GENERALIZED REDUCED-POTENTIAL CURVE METHOD AND ITS APPLICATIONS

The generalized reduced-potential curve (GRPC) is defined and analyzed. A special form of the GRPC formula is defined with respect to the reduced-potential curve (RPC) employed previously (parametrized formula). It is shown that the definition of the reduced potential used by Ferrante et al. [Phys. Rev. Lett. 50, 1385 (1983)] and Tellinghuisen et al. [Phys. Rev. A 39, 925 (1989)] is equivalent to the old definition of Frost and Musulin (FM) [J. Am. Chem. Soc. 76, 2045 (1954)] that is obtained from the GRPC as a limit case. It is further shown that the FM reduced potential cannot be used for a systematic comparative study of the potentials of diatomic molecules (which, however, may be successfully made in the RPC scheme), nor can the FM formula be employed to obtain accurate approximations of the potentials. On the other hand, it is demonstrated by a series of examples that very accurate approximation methods for the extensions of the potentials may be defined with the use of the GRPC formula in the framework of the RPC scheme. A parametrized RPC formula appears to be a good GRPC formula: For the inner wing, the one-parameter approximation already leads to a degree of accuracy that seems satisfactory also to a spectroscopist (limit of error in the internuclear distance less than 0.001). One-parameter approximations of potentials published previously are evaluated and shown to have reached a satisfactory degree of accuracy also in the outer wing (limit of error in energy less than 3 cm-1). The GRPC method is also employed to obtain an essentially more accurate approximation from theoretical ab initio calculated potentials. The potentials obtained with the aid of the GRPC method may then be used for the calculation of the spectra. © 1990 The American Physical Society.