Calculations of sub-μhartree accuracy employing explicitly correlated Gaussian lobe functions produce comprehensive data on the energy E(ω), its components, and the one-electron properties of the two lowest-energy states of the three-electron harmonium atom. The energy computations at 19 values of the confinement strength ω ranging from 0.001 to 1000.0, used in conjunction with a recently proposed robust interpolation scheme, yield explicit approximants capable of estimating E(ω) and the potential energy of the harmonic confinement within a few tenths of μhartree for any ω ⩾ 0.001, the respective errors for the kinetic energy and the potential energy of the electron-electron repulsion not exceeding 2 μhartrees. Thanks to the correct ω → 0 asymptotics incorporated into the approximants, comparable accuracy is expected for values of ω smaller than 0.001. Occupation numbers of the dominant natural spinorbitals and two different measures of electron correlation are also computed.
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The convergence of the computed energies is illustrated by the following examples: For the 2P− state, one obtains E(10.0) = 61.13852568, 61.13852556, and 61.13852553, for M = 39, 69, and 152, respectively, which yields the extrapolated value of 61.13852552 based upon a [1/1] Padé approximant. Similarly, one obtains E(0.1) = 1.05944965, 1.05944933, and 1.05944923 (for M = 36, 71, and 166), and E(0.001) = 0.03484805, 0.03484604, and 0.03484583 (for M = 39, 100, and 225), which results in the respective extrapolated energies of 1.05944918 and 0.03484571. For the 4P+ state, the analogous data for E(0.001) read 0.03488111, 0.03487876, and 0.03487830 (for M = 225, 572, and 880), which corresponds to the extrapolated energy of 0.03487750.
© 2012 American Institute of Physics.
2012
American Institute of Physics
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