Nonadiabatic Excited-State Molecular Dynamics Modeling of Photoinduced Dynamics in Conjugated Molecules

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.

Surface hopping simulations on charge photogeneration in conjugated polymers

The mechanism of charge photogeneration in neat conjugated polymers has long been controversial and a unified explanation has not been achieved so far. In this paper, we use a surface hopping method to simulate the excited-state dynamics of a system composed of five π-stacked polymer chains. In this system, polaron pairs (PPs) with large electron-hole distance can be seen as free charges. The surface hopping method is based on the Pariser-Parr-Pople (PPP) Hamiltonian and the excited states of the system are calculated with configuration interaction singles (CIS) formalism. During the simulations, the yields of PPs and free charges are calculated using a statistical method. By comparison, it is found that impurity and excess energy have significant effects on the yields of PPs and free charges. Free charges are difficult to be generated in neat systems with small excess energy. Free charges come from direct dissociation of high-energy excitons.

Practical phase-space electronic Hamiltonians for ab initio dynamics

Modern electronic structure theory is built around the Born-Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ') and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, ĤPS(X,P). While classical Born-Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

A Local Diabatisation Method for Two-State Adiabatic Conical Intersections

A methodology to locally characterize conical intersections (CIs) between two adiabatic electronic states for which no nonadiabatic coupling (NAC) vectors are available is presented. Based on the Hessian and gradient at the CI, the branching space coordinates are identified. The potential energy surface around the CI in the branching space is expressed in the diabatic representation, from which the NAC vectors can be calculated in a wave-function-free, energy-based approach. To demonstrate the universality of the developed methodology, the minimum-energy CI (MECI) between the first (S1) and second (S2) singlet excited states of formamide is investigated at the state-averaged complete active space self-consistent field (SA-CASSCF) and extended multistate complete active space second-order perturbation theory (XMS-CASPT2) levels of theory. In addition, the asymmetrical MECI between the ground state (S0) and S1 of cyclopropanone is evaluated using SA-CASSCF, as well as (ME)CIs between the S1 and S2 states of benzene using SA-CASSCF and time-dependent density functional theory (TDDFT). Finally, a CI between the S1 and S2 excited states of thiophene was analyzed using TDDFT.

Excitation Energy Transfer between Higher Excited States of Photosynthetic Pigments: 2. Chlorophyll b is a B Band Excitation Trap

Chlorophylls (Chls) are known for fast, subpicosecond internal conversion (IC) from ultraviolet/blue absorbing ("B" or "Soret" states) to the energetically lower, red light-absorbing Q states. Consequently, excitation energy transfer (EET) in photosynthetic pigment-protein complexes involving the B states has so far not been considered. We present, for the first time, a theoretical framework for the existence of B-B EET in tightly coupled Chl aggregates such as photosynthetic pigment-protein complexes. We show that according to a Förster resonance energy transport (FRET) scheme, unmodulated B-B EET has an unexpectedly high range. Unsuppressed, it could pose an existential threat-the damage potential of blue light for photochemical reaction centers (RCs) is well-known. This insight reveals so-far undescribed roles for carotenoids (Crts, cf. previous article in this series) and Chl b (this article) of possibly vital importance. Our model system is the photosynthetic antenna pigment-protein complex (CP29). The focus of the study is on the role of Chl b for EET in the Q and B bands. Further, the initial excited pigment distribution in the B band is computed for relevant solar irradiation and wavelength-centered laser pulses. It is found that both accessory pigment classes compete efficiently with Chl a absorption in the B band, leaving only 40% of B band excitations for Chl a. B state population is preferentially relocated to Chl b after excitation of any Chls, due to a near-perfect match of Chl b B band absorption with Chl a B state emission spectra. This results in an efficient depletion of the Chl a population (0.66 per IC/EET step, as compared to 0.21 in a Chl a-only system). Since Chl b only occurs in the peripheral antenna complexes of plants and algae, and RCs contain only Chl a, this would automatically trap potentially dangerous B state population in the antennae, preventing forwarding to the RCs.

