Significance of the Pariser Approximation on the One-Center Electron Repulsion Integral

The one‐center electron repulsion integral (χ_pχ_p | χ_pχ_p) as obtained by $${\mathrm{(\chi }}_p{\chi }_p{\mathrm{\hspace{0.17em}|\hspace{0.17em}\chi }}_p{\chi }_p\mathrm{)=I-A,}$$ where I and A are the ionization potential and the electron affinity of an appropriate valence state, is shown to be the one for the negative ion rather than for the neutral atom. The argument is based on the assumptions that an energy integral for the neutral atom equals the arithmetic mean of the corresponding integral for the positive and the negative ions and that Koopmans' theorem is correct. The validity of the assumptions is discussed. The implication of the present conclusion in the semiempirical MO theory is also discussed.