Synthetic Control of Exciton Dynamics in Bioinspired Cofacial Porphyrin Dimers

Instantaneous Marcus theory for photoinduced charge transfer dynamics in multistate harmonic model systems

Modeling the dynamics of photoinduced charge transfer (CT) in condensed phases presents challenges due to complicated many-body interactions and the quantum nature of electronic transitions. While traditional Marcus theory is a robust method for calculating CT rate constants between electronic states, it cannot account for the nonequilibrium effects arising from the initial nuclear state preparation. In this study, we employ the instantaneous Marcus theory (IMT) to simulate photoinduced CT dynamics. IMT incorporates nonequilibrium structural relaxation following a vertical photoexcitation from the equilibrated ground state, yielding a time-dependent rate coefficient. The multistate harmonic (MSH) model Hamiltonian characterizes an organic photovoltaic carotenoid-porphyrin-fullerene triad dissolved in explicit tetrahydrofuran solvent, constructed by mapping all-atom inputs from molecular dynamics simulations. Our calculations reveal that the electronic population dynamics of the MSH models obtained with IMT agree with the more accurate quantum-mechanical nonequilibrium Fermi's golden rule. This alignment suggests that IMT provides a practical approach to understanding nonadiabatic CT dynamics in condensed-phase systems.

Electron transfer rate modulation with mid-IR in butadiyne-bridged donor-bridge-acceptor compounds

Controlling electron transfer (ET) processes in donor-bridge-acceptor (DBA) compounds by mid-IR excitation can enhance our understanding of the ET dynamics and may find practical applications in molecular sensing and molecular-scale electronics. Alkyne moieties are attractive to serve as ET bridges, as they offer the possibility of fast ET and present convenient vibrational modes to perturb the ET dynamics. Yet, these bridges introduce complexity because of the strong torsion angle dependence of the ET rates and transition dipoles among electronic states and a shallow torsion barrier. In this study, we implemented ultrafast 3-pulse laser spectroscopy to investigate how the ET from the dimethyl aniline (D) electron donor to the N-isopropyl-1,8-napthalimide (NAP) electron acceptor can be altered by exciting the CC stretching mode (νCC) of the butadiyne bridge linking the donor and acceptor. The electron transfer was initiated by electronically exciting the acceptor moiety at 400 nm, followed by vibrational excitation of the alkyne, νCC, and detecting the changes in the absorption spectrum in the visible spectral region. The experiments were performed at different delay times t1 and t2, which are the delays between UV-mid-IR and mid-IR-Vis pulses, respectively. Two sets of torsion-angle conformers were identified, one featuring a very fast mean ET time of 0.63 ps (group A) and another featuring a slower mean ET time of 4.3 ps (group B), in the absence of the mid-IR excitation. TD-DFT calculations were performed to determine key torsion angle dependent molecular parameters, including the electronic and vibrational transition dipoles, transition frequencies, and electronic couplings. To describe the 3-pulse data, we developed a kinetic model that includes a locally excited, acceptor-based S2 state, a charge separated S1 state, and their vibrationally excited counterparts, with either excited νCC (denoted as S1Atr, S1Btr, S2Atr, and S2Btr, where tr stands for the excited triplet bond, νCC) or excited daughter modes of the νCC relaxation (S1Ah, S1Bh, S2Ah, and S2Bh, where h stands for vibrationally hot species). The kinetic model was solved analytically, and the species-associated spectra (SAS) were determined numerically using a matrix approach, treating first the experiments with longer t1 delays and then using the already determined SAS for modeling the experiments with shorter t1 delays. Strong vibronic coupling of νCC and of vibrationally hot states makes the analysis complicated. Nevertheless, the SAS were identified and the ET rates of the vibrationally excited species, S2Atr, S2Btr and S2Bh, were determined. The results show that the ET rate for the S2A species is ca. 1.2-fold slower when the νCC mode is excited. The ET rate for species S2B is slower by ca. 1.3-fold if the compound is vibrationally hot and is essentially unchanged when the νCC mode is excited. The SAS determined for the tr and h species resemble the SAS for their respective precursor species in the 2-pulse transient absorption experiments, which validates the procedure used and the results.

