Ground‐State Energy of Lithium and Three‐Electron Ions by Perturbation Theory

Shirley Seung and E. Bright Wilson Jr.

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• Department of Chemistry, Harvard University, Cambridge, Massachusetts

ABSTRACT

Perturbation theory has been applied to the calculation of the energy of the (1s)22s 2S ground state of the lithium atom and three‐electron ion series, with the entire interelectron repulsion potential employed as the perturbation. The wavefunction to first order has been written down in terms of variation perturbation first‐order wavefunctions for the three states of the two‐electron ion: (1s)2 1S, 1s2s 1S, and 1s2s 3S. From the first‐order wavefunction, the second‐order and third‐order contributions to the energy have been calculated. The results are that the nonrelativistic Schrödinger energy for the ground state of two‐electron ions (with fixed nucleus) is given by E(Z)=−1.125Z2+1.022805Z−0.4083–0.0230(1/Z)+O(1/Z2)${\text{E(Z)=−1.125Z}}^2{\text{+1.022805Z−0.4083–0.0230(1/Z)+O(1/Z}}^2)$ a.u. The term in Z0 is in agreement with an empirical value within the uncertainty of the latter. The above expression gives an overall energy better for the larger values of Z than any existing direct variation or configuration interaction calculation and shows that the perturbation expansion is quite rapidly convergent, at least for three electrons. New wavefunctions to first order for the 1s2s 1S and 1s2s 3S states of the two‐electron ions were obtained by the variation‐perturbation procedure at several levels of approximation. In particular, for the 1S functions, steps were taken to ensure that the perturbation part was orthogonal to the unperturbed function and that the correct relationship to the ground state was maintained.

https://sci-hub.tw/https://aip.scitation.org/doi/abs/10.1063/1.1701800