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.

2D excitons as primary energy carriers in organic crystals: the case of oligoacenes.

A number of organic crystals show anisotropic excitonic couplings, with weak interlayer interactions between molecules that are more strongly coupled within the layers. The resulting energy carriers are intralayer 2D excitons that diffuse along the interlayer direction. We model this analytically for infinite layers and using quantum-chemical calculations of the electronic couplings for anthracene clusters. We show that the exciton hopping rates and diffusion lengths depend in a subtle manner on the size and shape of the interacting aggregates, temperature, and the presence of energetic disorder.

Saturation of cubic optical nonlinearity in long-chain polyene oligomers.

The scaling of the cubic nonlinearity gamma with chain length in polyenic molecules has received considerable theoretical attention. Earlier experimental investigations have been restricted to oligomers with fewer than 20 double bonds because of problems associated with the synthesis and solubility of conjugated molecules. These synthetic difficulties have been overcome in the present study by the use of modern living polymerization techniques. Solution measurements of gamma as a function of chain length in long-chain (up to 240 double bonds) model polyene oligomers are reported. A saturation of the increase of gamma with chain length is observed, and the onset of this saturation occurs for chain lengths considerably longer than predicted from theory.

Shared-mode assisted resonant energy transfer in the weak coupling regime.

Recent work has suggested that correlations in the environments of chromophores can lead to a change in the dynamics of excitation transfer in both the coherent and incoherent limits. An example of this effect that is relevant to many single molecule experiments occurs in the standard Forster model for resonant energy transfer (RET). The standard formula for the FRET rate breaks down when the electronic excitations on weakly interacting donor and acceptor couple to the same vibrational modes. The transfer rate can then no longer be factored into donor emission and acceptor absorption lineshapes, but must be recast in terms of a renormalized phonon reorganization energy accounting for the magnitude and sign of the excitation-vibration couplings. In this paper, we derive theoretically how the FRET rate depends on the shared mode structure and coupling, examine the simplified case of Gaussian lineshapes and then provide a quantitative calculation for a system of current interest.

Toolbox for analyzing finite two-state trajectories.

In many experiments, the aim is to deduce an underlying multisubstate on-off kinetic scheme (KS) from the statistical properties of a two-state trajectory. However, a two-state trajectory that is generated from an on-off KS contains only partial information about the KS, and so, in many cases, more than one KS can be associated with the data. We recently showed that the optimal way to solve this problem is to use canonical forms of reduced dimensions (RDs). RD forms are on-off networks with connections only between substates of different states, where the connections can have nonexponential waiting time probability density functions (WT-PDFs). In theory, only a single RD form can be associated with the data. To utilize RD forms in the analysis of the data, a RD form should be associated with the data. Here, we give a toolbox for building a RD form from a finite time, noiseless, two-state trajectory. The methods in the toolbox are based on known statistical methods in data analysis, combined with statistical methods and numerical algorithms designed specifically for the current problem. Our toolbox is self-contained-it builds a mechanism based only on the information it extracts from the data, and its implementation is fast (analyzing a 10;{6}cycle trajectory from a 30-parameter mechanism takes a couple of hours on a PC with a 2.66GHz processor). The toolbox is automated and is freely available for academic research upon electronic request.

Path-probability density functions for semi-Markovian random walks.

In random walks, the path representation of the Green's function is an infinite sum over the length of path probability density functions (PDFs). Recently, a closed-form expression for the Green's function of an arbitrarily inhomogeneous semi-Markovian random walk in a one-dimensional (1D) chain of L states was obtained by utilizing path-PDFs calculations. Here we derive and solve, in Laplace space, the recursion relation for the n order path PDF for the same system. The recursion relation relates the n order path PDF to L/2 (round towards zero for an odd L) shorter path PDFs and has n independent coefficients that obey a universal formula. The z transform of the recursion relation straightforwardly gives the generating function for path PDFs, from which we recover the Green's function of the random walk, but, moreover, derive an explicit expression for any path PDF of the random walk. These expressions give the most detailed description of arbitrarily inhomogeneous semi-Markovian random walks in 1D.

Memory effects on the convergence properties of the Jarzynski equality.

