Through-Bond and Through-Space Coupling in Photoinduced Electron and Energy Transfer: An ab Initio and Semiempirical Study

Controllable Electron Transfer in Mixed-Valence Bridged Norbornylogous Compounds: Ab Initio Calculation Combined with a Parametric Model and Through-Bond and Through-Space Interpretation

In the context of a computationally guided approach to the controllable electron transfer in mixed-valence (MV) systems, in this article, we study the electron transfer (ET) in the series of oxidized norbornadiene C₇H₈ (I) and its polycyclic derivatives, C₁₂H₁₂ (II), C₁₇H₁₆, (III), C₂₇H₂₄ (IV), and C₃₂H₂₈ (V), with variable lengths of the bridge connecting redox sites. The work combines an ab initio CASSCF evaluation of the electronic structure of systems I-V with the parametric description in the framework of the biorbital two-mode vibronic model. The model involves coupling with the "breathing" mode and intercenter vibration modulating the distances between the redox fragments. The ab initio calculations were performed for two types of optimized structures of I-V: (a) charge-localized global minimum (C_s) and (b) symmetric configuration (C_2v) with the delocalized charge. This allows one to estimate the potential barrier separating charge-localized configurations as well as vibronic coupling parameters and the electron transfer integral. Along with the adiabatic approach, the quantum-mechanical analysis of the vibronic levels has been applied to precisely estimate the quantum effect of tunneling splitting. We estimate the "through-space" and "through-bond" contributions to the parameters interrelated with the charge transfer (CT). The through-space effect proves to be a major factor of ET at a short distance between the redox centers, whereas the through-bond contribution is dominant at a long distance. Vibronic coupling under the condition of through-space ET leads to the localization of the positive charge on the π-chromophore, while the through-bond component of ET results in compensating σ-shifts and subsequent charge delocalization over the bridge. The limitations of the parametric approach were discussed in the context of the two components contributing to the ET. Particularly, the bridge polarization in the course of through-bond ET proves to be beyond the basis of the employed parametric model.

Chemical Tuning of Exciton versus Charge-Transfer Excited States in Conformationally Restricted Arylene Cages

Covalent assemblies of conjugated organic chromophores provide the opportunity to engineer new excited states with novel properties. In this work, a newly developed triple-stranded cage architecture, in which meta-substituted aromatic caps serve as covalent linking groups that attach to both top and bottom of the conjugated molecule walls, is used to tune the properties of thiophene oligomer assemblies. Benzene-capped and triazine-capped 5,5'-(2,2-bithiophene)-containing arylene cages are synthesized and characterized using steady-state and time-resolved spectroscopic methods. The conformational freedom and electronic states are analyzed using time-dependent density functional theory. The benzene cap acts as a passive spacer whose electronic states do not mix with those of the chromophore walls. The excited state properties are dominated by through-space interactions between the chromophore subunits, generating a neutral Frenkel H-type exciton state. This excitonic state undergoes intersystem crossing on a 200 ps time scale while the fluorescence output is suppressed by a factor of 2 due to a decreased radiative rate. Switching to a triazine cap enables electron transfer from the chromophore-linker after the initial excitation to the exciton state, leading to the formation of a charge-transfer state within 10 ps. This state can avoid intersystem crossing and exhibits red-shifted fluorescence with enhanced quantum yield. The ability to interchange structural modules with different electronic properties while retaining the overall cage morphology provides a new approach for tuning the properties of discrete chromophore assemblies.

Exciton transfer free energy from Car-Parrinello molecular dynamics

A computational approach is presented which allows the calculation of free energies profiles for exciton transfer processes within the framework of ab initio molecular dynamics (AIMD) simulations, sampling both the electronic and the nuclear degrees of freedom. To achieve this, restraining potentials are imposed on the centres of maximally localized Wannier orbitals. The resulting quantum-mechanical orbital forces are derived analytically and implemented in an AIMD program. In analogy to classical umbrella sampling techniques, these restraints are used to control an exciton transfer by incrementally moving the Wannier centres corresponding to the electron-hole pair along a suitable reaction coordinate. The new method is applied to study exciton transfer between two stacked penta(3-methylthiophene) molecules as a function of intermolecular distance. From the resulting free energy profiles, exciton transfer rates and diffusion constants are estimated, which prove to be in line with experimental results.

