# CORRELATED ORBITALS FOR HELIUM-LIKE $SYSTEMS^{*}$

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 Title: CORRELATED ORBITALS FOR HELIUM-LIKE $SYSTEMS^{*}$ Creators: Roothaan, C. C. J.; Weiss, A. Issue Date: 1958 Publisher: Ohio State University Abstract: “Trial wave functions of the form $\phi({r}_{1})\phi({r}_{2})\chi({r}_{12})$ and $[\phi({r}_{1})\psi({r}_{2})+\phi({r}_{1})\psi({r}_{2})\chi({r}_{12})]$ have been used to represent the wave functions of the isoelectronic helium scries. The functions $\phi$ and $\psi$ are taken in the forme ${e}^{-\zeta{r}}\Sigma_{\lambda}{a}_{\lambda}{r}^\lambda$ and $\chi$ in the form $\Sigma_{\lambda}{c}_{\lambda}{r}_{12}^\lambda;\zeta, {a}_{\lambda}$ and ${c}_{l}ambda$ were determined by minimizing the energy. Preliminary results indicate that about five terms for each expansion is equivalent to a full variational calculation of $\phi , \psi$ and $\chi$. For helium, the best closed-shell wave function accounts for 02%, and the best open-shell wave function for 98.6% of the correlation energy.” Description: $^{*}$This work was assisted in part by contraets with The Office of Naval Rescarch and the Air Force Office Scientific Research and a grant from the National Science Foundation. Author Institution: Laboratory of Molecular Structure and Spectra, Department of Physics, The University of Chicago URI: http://hdl.handle.net/1811/7741 Other Identifiers: 1958-H-01