One-Electron Reduced Density Matrices forLi(P2)andB(P2)

Abstract

The one-electron reduced density matrix (one-matrix) is reported for the Weiss $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}P\right)$ configuration interaction (CI) wave function and for the $\mathrm{B}\left({}_{}{}^2{}_{}{}^{}P\right)$ polarization, first-order, and 187-term CI functions of Schaefer, Harris, and Klemm. The one-matrix of the $\mathrm{Li}\left({}_{}{}^2{}_{}{}^{}P\right)$ function demonstrated none of the symmetry mixing expected of a ${}_{}{}^2{}_{}{}^{}P$ state due to the "${}_{}{}^2{}_{}{}^{}S$-type" restrictions imposed on the wave function. Both the 187-term and first-order wave functions for $\mathrm{B}\left({}_{}{}^2{}_{}{}^{}P\right)$ do not fully describe the hyperfine structure because the 187-term function lacks an adequate basis and the first-order function systematically excludes some important radial-type correlation terms in the $L$ shell. By including a few such terms, this function could represent an effective systematic approach to hyperfine-structure determinations. The polarization function excludes too many important terms to be reliable. These studies indicate that the polarization to the $1s$ and $2s$ orbitals decreased with the inclusion of more correlation in the wave function and that the inclusion of the $2s-2p$ near-degeneracy effect did materially influence the forms of the dominant natural spin orbitals. Pertinent suggestions are presented for constructing improved CI wave functions for $\mathrm{B}\left({}_{}{}^2{}_{}{}^{}P\right)$.