Lower Rydberg 2D states of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions

Very accurate variational nonrelativistic calculations are performed for the five lowest Rydberg 2D states (1s2nd1, n = 3, . . . ,7) of the lithium atom (7Li). The finite-nuclear-mass approach is employed and the wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian function. Four thousand Gaussians are used for each state. The calculated relative energies of the states determined with respect to the 2S 1s22s1 ground state are systematically lower than the experimental values by about 2.5 cm−1. As this value is about the same as the difference between the experimental relative energy between 7Li+ and 7Li in their ground-state energy and the corresponding calculated nonrelativistic relative energy, we attribute it to the relativistic effects not included in the present calculation

1D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions

Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five 1D states (1s2 2p2, 1s2 2s1 3d1, 1s2 2s1 4d1, 1s2 2s1 5d1, and 1s2 2s1 6d1) of the beryllium atom (9Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular state

Analytical energy gradient in variational calculations of the two lowest 3P states of the carbon atom with explicitly correlated Gaussian basis functions

Variational calculations of ground and excited bound states on atomic and molecular systems performed with basis functions that explicitly depend on the interparticle distances can generate very accurate results provided that the basis function parameters are thoroughly optimized by the minimization of the energy. In this work we have derived the algorithm for the gradient of the energy determined with respect to the nonlinear exponential parameters of explicitly correlated Gaussian functions used in calculating n-electron atomic systems with two p-electrons and n−2 s-electrons. The atomic Hamiltonian we used was obtained by rigorously separating out the kinetic energy of the center of mass motion from the laboratory-frame Hamiltonian and explicitly depends on the finite mass of the nucleus. The advantage of having the gradient available in the variational minimization of the energy is demonstrated in the calculations of the ground and the first excited 3P state of the carbon atom. For the former the lowest energy upper bound ever obtained is reporte

Refinement of the experimental energy levels of higher 2D Rydberg states of the lithium atom with very accurate quantum mechanical calculations

Very accurate variational non-relativistic calculations are performed for four higher Rydberg 2D states (1s2nd1, n = 8, . . . , 11) of the lithium atom (7Li). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions and finite nuclear mass is used. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The results of the calculations allow for refining the experimental energy levels determined with respect to the 2S 1s22s1 ground stat

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 2D states (1s2nd, n= 6, . . . , 11) of the 7Li and 6Li 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 2D 1s2nd states for 7Li and 6Li with n up to 3

1D states of the beryllium atom: Quantum mechanical nonrelativistic calculations employing explicitly correlated Gaussian functions

Very accurate finite-nuclear-mass variational nonrelativistic calculations are performed for the lowest five 1D states (1s2 2p2, 1s2 2s1 3d1, 1s2 2s1 4d1, 1s2 2s1 5d1, and 1s2 2s1 6d1) of the beryllium atom (9Be). The wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian functions. The exponential parameters of the Gaussians are optimized using the variational method with the aid of the analytical energy gradient determined with respect to those parameters. The calculations exemplify the level of accuracy that is now possible with Gaussians in describing bound states of a four-electron system where some of the electrons are excited into higher angular state

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 resul

Lower Rydberg 2D states of the lithium atom: Finite-nuclear-mass calculations with explicitly correlated Gaussian functions

Very accurate variational nonrelativistic calculations are performed for the five lowest Rydberg 2D states (1s2nd1, n = 3, . . . ,7) of the lithium atom (7Li). The finite-nuclear-mass approach is employed and the wave functions of the states are expanded in terms of all-electron explicitly correlated Gaussian function. Four thousand Gaussians are used for each state. The calculated relative energies of the states determined with respect to the 2S 1s22s1 ground state are systematically lower than the experimental values by about 2.5 cm−1. As this value is about the same as the difference between the experimental relative energy between 7Li+ and 7Li in their ground-state energy and the corresponding calculated nonrelativistic relative energy, we attribute it to the relativistic effects not included in the present calculation

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 resul