Propagator matrices as matrices of power series. I: Its zeroth order and the Pople Santry model

Abstract

The implementation and calculation of the principal propagator matrix elements as a power's series are presented. The scheme is applied to singlet- and triplet-type properties at random phase approach (RPA) level of approximation. Its application to both the polarizability and the J-NMR spectroscopic parameter by using localized molecular orbitals shows (i) any element of the principal propagator matrix can be expressed as a series, (ii) each series has a different rate of convergence which depends on the type of property analyzed, the model compound and the relative magnitude of the first element of that series, (iii) the Pople–Santry model is related with the first element of each series, (iv) convergence also depends on stability conditions, and (v) this scheme can easily be applied to ab initio post-RPA calculation of molecular properties.