The atomic three‐body problem. An accurate lower bond calculation using wave functions with logarithmic terms

Abstract

Accurate lower and upper bounds for the nonrelativistic ground state energies E, of the real systems ,He, H-, D-, and T-were calculated by the method of variance minimization using wave functions which include logarithmic terms. In addition, an analogous treatment with an infinite mass approximation for H-, He, and the isoelectronic series up to 2 = 10 was carried out. Especially for H-and He the results (a.u.) are given by -0.52775101712297, < E,(H-) < -0.52775101654373,These values have an absolute error smaller than 1.28 . lo-, cm-' for H-and 3.10 .cm-' for He. Moreover it is shown that a variation of nuclear mass m, for the H-species does not produce a second discrete eigenvalue.

Finite-element-method expectation values for correlated two-electron wave functions

“…Examples are the high-precision variational calculation of Drake [4] and the very accurate 401 term 1/Z expansion of Baker, Freund, Hill, and Morgan [5] (see [5] for a review). The recent upper bound energy of Thakkar and Khoga [6] lying 2.3 femtoHartree above this value is identical with the sharp lower-energy bound of Kleindienst and Emrich [7] up to the first 14 digits. A precise direct numerical treatment of the 3D partial differential equation is still lacking.…”

Accurately solving the electronic Schrödinger equation of atoms and molecules using explicitly correlated (r12-)MR-CI. II. Ground-state energies of first-row atoms and positive atomic ions

“…As a basis set, we first substituted the sp part of the aug-cc-pV5Z set 39 by Klobukowski's ͓14s͔ 30 and Partridge's ͓9 p͔ 31 sets and logarithmically extrapolated ͑i.e., ␣ nϩ1 ª␣ n 2 /␣ nϪ1 ) one diffuse s, respective p function. The resulting energy turned out to be 71 E h too high with respect to the exact value, 40,41 with the partial wave expansion already being converged to 5 E h in the spd set. We therefore decided to reoptimize the ͓4d3 f 2g͔ part using even-tempered sets ͑see, e.g., Ref.…”

Correlated one- and two-electron densities of low-lying S-states in helium-like atoms

“…For two-electron atoms and ions, different correlated wavefunctions are known (Accad et a1 1971, Baker et a1 1990, Kleindienst and Emrich 1990, Drake 1993, Drake and Yan 1994. The high accuracy of the energy eigenvalue predicted by these solutions, as well as the cuspcondition tests (Arias de Saavedra er a1 1994a,b), allows us to think that these results will be very close to the exact non-relativistic solution of the two-electron atom.…”