Adiabatic correction to the energy of molecular systems: the CPHF equivalent of the Born–Handy formula

The Born–Handy formula, recently shown by Kutzelnigg to be a rigorous expression for the calculation of the adiabatic correction, has been, on the level of a ground state SCF wavefunction, reformulated and linked to the coefficients of the standard coupled perturbed Hartree–Fock (CPHF) method. The contribution of the electron correlation via second-order perturbation theory is also presented. The solution of the corresponding secular equation of the nuclear motion enables the calculation of the adiabatic correction over the particular normal modes. The method offers the possibility of extending high-precision calculations of the adiabatic correction to more complex systems. Test calculations have been performed for H2, HD and D2 and the results are in satisfactory agreement with the exact figures.