Second-order dispersion interactions in π-conjugated polymers.

We calculate the ground state and excited state second-order dispersion interactions 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-state dispersion interaction, ΔE(GS), satisfies, ΔE(GS)∼L(2)/R(6) for L ≪ R and ΔE(GS)∼L/R(5) 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, ΔE(n), satisfies, ΔE(n) ∼ L∕R(6) for R(c) < L ≪ R and ΔE(n) ∼ L(0)∕R(5) for R(c) < R ≪ L. For R < R(c) < L, ΔE(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 ΔE(n). For example, for poly(para-phenylene), ΔE(n = 1) ≃ 0.1 eV, ΔE(n = 2) ≃ 0.6 eV, and ΔE(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 ΔE(n) on inter-chain separation implies a strong dependency of ΔE(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-state dispersion 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.