Photoinduced electron transfer from zinc meso-tetraphenylporphyrin to a one-dimensional perylenediimide aggregate: Probing anion delocalization effects

Organic photovoltaics incorporating non-fullerene acceptors based on perylenediimide (PDI) now rival fullerene acceptor-based devices in performance, although the mechanisms of charge generation in PDI-based devices are not yet fully understood. Fullerene-based systems are proposed to undergo electron transfer directly from the photoexcited donor into a band of delocalized acceptor states, thus increasing charge generation efficiency. Similarly, anion delocalization has been shown to enhance the rate of electron transfer from a photoexcited donor to two electronically coupled PDI acceptors. Here we investigate how additional electron acceptors may further increase the rate of electron transfer from the donor zinc meso-tetraphenylporphyrin (ZnTPP) to an aggregate of PDI acceptors (PDI[Formula: see text]. Femtosecond transient visible and mid-infrared absorption spectroscopies show that the rate of electron transfer from 1*ZnTPP to the PDI assembly ZnTPP2-PDI3 is statistically identical to that of the previously examined ZnTPP-PDI2. A Marcus theory analysis indicates that the parameters governing electron transfer are nearly identical for the two molecules, suggesting that the maximum electron transfer rate enhancement has been achieved in a cofacial PDI dimer because the ZnTPP directly couples to the first two PDI acceptors whereas the coupling to the third PDI is too weak.

Using Structurally Well-Defined Norbornyl-Bridged Acene Dimers to Map a Mechanistic Landscape for Correlated Triplet Formation in Singlet Fission

Structurally well-defined TIPS-acetylene substituted tetracene (TIPS-BT1') and pentacene (TIPS-BP1') dimers utilizing a [2.2.1] bicyclic norbornyl bridge have been studied-primarily using time-resolved spectroscopic methods-to uncover mechanistic details about primary steps in singlet fission leading to formation of the biexcitonic ¹TT state as well as decay pathways to the ground state. For TIPS-BP1' in room-temperature toluene, ¹TT formation is rapid and complete, occurring in 4.4 ps. Decay to the ground state in 100 ns is the primary loss pathway for ¹TT in this system. For TIPS-BT1', the ¹TT is also observed to form rapidly (with a time constant of 5 ps), but in this case it occurs in concert with establishment of an excited-state equilibrium ( K ∼ 1) with the singlet exciton state S₁ at an energy of 2.3 eV above the ground state. The equilibrated states survive for 36 ns and are lost to ground state through both radiative and nonradiative pathways via the S₁ and nonradiative pathways via the ¹TT. The rapidity of ¹TT formation in TIPS-BT1' is at first glance surprising. However, our analysis suggests that the few-parameter rate constant expression of Marcus theory explains both individual and comparative findings in the set of systems, thus establishing benchmarks for diabatic coupling and reorganization energy needed for efficient ¹TT formation. Finally, a comparison of TIPS-BT1' with previous results obtained for a close constitutional isomer (TIPS-BT1) differing in the placement of TIPS-acetylene side groups suggests that the magnitude of exchange interaction in the correlated triplet manifold plays a critical role dictating ¹TT yield in the tetracenic systems.

