Abstract: The internal interaction potential of diatomic molecular system is analyzed and compared. The Murrell-Sorbian potential is used. We use Taylor perturbation theory to solve the corresponding stationary Schrodinger equation and to take the radial matrix diagonal element brief form in three-dimensional harmonic oscillator potential energy representation as well as to get first-order perturbation energy. Then the vibration-rotational energy level of the analytical form in the diatomic molecular system is obtained. The low energy level and spectral theory result are consistent with the experimental results.

Key words: level, M-S molecular potential energy function, Taylor perturbation method, radial matrix elements, three-dimensional harmonic oscillator energy representation