Vibrational corrections to properties at arbitrary reference geometry

We demonstrate how vibrational contributions to any (static) electric property may be computed with respect to an arbitrary reference geometry which, at a given level of electronic structure theory, need not correspond to the associated minimum energy geometry. Within the harmonic approximation, it is shown that the formulas for the vibrational contributions can be extended to include a second-order corrective term, which is a function of the energy gradient and the (nuclear) first derivatives of the property in question. Taking the BH molecule as a test case, we illustrate that the order of magnitude of the correction increases with order of property (i.e., mu approximate to 10(-2) --> gamma approximate to 10(1)-10(2)), and that this value is equivalent to the difference in (pure) electronic contributions evaluated with respect to the optimum and nonoptimum geometries. Furthermore, we show that for a diatomic, vibrational [zero-point vibrational average (ZPVA) and pure] contributions computed at a nonoptimum geometry may be readily corrected to give the optimum geometry values. Thus we provide a route for obtaining total (electronic + vibrational) properties associated with a minimum energy geometry, using information calculated at a nonoptimum geometry. (C) 2000 American Institute of Physics. [S0021-9606(00)31004-2].