Stabilization of Charge-Transfer Excited States in Biological Systems: A Computational Focus on the Special Pair in Photosystem II Reaction Centers.

Charge-transfer (CT) excited states play an important role in many biological processes. However, many computational approaches often inadequately address the equilibration effects of nuclear and environmental degrees of freedom on these states. One prominent example of systems in which CT states are of utmost importance is reaction centers (RC) in photosystems. Here we use a multiscale approach combined with time-dependent density functional theory to explore the lowest CT excited state of the special pair PD1-PD2 in the Photosystem II-RC of a cyanobacterium. We find that the nonequilibrium CT excited state resides near the Soret band, making an exciton the lowest-energy excited state. However, accounting for nuclear and state-specific dielectric equilibration along the CT potential energy surface (PES), the CT state PD1--PD2+ stabilizes energetically below the excitonic state. This underscores the crucial role of state-specific solvation in mapping the PES of CT states, as demonstrated in a simplified dimer model.

Twisting Aromaticity and Photoinduced Dynamics in Hexapole Helicenes.

Curved aromatic molecules are attractive electronic materials, where an additional internal strain uniquely modifies their structure, aromaticity, dynamics, and optical properties. Helicenes are examples of such twisted conjugated systems. Herein, we analyze the photoinduced dynamics in different stereoisomers of a hexapole helicene by using nonadiabatic excited-state molecular dynamics simulations. We explore how changes in symmetry and structural distortion modulate the intramolecular energy redistribution. We find that distinct helical assembly leads to different rigid distorted structures that in turn impact the nonradiative energy relaxation and ultimately formation of the self-trapped exciton. Subsequently, the value of the twisting angles relative to the central triphenylene core structure controls the global molecular aromaticity and electronic localization during the internal conversion process. Our work sheds light on how the future synthesis of novel curved aromatic compounds can be directed to attain specific desired electronic properties through the modulation of their twisted aromaticity.

X-ray and Optical Circular Dichroism as Local and Global Ultrafast Chiral Probes of [12]Helicene Racemization.

Chirality is a fundamental molecular property that plays a crucial role in biophysics and drug design. Optical circular dichroism (OCD) is a well-established chiral spectroscopic probe in the UV-visible regime. Chirality is most commonly associated with a localized chiral center. However, some compounds such as helicenes (Figure 1) are chiral due to their screwlike global structure. In these highly conjugated systems, some electric and magnetic allowed transitions are distributed across the entire molecule, and OCD thus probes the global molecular chirality. Recent advances in X-ray sources, in particular the control of their polarization and spatial profiles, have enabled X-ray circular dichroism (XCD), which, in contrast to OCD, can exploit the localized and element-specific nature of X-ray electronic transitions. XCD therefore is more sensitive to local structures, and the chirality probed with it can be referred to as local. During the racemization of helicene, between opposite helical structures, the screw handedness can flip locally, making the molecule globally achiral while retaining a local handedness. Here, we use the racemization mechanism of [12]helicene as a model to demonstrate the capabilities of OCD and XCD as time-dependent probes for global and local chiralities, respectively. Our simulations demonstrate that XCD provides an excellent spectroscopic probe for the time-dependent local chirality of molecules.

NEXMD v2.0 Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present NEXMD version 2.0, the second release of the NEXMD (Nonadiabatic EXcited-state Molecular Dynamics) software package. Across a variety of new features, NEXMD v2.0 incorporates new implementations of two hybrid quantum-classical dynamics methods, namely, Ehrenfest dynamics (EHR) and the Ab-Initio Multiple Cloning sampling technique for Multiconfigurational Ehrenfest quantum dynamics (MCE-AIMC or simply AIMC), which are alternative options to the previously implemented trajectory surface hopping (TSH) method. To illustrate these methodologies, we outline a direct comparison of these three hybrid quantum-classical dynamics methods as implemented in the same NEXMD framework, discussing their weaknesses and strengths, using the modeled photodynamics of a polyphenylene ethylene dendrimer building block as a representative example. We also describe the expanded normal-mode analysis and constraints for both the ground and excited states, newly implemented in the NEXMD v2.0 framework, which allow for a deeper analysis of the main vibrational motions involved in vibronic dynamics. Overall, NEXMD v2.0 expands the range of applications of NEXMD to a larger variety of multichromophore organic molecules and photophysical processes involving quantum coherences and persistent couplings between electronic excited states and nuclear velocity.

Impact of the core on the inter-branch exciton exchange in dendrimers.

