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Extra info for Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8
Hence, the orbitals of X can be approximately characterized by the quantum numbers = O(a), 3, = l ( r ) and so on. If the atom X is a closed-shell halide or oxide ligand, the outermost 9 shell divides into two degenerate r-orbitals and one a-orbital. The six u-orbitals of the cluster MX,, directed along the coordinate axes towards M, transform as the six highest orbitals of Eq. (2) having the symmetry types yn = a,,, tlu, and e,. Consequently, the empty sand @-orbitals of M and the set of two d-orbitals forming the higher sub-shell become the a-anti-bonding components of a set of six a-bonding orbitals filled by twelve electrons.
References 1. For a review see Craig, D. P.. and Walmsley, S. , Physics and Chemistry of the Organic Solid State, Interscience, New York, 1963, Ch. 10. 2. McClure, D. , J. Chem. Phys. 22, 1668 (1954). 3. Choudhury, N. , and Ganguly, S. , Proc. Roy. Soc. (Lmdon) A259, 419 (1960). 4. Craig, D. , Proc. Roy. Soc. 271, 207 (1963). 5. Santry, D. , Thesis, University of London, 1962. 6. Craig, D. , and Philpott, M. , in press. 7. Koster, G. , and Slater, J. , Phys. Rev. 96, 1208 (1954); and earlier papers.
11. Pure Crystals In molecular crystals the forces between molecules are much smaller than those within molecules. It is for this reason adequate in dealing with the low electronically excited states to use the free-molecule wave functions and to treat crystal perturbations on them only in a higher approximation. Accordingly we shall denote by v, vl, y2, . ,v", . , the several electronic states of the free molecules, and show by subscripts ( i , j )the location of the chosen molecule in the crystal.