Electronic Couplings versus Thermal Fluctuations in the Internal Conversion of Perylene Diimides: The Battle to Localize the Exciton.

Energy transfer processes among units of light-harvesting homo-oligomers impact the efficiency of these materials as components in organic optoelectronic devices such as solar cells. Perylene diimide (PDI), a prototypical dye, features exceptional light absorption and highly tunable optical and electronic properties. These properties can be modulated by varying the number of PDI units and linkers between them. Herein, atomistic nonadiabatic excited state molecular dynamics is used to explore the energy transfer during the internal conversion of acetylene and diacetylene bridged dimeric and trimeric PDIs. Our simulations reveal a significant impact of the bridge type on the transient exciton localization/delocalization between units of PDI dimers. After electronic relaxation, larger exciton delocalization occurs in the PDI dimer connected by the diacetylene bridge with respect to the one connected by the shorter acetylene bridge. These changes can be rationalized by the Frenkel exciton model. We outline a technique for deriving parameters for this model using inputs provided by nonadiabatic dynamics simulations. Frenkel exciton description reveals an interplay between the relative strengths of the diagonal and off-diagonal disorders. Moreover, atomistic simulations and the Frenkel exciton model of the PDI trimer systems corroborate in detail the localization properties of the exciton on the molecular units during the internal conversion to the lowest-energy excited state when the units become effectively decoupled. Overall, atomistic nonadiabatic simulations in combination with the Frenkel exciton model can serve as a predictive framework for analyzing and predicting desired exciton traps in PDI-based oligomers designed for organic electronics and photonic devices.

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.

Infinitene: Computational Insights from Nonadiabatic Excited State Dynamics.

Progress in organic synthesis opens exploration of a rich diversity of molecules with interesting new structural topologies. This is the case of a recently synthesized helically twisted figure-eight molecule coined infinitene. The molecule belongs to a numerous family of looped polyarenes, where the degree of π-conjugation is controlled by high strain energies and steric hindrances. A particular balance of these ingredients leads to unusual optoelectronic properties potentially suitable for a range of applications in nanoelectronics and photonics. Due to its recent discovery, the photophysical properties of infinitene remain unexplored. In this Letter, atomistic nonadiabatic excited state molecular dynamics modeling unveils unique features of intramolecular electronic and vibrational energy relaxation and redistribution that take place after molecular photoexcitation. Our results detail relationships between optical and electronic properties providing useful knowledge for future molecular designs related to infinitene.

Exciton-vibrational dynamics induces efficient self-trapping in a substituted nanoring.

Cycloparaphenylenes, being the smallest segments of carbon nanotubes, have emerged as prototypes of the simplest carbon nanohoops. Their unique structure-dynamics-optical properties relationships have motivated a wide variety of synthesis of new related nanohoop species. Studies of how chemical changes, introduced in these new materials, lead to systems with new structural, dynamics and optical properties, expand their functionalities for optoelectronics applications. Herein, we study the effect that conjugation extension of a cycloparaphenylene through the introduction of a satellite tetraphenyl substitution has on its structural and dynamical properties. Our non-adiabatic excited state molecular dynamics simulations suggest that this substitution accelerates the electronic relaxation from the high-energy band to the lowest excited state. This is partially due to efficient conjugation achieved between specific phenyl units as introduced by the tetraphenyl substitution. We observe a particular exciton redistribution during relaxation, in which the tetraphenyl substitution plays a significant role. As a result, an efficient inter-band energy transfer takes place. Besides, the observed phonon-exciton interplay induces a significant exciton self-trapping. Our results encourage and guide the future studies of new phenyl substitutions in carbon nanorings with desired optoelectronic properties.

Vibronic Photoexcitation Dynamics of Perylene Diimide: Computational Insights.

Perylene diimide (PDI) represents a prototype material for organic optoelectronic devices because of its strong optical absorbance, chemical stability, efficient energy transfer, and optical and chemical tunability. Herein, we analyze in detail the vibronic relaxation of its photoexcitation using nonadiabatic excited-state molecular dynamics simulations. We find that after the absorption of a photon, which excites the electron to the second excited state, S2, induced vibronic dynamics features persistent modulations in the spatial localization of electronic and vibrational excitations. These energy exchanges are dictated by strong vibronic couplings that overcome structural disorders and thermal fluctuations. Specifically, the electronic wavefunction periodically swaps between localizations on the right and left sides of the molecule. Within 1 ps of such dynamics, a nonradiative transition to the lowest electronic state, S1, takes place, resulting in a complete delocalization of the wavefunction. The observed vibronic dynamics emerges following the electronic energy deposition in the direction that excites a combination of two dominant vibrational normal modes. This behavior is maintained even with a chemical substitution that breaks the symmetry of the molecule. We believe that our findings elucidate the nature of the complex dynamics of the optically excited states and, therefore, contribute to the development of tunable functionalities of PDIs and their derivatives.