Expanded Theory of H- and J-Molecular Aggregates: The Effects of Vibronic Coupling and Intermolecular Charge Transfer

The electronic excited states of molecular aggregates and their photophysical signatures have long fascinated spectroscopists and theoreticians alike since the advent of Frenkel exciton theory almost 90 years ago. The influence of molecular packing on basic optical probes like absorption and photoluminescence was originally worked out by Kasha for aggregates dominated by Coulombic intermolecular interactions, eventually leading to the classification of J- and H-aggregates. This review outlines advances made in understanding the relationship between aggregate structure and photophysics when vibronic coupling and intermolecular charge transfer are incorporated. An assortment of packing geometries is considered from the humble molecular dimer to more exotic structures including linear and bent aggregates, two-dimensional herringbone and "HJ" aggregates, and chiral aggregates. The interplay between long-range Coulomb coupling and short-range charge-transfer-mediated coupling strongly depends on the aggregate architecture leading to a wide array of photophysical behaviors.

Photophysical properties of acetylene-linked syn bimane oligomers: a molecular photonic wire

Computational studies using correlated wave function methods and density functional theory were carried out on a series of acetylene-linked bimane oligomers with particular emphasis on their excitonic properties and implications for intra-chain excitation energy transfer (EET). The low energy barriers found for the rotation of bimane subunits about the longitudinal axis are such that the π-conjugation is easily disrupted. Nevertheless, a distinctive feature of the oligomer lies in the parallel alignment of the S₁ transition dipole along the longitudinal axis, which sustains electronic coupling between adjacent bimane subunits over a range of torsional angles and is crucial for driving intra-chain EET. Using a model that comprises hexameric donor and acceptor fragments, we evaluated electronic couplings and spectral overlaps, and applied Fermi's golden rule (in the weak electronic coupling regime) to approximate the lower limit of intra-chain EET in an acetylene-linked bimane photonic wire.

Photoinduced Electron Transfer in Organic Solar Cells

Electron transfer (ET) is the key process in light-driven charge separation reactions in organic solar cells. The current review summarizes the progress in theoretical modelling of ET in these materials. First we give an account of ET, with a description originating from Marcus theory. We systematically go through all the relevant parameters and show how they depend on different material properties, and discuss the consequences such dependencies have for the performance of the devices. Finally, we present a set of visualization methods which have proven to be very useful in analyzing the elementary processes in absorption and charge separation events. Such visualization tools help us to understand the properties of the photochemical and photobiological systems in solar cells.

DFT-based Green's function pathways model for prediction of bridge-mediated electronic coupling

New LMO-GFM methodology enables intuitive understanding of electron tunneling in terms of through-bond and through-space interactions.

Photodynamic behavior of electronic coupling in a N-methylformamide dimer

The role of the bridging water molecules has been studied during the excited state photodynamics of a N-methylformamide dimer in complex with water molecules employing the complete active space self-consistent field (CASSCF) and CAS perturbation theory (CASPT2) methods.

Tunable electronic coupling and driving force in structurally well-defined tetracene dimers for molecular singlet fission: a computational exploration using density functional theory

Singlet fission (SF), a process by which two excited states are formed in a chromophoric system following the absorption of a single photon, has the potential to increase the theoretical efficiency of solar energy conversion devices beyond the single-junction Shockley-Quiesser limit. Although SF is observed with high yield in the solid state of certain molecules, linearly linked dimers based on these same constituents exhibit small yields in part due to small interchromophore electronic coupling. Previous work from our group demonstrated enhancement of SF yield in polycrystalline tetracene (Tc) via excitation of intermolecular motions, which increased direct overlap of monomer π-systems. In this current work, a series of norbornyl-bridged bistetracene (BT) dimers are investigated using DFT and the ability to control SF thermodynamics along with important interchromophore electronic coupling parameters via bridging geometry is shown. Although the electronic coupling of a series of C2v-symmetric dimers (BT1-BT3) that differ in norbornyl bridge length is larger than in previously studied Tc dimers, a key nonhorizontal electron-transfer (ET) matrix element used in determining the SF rate is zero due to symmetry. In these systems, SF may be expected but electronic excitation will require coupling to vibrational modes that break symmetry. Singly bridged dimer isomers BT1-trans and BT1-cis, which break the C2v symmetry of BT1 by exploiting attachment of the norbornyl bridge at the 1,2 instead of the 2,3 Tc positions, are expected to be significantly more favorable for SF due to an exoergic driving force, increased electronic coupling, a lower charge-transfer-state energy (particularly in the case of BT1-cis), and nonhorizontal ET matrix elements that are nonzero.

