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Extra resources for Advances in Chemical Physics, Vol. 74
32) where b + b' is given its classical significance. 33) This problem is that of diagonal disorder (see Section IV). 34) Applying the results of Section IV,we find the two well-known limit results: At high temperature, A >> B, the excitonic coherence is thermalized; the lattice is an assembly of incoherent molecules with a response consisting of localized excitations with gaussian shape. C)in terms of the absorption of excitonic states, momentarily trapped in a lattice thermal fluctuation, when local interactions are not strong enough to create self-trapped excitons.
Then we obtain 6s branches of phonons in a crystal with s molecules per unit cell. In these 6s branches, 6s-3 are optical phonon branches and 3 acoustical phonon branches; for the latter Rs(k)k~oc,I kl (c, being the sound velocity in branch s). For directions of k of high symmetry the acoustical branches are divided into one longitudinal and two transverse branches. In genera1 the optical branches correspond to mixed motions of translation and rotation. Nevertheless, for centrosymmetric crystals where the center of the molecule is center of symmetry, for k = 0, the translation optical modes are of u symmetry, while the rotation modes are of g symmetry and are called librations.
66) = JNa,IK)E,,,, As a consequence of the translational invariance of the matrix ae,J K ) is an eigenstate, so that the induced dipoles build up a plane wave IK). 69) Here a;’ denotes the inverse polarizability tensor of the unit cell. For example, in a crystal with two molecules per unit cell, a; is a 2 x 2 matrix of tensors [(a; 1)12 =(a; 1 ) 2 1 = 0,a; = inverse polarizability ofmolecule i] and 4 is a 2 x 2 matrix of the dipolar sums. 69) for E is quite general in the sense that it gives the response of the crystal to an external field of any wave vector.