Efficient computation of compliance matrices in redundant internal coordinates from Cartesian Hessians for nonstationary points

We present an extension to the theory of compliance matrices, which is valid for arbitrary nonstationary points on the potential energy hypersurface. It is shown that compliance matrices computed as the inverse of the covariant Hessian matrix obey the same invariance properties with respect to different internal coordinate systems as they do for stationary points. Furthermore, we demonstrate how the computation of compliance matrices in arbitrary sets of redundant internal coordinates starting from a Cartesian Hessian can be achieved efficiently, and we discuss their potential usefullness in geometry optimization processes. (C) 2010 American Institute of Physics. [doi:10.1063/1.3413528]