Application of the finite-difference boundary value method to the calculation of Born–Oppenheimer vibrational eigenenergies for the double-minimum E,F 1Σ+g state of the hydrogen molecule

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Abstract
The finite‐difference boundary value method is applied to the calculation of Born–Oppenheimer vibrational energies and expectation values of R−2 for an excited state of H2. We estimate the accuracy attainable by this method, point out a systematic error in the previous calculations of Tobin and Hinze, and correct several unjustified statements in the literature. Finally we point out that there is a large uncertainty in the final results due to choice of interpolation scheme.