### Abstract

We calculate the ground state and excited state second-order dispersioninteractions between parallel π-conjugated polymers. The unperturbed eigenstates and energies are calculated from the Pariser-Parr-Pople model using CI-singles theory. Based on large-scale calculations using the molecular structure of *trans*-polyacetylene as a model system and by exploiting dimensional analysis, we find that: (1) For inter-chain separations, *R*, greater than a few lattice spacings, the ground-statedispersioninteraction,, satisfies, for *L* ≪ *R* and for *R* ≪ *L*, where *L* is the chain length. The former is the London fluctuating dipole-dipole interaction while the latter is a fluctuating line dipole-line dipole interaction. (2) The excited state screening interaction exhibits a crossover from fluctuating monopole-line dipole interactions to either fluctuating dipole-dipole or fluctuating line dipole-line dipole interactions when *R* exceeds a threshold *R* _{ c }, where *R* _{ c } is related to the root-mean-square separation of the electron-hole excitation. Specifically, the excited state screening interaction, Δ*E* _{ n }, satisfies, Δ*E* _{ n } ∼ *L*/*R* ^{6} for *R* _{ c } < *L* ≪ *R* and Δ*E* _{ n } ∼ *L* ^{0}/*R* ^{5} for *R* _{ c } < *R* ≪ *L*. For *R* < *R* _{ c } < *L*, Δ*E* _{ n } ∼ *R* ^{−ν}, where ν ≃ 3. We also investigate the relative screening of the primary excited states in conjugated polymers, namely the *n* = 1, 2, and 3 excitons. We find that a larger value of *n* corresponds to a larger value of Δ*E* _{ n }. For example, for poly(para-phenylene), Δ*E* _{ n = 1} ≃ 0.1 eV, Δ*E* _{ n = 2} ≃ 0.6 eV, and Δ*E* _{ n = 3} ≃ 1.2 eV (where *n* = 1 is the 1^{1} *B* _{1} state, *n* = 2 is the *m* ^{1} *A* state, and *n* = 3 is the *n* ^{1} *B* _{1} state). Finally, we find that the strong dependence of Δ*E* _{ n } on inter-chain separation implies a strong dependency of Δ*E* _{ n } on density fluctuations. In particular, a 10% density fluctuation implies a fluctuation of 13 meV, 66 meV, and 120 meV for the 1^{1} *B* _{1}, *m* ^{1} *A* state, and *n* ^{1} *B* _{1} states of poly(para-phenylene), respectively. Our results for the ground-statedispersion are applicable to all types of conjugated polymers. However, our excited state results are only applicable to conjugated polymers, such as the phenyl-based class of light emitting polymers, in which the primary excitations are particle-hole (or ionic) states.

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