NWChem: Recent and Ongoing Developments

This paper summarizes developments in the NWChem computational chemistry suite since the last major release (NWChem 7.0.0). Specifically, we focus on functionality, along with input blocks, that is accessible in the current stable release (NWChem 7.2.0) and in the "master" development branch, interfaces to quantum computing simulators, interfaces to external libraries, the NWChem github repository, and containerization of NWChem executable images. Some ongoing developments that will be available in the near future are also discussed.

Surface hopping simulations on charge separation in an organic donor-acceptor system

Charge separation in organic solar cells is a long-lasting and heavily debated issue. Here, we use the surface hopping method based on the Pariser-Parr-Pople (PPP) Hamiltonian and configuration interaction singles (CIS) approximation to simulate the charge separation process in an organic donor-acceptor system. The system is composed of one donor polymer chain and four acceptor polymer chains, and they are all stacked face-to-face. We let the system to relax from a photoexcited state, and then we observed that the electron is transferred from the donor chain to different acceptor chains and the hole is left on the donor chain, forming polaron pairs with different electron-hole distances. By performing statistical analysis on a number of trajectories, we found that the electron and the hole are fully separated before the system relaxes to its lowest excited state. The yield of free charges shows a significant dependence on the donor-acceptor band offset which provides the driving force for charge separation, while showing negligible dependence on the photoexcitation energy. The external electric field has a remarkable effect on the yield of free charges.

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.

Exact non-adiabatic coupling vectors for the time-dependent density functional based tight-binding method

We report on non-adiabatic coupling vectors between electronic excited states for the time-dependent-density functional theory based tight-binding (TD-DFTB) method. The implementation includes orbital relaxation effects that have been previously neglected and covers also the case of range-separated exchange-correlation functionals. Benchmark calculations with respect to first principles TD-DFT highlight the large dependence of non-adiabatic couplings on the functional. Closer investigations of the topology around a conical intersection between excited states show that TD-DFTB delivers near-exact values of the Berry phase, which paves the way for consistent non-adiabatic molecular dynamics simulations for large systems.

From a one-mode to a multi-mode understanding of conical intersection mediated ultrafast organic photochemical reactions

This review discusses how ultrafast organic photochemical reactions are controlled by conical intersections, highlighting that decay to the ground-state at multiple points of the intersection space results in their multi-mode character.

Modeling Photolytic Decomposition of Energetically Functionalized Dodecanes

The photolytic stability of explosives and energetic functional groups is of importance for those who regularly handle or are exposed to explosives in typical environmental conditions. This study models the photolytic degradation of dodecane substituted with various energetic functional groups: azide, nitro, nitrate ester, and nitramine. For the studied molecules, it was found that excitons localize on the energetic functional group, no matter where they were initially formed, and thus, the predominant degradation pathway involves the degradation of the energetic functional group. The relative trends for both 4 and 8 eV excitation energies followed with what is expected from the relative stability of the energetic functional groups to thermal and sub-shock degradation. The one notable exception was the azide functional group; more work should be done to further understand the photolytic effects on the azide functional group.

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.

Adiabatic Excited-State Molecular Dynamics with an Explicit Solvent: NEXMD-SANDER Implementation

We present a method to link the Nonadiabatic EXcited-state Molecular Dynamics (NEXMD) package to the SANDER package supplied by AMBERTOOLS to provide excited-state adiabatic quantum mechanics/molecular mechanics (QM/MM) simulations. NEXMD is a computational package particularly developed to perform simulations of the photoexcitation and subsequent nonadiabatic electronic and vibrational energy relaxation in large multichromophoric conjugated molecules involving several coupled electronic excited states. The NEXMD-SANDER exchange has been optimized in order to achieve excited-state adiabatic dynamics simulations of large conjugated materials in a QM/MM environment, such as an explicit solvent. Dynamics of a substituted polyphenylene vinylene oligomer (PPV3-NO₂) in vacuum and different explicit solvents has been used as a test case by performing comparative analysis of changes in its optical spectrum, state-dependent conformational changes, and quantum bond orderings. The method has been tested and compared with respect to previous implicit solvent implementations. Also, the impact on the expansion of the QM region by including a variable number of solvent molecules has been analyzed. Altogether, these results encourage future implementations of NEXMD simulations using the same combination of methods.