In this paper we consider solvable model systems on which finite-time work is done. For the systems and changes in state considered, there is no entropic change and the ensuing work distribution is Gaussian. We focus on the fluctuations in the work for such systems, arising from system-bath interactions and finite system recurrences, and study the resulting effect of dynamical broadening on the corresponding distribution P(e{-beta{0}W}) . This allows us to describe the dependence of P(e{-beta{0}W}) on time and system-bath interactions. From the long-time behavior of the work fluctuations and P(e{-beta{0}W}) , we clarify both (i) when a stochastic treatment of the dynamics may be legitimately invoked and (ii) how information on the system-bath interaction for stochastic, near-equilibrium, systems may be extracted for such processes where a final temperature is well defined.

Markovian approximation in the relaxation of open quantum systems.

In this paper, we examine the validity of the Markovian approximation and the slippage scheme used to incorporate short time transient memory effects in the Markovian master equations (Redfield equations). We argue that for a bath described by a spectral function, J(omega), that is dense and smoothly spread out over the range omega(d), a time scale of tau(b) approximately 1/omega(d) exists; for times of t > tau(b), the Markovian approximation is applicable. In addition, if J(omega) decays to zero reasonably fast in both the omega --> 0 and omega --> infinity limits, then the bath relaxation time, tau(b), is determined by the width of the spectral function and is weakly dependent on the temperature of the bath. On the basis of this criterion of tau(b), a scheme to incorporate transient memory effects in the Markovian master equation is suggested. Instead of using slipped initial conditions, we propose a concatenation scheme that uses the second-order perturbation theory for short time dynamics and the Markovian master equation at long times. Application of this concatenation scheme to the spin-boson model shows that it reproduces the reduced dynamics obtained from the non-Markovian master equation for all parameters studied, while the simple slippage scheme breaks down at high temperatures.

Utilizing redox-chemistry to elucidate the nature of exciton transitions in supramolecular dye nanotubes.

Supramolecular assemblies that interact with light have recently garnered much interest as well-defined nanoscale materials for electronic excitation energy collection and transport. However, to control such complex systems it is essential to understand how their various parts interact and whether these interactions result in coherently shared excited states (excitons) or in diffusive energy transport between them. Here, we address this by studying a model system consisting of two concentric cylindrical dye aggregates in a light-harvesting nanotube. Through selective chemistry we are able to unambiguously determine the supramolecular origin of the observed excitonic transitions. These results required the development of a new theoretical model of the supramolecular structure of the assembly. Our results demonstrate that the two cylinders of the nanotube have distinct spectral responses and are best described as two separate, weakly coupled excitonic systems. Understanding such interactions is critical to the control of energy transfer on a molecular scale, a goal in various applications ranging from artificial photosynthesis to molecular electronics.

Universal properties of mechanisms from two-state trajectories.

Finding the underlying mechanism from the statistical properties of an experimental two-state trajectory generated from dynamics in a complex on-off multisubstate kinetic scheme (KS) is the aim of many experiments. Since the data explicitly shows only transitions between substates of different states, information about the KS is lost, resulting in equivalence of KSs, i.e., the occurrence of different KSs that lead to the same data, in a statistical sense. In order to deal with this phenomenon, a canonical (unique) form of reduced dimensions (RD) is built from the data. RD forms are on-off networks with connections only between substates of different states, where the connections usually have nonexponential waiting time probability density functions. In this paper, we give a list of (about 50) relationships between properties of the data, the topology of reduced dimension forms, and features of KSs. Many of these relationships involve symmetries in RD forms, KSs, and the data and irreversible transitions in KSs. These relationships are useful both in theoretical analysis of on-off KSs and in the analysis of the data.

Coherence in the B800 ring of purple bacteria LH2.

We study the quantum coherence in the B800 ring and how it affects the dynamics of excitation energy transfer (EET) in photo-synthetic light-harvesting systems. From an analysis of the spectrum, we determine the disorder parameters for the B800 ring and show that the relatively weak electronic coupling between B800 pigments subtly changes the dynamics of EET and improves the uniformity and robustness of B800 --> B850 EET at room temperature, an example of how a multichromophoric assembly can exploit coherence to optimize the efficiency of photosynthesis. A molecular-level description for the dynamics of EET in the light-harvesting system may prove useful for understanding other nanoscale molecular assemblies and designing efficient nanoscale optical devices.