Theory of Atomic Structure Including Electron Correlation. I. Three Kinds of Correlation in Ground and Excited Configurations

There are novel correlation effects in excited states and configurations unlike those in closed shells. A theory for general nonclosed shells, and a method for calculation, are developed by separating the correlations into three mathematically and physically distinct types: (1) "internal," (2) "polarization plus semi-internal," and (3) "all-external" correlations. The first two of these are unique to open shells and strongly dependent on number of electrons, symmetry, and $Z$. They are however shown to be calculable by a finite configuration interaction method, and their energy contributions and wave functions are computed using a fully automatic program for 113 states of $1s^{2}2s^{n}2p^m(n=0, 1, 2; m=0, 1,\dots , 6)$ configurations for $Z=5\mathrm{} \mathrm{through} 11$. Both effects are found to be important in magnitude. The detailed wave functions obtained, which include those of positive and negative ions and of highly excited states containing inner $2s$ holes, are useful for obtaining atomic properties such as transition probabilities. The remaining all-external correlation energy is found to be, as predicted by the present theory, just like the correlation in closed shells, i.e., mainly made up of transferable pair correlations (evaluated in Paper II) and approximately transferable through $Z$ in a given isoelectronic sequence.