| Abstract | Crawford's A matrix in the theory of molecular vibrations is, in a sense, the inverse of Wilson's B matrix, but is not unique because B is rectangular. We consider the general form of A and then use the Eckart conditions to obtain the solution A = M-1BTG-1, which has been widely used. Although the internal-coordinate harmonic force constants F = ATFXA, where FX are the Cartesian force constants, are superficially isotope-dependent, we show that this dependence vanishes. More generally, solutions of the form A = WBT(BWBT)-1, where W is an arbitrary nonsingular square matrix, are shown to give an f matrix that is independent of W. |
|---|
