations in terms of the single rotation angle are especially perspicuous. We shall illustrate the application to the determination of the force constants of $C2H4$ and the bond-moment parameters of $CF2$ and $C2F4$.