The role of the environment in electronic energy transfer: a molecular modeling perspective

The key role of the environment in electronic energy transfer has been underscored in recent experimental and theoretical studies. In this perspective, we provide an overview of novel quantum-mechanical methodologies aimed at describing environment effects in energy transfers. The techniques described include continuum dielectric and atomistic descriptions of the surroundings. We discuss the advantages and limitations of each technique, as well as the main insights that have emerged from their application to solvated dyads and photosynthetic pigment-protein complexes. We finally highlight the aspects that still need to be solved in order to provide a full theoretical route to the study of energy transfer phenomena in complex environments.

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.

The electronic couplings in electron transfer and excitation energy transfer

The transport of charge via electrons and the transport of excitation energy via excitons are two processes of fundamental importance in diverse areas of research. Characterization of electron transfer (ET) and excitation energy transfer (EET) rates are essential for a full understanding of, for instance, biological systems (such as respiration and photosynthesis) and opto-electronic devices (which interconvert electric and light energy). In this Account, we examine one of the parameters, the electronic coupling factor, for which reliable values are critical in determining transfer rates. Although ET and EET are different processes, many strategies for calculating the couplings share common themes. We emphasize the similarities in basic assumptions between the computational methods for the ET and EET couplings, examine the differences, and summarize the properties, advantages, and limits of the different computational methods. The electronic coupling factor is an off-diagonal Hamiltonian matrix element between the initial and final diabatic states in the transport processes. ET coupling is essentially the interaction of the two molecular orbitals (MOs) where the electron occupancy is changed. Singlet excitation energy transfer (SEET), however, contains a Frster dipole-dipole coupling as its most important constituent. Triplet excitation energy transfer (TEET) involves an exchange of two electrons of different spin and energy; thus, it is like an overlap interaction of two pairs of MOs. Strategies for calculating ET and EET couplings can be classified as (1) energy-gap-based approaches, (2) direct calculation of the off-diagonal matrix elements, or (3) use of an additional operator to describe the extent of charge or excitation localization and to calculate the coupling value. Some of the difficulties in calculating the couplings were recently resolved. Methods were developed to remove the nondynamical correlation problem from the highly precise coupled cluster models for ET coupling. It is now possible to obtain reliable ET couplings from entry-level excited-state Hamiltonians. A scheme to calculate the EET coupling in a general class of systems, regardless of the contributing terms, was also developed. In the past, empirically derived parameters were heavily invoked in model description of charge and excitation energy drifts in a solid-state device. Recent advances, including the methods described in this Account, permit the first-principle quantum mechanical characterization of one class of the parameters in such descriptions, enhancing the predictive power and allowing a deeper understanding of the systems involved.

Fresh look at electron-transfer mechanisms via the donor/acceptor bindings in the critical encounter complex

