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Extra resources for Advances in Chemical Physics, Vol. 74
This approximation is well adapted to the intramolecular vibrations and, to a less degree, to the libration modes, particularly to optical modes. 15), when the frequency change upon excitation is neglected. 15). This approximation amounts to considering only the R , dependence of the local energy Dnm. We find that the xs do not depend on q. 30) The B(b) are operators of excitons (vibrations); the Vnmare intermolecular interactions; t, a dimensionless parameter, characterizes the linear coupling.
37b) - (cf. Appendix C). 40) we obtain the ground state with E’j = 0, and the excited state with i t E = 1, with its new frequency a,, and with a shift of the fundamental vibration, due in part to the change of the zero-point energy (hR,/2 - hf2,/2) and in part to the Franck-Condon shift giving the energy stabilization - E F C . )-”28’”16) represents the state 1:’) when BtB = 0, and the state 1:) when BtB = 1. 38) as combinations of the renormalized excitation operators. b. T h e Vibronic Exciton.
A brief discussion of the method of Ewald allows us to distinguish, in the dipolar sums, the dispersion due to short-range forces (coulombic interactions between neighboring molecules) and the nonanalytic dispersion due to longrange forces originating both from long-range coulombic interactions and from retarded interactions. The structure at K = 0 of the elementary excitations, depending on the direction of the wave vector (nonanalyticity), is thus shown to be the signature of the infinite range of the dipole-dipole interactions.