Theory of Atomic Structure Including Electron Correlation. II. All-External Pair Correlations in the Various States and Ions of B, C, N, O, F, Ne, and Na, and Prediction of Electron Affinities and Atomic Excitation Energies

The first paper of this series showed that the portion of the total correlation energy, which remains after two types of correlation effects specific to $N$ (number of electrons), symmetry state, and $Z$ are taken out, is quite similar in nature to correlation in closed shells. This remainder, the "all-external energy" is expected to be by and large made up of pair correlations whose values are transferable through $N$, symmetry state, and $Z$ as predicted in the theory by Sinanoğlu. The present paper analyzes the all-external correlation energies of B, C, N, O, F, Ne, and Na into their irreducible all-external pair components. The predicted additivity and transferability of all-external pairs are found to hold within the error limits of experimental correlation energies. A set of such pair-correlation values applicable to a great many states and ions of $1s^{n}2s^{m}2p^k$ type are obtained. Together with the calculated values of the two other types of correlation effects, these yield nonrelativistic atomic energies to a root-mean-square deviation of 0.05 eV. A semiempirical method for the prediction of atomic energy levels of general nonclosed-shell species, excited configurations and states as well as ground states is presented. The method is applied to predictions of electron affinities, excited states of negative ions, excitation energies, intermultiplet separations, and term-splitting ratios. Results of the method are compared with experiment and other semiempirical and nonempirical methods.