Organic dendrimers with π conjugated systems are capable of capturing solar energy as a renewable source for human use. Nonetheless, further study regarding the relationship between the structure and the energy transfer mechanism in these types of molecules is still necessary. In this work, nonadiabatic excited state molecular dynamics (NEXMD) were carried out to study the intra- and inter-branch exciton migration in two tetra-branched dendrimers, C(dSSB)4 and Ad(BuSSB)4, which differ in their respective carbon and adamantane core. Both systems undergo a ladder decay mechanism between excited states, with back-and-forth transitions between S1 and S2. Despite presenting very similar absorption-emission spectra, differences in the photoinduced energy relaxation are observed. The size of the core impacts the inter-branch energy exchange and transient exciton localization/delocalization, which ultimately condition the relative energy relaxation rates, being faster in Ad(BuSSB)4 with respect to C(dSSB)4. Nevertheless, the photoinduced processes lead to a progressive final exciton-self-trapping in one of the branches of both dendrimers, which is a desirable feature in organic photovoltaic applications. Our results can inspire the design of more efficient dendrimers with the desired magnitude of inter-branch exciton exchange and localization/delocalization according to changes in their core.

Monitoring vibronic coherences and molecular aromaticity in photoexcited cyclooctatetraene with an X-ray probe: a simulation study.

Understanding conical intersection (CI) dynamics and subsequent conformational changes is key for exploring and controlling photo-reactions in aromatic molecules. Monitoring of their time-resolved dynamics remains a formidable experimental challenge. In this study, we simulate the photoinduced S3 to S1 non-adiabatic dynamics of cyclooctatetraene (COT), involving multiple CIs with relaxation times in good agreement with experiment. We further investigate the possibility to directly probe the CI passages in COT by off-resonant X-ray Raman spectroscopy (TRUECARS) and time-resolved X-ray diffraction (TRXD). We find that these signals sensitively monitor key chemical features during the ultrafast dynamics. First, we distinguish two CIs by using TRUECARS signals with their appearances at different Raman shifts. Second, we demonstrate that TRXD, where X-ray photons scatter off electron densities, can resolve ultrafast changes in the aromaticity of COT. It can further distinguish between planar and non-planar geometries explored during the dynamics, as e.g. two different tetraradical-type CIs. The knowledge gained from these measurements can give unique insight into fundamental chemical properties that dynamically change during non-adiabatic passages.

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.

Charge-Transfer Luminescence in a Molecular Donor-Acceptor Complex: Computational Insights.

Donor-acceptor molecular complexes are a popular class of materials utilizing charge-transfer states for practical applications. A recent class of donor-acceptor dyads based on the fluorescent BODIPY functionalized with triphenylamine (TPA) shows the peculiar property of dual fluorescence. It is hypothesized that instead of the sensitized charge-transfer state being optically dark, it provides an additional bright radiative pathway. Here we use time-dependent density functional theory to characterize the energetic alignment of excitonic and charge-transfer states in a BODIPY-TPA molecular complex. We observe that using a long-range exchange corrected functional in combination with state-specific solvation scheme gives a qualitatively correct alignment of the exciton and charge-transfer states and an enhancement in oscillator strength for the equilibrium solvated charge-transfer state, in agreement with experiment. This work provides rationalization of charge-transfer state emission and provides a foundation to explore charge-transfer using ab initio excited-state nonadiabatic dynamics.

Ultrafast coherent photoexcited dynamics in a trimeric dendrimer probed by X-ray stimulated-Raman signals.

The photoinduced ultrafast coherent inter-chromophore energy redistribution in a triarylamine trimer is explored using nonadiabatic excited state molecular dynamics followed by simulations of X-ray Raman signals. The nitrogencentered system ensures strong interchromophore interactions and, thus, the presence of coherences. Nevertheless, the multitude of non-deterministic photoinduced pathways during the ultrafast inter-branch migration of the excitation results in random confinement on some branches and, therefore, spatial exciton scrambling and loss of phase information at long times. We show that the vibronic coherence dynamics evolving into the incoherent scrambling mechanism on ultrafast 50 fs timescale, is accurately probed by the TRUECARS X-ray stimulated Raman signal. In combination with previous results, where the technique has revealed long-lived coherences in a rigid heterodimer, the signal is most valuable for detecting ultrafast molecular coherences or their absence. We demonstrate that X-ray Raman spectroscopy is a useful tool in the chemical design of functional molecular building blocks.

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.

Monitoring molecular vibronic coherences in a bichromophoric molecule by ultrafast X-ray spectroscopy.

