Cartesian internal coordinates: translational and rotational invariance

Abstract

Using translational and rotational invariance conditions for energy derivatives, we show that at a nonstationary point on the molecular potential energy surface the Hessian has at least three zero eigenvalues. Only at a stationary point can there be shown to be six (five for collinear geometries) zero eigenvalues. An infinitesimal transformation is defined such that the six (five for collinear geometries) transformed dependent Cartesian-like coordinates have zero gradients. From the form of this infinitesimal transformation, a translation-rotation free surface walking algorithm is defined. Numerical tests show that this surface walking procedure is practical for both non-collinear and collinear molecules.