Errors in the calculations of first‐order and second‐order energy perturbations

We consider the calculation of first‐order and second‐order atomic and molecular properties from approximate ground‐state wave‐functions by using variational procedures for solving the first‐ and second‐order perturbation equations. We evaluate the errors in the final results due to the error in the unperturbed wave‐function and to the errors caused by the approximations in solving the perturbation equations. By combining slightly different results we can eliminate all first‐order errors. Our analysis covers situations where perturbation expansions of the error in the ground‐state wave‐function are not feasible and it includes the effects due to approximations in solving the perturbation equations.