Multistate Reaction Coordinate Model for Charge and Energy Transfer Dynamics in the Condensed Phase

Constructing multistate model Hamiltonians from all-atom electronic structure calculations and molecular dynamics simulations is crucial for understanding charge and energy transfer dynamics in complex condensed phases. The most popular two-level system model is the spin-boson Hamiltonian, where the nuclear degrees of freedom are represented as shifted normal modes. Recently, we proposed the general multistate nontrivial extension of the spin-boson model, i.e., the multistate harmonic (MSH) model, which is constructed by extending the spatial dimensions of each nuclear mode so as to satisfy the all-atom reorganization energy restrictions for all pairs of electronic states. In this work, we propose the multistate reaction coordinate (MRC) model with a primary reaction coordinate and secondary bath modes as in the Caldeira-Leggett form but in extended spatial dimensions. The MRC model is proven to be equivalent to the MSH model and offers an intuitive physical picture of the nuclear-electronic feedback in nonadiabatic processes such as the inherent trajectory of the reaction coordinate. The reaction coordinate is represented in extended dimensions, carrying the entire reorganization energies and bilinearly coupled to the secondary bath modes. We demonstrate the MRC model construction for photoinduced charge transfer in an organic photovoltaic caroteniod-porphyrin-C60 molecular triad dissolved in tetrahydrofuran as well as excitation energy transfer in a photosynthetic light-harvesting Fenna-Matthews-Olson complex. The MRC model provides an effective and robust platform for investigating quantum dissipative dynamics in complex condensed-phase systems since it allows a consistent description of realistic spectral density, state-dependent system-bath couplings, and heterogeneous environments due to static disorder in reorganization energies.

Vibrational Funnels for Energy Transfer in Organic Chromophores

Photoinduced intramolecular energy transfers in multichromophoric molecules involve nonadiabatic vibronic channels that act as energy transfer funnels. They commonly take place through specific directions of motion dictated by the nonadiabatic coupling vectors. Vibrational funnels may support persistent coherences between electronic states and sometimes delineate the presence of minor alternative energy transfer pathways. The ultimate confirmation of their role on the interchromophoric energy transfer can be achieved by performing nonadiabatic excited-state molecular dynamics simulations by selectively freezing the nuclear motions in question. Our results point out this strategy as a useful tool to identify and evaluate the impact of these vibrational funnels on the energy transfer processes and guide the in silico design of materials with tunable properties and enhanced functionalities. Our work encourages applications of this methodology to different chemical and biochemical processes such as reactive scattering and protein conformational changes, to name a few.

Highly Coupled Heterobicycle-Fused Porphyrin Dimers: Excitonic Coupling and Charge Separation with Coordinated Fullerene, C60

Porphyrin dimers have been widely explored and studied owing to their importance in photosynthetic systems. A vast variety of dimers linked by different groups and at different angles have been synthesized and studied; however, the means by which to synthesize rigidly fused porphyrins with direct conjugation of the chromophores remains limited. Such a class of porphyrins may possess interesting properties that unconjugated or stacked dimers may not exhibit. In this study, bisbenzimidazole-fused porphyrin dimers and their mono- and bis-zinc derivatives are synthesized and characterized. As a consequence of excitonic coupling, these dimers exhibit a split Soret band irrespective of the metal ion in the porphyrin cavity. Steady-state fluorescence and excitation spectra followed by femtosecond transient absorption spectral studies of the heterometallated dimer, (free-base and zinc porphyrin) reveals the occurrence of efficient singlet-singlet energy transfer (>95 % efficiency and rate constant >10¹²  s^-1 ) within the dyad. Further, donor-acceptor conjugates were formed by metal-ligand axial coordination of phenyl imidazole functionalized C₆₀ and were characterized by a variety of physicochemical techniques. Excited state charge separation from both singlet and triplet excited states of ZnP in the conjugates has been established. The lifetime of the final charge-separated state was in the 30-40 μs range revealing charge stabilization. Interestingly, no charge separation in the conjugate derived from the heterometallated dimer was observed wherein excitation transfer dominated the process. The present study brings out the importance of the rigid π-spacer connecting porphyrin dimers in governing the energy and electron transfer events when coupled with an electron acceptor.