The role of quantum-mechanical coherences in the elementary photophysics of functional optoelectronic molecular materials is currently under active study. Designing and controlling stable coherences arising from concerted vibronic dynamics in organic chromophores is the key for numerous applications. Here, we present fundamental insight into the energy transfer properties of a rigid synthetic heterodimer that has been experimentally engineered to study coherences. Quantum non-adiabatic excited state simulations are used to compute X-ray Raman signals, which are able to sensitively monitor the coherence evolution. Our results verify their vibronic nature, that survives multiple conical intersection passages for several hundred femtoseconds at room temperature. Despite the contributions of highly heterogeneous evolution pathways, the coherences are unambiguously visualized by the experimentally accessible X-ray signals. They offer direct information on the dynamics of electronic and structural degrees of freedom, paving the way for detailed coherence measurements in functional organic materials.

An Ab Initio Multiple Cloning Method for Non-Adiabatic Excited-State Molecular Dynamics in NWChem.

The recently developed ab initio multiple cloning (AIMC) approach based on the multiconfigurational Ehrenfest (MCE) method provides a powerful and accurate way of describing the excited-state dynamics of molecular systems. The AIMC method is a controlled approximation to nonadiabatic dynamics with a particular strength in the proper description of decoherence effects because of the branching of vibrational wavepackets at a level crossing. Here, we report a new implementation of the AIMC algorithm in the open source NWChem computational chemistry program. The framework combines linear-response time-dependent density functional theory with Ehrenfest mean-field theory to determine the equations of motion for classical trajectories. The multidimensional wave function is decomposed into a superposition of Gaussian coherent states guided by Ehrenfest trajectories (i.e., MCE approach), which can clone with fully quantum mechanical amplitudes and phases. By using an efficient time-derivative based nonadiabatic coupling approach within the AIMC method, all observables are calculated on-the-fly in the nonadiabatic molecular dynamics process. As a representative example, we apply our implementation to study the ultrafast photoinduced electronic and vibrational energy transfer in a pyridine molecule. The effects of the cloning procedure on electronic and vibrational coherence, relaxation and unidirectional energy transfer are discussed. This new AIMC implementation provides a high-level nonadiabatic molecular dynamics framework for simulating photoexcited dynamics in complex molecular systems and experimentally relevant ultrafast spectroscopic probes, such as nonlinear coherent optical and X-ray signals.

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.

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.

NEXMD Software Package for Nonadiabatic Excited State Molecular Dynamics Simulations.

We present a versatile new code released for open community use, the nonadiabatic excited state molecular dynamics (NEXMD) package. This software aims to simulate nonadiabatic excited state molecular dynamics using several semiempirical Hamiltonian models. To model such dynamics of a molecular system, the NEXMD uses the fewest-switches surface hopping algorithm, where the probability of transition from one state to another depends on the strength of the derivative nonadiabatic coupling. In addition, there are a number of algorithmic improvements such as empirical decoherence corrections and tracking trivial crossings of electronic states. While the primary intent behind the NEXMD was to simulate nonadiabatic molecular dynamics, the code can also perform geometry optimizations, adiabatic excited state dynamics, and single-point calculations all in vacuum or in a simulated solvent. In this report, first, we lay out the basic theoretical framework underlying the code. Then we present the code's structure and workflow. To demonstrate the functionality of NEXMD in detail, we analyze the photoexcited dynamics of a polyphenylene ethynylene dendrimer (PPE, C30H18) in vacuum and in a continuum solvent. Furthermore, the PPE molecule example serves to highlight the utility of the getexcited.py helper script to form a streamlined workflow. This script, provided with the package, can both set up NEXMD calculations and analyze the results, including, but not limited to, collecting populations, generating an average optical spectrum, and restarting unfinished calculations.

Exploring Conformational Space with Thermal Fluctuations Obtained by Normal-Mode Analysis.

Proteins in their native states can be represented as ensembles of conformers in dynamical equilibrium. Thermal fluctuations are responsible for transitions between these conformers. Normal-modes analysis (NMA) using elastic network models (ENMs) provides an efficient procedure to explore global dynamics of proteins commonly associated with conformational transitions. In the present work, we present an iterative approach to explore protein conformational spaces by introducing structural distortions according to their equilibrium dynamics at room temperature. The approach can be used either to perform unbiased explorations of conformational space or to explore guided pathways connecting two different conformations, e.g., apo and holo forms. In order to test its performance, four proteins with different magnitudes of structural distortions upon ligand binding have been tested. In all cases, the conformational selection model has been confirmed and the conformational space between apo and holo forms has been encompassed. Different strategies have been tested that impact on the efficiency either to achieve a desired conformational change or to achieve a balanced exploration of the protein conformational multiplicity.

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.