Correlation Energies of the Lithium Sequence

The nonrelativistic eigenvalues of the $1s^{2}2p{}_{}{}^2{}_{}{}^{}P$ states of the lithium sequence are calculated to be $E\left(Z\right)=-1.125\mathrm{}{Z}^2+1.09352614Z-0.52717136+\mathrm{O}\left(Z^{-1\mathrm{}}\right)$ a.u., where $Z$ is the nuclear charge; and the energy of the $1s^{2}2p{}_{}{}^2{}_{}{}^{}P-1\mathrm{}{s}^{2}2s{}_{}{}^2{}_{}{}^{}S$ transition is calculated to be $\Delta E\left(Z\right)=0.07072093Z-0.11902237+\mathrm{O}\left(Z^{-1\mathrm{}}\right)$ a.u. For large nuclear charges, the addition of a $2p$ electron to the $1s^2{}_{}{}^1{}_{}{}^{}S$ core increases the magnitude of the correlation energy by 0.30 eV to give a value of 1.57 eV, most of which arises from the electron-pair energies.