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Additional resources for Advances in Chemical Physics: The Application of Wave Mechanical Methods to the Study of Molecular Properties, Volume 8
J-(m - 1)/2 (m odd) and p = 0, &l, m/2 (m even). If the coupling constant j3 is negative (as it is in the analogous MO calculation), the level Y = 0 lies at the bottom of the band and the lowest mixed-crystal level will come from the Y = 0 manifold. For positive j3 the lowest level is that for Y = n/2 : if m is even this also belongs to the Y = 0 manifold and if m is odd it belongs to the Y = n12m manifold. 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.
RpT of the host are Awl . . b THEORY OF MIXED-CRYSTAL SPECTRA 31 + of a guest molecule’of trap depth 6 is Aw 6, where, for later convenience, 6 is negative. The method of finding the stationary states of a mixed crystal is to diagonalize the energy in a basis of localized excitation functions each of which is derived from the functions (2) by substituting guest wave functions for host functions on the appropriate sites. The diagonal elements in the energy matrix are in these cases Awl + D + 6 instead of Awl + D , D being the difference in van der Waals energy between ground and excited states in the crystal lattice.
P. CRAIG be applied as usual for crystals, the system being essentially one of n molecules arranged on the circumference of a circle. The ground-state wave function of the mixed crystals is the product of unexcited free-molecule functions (4) @a= voviVa -- --- ~m-i~)m * ~am-1~2m - ~ n - 1 (4) The localized excitation wave functions are the analogues of expressions (2), namely (5) for excitation localized on a host 6, = TOT1 y u * =vov1. * -- 1 V, - * Ym-lYm --- - Yu - Ym-1Vm * 1 * (5) (6) molecule and (6)on a guest.