Photochemical spin-state control of binding configuration for tailoring organic color center emission in carbon nanotubes

Incorporating fluorescent quantum defects in the sidewalls of semiconducting single-wall carbon nanotubes (SWCNTs) through chemical reaction is an emerging route to predictably modify nanotube electronic structures and develop advanced photonic functionality. Applications such as room-temperature single-photon emission and high-contrast bio-imaging have been advanced through aryl-functionalized SWCNTs, in which the binding configurations of the aryl group define the energies of the emitting states. However, the chemistry of binding with atomic precision at the single-bond level and tunable control over the binding configurations are yet to be achieved. Here, we explore recently reported photosynthetic protocol and find that it can control chemical binding configurations of quantum defects, which are often referred to as organic color centers, through the spin multiplicity of photoexcited intermediates. Specifically, photoexcited aromatics react with SWCNT sidewalls to undergo a singlet-state pathway in the presence of dissolved oxygen, leading to ortho binding configurations of the aryl group on the nanotube. In contrast, the oxygen-free photoreaction activates previously inaccessible para configurations through a triplet-state mechanism. These experimental results are corroborated by first principles simulations. Such spin-selective photochemistry diversifies SWCNT emission tunability by controlling the morphology of the emitting sites.

Chemical functionalization of the sidewalls of single-wall carbon nanotubes (SWCNTs) is an emerging route to introduce fluorescent quantum defects and tailor the emission properties. Here, authors demonstrate that spin-selective photochemistry diversifies SWCNT emission tunability by controlling the morphology of the emitting sites.

Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods

We benchmark a set of quantum-chemistry methods, including multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational-Ehrenfest dynamics, against exact quantum-many-body techniques by studying real-time dynamics in the Holstein model. This is a paradigmatic model in condensed matter theory incorporating a local coupling of electrons to Einstein phonons. For the two-site and three-site Holstein model, we discuss the exact and quantum-chemistry methods in terms of the Born-Huang formalism, covering different initial states, which either start on a single Born-Oppenheimer surface, or with the electron localized to a single site. For extended systems with up to 51 sites, we address both the physics of single Holstein polarons and the dynamics of charge-density waves at finite electron densities. For these extended systems, we compare the quantum-chemistry methods to exact dynamics obtained from time-dependent density matrix renormalization group calculations with local basis optimization (DMRG-LBO). We observe that the multitrajectory Ehrenfest method, in general, only captures the ultrashort time dynamics accurately. In contrast, the surface-hopping method with suitable corrections provides a much better description of the long-time behavior but struggles with the short-time description of coherences between different Born-Oppenheimer states. We show that the multiconfigurational Ehrenfest method yields a significant improvement over the multitrajectory Ehrenfest method and can be converged to the exact results in small systems with moderate computational efforts. We further observe that for extended systems, this convergence is slower with respect to the number of configurations. Our benchmark study demonstrates that DMRG-LBO is a useful tool for assessing the quality of the quantum-chemistry methods.

Incorporating Berry Force Effects into the Fewest Switches Surface-Hopping Algorithm: Intersystem Crossing and the Case of Electronic Degeneracy

We present a preliminary surface-hopping approach for modeling intersystem crossing (ISC) dynamics between four electronic states: one singlet and one (triply degenerate) triplet. In order to incorporate all Berry force effects, the algorithm requires that, when moving along an adiabatic surface associated with the triplet manifold, one must also keep track of a quasi-diabatic index (akin to a "m_s" quantum number) for each trajectory. For a simple model problem, we find that a great deal of new physics can be captured by our algorithm, setting the stage for larger, more realistic (or perhaps even ab initio) simulations in the future.