Seminal insights provided by the iconic R. S. Mulliken and his "charge-transfer" theory, H. Taube and his "outer/inner-sphere" mechanisms, R. A. Marcus and his "two-state non-adiabatic" theory, and N. S. Hush and his "intervalence" theory are each separately woven into the rich panoramic tapestry constituting chemical research into electron-transfer dynamics, and its mechanistic dominance for the past half century and more. In this Account, we illustrate how the simultaneous melding of all four key concepts allows sharp focus on the charge-transfer character of the critical encounter complex to evoke the latent facet of traditional electron-transfer mechanisms. To this end, we exploit the intervalence (electronic) transition that invariably accompanies the diffusive encounter of electron-rich organic donors (D) with electron-poor acceptors (A) as the experimental harbinger of the collision complex, which is then actually isolated and X-ray crystallographically established as loosely bound pi-stacked pairs of various aromatic and olefinic donor/acceptor dyads with uniform interplanar separations of r(DA) = 3.1 +/- 0.2 A. These X-ray structures, together with the spectral measurements of their intervalence transitions, lead to the pair of important electron-transfer parameters, H(DA) (electronic coupling element) versus lambdaT (reorganization energy), the ratio of which generally defines the odd-electron mobility within such an encounter complex in terms of the resonance stabilization of the donor/acceptor assembly [D, A] as opposed to the reorganization-energy penalty required for its interconversion to the electron-transfer state [D(+*), A(-*)]. We recognize the resonance-stabilization energy relative to the intrinsic activation barrier as the mechanistic binding factor, Q = 2H(DA)/lambdaT, to represent the quantitative measure of the highly variable continuum of inner-sphere/outer-sphere interactions that are possible within various types of precursor complexes. First, Q << 1 identifies one extreme mechanism owing to slow electron-transfer rates that result from the dominance of the intrinsic activation barrier (lambdaT) between the encounter and successor complexes. At the other extreme of Q > or = 1, the overwhelming dominance of the resonance stabilization (H(DA)) predicts the odd-electron mobility between the donor and acceptor to occur without an activation barrier such that bimolecular electron transfer is coincident with their diffusional encounter. In between lies a potentially infinite set of states, 0 < Q < 1 with opposing attractive and destabilizing forces that determine the location of the bound transition states along the reaction coordinate. Three prototypical potential-energy surfaces evolve as a result of progressively increasing the donor/acceptor bindings (H(DA)) extant in the precursor complex (at constant lambdaT). In these cases, the "outer-sphere" mechanism is limited by the weak donor/acceptor coupling that characterizes the now classical Marcus outer-sphere mechanism. Next, the "inner-sphere" mechanism derives from moderate (localized) donor/acceptor bindings and includes the mechanistic concept of the bridged-activated complex introduced by Taube for a wide variety of ligand-based redox dyads. Finally, the "interior" mechanism is also another subclass of the Taube (inner-sphere) classification, and it lies at the other extreme of very fast electron-transfer rate processes (heretofore unrecognized), arising from the spontaneous annihilation of the donor/acceptor dyad to the delocalized (electron-transfer) complex as it descends barrierlessly into the chemical "black hole" that is rate-limited solely by diffusion.

Novel organic materials through control of multichromophore interactions

The function of organic semiconducting and light-harvesting materials depends on the organization of the individual molecular components. Our group has tackled the problem of through-space delocalization via the design and synthesis of bichromphoric pairs held in close proximity by the [2.2]paracyclophane core. The linear and nonlinear optical properties of these molecules provide a challenge to theory. They are also useful in delineating the problem of intermolecular contacts in molecular conductivity measurements. Another area of research described here concerns conjugated polyelectrolytes. These macromolecules combine the properties of organic semiconductors and conventional polyelectrolytes. We have used these materials in the development of optically amplified biosensors and have also incorporated them into organic optoelectronic devices. Of particular interest to us is to derive useful structure/property relationships via molecular design that address important basic scientific problems and technological challenges.

Towards a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems. II. The through-bond contribution

In this paper we present a quantum-mechanical investigation on the mechanisms which promote intramolecular EET coupling. This investigation is done by using a new computational strategy in which we combine a configuration-interaction and a linear response approach. The combined use of these two methods allows a direct identification and a quantification of both "direct" (coulomb and exchange) and through-bond (superexchange and charge-transfer) contributions. In addition, solvent effects are introduced using the polarizable continuum model. The method is applied to a family of naphthalene-bridge-naphthalene and naphthalene-bridge-anthracene systems, and the results obtained are compared with experiments. The results found suggest that the through-bond charge-transfer effects are not significant when the EET goes through permitted excitations on distant chromophores (see DN4 and DN6) while they become as important as (or even more important than) the covalent terms for EETs involving weakly allowed excitations (see A6N). By contrast, the presence of a very short bridge (in DN2) allows a very efficient delocalization of the excitation energy which is also largely modified by the presence of a solvent.

