Abstract
The wave functions for the singlet and triplet states of a two-electron system in a given nuclear framework are investigated as superpositions of configurations and are shown to be transformationally equivalent to quadratic forms having certain ranks and signatures. By introducing the "natural orbitals" diagonalizing the generalized first-order density matrix, the total wave functions may also be brought to principal form. If the basis contains one-electron functions, the singlet and triplet wave functions contain respectively and configurations, but the transformation to natural orbitals reduces the number of terms to and [], respectively. The natural expansion having the best convergence is also characterized by another important extremum property. The approximate wave function of rank having the smallest quadratic deviation from the exact eigenfunction is obtained by interrupting the natural expansion of the eigenfunction after terms and renormalizing the result. For the singlet state, the wave function of rank two and signature zero has a special importance as giving a simple extension of the visual one-electron picture to include a large part of the correlation effects. The theory is illustrated by some results on helium obtained by using radial configuration interaction.
- Received 21 November 1955
DOI:https://doi.org/10.1103/PhysRev.101.1730
©1956 American Physical Society