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.
High precision atomic theory for Li and Be+: QED shifts and isotope shifts.
High-precision results are presented for calculations of the nonrelativistic energies, relativistic corrections, and quantum electrodynamic corrections for the 2 2S, 2 2P, and 3 2S states of Li and Be+, using nonrelativistic wave functions expressed in Hylleraas coordinates. Bethe logarithms are obtained for the states of Be+. Finite mass corrections are calculated with sufficient accuracy to extract the nuclear charge radius from measurements of the isotope shift for the 2 2S-2 2P and 2 2S-3 2S transitions. The calculated ionization potential for Be+ is 146 882.923+/-0.005 cm{-1}.
Closed Form of Infinite Series Used in Some Atomic Integrals Containing r12, r13, and r23
In an excellent scheme recently developed for evaluating the integral ∫f_1(r_1)f_2(r_2)f_3(r_3)g_1(r_(12))g_2(r_(23))g_3(r_(13))(dv) met in the calculation of correlated atomic wavefunctions, certain functions required in the computational scheme had to be evaluated by an infinite series expansion. As many as 40 terms may be needed in each of the three required infinite summations to get eight significant figures. We give a closed form expression for such functions avoiding all infinite sums. The new result is very compact and avoids the previous difficulty of numerical stability.