Back-and-Forth Energy Transfer during Electronic Relaxation in a Chlorin-Perylene Dyad.

Donor-acceptor dyads represent a practical approach to tuning the photophysical properties of linear conjugated polymers in materials chemistry. Depending on the absorption wavelength, the acceptor and donor roles can be interchanged, and as such, the directionality of the energy transfer can be controlled. Herein, nonadiabatic excited state molecular dynamics simulations have been performed in an arylethylene-linked perylene-chlorin dyad. After an initial photoexcitation at the Soret band of chlorin, we observe an ultrafast sequential electronic relaxation to the lowest excited state. This process is accomplished through an efficient round-trip chlorin-to-perylene-to-chlorin energy transfer. It is characterized by successive intermittent localized and delocalized vibronic dynamics. Nonradiative relaxation takes place mainly through energy transfer events with perylene acting as a "heat sink" through which the nonradiative relaxation is efficiently funneled, and the excess energy is dispersed in a larger space of vibrational degrees of freedom. Thus, our findings suggest the use of donor-acceptor dyads as a useful strategy when one needs to deactivate an electronic excitation.

Excitation Energy Transfer between bodipy Dyes in a Symmetric Molecular Excitonic Seesaw.

We examine the redistribution of energy between electronic and vibrational degrees of freedom that takes place between a π-conjugated oligomer, a phenylene-butadiynylene, and two identical boron-dipyrromethene (bodipy) end-caps using femtosecond transient absorption spectroscopy, single-molecule spectroscopy, and nonadiabatic excited-state molecular dynamics (NEXMD) modeling techniques. The molecular structure represents an excitonic seesaw in that the excitation energy on the oligomer backbone can migrate to either one end-cap or the other, but not to both. The NEXMD simulations closely reproduce the characteristic time scale for redistribution of electronic and vibrational energy of 2.2 ps and uncover the vibrational modes contributing to the intramolecular relaxation. The calculations indicate that the dihedral angle between the bodipy dye and the oligomer change upon excitation of the oligomer. Single-molecule experiments reveal a difference in photoluminescence lifetime of the bodipy dyes depending on whether they are excited by direct absorption or by redistribution of energy from the backbone. This difference in lifetime may be attributed to the difference in dihedral angle. The simulations also suggest that a strong coupling can occur between the two end-caps, giving rise to a reversible shuttling of excitation energy between them. Strong coupling should lead to a pronounced loss in polarization memory of the fluorescence since the oligomer backbone tends to be slightly distorted and the two bodipy transition dipoles have different orientations. A sensitive single-molecule technique is presented to test for such coupling. However, although redistribution of electronic and vibrational energy between the end-caps can occur, it appears to be unidirectional and irreversible, suggesting that an additional localization mechanism is at play which is, as yet, not fully accounted for in the simulations.

Nonadiabatic Excited-State Molecular Dynamics Methodologies: Comparison and Convergence.

Direct atomistic simulation of nonadiabatic molecular dynamics is a challenging goal that allows important insights into fundamental physical phenomena. A variety of frameworks, ranging from fully quantum treatment of nuclei to semiclassical and mixed quantum-classical approaches, were developed. These algorithms are then coupled to specific electronic structure techniques. Such diversity and lack of standardized implementation make it difficult to compare the performance of different methodologies when treating realistic systems. Here, we compare three popular methods for large chromophores: Ehrenfest, surface hopping, and multiconfigurational Ehrenfest with ab initio multiple cloning (MCE-AIMC). These approaches are implemented in the NEXMD software, which features a common computational chemistry model. The resulting comparisons reveal the method performance for population relaxation and coherent vibronic dynamics. Finally, we study the numerical convergence of MCE-AIMC algorithms by considering the number of trajectories, cloning thresholds, and Gaussian wavepacket width. Our results provide helpful reference data for selecting an optimal methodology for simulating excited-state molecular dynamics.

