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.
Prediction of 2D Rydberg energy levels of 6Li and 7Li based on very accurate quantum mechanical calculations performed with explicitly correlated Gaussian functions.
Very accurate variational nonrelativistic finite-nuclear-mass calculations employing all-electron explicitly correlated Gaussian basis functions are carried out for six Rydberg (2)D states (1s(2)nd, n = 6, [ellipsis (horizontal)], 11) of the (7)Li and (6)Li isotopes. The exponential parameters of the Gaussian functions are optimized using the variational method with the aid of the analytical energy gradient determined with respect to these parameters. The experimental results for the lower states (n = 3, ..., 6) and the calculated results for the higher states (n = 7, ..., 11) fitted with quantum-defect-like formulas are used to predict the energies of (2)D 1s(2)nd states for (7)Li and (6)Li with n up to 30.
Calculation of some integrals for the atomic three-electron problem.
An analysis is presented for the evaluation of integrals of the form ∫r 1 i r 2 j r 3 k r 23 -2 r m 31 r n 12 exp(-αr 1 -βr 2 -γr 3 )dr 1 dr 2 dr 3 which arise in the de atomic three-electron systems. All convergent integrals with i≥-2, j≥-2, k≥-2, m≥-1, and n≥-1 are discussed