An algorithm for calculating atomic D states with explicitly correlated gaussian functions.
An algorithm for the variational calculation of atomic D states employing n-electron explicitly correlated gaussians is developed and implemented. The algorithm includes formulas for the first derivatives of the hamiltonian and overlap matrix elements determined with respect to the gaussian nonlinear exponential parameters. The derivatives are used to form the energy gradient which is employed in the variational energy minimization. The algorithm is tested in the calculations of the two lowest D states of the lithium and beryllium atoms. For the lowest D state of Li the present result is lower than the best previously reported result.
An algorithm for quantum mechanical finite-nuclear-mass variational calculations of atoms with L = 3 using all-electron explicitly correlated Gaussian basis functions.
A new algorithm for quantum-mechanical nonrelativistic calculation of the Hamiltonian matrix elements with all-electron explicitly correlated Gaussian functions for atoms with an arbitrary number of s electrons and with three p electrons, or one p electron and one d electron, or one f electron is developed and implemented. In particular the implementation concerns atomic states with L = 3 and M = 0. The Hamiltonian used in the approach is obtained by rigorously separating the center-of-mass motion from the laboratory-frame all particle Hamiltonian, and thus it explicitly depends on the finite mass of the nucleus. The approach is employed to perform test calculations on the lowest (2)F state of the two main isotopes of the lithium atom, (7)Li and (6)Li.
Projection-operator calculations of the lowest e--He resonance.
Results for the lowest (Schulz) autodetaching state of ${\mathrm{He}}^{\mathrm{\ensuremath{-}}}$ [1s(2s${)}^{2}$] are reported. The calculation utilizes the full projection-operator formalism as explicitly developed by Temkin and Bhatia [Phys. Rev. A 31, 1259 (1985)]. Eigenvalues, scrE=〈\ensuremath{\Phi}\ensuremath{\Vert}QHQ\ensuremath{\Vert}\ensuremath{\Phi}〉, are calculated using projection operators Q depending on increasingly elaborate target wave functions going up to a 10-term Hylleraas-form, and a configuration-interaction total wave function \ensuremath{\Phi} of 40 configurations. Results are well converged, but our best value is \ensuremath{\sim}0.13 eV above the experimental position at 19.37 eV. We conclude that the shift (\ensuremath{\Delta}) in the Feshbach formalism gives a large contribution (relative to the width) to the position ${E}_{r}$ (=scrE+\ensuremath{\Delta}). An appendix is devoted to the evaluation of the most complicated type of three-center integral involved in the calculation.