Exciton Spatial Dynamics and Self-Trapping in Carbon Nanocages.

Three-dimensional cage-shaped molecules formed from chainlike structures hold potential as unique optoelectronic materials and host compounds. Their optical, structural, and dynamical features are tunable by changes in shape and size. We perform a comparison of these properties for three sizes of strained conjugated [n.n.n]carbon nanocages composed of three paraphenylene chains (bridges) of length n = 4, 5, or 6. The exciton intramolecular redistribution occurring during nonradiative relaxation has been explored using nonadiabatic excited-state molecular dynamics. Our results provide atomistic insight into the conformational features associated with the observed red- and blue-shift trends in the absorption and fluorescence spectra, respectively, with increasing nanocage size. Their internal conversion processes involve intramolecular energy transfer that leads to exciton self-trapping on a few phenylene units at the center of a single bridge. The dependence of these dynamical features on the size of the nanocage can be used to tune their host-guest chemical properties and their use for organic electronics and catenane-like applications.

Experimental and theoretical study of energy transfer in a chromophore triad: What makes modeling dynamics successful?

Simulation of electronic dynamics in realistically large molecular systems is a demanding task that has not yet achieved the same level of quantitative prediction already realized for its static counterpart. This is particularly true for processes occurring beyond the Born-Oppenheimer regime. Non-adiabatic molecular dynamics (NAMD) simulations suffer from two convoluted sources of error: numerical algorithms for dynamics and electronic structure calculations. While the former has gained increasing attention, particularly addressing the validity of ad hoc methodologies, the effect of the latter remains relatively unexplored. Indeed, the required accuracy for electronic structure calculations to reach quantitative agreement with experiment in dynamics may be even more strict than that required for static simulations. Here, we address this issue by modeling the electronic energy transfer in a donor-acceptor-donor (D-A-D) molecular light harvesting system using fewest switches surface hopping NAMD simulations. In the studied system, time-resolved experimental measurements deliver complete information on spectra and energy transfer rates. Subsequent modeling shows that the calculated electronic transition energies are "sufficiently good" to reproduce experimental spectra but produce over an order of magnitude error in simulated dynamical rates. We further perform simulations using artificially shifted energy gaps to investigate the complex relationship between transition energies and modeled dynamics to understand factors affecting non-radiative relaxation and energy transfer rates.

Let Digons be Bygones: The Fate of Excitons in Curved π-Systems.

We explore the diverse origins of unpolarized absorption and emission of molecular polygons consisting of π-conjugated oligomer chains held in a bent geometry by strain controlled at the vertex units. For this purpose, we make use of atomistic nonadiabatic excited-state molecular dynamics simulations of a bichromophore molecular polygon (digon) with bent chromophore chains. Both structural and photoexcited dynamics were found to affect polarization features. Bending strain induces exciton localization on individual chromophore units of the conjugated chains. The latter display different transition dipole moment orientations, a feature not present in the linear oligomer counterparts. In addition, bending makes exciton localization very sensitive to molecular distortions induced by thermal fluctuations. The excited-state dynamics reveals an ultrafast intramolecular energy redistribution that spreads the exciton equally among spatially separated chromophore fragments within the molecular system. As a result, digons become virtually unpolarized absorbers and emitters, in agreement with recent experimental studies on the single-molecule level.

An ab initio multiple cloning approach for the simulation of photoinduced dynamics in conjugated molecules.

We present a new implementation of the Ab Initio Multiple Cloning (AIMC) method, which is applied for non-adiabatic excited-state molecular dynamics simulations of photoinduced processes in conjugated molecules. Within our framework, the multidimensional wave-function is decomposed into a superposition of a number of Gaussian coherent states guided by Ehrenfest trajectories that are suited to clone and swap their electronic amplitudes throughout the simulation. New generalized cloning criteria are defined and tested. Because of sharp changes of the electronic states, which are common for conjugated polymers, the electronic parts of the Gaussian coherent states are represented in the Time Dependent Diabatic Basis (TDDB). The input to these simulations in terms of the excited-state energies, gradients and non-adiabatic couplings, is calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. As a test case, we consider the photoinduced unidirectional electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer between dendritic branches are discussed.

Phonon bottleneck and long-lived excited states in π-conjugated pyrene hoop.

