Exciton delocalization in conjugated polymer systems is determined by polymer conformations and packing. Since exciton delocalization determines the photoluminescent vibronic progression, optical spectroscopy provides an indirect link to polymer multiscale structures. This perspective describes our current theoretical understanding of how exciton delocalization in π-conjugated polymers determines their optical spectroscopy and further shows how exciton delocalization is related to conformational and environmental disorder. If the multiscale structures in conjugated polymer systems are known, then using first-principles modeling of excitonic processes it is possible to predict a wide-range of spectroscopic observables. We propose a reverse-engineering protocol of using these experimental observables in combination with theoretical and computational modeling to determine the multiscale polymers structures, thus establishing quantitative structure-function predictions.

The theory of optical transitions developed in Barford and Marcus ["Theory of optical transitions in conjugated polymers. I. Ideal systems," J. Chem. Phys. 141, 164101 (2014)] for linear, ordered polymer chains is extended in this paper to model conformationally disordered systems. Our key result is that in the Born-Oppenheimer regime the emission intensities are proportional to S(1)/⟨IPR⟩, where S(1) is the Huang-Rhys parameter for a monomer. ⟨IPR⟩ is the average inverse participation ratio for the emitting species, i.e., local exciton ground states (LEGSs). Since the spatial coherence of LEGSs determines the spatial extent of chromophores, the significance of this result is that it directly relates experimental observables to chromophore sizes (where ⟨IPR⟩ is half the mean chromophore size in monomer units). This result is independent of the chromophore shape, because of the Born-Oppenheimer factorization of the many body wavefunction. We verify this prediction by density matrix renormalization group (DMRG) calculations of the Frenkel-Holstein model in the adiabatic limit for both linear, disordered chains and for coiled, ordered chains. We also model optical spectra for poly(p-phenylene) and poly(p-phenylene-vinylene) oligomers and polymers. For oligomers, we solve the fully quantized Frenkel-Holstein model via the DMRG method. For polymers, we use the much simpler method of solving the one-particle Frenkel model and employ the Born-Oppenheimer expressions relating the effective Franck-Condon factor of a chromophore to its inverse participation ratio. We show that increased disorder decreases chromophore sizes and increases the inhomogeneous broadening, but has a non-monotonic effect on transition energies. We also show that as planarizing the polymer chain increases the exciton band width, it causes the chromophore sizes to increase, the transition energies to decrease, and the broadening to decrease. Finally, we show that the absorption spectra are more broadened than the emission spectra and that the broadening of the absorption spectra increases as the chains become more coiled. This is primarily because absorption occurs to both LEGSs and quasi-extended exciton states (QEESs), and QEES acquire increased intensity as chromophores bend, while emission only occurs from LEGSs.

We describe a theory of linear optical transitions in conjugated polymers. The theory is based on three assumptions. The first is that the low-lying excited states of conjugated polymers are Frenkel excitons coupled to local normal modes, described by the Frenkel-Holstein model. Second, we assume that the relevant parameter regime is ℏω ≪ J, i.e., the adiabatic regime, and thus the Born-Oppenheimer factorization of the electronic and nuclear degrees of freedom is generally applicable. Finally, we assume that the Condon approximation is valid, i.e., the exciton-polaron wavefunction is essentially independent of the normal modes. Using these assumptions we derive an expression for an effective Huang-Rhys parameter for a chain (or chromophore) of N monomers, given by S(N) = S(1)/IPR, where S(1) is the Huang-Rhys parameter for an isolated monomer. IPR is the inverse participation ratio, defined by IPR = (∑(n)|Ψ(n)|(4))(-1), where Ψ(n) is the exciton center-of-mass wavefunction. Since the IPR is proportional to the spread of the exciton center-of-mass 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 Franck-Condon factor, F(0v)(N) = S(N)(v)exp ( - S(N))/v! for the vth vibronic manifold. We show that the 0 - 0 and 0 - 1 optical intensities are proportional to F00(N) and F01(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 higher-lying 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 Born-Oppenheimer 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 phenyl-based polymers, the critical value of N is ~20 monomers.

Identifying non-classicality unambiguously and inexpensively is a long-standing open challenge in physics. The No-Signalling-In-Time protocol was developed as an experimental test for macroscopic realism, and serves as a witness of quantum coherence in isolated quantum systems by comparing the quantum state to its completely dephased counterpart. We show that it provides a lower bound on a certain resource-theoretic coherence monotone. We go on to generalise the protocol to the case where the system of interest is coupled to an environment. Depending on the manner of the generalisation, the resulting witness either reports on system coherence alone, or on a disjunction of system coherence with either (i) the existence of non-classical system-environment correlations or (ii) non-negligible dynamics in the environment. These are distinct failure modes of the Born approximation in non-isolated systems.