Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ, United Kingdom.
J Chem Phys. 2011 Jun 21;134(23):234101. doi: 10.1063/1.3600342.
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.
我们计算了平行π-共轭聚合物的基态和激发态二阶色散相互作用。未受扰的本征态和能量是使用 CI-单态理论从 Pariser-Parr-Pople 模型计算得出的。基于使用反式聚乙炔的分子结构作为模型系统的大规模计算，并利用维度分析，我们发现：（1）对于链间分离，R 大于几个晶格间距，基态色散相互作用，ΔE(GS)，满足，对于 L << R，ΔE(GS)∼L(2)/R(6)，对于 R << L，ΔE(GS)∼L/R(5)，其中 L 是链长。前者是伦敦波动偶极子-偶极子相互作用，而后者是波动线偶极子-线偶极子相互作用。（2）激发态屏蔽相互作用表现出从波动单极子-线偶极子相互作用到波动偶极子-偶极子或波动线偶极子-线偶极子相互作用的交叉，当 R 超过一个阈值 R(c) 时，其中 R(c) 与电子-空穴激发的均方根分离有关。具体来说，激发态屏蔽相互作用，ΔE(n)，对于 R(c) < L << R，满足ΔE(n) ∼ L∕R(6)，对于 R(c) < R << L，满足ΔE(n) ∼ L(0)∕R(5)。对于 R < R(c) < L，ΔE(n) ∼ R(-ν)，其中 ν ≃ 3。我们还研究了共轭聚合物中主要激发态的相对屏蔽，即 n = 1、2 和 3 激子。我们发现，较大的 n 值对应于较大的ΔE(n)值。例如，对于聚对苯撑，ΔE(n = 1) ≃ 0.1 eV，ΔE(n = 2) ≃ 0.6 eV，ΔE(n = 3) ≃ 1.2 eV（其中 n = 1 是 1(1)B(1)态，n = 2 是 m(1)A 态，n = 3 是 n(1)B(1)态）。最后，我们发现ΔE(n)对链间分离的强烈依赖性意味着ΔE(n)对密度波动的强烈依赖性。特别是，对于聚对苯撑的 1(1)B(1)、m(1)A 态和 n(1)B(1)态，10%的密度波动分别意味着 13 meV、66 meV 和 120 meV 的波动。我们对基态色散的结果适用于所有类型的共轭聚合物。然而，我们的激发态结果仅适用于共轭聚合物，例如基于苯基的发光聚合物类，其中主要激发态是粒子-空穴（或离子）态。