Electronic Structure Methods for the Description of Nonadiabatic Effects and Conical Intersections

Nonadiabatic effects are ubiquitous in photophysics and photochemistry, and therefore, many theoretical developments have been made to properly describe them. Conical intersections are central in nonadiabatic processes, as they promote efficient and ultrafast nonadiabatic transitions between electronic states. A proper theoretical description requires developments in electronic structure and specifically in methods that describe conical intersections between states and nonadiabatic coupling terms. This review focuses on the electronic structure aspects of nonadiabatic processes. We discuss the requirements of electronic structure methods to describe conical intersections and nonadiabatic couplings, how the most common excited state methods perform in describing these effects, and what the recent developments are in expanding the methodology and implementing nonadiabatic couplings.

Nonadiabatic Molecular Dynamics Study of the Relaxation Pathways of Photoexcited Cyclooctatetraene

In the current study, we present nonadiabatic (NAMD) and adiabatic molecular dynamics simulations of the transition-state dynamics of photoexcited cyclooctatetraene (COT). The equilibrium-state structure and absorption spectra are analyzed using the semiempirical Austin Model 1 potential. The NAMD simulations are obtained by a surface-hopping algorithm. We analyzed in detail an active excited to ground state relaxation pathway accompanied by an S₂/S₃(D_2d) → S₁(D_8h) → S₀(D_4h) → S₀(D_2d) double-bond shifting mechanism. The simulated excitation lifetime is in good agreement with experiment. The first excited singlet state S₁ plays a crucial role in the photochemistry. The obtained critical molecular conformations, energy barrier, and transition-state lifetime results will provide a basis for further investigations of the bond-order inversion and photoswitching process of COT.

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.

Three-state harmonic models for photoinduced charge transfer

A widely used strategy for simulating the charge transfer between donor and acceptor electronic states in an all-atom anharmonic condensed-phase system is based on invoking linear response theory to describe the system in terms of an effective spin-boson model Hamiltonian. Extending this strategy to photoinduced charge transfer processes requires also taking into consideration the ground electronic state in addition to the excited donor and acceptor electronic states. In this paper, we revisit the problem of describing such nonequilibrium processes in terms of an effective three-state harmonic model. We do so within the framework of nonequilibrium Fermi's golden rule (NE-FGR) in the context of photoinduced charge transfer in the carotenoid-porphyrin-C₆₀ (CPC₆₀) molecular triad dissolved in explicit tetrahydrofuran (THF). To this end, we consider different ways for obtaining a three-state harmonic model from the equilibrium autocorrelation functions of the donor-acceptor, donor-ground, and acceptor-ground energy gaps, as obtained from all-atom molecular dynamics simulations of the CPC₆₀/THF system. The quantum-mechanically exact time-dependent NE-FGR rate coefficients for two different charge transfer processes in two different triad conformations are then calculated using the effective three-state model Hamiltonians as well as a hierarchy of more approximate expressions that lead to the instantaneous Marcus theory limit. Our results show that the photoinduced charge transfer in CPC₆₀/THF can be described accurately by the effective harmonic three-state models and that nuclear quantum effects are small in this system.

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.

A general approach to study molecular fragmentation and energy redistribution after an ionizing event

We propose to combine quantum chemical calculations, statistical mechanical methods, and photoionization and particle collision experiments to unravel the redistribution of internal energy of the furan cation and its dissociation pathways. This approach successfully reproduces the relative intensity of the different fragments as a function of the internal energy of the system in photoelectron-photoion coincidence experiments and the different mass spectra obtained when ions ranging from Ar+ to Xe25+ or electrons are used in collision experiments. It provides deep insights into the redistribution of the internal energy in the ionized molecule and its influence on the dissociation pathways and resulting charged fragments. The present pilot study demonstrates the efficiency of a statistical exchange of excitation energy among various degrees of freedom of the molecule and proves that the proposed approach is mature to be extended to more complex systems.

