Exciton Superexchange, Resonance Pairs, and Complete Exciton Band Structure of B12u Naphthalene

Abstract

A method for the determination of complete exciton band structures in molecular crystals is given. Pairwise exciton interactions are derived from resonance‐pair data using an exciton “superexchange” approach. Koster and Slater's impurity cluster formulation is found to be applicable to nontrivial interchange symmetry systems, within the “restricted Frenkel–Davydov” theory. The derivation starts from the recent general formulation for isotopically mixed crystals of arbitrary concentrations. The resonance pair states are given by the second‐order self‐energy of the mixed crystal Green's function. General symmetry arguments and moment sum rules have been worked out for resonance pairs. It is demonstrated for naphthalene‐h8 resonance pairs in naphthalene‐d8 that superexchange corrections are not only inevitable for the 1B2u1B2u pair states but that they can also be utilized to assign experimental pairwise interactions to definite crystal directions, i.e., specific pairs. The naphthalene first singlet excited state 0–0 vibronic exciton band is successfully described by the “restricted Frenkel–Davydov” dispersion relation: ϵ(k±)=∑eMeexp(ik⋅Re±∑iMiexp(ik⋅Ri), where e = a,b,c,(a + c)e=a,b,c,(a+c) and i = ½(a + b),[½(a + b) + c]i=12(a+b),[12(a+b)+c]. Three sets of MM's that are consistent with all resonance‐pair and monomer mixed crystal data are tabulated. The only one consistent with a multipole expansion gives for the MeMe's and MiMi's, respectively, − 0.6, − 3.9, − 3.7, 6.1, and 18.0, 2.0 cm−1. This point multipole expansion is safely limited to nonnearest‐neighbor interactions and truncated beyond transition octopoles (Q31c = 7Q31c=7 and Q33c = 72Å3Q33c=72Å3). The translational shift is − 4.5 ± 4 cm−1, and the hot‐band density‐of‐states function has been independently reproduced from the mixed crystal data, indicating that exciton–phonon coupling is small. The results are compared with ab initio calculations and new criteria for theoretical computations are suggested