Ab Initio Implementation of the Frenkel-Davydov Exciton Model: A Naturally Parallelizable Approach to Computing Collective Excitations in Crystals and Aggregates

A fragment-based method for computing vertical excitation energies of molecular clusters is introduced based on an ab initio implementation of a Frenkel-Davydov exciton model consisting of singly excited monomer basis states. Our strategy is to construct and diagonalize the exact Hartree-Fock Hamiltonian in such a basis. Matrix elements between nonorthogonal determinants are computed via the corresponding orbital transformation and the resulting generalized eigenvalue problem is solved to determine collective excitation energies and wave functions. The basis may be expanded to include higher-lying fragment excited states in order to account for interfragment polarization effects. Absolute errors of less than or similar to 0.1 eV (relative to supersystem methods) are achievable for systems such as water clusters and crystalline arrays of organic chromophores such as pentacene and napthalenediimide. Preliminary tests for a nine-chromophore subunit of an organic nanotube suggest that it is possible to target the optically bright state, even when it is a high-lying excitation, by using carefully selected basis states. The highly parallel nature of this method provides a foundation for further developments to treat collective excitations in large molecular assemblies.