Some applications of the virial theorem to molecular force fields: The zero virial reaction coordinate and diatomic potentials from the normalized kinetic field functions

For a fixed‐angle potential energy surface (PES), W (Q), following the zero virial path (zvp), on which Σ W (Q) u ▽ u = 0, provides an efficient way for locating the transition state and generating a good approximation to the minimum‐energy reaction path; vector Q = (Q 1 ,…, Q N ) stands for nuclear coordinates. An algorithm which employs the zvp following is proposed for exploring PESs when starting from the reactant (or product) region. It seems that this approach allows one to avoid some discontinuities in the reaction coordinate, which often result from the “bottom‐following” procedures. The implications of the integral forms of the virial theorem are examined and a new way of constructing potential energy functions W (R) for diatomic molecules is proposed. It starts with the normalization of the kinetic component T (R) of the potential: f∞ [ T(R) ‐ T (∞)] dR ∞ Z A Z B , where Z A and Z B are the nuclear charges and R is the internuclear distance. The modified potentials are derived for four different analytical representations of T(R), T X (R) (X = M, R, RM, and HH) by the Morse, Rydberg, Rosen‐Morse, and Hulbert‐Hirschfelder functions, respectively. The three‐parameter modified potentials ( X = M, R, and RM) are tested against known spectroscopic data for H + 2 and H 2 . The modified potentials require one less experimental constant to fit the potential parameters than do their original analogs. It follows that the Morse and Rydberg functions constitute satisfactory representations of the kinetic component T(R) , and that enforcing its normalization improves predictions of spectroscopic constants and relations between them.