Application of the finite-difference boundary value method to the calculation of Born-Oppenheimer vibrational eigenenergies for the double-minimum E,F¹Σ_g⁺ state of the hydrogen molecule

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.