R. Silbey

Beyond Förster Resonance Energy Transfer in Biological and Nanoscale Systems

After photoexcitation, energy absorbed by a molecule can be transferred efficiently over a distance of up to several tens of angstroms to another molecule by the process of resonance energy transfer, RET (also commonly known as electronic energy transfer, EET). Examples of where RET is observed include natural and artificial antennae for the capture and energy conversion of light, amplification of fluorescence-based sensors, optimization of organic light-emitting diodes, and the measurement of structure in biological systems (FRET). Forster theory has proven to be very successful at estimating the rate of RET in many donor-acceptor systems, but it has also been of interest to discover when this theory does not work. By identifying these cases, researchers have been able to obtain, sometimes surprising, insights into excited-state dynamics in complex systems. In this article, we consider various ways that electronic energy transfer is promoted by mechanisms beyond those explicitly considered in Forster RET theory. First, we recount the important situations when the electronic coupling is not accurately calculated by the dipole-dipole approximation. Second, we examine the related problem of how to describe solvent screening when the dipole approximation fails. Third, there are situations where we need to be careful about the separability of electronic coupling and spectral overlap factors. For example, when the donors and/or acceptors are molecular aggregates rather than individual molecules, then RET occurs between molecular exciton states and we must invoke generalized Forster theory (GFT). In even more complicated cases, involving the intermediate regime of electronic energy transfer, we should consider carefully nonequilibrium processes and coherences and how bath modes can be shared. Lastly, we discuss how information is obscured by various forms of energetic disorder in ensemble measurements and we outline how single molecule experiments continue to be important in these instances.

A nonempirical effective Hamiltonian technique for polymers: Application to polyacetylene and polydiacetylene

The recently proposed ab initio effective Hamiltonian technique is extended to polymer calculations and applied to various conformations of polyacetylene (all‐trans, cis‐transoid, and trans‐cisoid) and polydiacetylene (acetylenic and butatrienic backbones). Band structures, density of states (DOS), and XPS theoretical spectra are presented. Comparison of the band structures and DOS with those obtained by ab initio SCF (self‐consistent‐field) Hartree–Fock calculations of double zeta quality is excellent. The XPS theoretical spectrum for all‐trans polyacetylene is in good agreement with experiment. In polyacetylene, it is found that the π bands are quite similar for all three backbone conformations, though the σ bands differ significantly. For polydiacetylene, low ionization potentials are predicted—a few tenths of an eV larger than polyacetylene for the acetylenic backbone and a few tenths of an eV smaller than polyacetylene for the butatrienic backbone.

Three-dimensional band structure and bandlike mobility in oligoacene single crystals: A theoretical investigation

Quantum-chemical calculations coupled with a tight binding band model are used to study the charge carrier mobilities in oligoacene crystals. The transfer integrals for all nonzero interactions in four crystalline oligoacenes (naphthalene, anthracene, tetracene, and pentacene) were calculated, and then used to construct the excess electron and hole band structures of all four oligoacene crystals in the tight binding approximation. From these band structures, thermal-averaged velocity–velocity tensors in the constant-free-time and the constant-free-path approximations for all four materials were calculated at temperatures ranging from 2 to 500 K. The bandwidths for these oligoacenes were found to be of the order of 0.1–0.5 eV. Furthermore, comparison of the thermal-averaged velocity–velocity tensors with the experimental mobility data indicates that the simple band model is applicable for temperatures only up to about 150 K. A small-polaron band model is also considered, but the exponential band narrowing ...

Exciton Migration in Molecular Crystals

The migration of Frenkel excitons in molecular crystals is studied theoretically, starting from the microscopic equations of motion for the exciton density. The migration process is found to be diffusionlike on a long time scale for all temperatures as long as the exciton–phonon coupling is present. If there is no exciton–phonon coupling, the migration is wavelike. A discussion of the relevant time scales for the wavelike (coherent) process and the diffusion (incoherent) process is given. Several different approximation techniques, based on the cumulant expansion, projection operator, and functional derivative methods, are shown to be mathematically equivalent as applied to this problem.

