Knowledge Bank

The effective-core-potential method of Goddard, et al.,$\mathrm{<mrow\; data-mjx-texclass="ORD">1</mrow>}$ and Kahn, $etal.,2$ has been modified to properly account for one-electron relativistic effects. These effective potentials (EP) are obtained from the numerical atomic Dirac-Hartree-Fock (DHF) calculations and may be written as $$ V^{R}{EP}=\sum\ell\sum_{j=\ell-\frac{1}{2}}^{\ell+\frac{1}{2}}\sum_{m=-j}^{m=j}V_{\ell j(r)|\ell jm><\ell jm|} $$ where$|\ell jm>$ is a two-component angular basis function that is a product of a two-component Pauli spinor and spherical harmonics. Numerical $V\ell j(r)\prime s$ are approximated as expansions in terms of Gaussian- or Slater-type functions. The use of these EP’s enables one to use the jj-coupling scheme for subsequent applications in all-valence-electron calculations on heavy atoms and their molecules. A standard atomic SCF program has been modified to accommodate these EP’s and Gaussian- and Slater-type base sets having proper j-angular dependence. Energy levels for many atomic states of Xe and Au were calculated. The study of Xe excited states indicates that the spin-orbit splittings are reasonably approximated and that the numerical DHF calculations are adequately reproduced. Au has been treated as a 1-, 11-, 19- and 33-valence electron atom to investigate the effects of re-definition of the core. Molecular calculations using these EP’s are in progress.