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The eigenvectors of the overlap matrix are shown to be maximum overlap orbitals (MO–O's). Naive MO methods, such as that due to Hückel, are shown often to reduce to the MO–O problem. The potential usefulness of MO–O's in the determination of atomic hybrid orbitals and as starting orbitals for SCF calculations is considered.

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Wavefunctions and energy levels for the triplet and higher excited singlet states of the U center are calculated using the point ion model of Gourary. The transition energy and oscillator strengths are computed. The calculations of Gourary for the first singlet transition are extended to include all the alkali halides for which experimental information is available including those having the CsCl structure as well as those having the NaCl structure. The theoretical calculations for the first singlet transition are approximately 15% smaller than the experimental values. The oscillator strengths which we compute for this transition agree with those of Gourary. The theoretical calculations for the first triplet transition predict that it will lie in the visible and near-infrared region of the spectra, i.e., from 0.8 to 1.8 eV. The oscillator strength calculated for this transition is less than for the singlet transition. The theoretical values of the transition energies and oscillator strengths for the second singlet and triplet transitions are also calculated.