Partially polaron-transformed quantum master equation for exciton and charge transport dynamics

Polaron-transformed quantum master equation (PQME) offers a unified framework to describe the dynamics of quantum systems in both limits of weak and strong couplings to environmental degrees of freedom. Thus, PQME serves as an efficient method to describe charge and exciton transfer/transport dynamics for a broad range of parameters in condensed or complex environments. However, in some cases, the polaron transformation (PT) being employed in the formulation invokes an over-relaxation of slow modes and results in premature suppression of important coherence terms. A formal framework to address this issue is developed in the present work by employing a partial PT that has smaller weights for low frequency bath modes. It is shown here that a closed form expression of a 2nd order time-local PQME including all the inhomogeneous terms can be derived for a general form of partial PT, although more complicated than that for the full PT. All the expressions needed for numerical calculation are derived in detail. Applications to a model of two-level system coupled to a bath of harmonic oscillators, with test calculations focused on those due to homogeneous relaxation terms, demonstrate the feasibility and the utility of the present approach.Comment: 17 pages, 5 figure

Delocalized excitons in natural light harvesting complexes

Natural organisms such as photosynthetic bacteria, algae, and plants employ complex molecular machinery to convert solar energy into biochemical fuel. An important common feature shared by most of these photosynthetic organisms is that they capture photons in the form of excitons typically delocalized over a few to tens of pigment molecules embedded in protein environments of light harvesting complexes (LHCs). Delocalized excitons created in such LHCs remain well protected despite being swayed by environmental fluctuations, and are delivered successfully to their destinations over hundred nanometer length scale distances in about hundred picosecond time scales. Decades of experimental and theoretical investigation have produced a large body of information offering insights into major structural, energetic, and dynamical features contributing to LHCs' extraordinary capability to harness photons using delocalized excitons. The objective of this review is (i) to provide a comprehensive account of major theoretical, computational, and spectroscopic advances that have contributed to this body of knowledge, and (ii) to clarify the issues concerning the role of delocalized excitons in achieving efficient energy transport mechanisms. The focus of this review is on three representative systems, Fenna-Matthews-Olson complex of green sulfur bacteria, light harvesting 2 complex of purple bacteria, and phycobiliproteins of cryptophyte algae. Although we offer more in-depth and detailed description of theoretical and computational aspects, major experimental results and their implications are also assessed in the context of achieving excellent light harvesting functionality. Future theoretical and experimental challenges to be addressed in gaining better understanding and utilization of delocalized excitons are also discussed.Comment: 53 pages, 15 figure

Modified Fermi's golden rule rate expressions

Fermi's golden rule (FGR) serves as the basis for many expressions of spectroscopic observables and quantum transition rates. The utility of FGR has been demonstrated through decades of experimental confirmation. However, there still remain important cases where the evaluation of a FGR rate is ambiguous or ill-defined. Examples are cases where the rate has divergent terms due to the sparsity in the density of final states or time dependent fluctuations of system Hamiltonians. Strictly speaking, assumptions of FGR are no longer valid for such cases. However, it is still possible to define modified FGR rate expressions that are useful as effective rates. The resulting modified FGR rate expressions resolve a long standing ambiguity often encountered in using FGR and offer more reliable ways to model general rate processes. Simple model calculations illustrate the utility and implications of new rate expressions.Comment: 11 pages, 4 figure

Fundamental trade-off between the speed of light and the Fano factor of photon current in three-level lambda systems

Electromagnetically induced slow-light medium is a promising system for quantum memory devices, but controlling its noise level remains a major challenge to overcome. This work considers the simplest model for such medium, comprised of three-level $\Lambda$-systems interacting with bosonic bath, and provides a new fundamental trade-off relation in light-matter interaction between the group velocity of light and the Fano factor of photon current due to radiative transitions. Considering the steady state limits of a newly derived Lindblad-type equation, we find that the Fano factor of the photon current maximizes to 3 at the minimal group velocity of light, which holds true universally regardless of detailed values of parameters characterizing the medium.Comment: 14 pages, 5 figure

General Chemical Reaction Network Theory for Olfactory Sensing Based on G-Protein-Coupled Receptors : Elucidation of Odorant Mixture Effects and Agonist-Synergist Threshold