Toward a molecular scale interpretation of excitation energy transfer in solvated bichromophoric systems

This paper presents a quantum-mechanical study of the intramolecular excitation energy transfer (EET) coupling in naphthalene-bridge-naphthalene systems in gas phase and in solution. ZINDO and TDDFT response schemes are compared using both an exact and an approximate solution. The approximate solution based on a perturbative approach uses the single chromophore properties to reconstruct the real system coupling thus neglecting possible through-bond effects which conversely are accounted for in the exact solution. The comparison of the results of the two approaches with the experiments allows a detailed analysis of the relative importance of through-bond and through-space effects as well as a more complete understanding of the modifications in the EET coupling with the size of the system, the chromophore-chromophore distance, and solvation.

Triplet-triplet energy-transfer coupling: Theory and calculation

Triplet-triplet (TT) energy transfer requires two molecular fragments to exchange electrons that carry different spin and energy. In this paper, we analyze and report values of the electronic coupling strengths for TT energy transfer. Two different methods were proposed and tested: (1) Directly calculating the off-diagonal Hamiltonian matrix element. This direct coupling scheme was generalized from the one used for electron transfer coupling, where two spin-localized unrestricted Hartree-Fock wave functions are used as the zero-order reactant and product states, and the off-diagonal Hamiltonian matrix elements are calculated directly. (2) From energy gaps derived from configuration-interaction-singles (CIS) scheme. Both methods yielded very similar results for the systems tested. For TT coupling between a pair of face-to-face ethylene molecules, the exponential attenuation factor is 2.59 A(-1)(CIS6-311+G(**)), which is about twice as large as typical values for electron transfer. With a series of fully stacked polyene pairs, we found that the TT coupling magnitudes and attenuation rates are very similar irrespective of their molecular size. If the polyenes were partially stacked, TT couplings were much reduced, and they decay more rapidly with distance than those of full-stacked systems. Our results showed that the TT coupling arises mainly from the region of close contact between the donor and acceptor frontier orbitals, and the exponential decay of the coupling with separation depends on the details of the molecular contacts. With our calculated results, nanosecond or picosecond time scales for TT energy-transfer rates are possible.

Ab Initio Characterization of Electron Transfer Coupling in Photoinduced Systems: Generalized Mulliken−Hush with Configuration-Interaction Singles

To calculate electronic couplings for photoinduced electron transfer (ET) reactions, we propose and test the use of ab initio quantum chemistry calculation for excited states with the generalized Mulliken-Hush (GMH) method. Configuration-interaction singles (CIS) is proposed to model the locally excited (LE) and charge-transfer (CT) states. When the CT state couples with other high lying LE states, affecting coupling values, the image charge approximation (ICA), as a simple solvent model, can lower the energy of the CT state and decouple the undesired high-lying local excitations. We found that coupling strength is weakly dependent on many details of the solvent model, indicating the validity of the Condon approximation. Therefore, a trustworthy value can be obtained via this CIS-GMH scheme, with ICA used as a tool to improve and monitor the quality of the results. Systems we tested included a series of rigid, sigma-linked donor-bridge-acceptor compounds where "through-bond" coupling has been previously investigated, and a pair of molecules where "through-space" coupling was experimentally demonstrated. The calculated results agree well with experimentally inferred values in the coupling magnitudes (for both systems studied) and in the exponential distance dependence (for the through-bond series). Our results indicate that this new scheme can properly account for ET coupling arising from both through-bond and through-space mechanisms.

