By William Barford
Writing for experimentalists, physicists, and theoretical and computational chemists, Barford (physics and astronomy, U. of Sheffield) examines the homes of conjugated polymers, explaining how electron-electron interactions and electron-lattice coupling ensure the categories and personality of the low-lying digital states, beginning with the best approximations if noninteracting electronics. He covers pi-electron theories of conjugated polymers, noninteracting electrons and interacting electrons (including electron-lattice coupling in either cases), electrons and digital approaches in conjugated polymers, optical methods in conjugated polymers, linear polyenes and trans-polyacetylene, and lightweight- emitting polymers.
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Additional resources for Electronic and Optical Properties of Conjugated Polymers
Example text
The first term on the righthand side is the change in the electronic kinetic energy arising from the changes in the bond lengths from their reference values. Similarly, the second term is the change in the electronic potential energy arising from the changes in bond lengths. Notice that a reduction in the bond lengths results in a decrease of the (negative) kinetic energy. Physically, this is caused by the increase in the magnitude of the negative hybridization integrals as the distances between neighbouring atoms decreases.
Physically, this is caused by the increase in the magnitude of the negative hybridization integrals as the distances between neighbouring atoms decreases. 41) where Vn ({un }) is the nuclear-nuclear potential energy associated with small displacements from the reference coordinates. The next step is to quantize the nuclear degrees of freedom as phonons, giving a fully quantum mechanical description of the electron and nuclear degrees of freedom. This step will be described in Chapter 7. 1 The nuclear-nuclear potential, Vn ({un }) We conclude this section by making some remarks on the nuclear-nuclear potential.
This is based on the assumption that the single-particle energy levels are particle-in-the-box energy levels, n = 2 n2 /2ma2 N 2 , where N is the number of sites. At half-filling, where the number of electrons equals the number of sites, this assumption then predicts that the single particle gap is ∆ = N/2+1 − N/2 ∼ 2 /ma2 N . As well as for noninteracting systems, as will be shown in Chapter 6, the optical gap in an interacting system also scales as 1/N 2 as N → ∞. 1 1/N Fig. 6. The charge gap, 2∆, for dimerized, linear chains versus the inverse chain length, and the square of the inverse chain length (inset).