This work presents a general chemical reaction network theory for olfactory sensing processes that employ G-protein-coupled receptors as olfactory receptors (ORs). The theory is applicable to general mixtures of odorants and an arbitrary number of ORs. Reactions of ORs with G-proteins, both in the presence and the absence of odorants, are explicitly considered. A unique feature of the theory is the definition of an odor activity vector consisting of strengths of odorant-induced signals from ORs relative to those due to background G-protein activity in the absence of odorants. It is demonstrated that each component of the odor activity defined this way reduces to a Michaelis-Menten form capable of accounting for cooperation or competition effects between different odorants. The main features of the theory are illustrated for a two-odorant mixture. Known and potential mixture effects, such as suppression, shadowing, inhibition, and synergy are quantitatively described. Effects of relative values of rate constants, basal activity, and G-protein concentration are also demonstrated

Nonadiabatic derivative couplings through multiple Franck-Condon modes dictate the energy gap law for near and short-wave infrared dye molecules

Near infrared (NIR, 700 - 1,000 nm) and short-wave infrared (SWIR, 1,000 - 2,000 nm) dye molecules exhibit significant nonradiative decay rates from the first singlet excited state to the ground state. While these trends can be empirically explained by a simple energy gap law, detailed mechanisms of the nearly universal behavior have remained unsettled for many cases. Theoretical and experimental results for two representative NIR/SWIR dye molecules reported here clarify an important mechanism of such nature. It is shown that the first derivative nonadiabatic coupling terms serve as major coupling pathways for nonadiabatic decay processes exhibiting the energy gap law behavior and that vibrational modes other than the highest frequency ones also make significant contributions to the rate. This assessment is corroborated by further theoretical comparison with possible alternative mechanisms of intersystem crossing to triplet states and also by comparison with experimental data for deuterated molecules

Nonequilibrium generalization of F\"{o}rster-Dexter theory for excitation energy transfer

F\"{o}rster-Dexter theory for excitation energy transfer is generalized for the account of short time nonequilibrium kinetics due to the nonstationary bath relaxation. The final rate expression is presented as a spectral overlap between the time dependent stimulated emission and the stationary absorption profiles, which allows experimental determination of the time dependent rate. For a harmonic oscillator bath model, an explicit rate expression is derived and model calculations are performed in order to examine the dependence of the nonequilibrium kinetics on the excitation-bath coupling strength and the temperature. Relevance of the present theory with recent experimental findings and possible future theoretical directions are discussed.Comment: published in {\it Chemical Physics} (special issue on Photoprocesses in Multichromophoric Molecular Assemblies

Comparative Computational Study of Electronic Excitations of Neutral and Charged Small Oligothiophenes and Their Extrapolations Based on Simple Models

This work reports electronic excitation energies of neutral and charged oligothiophenes (OTn) with repeat unit n = 2–6 computed by routinely used semiempirical and time-dependent density functional theory (TD-DFT) methods. More specifically, for OTn, OTn+, and OTn–, we calculated vertical transition energies for electronic absorption spectroscopy employing the Zerner’s version of intermediate neglect differential overlap method for structures optimized by the PM6 semiempirical method and the TD-DFT method with three different functionals, B3LYP, BVP86, and M06-2X, for structures optimized by the ground-state DFT method employing the same functionals. We also calculated vertical transition energies for the emission spectroscopy from the lowest singlet excited states by employing the TD-DFT method for the structures optimized for the lowest singlet excited states. In addition to computational results in vacuum, solution phase data calculated at the level of polarizable continuum model are reported and compared with available experimental data. Most of the data are fitted reasonably well by two simple model functions, one based on a Frenkel exciton theory and the other based on the model of independent electrons in a box with sinusoidal modulation of potential. Despite similar levels of fitting performance, the two models produce distinctively different asymptotic values of excitation energies. Comparison of these with available experimental and computational data suggests that the values based on the exciton model, while seemingly overestimating, are closer to true values than those based on the other model. This assessment is confirmed by additional calculations for a larger oligomer. The fitting parameters offer new means to understand the relationship between electronic excitations of OTs and their sizes and suggest the feasibility of constructing simple coarse-grained exciton-bath models applicable for aggregates of OTs