Journal zyxwvutsrqponmlkjihgfedcbaZYXWVUTSRQPONMLKJIHGFEDCBA of Mok w .&r Structure (Theo&em), 254 (1992) 135-144 Elsevier Science Publishers B.V., Amsterdam 135 zyxwvu A numerical procedure to obtain accurate potential energy curves for diatomic molecules Alfred0 Aguado, Joaquin Juan Camacho and Miguel Paniagua Departamento de Quimica Fisica, Facultad de Ciencias C-XIV, Universidad Autdnoma de Madrid, 28049 Madrid (Spain) (Received 14 September 1990) Abstract The potential energy curves for the X’Z+ state of W60 and ‘Li’H were obtained by fitting the Rydberg-Klein-Rees potential in the Chebyshev sense (minimum-maximum approximation) to a simple functional form very similar to a perturbed-Morse-oscillator potential but with a minor number of parameters. Using Hermite orthogonal functions (eigenfunctions of the harmonic os- cillator) as the basis set we solved variationally the radial Schriidinger equation to obtain the vibrational energies E, and the rotational constants B,. Using the potential thus determined and the proposed basis set, the matrix elements of the Hamiltonian may be calculated analytically, presenting only round-off errors. The agreement between the calculated and experimentally de- termined E, and B, values is good, the self-consistency of our potentials being very similar to that obtained by other authors. INTRODUCTION The correct representation of the Born-Oppenheimer potential energy of a diatomic molecule as a function of the internuclear distance is of fundamental importance in, for example, molecular dynamics, spectral phenomena, kinetics mechanisms, and the understanding of stellar structure. A large part of the information about a molecular structure is summarized by the potential energy curves of the molecule. In recent years, increasing attention has been given to the problem of the most convenient and accurate representation of the poten- tial energy curves of diatomic molecules through some type of analytical func- tion. These functions are usually obtained in one of three forms: (i) an empir- ical function, (ii) a power series expansion, or (iii) Pad6 approximants. Empirical functions [l-11] are normally simple and easy to use but the assumption of a single functional form produces important deviations from the “true” potential energy curve. Power-series expansions zyxwvutsrqponmlkjihg [12-191 can be used to give a very accurate potential energy curve close to the minimum zone and, if the series converges, it is possible to represent the potential energy for OlSS-1280/92/$05.00 0 1992 Elsevier Science Publishers B.V. All rights reserved.