Some situations in the determination of molecular wave functions require to go beyond the Born-Oppenheimer (BO) approximation, with the wave function written as the product of an electronic wave function depending parametrically on the nuclear coordinates and a nuclear wave function. Such situations are usually treated by combining BO products. This form of the wave function leads to coupled equations which determine the nuclear factors of these products. There is another possibility: writing the exact molecular wave function as a single product having formally the same structure as a BO product. This approach has been at the origin of recent developments. We reconsider this problem with the aim of looking at the solutions of the coupled equations which determine the electronic factor of the factorization scheme. It is shown that these coupled equations can be reduced precisely to those encountered with the usual combination of diabatic BO products. Published by AIP Publishing.
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