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.

Photoexcitation dynamics in perylene diimide dimers

We utilize first-principles theory to investigate photo-induced excited-state dynamics of functionalized perylene diimide. This class of materials is highly suitable for solar energy conversion because of the strong optical absorbance, efficient energy transfer, and chemical tunability. We couple time-dependent density functional theory to a recently developed time-resolved non-adiabatic dynamics approach based on a semi-empirical description. By studying the monomer and dimer, we focus on the role stacking plays on the time-scales associated with excited-state non-radiative relaxation from a high excitonic state to the lowest energy exciton. We predict that the time-scale for energy conversion in the dimer is significantly faster than that in the monomer when equivalent excited states are accounted for. Additionally, for the dimer, the decay from the second to the nearly degenerate lowest energy excited-state involves two time-scales: a rapid decay on the order of ∼10 fs followed by a slower decay of ∼100 fs. Analysis of the spatial localization of the electronic transition density during the internal conversion process points out the existence of localized states on individual monomers, indicating that the strength of thermal fluctuations exceeds electronic couplings between the states such that the exciton hops between localized states throughout the simulation.

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.

Photoexcited energy relaxation and vibronic couplings in π-conjugated carbon nanorings

Conjugated carbon nanorings exhibit unique photophysical properties that, combined with their tunable sizes and conformations, make them suitable for a variety of practical applications. These properties are intimately associated to their strained, bent and sterically hindered cyclic structures. Herein we perform a comparative analysis of the photoinduced dynamics in carbon nanorings composed of nine phenyl units([9]CPP) and nine naphthyl units ([9]CN) respectively. The sterically demanding naphthyl units lead to large dihedral angles between neighboring units. Nevertheless, the ultrafast electronic and vibrational energy relaxation and redistribution is found to be similar for both systems. We observe that vibronic couplings, introduced by nonadiabatic energy transfer between electronic excited states, ensure the intramolecular vibrational energy redistribution through specific vibrational modes. The comparative impact of the internal conversion process on the exciton spatial localization and intra-ring migration indicates that naphthyl units in [9]CN achieve more efficient but less dynamical self-trapping compared to that of phenyl units in [9]CPP. That is, during the photoinduced process, the exciton in [9]CN is more static and localized than the exciton in [9]CPP. The internal conversion processes take place through a specific set of middle- to high-frequency normal modes, which directly influence the spatial exciton redistribution during the internal conversion, self-trapping and intra-ring migration.

Non-adiabatic Excited-State Molecular Dynamics: Theory and Applications for Modeling Photophysics in Extended Molecular Materials

Optically active molecular materials, such as organic conjugated polymers and biological systems, are characterized by strong coupling between electronic and vibrational degrees of freedom. Typically, simulations must go beyond the Born-Oppenheimer approximation to account for non-adiabatic coupling between excited states. Indeed, non-adiabatic dynamics is commonly associated with exciton dynamics and photophysics involving charge and energy transfer, as well as exciton dissociation and charge recombination. Understanding the photoinduced dynamics in such materials is vital to providing an accurate description of exciton formation, evolution, and decay. This interdisciplinary field has matured significantly over the past decades. Formulation of new theoretical frameworks, development of more efficient and accurate computational algorithms, and evolution of high-performance computer hardware has extended these simulations to very large molecular systems with hundreds of atoms, including numerous studies of organic semiconductors and biomolecules. In this Review, we will describe recent theoretical advances including treatment of electronic decoherence in surface-hopping methods, the role of solvent effects, trivial unavoided crossings, analysis of data based on transition densities, and efficient computational implementations of these numerical methods. We also emphasize newly developed semiclassical approaches, based on the Gaussian approximation, which retain phase and width information to account for significant decoherence and interference effects while maintaining the high efficiency of surface-hopping approaches. The above developments have been employed to successfully describe photophysics in a variety of molecular materials.