In the last decade, recent synthetic advances have launched carbon-based π-conjugated hoops to the forefront of theoretical and experimental investigation not only for their potential use as bottom-up templates for carbon nanotube (CNT) growth, but also for the interesting excitonic effects arising from the cyclic geometry, unique π-system orientation, and unusual electronic interactions and couplings. In particular, cyclic materials based on pyrene, a common component in organic electronics, are popular candidates for the future design of π-conjugated nanorings for optoelectronic applications. Understanding the photophysical response in cyclic oligopyrenes can be achieved using non-adiabatic excited state molecular dynamics (NA-ESMD). Through NA-ESMD modeling, we reveal details of the nonradiative relaxation processes in the circular pyrene tetramer [4]cyclo-2,7-pyrenylene ([4]CPY) where we find that the strong non-adiabatic coupling combined with the dense manifold of excited states creates an internal conversion mechanism dominated by ultrafast sequential quantum transitions. However, we observe two long-lived electronic excited states that introduce a phonon bottleneck in the electronic relaxation process. In fact, the timescale for the electronic relaxation is almost exclusively dominated by the lifetimes of the long-lived states. We find that the states associated with the phonon bottleneck are separated from lower energy states by large energy gaps and are characterized by localization on a single pyrene unit resulting in a spatial mismatch with strongly delocalized neighboring states.

Interference of Interchromophoric Energy-Transfer Pathways in π-Conjugated Macrocycles.

The interchromophoric energy-transfer pathways between weakly coupled units in a π-conjugated phenylene-ethynylene macrocycle and its half-ring analogue have been investigated using the nonadiabatic excited-state molecular dynamics approach. To track the flow of electronic transition density between macrocycle units, we formulate a transition density flux analysis adapted from the statistical minimum flow method previously developed to investigate vibrational energy flow. Following photoexcitation, transition density is primarily delocalized on two chromophore units and the system undergoes ultrafast energy transfer, creating a localized excited state on a single unit. In the macrocycle, distinct chromophore units donate transition density to a single acceptor unit but do not interchange transition density among each other. We find that energy transfer in the macrocycle is slower than in the corresponding half ring because of the presence of multiple interfering energy-transfer pathways. Simulation results are validated by modeling the fluorescence anisotropy decay.

Non-adiabatic excited state molecular dynamics of phenylene ethynylene dendrimer using a multiconfigurational Ehrenfest approach.

Photoinduced dynamics of electronic and vibrational unidirectional energy transfer between meta-linked building blocks in a phenylene ethynylene dendrimer is simulated using a multiconfigurational Ehrenfest in time-dependent diabatic basis (MCE-TDDB) method, a new variant of the MCE approach developed by us for dynamics involving multiple electronic states with numerous abrupt crossings. Excited-state energies, gradients and non-adiabatic coupling terms needed for dynamics simulation are calculated on-the-fly using the Collective Electron Oscillator (CEO) approach. A comparative analysis of our results obtained using MCE-TDDB, the conventional Ehrenfest method and the surface-hopping approach with and without decoherence corrections is presented.

Photoexcited Energy Transfer in a Weakly Coupled Dimer.

Nonadiabatic excited-state molecular dynamics (NA-ESMD) simulations have been performed in order to study the time-dependent exciton localization during energy transfer between two chromophore units of the weakly coupled anthracene dimer dithia-anthracenophane (DTA). Simulations are done at both low temperature (10 K) and room temperature (300 K). The initial photoexcitation creates an exciton which is primarily localized on a single monomer unit. Subsequently, the exciton experiences an ultrafast energy transfer becoming localized on either one monomer unit or the other, whereas delocalization between both monomers never occurs. In half of the trajectories, the electronic transition density becomes completely localized on the same monomer as the initial excitation, while in the other half, it becomes completely localized on the opposite monomer. In this article, we present an analysis of the energy transfer dynamics and the effect of thermally induced geometry distortions on the exciton localization. Finally, simulated fluorescence anisotropy decay curves for both DTA and the monomer unit dimethyl anthracene (DMA) are compared. Our analysis reveals that changes in the transition density localization caused by energy transfer between two monomers in DTA is not the only source of depolarization and exciton relaxation within a single DTA monomer unit can also cause reorientation of the transition dipole.

Signature of nonadiabatic coupling in excited-state vibrational modes.

