Correlation Energy of Atomic Nitrogen

The Brueckner-Goldstone many-body perturbation theory is applied to study the electronic structure of the atomic nitrogen in its ground ${}_{}{}^4{}_{}{}^{}S$ state. A complete orthonormal set of the $V^{N-1\mathrm{}}$ single-particle states with angular symmetry up to $l=5\mathrm{}$ is explicitly used to calculate the correlation-energy diagrams. The contribution from higher $l(>5\mathrm{})\mathrm{}$ is estimated by a hydrogenic approximation of the continuum wave functions. Our final correlation energy is -0.1895 ± 0.003 a.u., as compared with -0.1886 ± 0.0094 a.u. from the semiempirical estimate made by Veillard and Clementi. The sum of the exchange-core-polarization and pair-correlation-energy diagrams give a total of -0.207 28 a.u., which is 110% of the semiempirical estimate. This contains a contribution of -0.006 10 a.u. (3.2%) from $l>\mathrm{}3\mathrm{}$ states and -0.058 25 a.u. (31%) from the excitations into the valence $2p$ orbitals, the latter arising from the open-shell nature of the nitrogen atom. The overestimate (10%) of the correlation energy is remedied by the pair-pair correlation of 0.011 37 a.u. (6%) and the many-electron (three and four) effect of 0.006 42 a.u. (3.4%). A comparison with earlier configuration-interaction results is also made.