Use of the virial theorem in construction of potential energy functions for diatomic molecules

Abstract

The nth-order diatomic potential energy functions W(T)n and W(V)n are constructed, by the integration of the virial theorem −W−R[dW/dR]=T and 2W+R[dW/dR]=V, respectively, using the nth-order truncations of the perturbational λ=1−(Re/R) power series expansions of the kinetic (T) and potential (V) parts of the vibrational potential. The resulting W(T)n potential is a linear combination of terms R−1, R−2,⋅⋅⋅,R−n, and (lnR)/R; the W(V)n potential is a linear combination of terms R−1, R−2,⋅⋅⋅,R−n, and (lnR)/R2. For n=2, predictions of W(T)2, W(V)2, and also the generalized two-logarithmic second-order potential W(T,V)2 [including both the (lnR)/R and (lnR)/R2 terms] are compared with experiment and the results obtained from the Morse and Clinton potentials. Second-order logarithmic potentials for the ground states of H2, CO, and HF are given and compared with the Kol/os and Wolniewicz potential for H2 and the RKR classical turning points for CO and HF. Convergence properties of the W(T)n and W(V)n potentials are tested using the ground state of H2 as an example.