Using analytical excited-state gradients, vibrational normal modes have been calculated at the minimum of the electronic excited-state potential energy surfaces for a set of extended conjugated molecules with different coupling between them. Molecular model systems composed of units of polyphenylene ethynylene (PPE), polyphenylenevinylene (PPV), and naphthacene/pentacene (NP) have been considered. In all cases except the NP model, the influence of the nonadiabatic coupling on the excited-state equilibrium normal modes is revealed as a unique highest frequency adiabatic vibrational mode that overlaps with the coupling vector. This feature is removed by using a locally diabatic representation in which the effect of NA interaction is removed. Comparison of the original adiabatic modes with a set of vibrational modes computed in the locally diabatic representation demonstrates that the effect of nonadiabaticity is confined to only a few modes. This suggests that the nonadiabatic character of a molecular system may be detected spectroscopically by identifying these unique state-specific high frequency vibrational modes.

Analysis of state-specific vibrations coupled to the unidirectional energy transfer in conjugated dendrimers.

The nonadiabatic excited-state molecular dynamics (NA-ESMD) method and excited-state instantaneous normal modes (ES-INMs) analyses have been applied to describe the state-specific vibrations that participate in the unidirectional energy transfer between the coupled chromophores in a branched dendrimeric molecule. Our molecule is composed of two-, three-, and four-ring linear poly(phenyleneethynylene) (PPE) units linked through meta-substitutions. After an initial laser excitation, an ultrafast sequential S(3) → S(2) → S(1) electronic energy transfer from the shortest to longest segment takes place. During each S(n) → S(n-1) (n = 3, 2) transition, ES-INM(S(n)) and ES-INM(S(n-1)) analyses have been performed on S(n) and S(n-1) states, respectively. Our results reveal a unique vibrational mode localized on the S(n) state that significantly matches with the corresponding nonadiabatic coupling vector d(n,(n-1)). This mode also corresponds to the highest frequency ES-INM(S(n)) and it is seen mainly during the electronic transitions. Furthermore, its absence as a unique ES-INM(S(n-1)) reveals that state-specific vibrations play the main role in the efficiency of the unidirectional S(n) → S(n-1) electronic and vibrational energy funneling in light-harvesting dendrimers.

Identification of unavoided crossings in nonadiabatic photoexcited dynamics involving multiple electronic states in polyatomic conjugated molecules.

Radiationless transitions between electronic excited states in polyatomic molecules take place through unavoided crossings of the potential energy surfaces with substantial non-adiabatic coupling between the respective adiabatic states. While the extent in time of these couplings are large enough, these transitions can be reasonably well simulated through quantum transitions using trajectory surface hopping-like methods. In addition, complex molecular systems may have multiple "trivial" unavoided crossings between noninteracting states. In these cases, the non-adiabatic couplings are described as sharp peaks strongly localized in time. Therefore, their modeling is commonly subjected to the identification of regions close to the particular instantaneous nuclear configurations for which the energy surfaces actually cross each other. Here, we present a novel procedure to identify and treat these regions of unavoided crossings between non-interacting states using the so-called Min-Cost algorithm. The method differentiates between unavoided crossings between interacting states (simulated by quantum hops), and trivial unavoided crossings between non-interacting states (detected by tracking the states in time with Min-Cost procedure). We discuss its implementation within our recently developed non-adiabatic excited state molecular dynamics framework. Fragments of two- and four-ring linear polyphenylene ethynylene chromophore units at various separations have been used as a representative molecular system to test the algorithm. Our results enable us to distinguish and analyze the main features of these different types of radiationless transitions the molecular system undertakes during internal conversion.

Nonadiabatic molecular dynamics simulations of the energy transfer between building blocks in a phenylene ethynylene dendrimer.

The ultrafast dynamics of electronic and vibrational energy transfer between two- and three-ring linear poly(phenylene ethynylene) units linked by meta-substitution is studied by nonadiabatic molecular dynamics simulations. The molecular dynamics with quantum transitions (1, 2) method is used including an "on the fly" calculation of the potential energy surfaces and electronic couplings. The results show that during the first 40 fs after a vertical photoexcitation to the S(2) state, the nonadiabatic coupling between S(2) and S(1) states causes a fast transfer of the electronic populations. A rapid decrease of the S(1)-S(2) energy gap is observed, reaching a first conical intersection at approximately 5 fs. Therefore, the first hopping events take place, and the S(2) state starts to depopulate. The analysis of the structural and energetic properties of the molecule during the jumps reveals the main role that the ethynylene triple bond plays in the unidirectional energy transfer process.