Estimated potential energy curves of diatomic molecules: A simplified procedure

A simplified method for evaluating f and g involved in the calculation of rmax and rmin for the electronic states of diatomic molecules, whose energy terms cannot be represented by a quadratic in v+ 1/2, is discussed. The method consists of dividing the observed vibrational term system into segments, each segment consisting of two vibrational levels, which can be represented by a quadratic in v+ 1/2 by the proper choice of constants omega i and omega xi, and thereby using the expressions of f and g derived by Rees for the quadratic equation, but with a slight modification. As a check, the potential energy curve of the B 3 Pi 0u+ state of the 79Br81Br molecule is constructed and compared with that calculated by Rees' elliptic function and RKRV methods. Further, the classical turning points are calculated for a few vibrational levels of the X 2 Sigma g+ state of N2+ and compared with those obtained by the RKRV method. The agreement is found to be excellent in both cases. Using the new procedure, true potential energy curves are also constructed for the X 1 Sigma g+ and C 1 Sigma u+ states of the P2 molecule.