Perturbation theory made efficient and effective for predictions of ionization potential and electron affinity

Ionization potential and electron affinity are essential molecular properties. The most straightforward method is to calculate them by taking the total energy differences of the initial and final states according to the definition. However, it often suffers from a serious convergence problem due to the requirement of the self-consistent field (SCF) calculations for the ionic states with non-Aufbau choices of occupations. In the present work, we have constructed a theoretical framework in view of perturbation theory to bypass the SCF calculations of the ionic states. To address the imbalance issue that arises from the precisely treated neutral ground state followed by the truncated perturbative treatment of the ionic states, an accurate yet effective method has been developed here, which adds back some terms from the higher order perturbations into the lower order to cancel out the most computationally cost terms in the truncated expansion, thus reaching a better convergence with less computation. The validity of the present methodology has been tested out by applying it to the Hartree-Fock (HF) method in combination with the correlation effect described at the second-order Møller-Plesset level in a frozen-orbital approximation. All the derivations in this work are given in a general framework, which are applicable not only to HF but also to a wide range of density functional theory methods from semi-local functionals to hybrid and doubly hybrid functionals.