The diagonal Born–Oppenheimer correction beyond the Hartree–Fock approximation

We report on evaluation of the diagonal Born–Oppenheimer correction (DBOC) to the electronic energy with Hartree–Fock (HF) and conventional correlated wave functions for general molecular systems. Convergence of both HF and configuration interaction (CI) DBOC with the one-particle basis seems to be rather fast, with triple-ζ quality correlation consistent sets of Dunning et al. sufficiently complete to approach the respective basis set limits for the DBOC of the ground state of $H2$ within 0.1 cm⁻¹. Introduction of electron correlation via the CI singles and doubles method has a substantial effect on the absolute value of the DBOC for $H2,$ $H2O,$ and BH in their ground states (ca. +13 cm⁻¹ out of 115 cm⁻¹, +22 cm⁻¹ out of 622 cm⁻¹, and +11 cm⁻¹ out of 370 cm⁻¹, respectively). The effect of the correlation correction to the DBOC on relative energies is small, e.g., the barrier to linearity of water changes by ca. 1 cm⁻¹; however, the value is difficult to converge to the ab initio limit. Based on recent results by Schwenke [J. Phys. Chem. A 105, 2352 (2001)] and our findings, we expect the correlation correction to the DBOC to have a substantial effect on spectroscopic properties of the ground state of water. The effect of DBOC on equilibrium bond distance $re$ and harmonic vibrational frequency $ωe$ of the ground state of BH is +0.0007 Å and −2 cm⁻¹, respectively. Surprisingly, the former is a much larger change than expected, and greater than errors due to residual incompleteness of electron correlation treatment and basis set in state-of-the-art conventional Born–Oppenheimer computations. The effect of using a correlated wave function for the DBOC evaluation on the above corrections to $re$ and $ωe$ is small.