Engineering giant excitonic coupling in bioinspired, covalently bridged BODIPY dyads

Strong excitonic coupling in photosynthetic systems is believed to enable efficient light absorption and quantitative charge separation, motivating the development of artificial multi-chromophore arrays with equally strong or even stronger excitonic coupling. However, large excitonic coupling strengths have typically been accompanied by fast non-radiative recombination, limiting the potential of the arrays for solar energy conversion as well as other applications such as fluorescent labeling. Here, we report giant excitonic coupling leading to broad optical absorption in bioinspired BODIPY dyads that have high photostability, excited-state lifetimes at the nanosecond scale, and fluorescence quantum yields of nearly 50%. Through the synthesis, spectroscopic characterization, and computational modeling of a series of dyads with different linking moieties, we show that the strongest coupling is obtained with diethynylmaleimide linkers, for which the coupling occurs through space between BODIPY units with small separations and slipped co-facial orientations. Other linkers allow for broad tuning of both the relative through-bond and through-space coupling contributions and the overall strength of interpigment coupling, with a tradeoff observed in general between the strength of the two coupling mechanisms. These findings open the door to the synthesis of molecular systems that function effectively as light-harvesting antennas and as electron donors or acceptors for solar energy conversion.

Long-range charge transport in homogeneous and alternating-rigidity chains

We study the interplay of intrinsic-electronic and environmental factors in long-range charge transport across molecular chains with up to N ∼ 80 monomers. We describe the molecular electronic structure of the chain with a tight-binding Hamiltonian. Thermal effects in the form of electron decoherence and inelastic scattering are incorporated with the Landauer–Büttiker probe method. In short chains of up to ten units, we observe the crossover between coherent (tunneling, ballistic) motion and thermally-assisted conduction, with thermal effects enhancing the current beyond the quantum coherent limit. We further show that unconventional (nonmonotonic with size) transport behavior emerges when monomer-to-monomer electronic coupling is made large. In long chains, we identify a different behavior, with thermal effects suppressing the conductance below the coherent-ballistic limit. With the goal to identify a minimal model for molecular chains displaying unconventional and effective long-range transport, we simulate a modular polymer with alternating regions of high and low rigidity. Simulations show that, surprisingly, while charge correlations are significantly affected by structuring environmental conditions, reflecting charge delocalization, the electrical resistance displays an averaging effect, and it is not sensitive to this patterning. We conclude by arguing that efficient long-range charge transport requires engineering both internal electronic parameters and environmental conditions.

All-Atom Nonadiabatic Semiclassical Mapping Dynamics for Photoinduced Charge Transfer of Organic Photovoltaic Molecules in Explicit Solvents

Direct all-atom simulation of nonadiabatic dynamics in disordered condensed phases like liquid solutions and amorphous solids has been challenging. The first all-atom simulation of the photoinduced charge-transfer dynamics of a prototypical organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad in explicit tetrahydrofuran is presented. Based on the Meyer-Miller mapping Hamiltonian, various semiclassical and mixed quantum-classical dynamics are employed, including the linearized semiclassical, symmetrical quasiclassical, mean-field Ehrenfest, classical mapping model, and spin-mapping model approaches. The all-atom nonadiabatic dynamics were compared to multi-state harmonic models with a globally shared bath, and the models built using the ensemble averages on the initial electronic state could reproduce the all-atom results. The solvent effect was found to be critical for the photoinduced charge transfer, and the time-dependent solute-solvent radial distribution functions revealed that only the nonadiabatic dynamics started with the effective forces on the initial electronic state could capture the correct nuclear dynamics. The proposed strategy for modeling condensed-phase nonadiabatic dynamics with atomistic details is readily applied to complex condensed-phase systems.

