Theory of optical transitions in conjugated polymers. I. Ideal systems
Abstract
We describe a theory of linear optical transitions in conjugated polymers. The theory is based on three assumptions. The first is that the lowlying excited states of conjugated polymers are Frenkel excitons coupled to local normal modes, described by the FrenkelHolstein model. Second, we assume that the relevant parameter regime is ℏω ≪ J, i.e., the adiabatic regime, and thus the BornOppenheimer factorization of the electronic and nuclear degrees of freedom is generally applicable. Finally, we assume that the Condon approximation is valid, i.e., the excitonpolaron wavefunction is essentially independent of the normal modes. Using these assumptions we derive an expression for an effective HuangRhys parameter for a chain (or chromophore) of N monomers, given by S(N) = S(1)/IPR, where S(1) is the HuangRhys parameter for an isolated monomer. IPR is the inverse participation ratio, defined by IPR = (∑{sub n}Ψ{sub n}{sup 4}){sup −1}, where Ψ{sub n} is the exciton centerofmass wavefunction. Since the IPR is proportional to the spread of the exciton centerofmass wavefunction, this is a key result, as it shows that S(N) decreases with chain length. As in molecules, in a polymer S(N) has two interpretations. First, ℏωS(N) is the relaxation energy of an excited state causedmore »
 Authors:
 Department of Chemistry, Physical and Theoretical Chemistry Laboratory, University of Oxford, Oxford OX1 3QZ (United Kingdom)
 (United Kingdom)
 Publication Date:
 OSTI Identifier:
 22310722
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Journal of Chemical Physics; Journal Volume: 141; Journal Issue: 16; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; ABSORPTION; BORNOPPENHEIMER APPROXIMATION; CENTEROFMASS SYSTEM; COUPLING; DEGREES OF FREEDOM; EMISSION; EXCITATION; EXCITED STATES; EXCITONS; MOLECULES; MONOMERS; POLYMERS; WAVE FUNCTIONS
Citation Formats
Barford, William, Email: william.barford@chem.ox.ac.uk, Marcus, Max, and Magdalen College, University of Oxford, Oxford OX1 4AU. Theory of optical transitions in conjugated polymers. I. Ideal systems. United States: N. p., 2014.
Web. doi:10.1063/1.4897984.
Barford, William, Email: william.barford@chem.ox.ac.uk, Marcus, Max, & Magdalen College, University of Oxford, Oxford OX1 4AU. Theory of optical transitions in conjugated polymers. I. Ideal systems. United States. doi:10.1063/1.4897984.
Barford, William, Email: william.barford@chem.ox.ac.uk, Marcus, Max, and Magdalen College, University of Oxford, Oxford OX1 4AU. 2014.
"Theory of optical transitions in conjugated polymers. I. Ideal systems". United States.
doi:10.1063/1.4897984.
@article{osti_22310722,
title = {Theory of optical transitions in conjugated polymers. I. Ideal systems},
author = {Barford, William, Email: william.barford@chem.ox.ac.uk and Marcus, Max and Magdalen College, University of Oxford, Oxford OX1 4AU},
abstractNote = {We describe a theory of linear optical transitions in conjugated polymers. The theory is based on three assumptions. The first is that the lowlying excited states of conjugated polymers are Frenkel excitons coupled to local normal modes, described by the FrenkelHolstein model. Second, we assume that the relevant parameter regime is ℏω ≪ J, i.e., the adiabatic regime, and thus the BornOppenheimer factorization of the electronic and nuclear degrees of freedom is generally applicable. Finally, we assume that the Condon approximation is valid, i.e., the excitonpolaron wavefunction is essentially independent of the normal modes. Using these assumptions we derive an expression for an effective HuangRhys parameter for a chain (or chromophore) of N monomers, given by S(N) = S(1)/IPR, where S(1) is the HuangRhys parameter for an isolated monomer. IPR is the inverse participation ratio, defined by IPR = (∑{sub n}Ψ{sub n}{sup 4}){sup −1}, where Ψ{sub n} is the exciton centerofmass wavefunction. Since the IPR is proportional to the spread of the exciton centerofmass wavefunction, this is a key result, as it shows that S(N) decreases with chain length. As in molecules, in a polymer S(N) has two interpretations. First, ℏωS(N) is the relaxation energy of an excited state caused by its coupling to the normal modes. Second, S(N) appears in the definition of an effective FranckCondon factor, F{sub 0v}(N) = S(N){sup v}exp ( − S(N))/v! for the vth vibronic manifold. We show that the 0 − 0 and 0 − 1 optical intensities are proportional to F{sub 00}(N) and F{sub 01}(N), respectively, and thus the ratio of the 0 − 1 to 0 − 0 absorption and emission intensities are proportional to S(N). These analytical results are checked by extensive DMRG calculations and found to be generally valid, particularly for emission. However, for large chain lengths higherlying quasimomentum exciton states become degenerate with the lowest vibrational excitation of the lowest exciton state. When this happens there is mixing of the electronic and nuclear states and a partial breakdown of the BornOppenheimer approximation, meaning that the ratio of the 0 − 0 to 0 − 1 absorption intensities no longer increases as fast as the IPR. When ℏω/J = 0.1, a value applicable to phenylbased polymers, the critical value of N is ∼20 monomers.},
doi = {10.1063/1.4897984},
journal = {Journal of Chemical Physics},
number = 16,
volume = 141,
place = {United States},
year = 2014,
month =
}

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