The diagonal correction to the Born–Oppenheimer approximation: Its effect on the singlet–triplet splitting of CH2 and other molecular effects

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Abstract
The prediction of the diagonal correction to the Born–Oppenheimer approximation is now possible by ab initio analytic methods, as has recently been shown by Yarkony and Lengsfield. At the general restricted Hartree–Fock (GRHF) level of approximation, the procedure is straightforward: solutions of the coupled perturbed Hartree–Fock equations (CPHF) and some overlap integrals are all that are required. This correction is evaluated for a series of small molecules with various basis sets: H2O, H2O+, CH2, HCF, H+5, and F2. It is interesting to observe that the value of this correction (0.11 kcal) for the singlet–triplet splitting of CH2 is larger than the relativistic correction, and that the theoretical value for Tnre (BO)≡9.23±0.20 kcal has come even closer to the best ab initio prediction of 9.4 kcal.