Pseudopotential Theory of Atoms and Molecules. I. A New Method for the Calculation of Correlated Pair Functions

It is shown that in all previously developed methods for the calculation of correlated pair functions the mathematical difficulties arise from the fact that the pair functions must be orthogonalized to the one‐electron spin orbitals by the orthogonality projection operator (1–Ω₁₂). Since this is an integral operator, if the pair functions are of Hylleraas type, containing $r_{12}$ , the orthogonalization will introduce integrals which are very time consuming to calculate. It is shown that the orthogonality projection operator can be transformed in good approximation into pseudopotentials, for which explicit expressions are derived. On the basis of this transformation a new method is developed for the calculation of correlated pair functions.