Variational calculation of the dynamics of a two level system interacting with a bath

A variational calculation of the dynamics of a two level system interacting with a bath is presented. The effective tunneling matrix element is renormalized by the interaction with the bath. For the case of a bath with ohmic dissipation (or infrared divergence), the variational calculation gives a vanishing tunneling at T=0 for critical values of the coupling and gives a highly unusual temperature dependence for the tunneling rate for large kT, all of which agree with recent path integral calculations. The present method also yields results for intermediate temperatures and coupling. This indicates that a judicious choice of the zeroth order Hamiltonian to include the major part of the coupling can lead to correct results even in low order perturbation theory.

Lifetime of an emitting molecule near a partially reflecting surface

A classical treatment of energy transfer in metal insulator systems is presented. The approach involves the calculation of the radiation field of an emitting molecule near a partially reflecting surface. The modification of the image theory result produces a large correction when the molecule is near the surface. This in turn produces a correction to the calculated lifetime of the molecule as a function of distance from the surface that differs substantially from previous theoretical descriptions of this system and brings the theory into good agreement with experiment.

Comments on the classical theory of energy transfer

Energy transfer from an emitting molecule to an absorbing half−space is considered from the viewpoint of electromagnetic theory. The lifetime of a dipole emitter in the presence of a mirror is determined through a calculation of the complex Poynting vector in the dielectric surrounding the dipole. This method has the advantage over previous approaches to this problem in that the radiative and nonradiative components of the lifetime expression may be rigorously separated. The influence on emitter lifetime of a mirror of finite thickness is also described. A simple expression is derived describing the energy transfer rate in these layered systems. It is shown that nonradiative energy transfer results from coupling of the near field of the dipole to the surface plasmon modes in the metallic absorber. The Forster energy transfer rate law is discussed in the context of the present theory.

The nature of singlet excitons in oligoacene molecular crystals

A theory for polarized absorption in crystalline oligoacenes is presented, which includes Frenkel exciton coupling, the coupling between Frenkel and charge-transfer (CT) excitons, and the coupling of all neutral and ionic excited states to the dominant ring-breathing vibrational mode. For tetracene, spectra calculated using all Frenkel couplings among the five lowest energy molecular singlet states predict a Davydov splitting (DS) of the lowest energy (0-0) vibronic band of only -32 cm(-1), far smaller than the measured value of 631 cm(-1) and of the wrong sign-a negative sign indicating that the polarizations of the lower and upper Davydov components are reversed from experiment. Inclusion of Frenkel-CT coupling dramatically improves the agreement with experiment, yielding a 0-0 DS of 601 cm(-1) and a nearly quantitative reproduction of the relative spectral intensities of the 0-n vibronic components. Our analysis also shows that CT mixing increases with the size of the oligoacenes. We discuss the implications of these results on exciton dissociation and transport.

New and proper integral equations for site-site equilibrium correlations in molecular fluids

We show that the often used site-site direct correlation function cannot be defined in terms of a sum over a subset of the diagrams in the interaction site cluster series for the equilibrium pair correlation functions of a molecular fluid. However, from an exact topological reduction, we arrive at a new class of site-site direct correct correlation functions that are properly defined in the diagrammatic sense. The class is composed of four topologically distinct functions which are related to each other and the pair correlation function through four coupled Ornstein-Zernike-like equations. These new integral equations are exact and provide a rigorous foundation for integral equation theories of molecular fluids. The formal solutions to the equations are constructed, and the utility of the formulation is illustrated by discussing one example of an approximate closure to the integral equations.

Ab initio effective Hamiltonian study of the electronic properties of conjugated polymers

The valence effective Hamiltonian technique is applied to a series of polymers to compute ionization potentials, bandwidths, and band gaps. The polymers considered represent systems of interest to the conducting polymers area and include various derivatives of polyacetylene and polyphenylene, polydiacetylene, polyacene, polybenzyl, and polyyne. The theoretical results for relative ionization potentials are in excellent agreement with available experimental estimates, as well as with the observed behavior of the electrical conductivity of these systems on exposure to weak (I2) versus strong (AsF5) electron acceptors. The bandwidths of the highest occupied band show a qualitative correlation to the conductivities achieved with acceptor doping. Band gaps for the planar systems considered are also in good agreement with experiment.