Ab initio effective core potential calculations for atoms and molecules including relativistic and correlation effects

Abstract

Numerical Dirac-Fock calculations with all electron and various different core-valence space partitionings are performed for the excitation energies of Cu, Ag and Au atom to assess the validity of frozen core approximation in heavy atom systems. Errors of effective core potential(ECP) calculations are analyzes. A modified ECP generating scheme which can generate a ECP from the valence space in which more than one valence orbitals per symmetry exist is proposed. A two-component Kramers`` restricted Hartree-Fock method(KRHF) has been developed for polyatomic molecules with closed shell configurations. The present KRHF program utilizes the relativistic effective core potentials with spin-orbit operators at the Hartree-Fock(HF) level and produces molecular spinors obeying the double group symmetry. The KRHF program enables the variational calculations of spin-orbit interactions at the HF level. KRHF calculations have been performed for HX, $X_2$, XY(X,Y=I, Br) and $CH_{3}I$ molecules. It is demonstrated that orbital energies of KRHF calculations are useful to interpret spin-orbit effects in photoelectron spectra. In all molecules studied, bond lengths are only slightly expanded, harmonic vibrational frequencies are reduced and bonding energies ar significantly decreased by incorporating spin-orbit interactions. Two-component Hartree-Fock method using relativistic effective core potentials(REP) is extended to include electric correlations by the second order M$ö$ller-Plesset perturbation theory(MP2). The present method simultaneously treats electron correlation and all the relativistic effects in REP including spin orbit effects. It is possible to estimate differential correlation effects on molecular properties due to the relativity and/or the spin-orbit interactions at the MP2 level using the present method. Test calculations have been performed for HX, $X_2$, XY (X,Y=Br,I), and $PbH_4$ molecules. Spin-orbit and electron correlation effects are rather small f...