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Additional info for Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8
Formally it is necessary to find linear combinations of the quotient functions which, when multiplied by the common factor @a, diagonalize the energy of a crystal D and Aw D 6 hamiltonian with diagonal elements Aw and molecular interaction energies in the non-diagonal places. The MO analogue is the familiar problem of finding energy levels and molecular orbitals for one electron in an LCAO basis by diagonalizing the energy of a molecular hamiltonian with diagonal + + + THEORY OF MIXED-CRYSTAL SPECTRA + 33 elements a and a 6 (for an "impurity atom") and by nondiagonal neighbour interactions p.
Note Added in Proof A certain revival of the ligand-field theory has recently taken place through the introduction of the angular overlap model [Jsrgensen, C. , and Schmidtke, H. , J . Chem. Phys. 39, 1422 (1963); Schmidtke, H. Naturjorsch. Teil a, in press; Schaffer, C. , and Jsrgensen, C. , submitted to Mol. ] and the observation that this model, somewhat related to the Huckel theory but'utilizing the hydrogenic form of the angular 2-functions in Eq. (l), has the same consequences as a contact term consisting of a singular potential acting close to each ligand nucleus.
For even m a sign change of /? inverts the I = 0 manifold symmetrically about the mean energy; for odd m the sign change sends the I = 0 manifold into the Y = nlm manifold. The levels are identical in energy in the two cases, but ordered differently with respect to their r values: this change is important in dealing with intensities, as we shall see. For a set guest concentration m, increasing the total number n of molecules merely adds new manifolds of levels to the secular equation, there being no interactions with existing manifolds.
Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8