Convergence of an s-wave calculation of the He ground state

The Configuration Interaction (CI) method using a large Laguerre basis restricted to l = 0 orbitals is applied to the calculation of the He ground state. The maximum number of orbitals included was 60. The numerical evidence suggests that the energy converges as Delta E^N approx A/N^(7/2) + B/N^(8/2) + >... where N is the number of Laguerre basis functions. The electron-electron delta-function expectation converges as Delta delta^N approx A/N^(5/2) + B/N^(6/2) + ... and the variational limit for the l = 0 basis is estimated as 0.1557637174(2) a_0^3. It was seen that extrapolation of the energy to the variational limit is dependent upon the basis dimension at which the exponent in the Laguerre basis was optimized. In effect, it may be best to choose a non-optimal exponent if one wishes to extrapolate to the variational limit. An investigation of the Natural Orbital asymptotics revealed the energy converged as Delta E^N approx A/N^6 + B/N^7 + ... while the electron-electron delta-function expectation converged as Delta delta^N approx A/N^4 + B/N^5 + >... . The asymptotics of expectation values other than the energy showed fluctuations that depended on whether $N$ was even or odd.Comment: 12 pages, 10 figures, revtex format, submitted to Int.J.Quantum Chemistr

Convergence of the partial wave expansion of the He ground state

The Configuration Interaction (CI) method using a very large Laguerre orbital basis is applied to the calculation of the He ground state. The largest calculations included a minimum of 35 radial orbitals for each l ranging from 0 to 12 resulting in basis sets in excess of 400 orbitals. The convergence of the energy and electron-electron delta-function with respect to J (the maximum angular momenta of the orbitals included in the CI expansion) were investigated in detail. Extrapolations to the limit of infinite in angular momentum using expansions of the type Delta X_J = A_X/(J+1/2)^p + B_X/(J+1/2)^(p+1) + ..., gave an energy accurate to 10^(-7) Hartree and a value of accurate to about 0.5%. Improved estimates of and , accurate to 10^(-8) Hartree and 0.01% respectively, were obtained when extrapolations to an infinite radial basis were done prior to the determination of the J -> infty limit. Round-off errors were the main impediment to achieving even higher precision since determination of the radial and angular limits required the manipulation of very small energy and differences.Comment: 11 pages, 7 figures, revtex format, submitted to Int.J.Quantum Chemistr

Emily Dickinson's "My life had stood a loaded gun" - An interdisciplinary analysis

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