Prediction of the nν2 inversional energy levels of the phosphine, arsine, and stibine molecules

Abstract

Effective inversion potential functions, V eff, of the PH 3, AsH 3, and SbH 3 molecules are constructed using the Frost-Musulin reduced potentials for description of the inversion potential functions and the harmonic approximation in order to account for the role of the (in-plane) vibrational motions. Consequently, the functions V eff involve eight free parameters [the equilibrium bond length, r X-H e ( X=P, As, Sb), the inversion barrier B, and six quadratic valence force constants, f ij ]. To determine V eff, we fix r X-H e and f ij at values taken from the literature and fit B to the experimental ν 2 band origins using a simple version of the nonrigid invertor Hamiltonian. The resulting potential functions are used with the same rotation-vibration theory to predict energies of the nν 2 inversional levels of the XH 3, XH 2D, XHD 2, XD 3, XH 2Mu, XHMu 2, and XMu 3 molecules, where Mu is muonium. In addition, inversion splittings of these levels are estimated by means of a simple WKB procedure.