NEW FUNCTIONAL FORM FOR REPRESENTING VIBRATIONAL EIGENENERGIES OF DIATOMIC-MOLECULES .2. APPLICATION TO H-2 GROUND-STATE

An expression previously proposed for representing vibrational eigenenergies E, as a function of quantum number ν is applied to the H 2 ground electronic state. The expression is Eν=D- (νD-ν)m[L/N], where D is the dissociation limit energy, vD and m are parameters, and [L/N] is a rational fraction in (νD-ν). We integrate the vibrational Schrödinger equation to obtain 15 Born-Oppenheimer (BO) Eν with reduced mass μ0=918.048 electron masses, and 77 BO E, with 25 μ0; error in E, attributable to the potential is estimated to be 0.02 cm -1. The proposed functional form with a variety of [L/N] is fitted to the 14 BO μ0 first differences ΔE(ν+1/2); with the exception of [4/0] all L+N=4 fits have an rms error in calculated ΔE of 0.02 cm-1. The proposed formula is then fitted to 15 BO differences including D-E14. The error in calculated D-E14 can be made negligible while the rms error in calculated energy differences remains 0.02 cm-1. Mass 25 μ0 is used to check applicability of the proposed functional form to a large number of levels; several fits yield all 76 δE with an rms error of only 0.04 cm-1. Finally, the proposed expression is applied to experimental vibrational energies. For these, better fits have an rms error of -0.07 cm-1, presumably due primarily to experimental errors. © 1979 American Institute of Physics.