Intervalence (Charge-Resonance) Transitions in Organic Mixed-Valence Systems. Through-Space versus Through-Bond Electron Transfer between Bridged Aromatic (Redox) Centers

Intervalence absorption bands appearing in the diagnostic near-IR region are consistently observed in the electronic spectra of mixed-valence systems containing a pair of aromatic redox centers (Ar(*)(+)/Ar) that are connected by two basically different types of molecular bridges. The through-space pathway for intramolecular electron transfer is dictated by an o-xylylene bridge in the mixed-valence cation radical 3(*)(+) with Ar = 2,5-dimethoxy-p-tolyl (T), in which conformational mobility allows the proximal syn disposition of planar T(*)(+)/T redox centers. Four independent experimental probes indicate the large through-space electronic interaction between such cofacial Ar(*)(+)/Ar redox centers from the measurements of (a) sizable potential splitting in the cyclic voltammogram, (b) quinonoidal distortion of T(*)(+)/T centers by X-ray crystallography, (c) "doubling" of the ESR hyperfine splittings, and (d) a pronounced intervalence charge-resonance band. The through (br)-bond pathway for intramolecular electron transfer is enforced in the mixed-valence cation radical 2a(*)(+) by the p-phenylene bridge which provides the structurally inflexible and linear connection between Ar(*)(+)/Ar redox centers. The direct comparison of intramolecular rates of electron transfer (k(ET)) between identical T(*)(+)/T centers in 3(*)(+) and 2a(*)(+)( )()indicates that through-space and through-bond mechanisms are equally effective, despite widely different separations between their redox centers. The same picture obtains for 3(*)(+) and 2a(*)(+)( )()from theoretical computations of the first-order rate constants for intramolecular electron transfer from Marcus-Hush theory using the electronic coupling elements evaluated from the diagnostic intervalence (charge-transfer) transitions. Such a strong coherence between theory and experiment also applies to the mixed-valence cation radical 7(*)(+), in which the aromatic redox S center is sterically encumbered by annulation.

Long-range resonance energy transfer in molecular systems

The current state of understanding of molecular resonance energy transfer (RET) and recent developments in the field are reviewed. The development of more general theoretical approaches has uncovered some new principles underlying RET processes. This review brings many of these important new concepts together into a generalization of Förster's original theory. The conclusions of studies investigating the various approximations in Förster theory are summarized. Areas of present and future activity are discussed. The review covers Förster theory for donor-acceptor pairs and electronic coupling for singlet-singlet, triplet-triplet, and superexchange-mediated energy transfer. This includes the transition density picture of Coulombic coupling as well as electronic coupling between molecular aggregates (excitons). Spectral overlaps and ensemble energy transfer rates in disordered aggregates, the role of dielectric properties of the medium, weak versus strong coupling, and new models for energy transfer in complex molecular assemblies are also described.

Multidimensional femtosecond correlation spectroscopies of electronic and vibrational excitations

Femtosecond visible and infrared analogues of multiple-pulse nuclear magnetic resonance techniques provide novel snapshot probes into the structure and electronic and vibrational dynamics of complex molecular assemblies such as photosynthetic antennae, proteins, and hydrogen-bonded liquids. A classical-oscillator description of these spectroscopies in terms of interacting quasiparticles (rather than transitions among global eigenstates) is developed and sets the stage for designing new pulse sequences and inverting the multidimensional signals to yield molecular structures. Considerable computational advantages and a clear physical insight into the origin of the response and the relevant coherence sizes are provided by a real-space analysis of the underlying coherence-transfer pathways in Liouville space.

Excitonic couplings and electronic coherence in bridged naphthalene dimers

The electronic excitations of naphthalene and a family of bridged naphthalene dimers are calculated and analyzed by using the Collective Electronic Oscillator method combined with the oblique Lanczos algorithm. All experimentally observed trends in absorption profiles and radiative lifetimes are reproduced. Each electronic excitation is linked to the corresponding real-space transition density matrix, which represents the motions of electrons and holes created in the molecule by photon absorption. Two-dimensional plots of these matrices help visualize the degree of exciton localization and explain the dependence of the electronic interaction between chromophores on their separation.