Approximate Natural Orbitals for Four-Electron Systems

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Abstract
Approximate natural orbitals for four‐electron wavefunctions for Be as calculated by Boys, Matsen, Watson, and Weiss and LiH as calculated by Ebbing are obtained by diagonalization of the appropriate first‐order reduced density matrices. The formalism for carrying out the process is extended to the case of a nonorthogonal basis. Occupation numbers are presented and compared for the functions reported. In addition, truncated natural expansions reproducing the original functions are tabulated. Natural‐orbital functions are tabulated. Natural‐orbital occupation numbers, the orbitals themselves, and the natural expansions are shown to have considerable value in comparing these functions. The nature of the approximations used in the individual functions is clarified by the analysis, and considerable insight is afforded to the nature of the physical system.
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