Interference between Franck-Condon and Herzberg-Teller Terms in the Condensed-Phase Molecular Spectra of Metal-Based Tetrapyrrole Derivatives

The commonly used Franck-Condon (FC) approximation is inadequate for explaining the electronic spectra of compounds that possess vibrations with substantial Herzberg-Teller (HT) couplings. Metal-based tetrapyrrole derivatives, which are ubiquitous natural pigments, often exhibit prominent HT activity. In this paper, we compare the condensed phase spectra of zinc-tetraphenylporphyrin (ZnTPP) and zinc-phthalocyanine (ZnPc), which exhibit vastly different spectral features in spite of sharing a common tetrapyrrole backbone. The absorption and emission spectra of ZnTPP are characterized by a lack of mirror symmetry and nontrivial temperature dependence. In contrast, mirror symmetry is restored, and the nontrivial temperature-dependent features disappear in ZnPc. We attribute these differences to FC-HT interference, which is less pronounced in ZnPc because of a larger FC component in the dipole moment that leads to FC-dominated transitions. A single minimalistic FC-HT vibronic model reproduces all the experimental spectral features of these molecules. These observations suggest that FC-HT interference is highly susceptible to chemical modification.

Photophysical Properties and Electronic Structure of Hydroporphyrin Dyads Exhibiting Strong Through-Space and Through-Bond Electronic Interactions

Electronic interactions between tetrapyrroles are utilized in natural photosynthetic systems to tune the light-harvesting and energy-/charge-transfer processes in these assemblies. Such interactions also can be employed to tailor the electronic properties of tetrapyrrolic dyads and larger arrays for use in materials science and biomedical research. Here, we have utilized static and time-resolved optical spectroscopy to characterize the optical absorption and emission properties of a set of chlorin and bacteriochlorin dyads with varying degrees of through-bond (TB) and through-space (TS) interactions between the constituent macrocycles. The dyads consist of two chlorins or two bacteriochlorins joined by a linker that utilizes a triple-double-triple-bond (enediyne) motif in which the double-bond portion is an ester-substituted ethylene or o-phenylene unit. The photophysical studies are coupled with density functional theory (DFT) calculations to probe the ground-state molecular orbital (MO) characteristics of the dyads and time-dependent DFT calculations (TDDFT) to elucidate excited-state properties. The latter include electronic characteristics of the singlet excited-state manifold and the absorption transitions to these states from the electronic ground state. A comparison of the MO and calculated spectral properties of each dyad with the linker present versus disrupted (by eliminating the double-bond portion) gives insight into the relative contributions of TB versus TS interactions to the electronic properties of the dyads. The results show that the TB and TS contributions are additive (constructively interfere), which is not always the case for molecular dyads. Most of the dyads have shorter lifetimes of the lowest singlet excited state compared to the parent monomer, which derives from increased S₁ → S₀ internal conversion. The enhancement is greater for the dyads in benzonitrile than in toluene. The studies provide insights into the nature of the electronic interactions between the constituents in the tetrapyrrole arrays and how these interactions dictate the spectral properties and excited-state decay characteristics.

Vibronic resonance along effective modes mediates selective energy transfer in excitonically coupled aggregates

We recently proposed effective normal modes for excitonically coupled aggregates that exactly transform the energy transfer Hamiltonian into a sum of one-dimensional Hamiltonians along the effective normal modes. Identifying physically meaningful vibrational motions that maximally promote vibronic mixing suggested an interesting possibility of leveraging vibrational-electronic resonance for mediating selective energy transfer. Here, we expand on the effective mode approach, elucidating its iterative nature for successively larger aggregates, and extend the idea of mediated energy transfer to larger aggregates. We show that energy transfer between electronically uncoupled but vibronically resonant donor-acceptor sites does not depend on the intermediate site energy or the number of intermediate sites. The intermediate sites simply mediate electronic coupling such that vibronic coupling along specific promoter modes leads to direct donor-acceptor energy transfer, bypassing any intermediate uphill energy transfer steps. We show that the interplay between the electronic Hamiltonian and the effective mode transformation partitions the linear vibronic coupling along specific promoter modes to dictate the selectivity of mediated energy transfer with a vital role of interference between vibronic couplings and multi-particle basis states. Our results suggest a general design principle for enhancing energy transfer through synergistic effects of vibronic resonance and weak mediated electronic coupling, where both effects individually do not promote efficient energy transfer. The effective mode approach proposed here paves a facile route toward four-wavemixing spectroscopy simulations of larger aggregates without severely approximating resonant vibronic coupling.