Crawford's A matrix in the theory of molecular vibrations is, in a sense, t
he 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 o
btain the solution A = M(-1)B(T)G(-1), which has been widely used. Although
the internal-coordinate harmonic force constants f = A(T)F(X)A, where F-x
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 sh
own to give an f matrix that is independent of W. (C) 2001 Academic Press.