Vibrational energy redistribution during donor–acceptor electronic energy transfer: criteria to identify subsets of active normal modes

Photoinduced electronic energy transfer in conjugated donor–acceptor systems is naturally accompanied by intramolecular vibrational energy redistributions accepting an excess of electronic energy.

How to calculate charge mobility in molecular materials from surface hopping non-adiabatic molecular dynamics - beyond the hopping/band paradigm

Charge transport in high mobility organic semiconductors is in an intermediate regime between small polaron hopping and band transport limits. We have recently shown that surface hopping non-adiabatic molecular dynamics is a powerful method for prediction of charge transport mechanisms in organic materials and for near-quantitative prediction of charge mobilities at room temperature where the effects of nuclear zero-point motion and tunneling are still relatively small [S. Giannini et al., Nat. Commun., 2019, 10, 3843]. Here we assess and critically discuss the extensions to Tully's original method that have led to this success: (i) correction for missing electronic decoherence, (ii) detection of trivial crossings and (iii) removal of decoherence correction-induced spurious charge transfer. If any one of these corrections is not included, the charge mobility diverges with system size, each for different physical reasons. Yet if they are included, convergence with system size, detailed balance and good internal consistency are achieved.

Conical Intersections at the Nanoscale: Molecular Ideas for Materials

The ability to predict and describe nonradiative processes in molecules via the identification and characterization of conical intersections is one of the greatest recent successes of theoretical chemistry. Only recently, however, has this concept been extended to materials science, where nonradiative recombination limits the efficiencies of materials for various optoelectronic applications. In this review, we present recent advances in the theoretical study of conical intersections in semiconductor nanomaterials. After briefly introducing conical intersections, we argue that specific defects in materials can induce conical intersections between the ground and first excited electronic states, thus introducing pathways for nonradiative recombination. We present recent developments in theoretical methods, computational tools, and chemical intuition for the prediction of such defect-induced conical intersections. Through examples in various nanomaterials, we illustrate the significance of conical intersections for nanoscience. We also discuss challenges facing research in this area and opportunities for progress.

Multistate hybrid time-dependent density functional theory with surface hopping accurately captures ultrafast thymine photodeactivation

We report an efficient analytical implementation of first-order nonadiabatic derivative couplings between arbitrary Born–Oppenheimer states in the hybrid time-dependent density functional theory (TDDFT) framework using atom-centered basis functions.

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.

A Versatile Computational Strategy To Characterize the Free-Energy Landscape of Excited States in Oligofluorenes

The π-rich rings of conjugated polymers and molecular rotors shape their typical properties, allowing a variety of chemical and photoresponsive phenomena. Herein, we present a computational method in the framework of classical simulations to estimate the free-energy gap between ground and excited states of oligofluorenes, which is a class of molecular rotors widely used in optoelectronic devices, because of the inner torsional rotation triggered by light irradiation. We devised multiple sets of free-energy simulations in combination with free-energy perturbation theory to predict the free-energy gap between the ground state and the first excited state. The computed excitation energies show good agreement with experiments. The approach presented herein allows one to achieve comprehensive sampling of the conformational landscape and accurate estimates of the excited state free-energy landscapes at the same time.

Coherent exciton-vibrational dynamics and energy transfer in conjugated organics

Coherence, signifying concurrent electron-vibrational dynamics in complex natural and man-made systems, is currently a subject of intense study. Understanding this phenomenon is important when designing carrier transport in optoelectronic materials. Here, excited state dynamics simulations reveal a ubiquitous pattern in the evolution of photoexcitations for a broad range of molecular systems. Symmetries of the wavefunctions define a specific form of the non-adiabatic coupling that drives quantum transitions between excited states, leading to a collective asymmetric vibrational excitation coupled to the electronic system. This promotes periodic oscillatory evolution of the wavefunctions, preserving specific phase and amplitude relations across the ensemble of trajectories. The simple model proposed here explains the appearance of coherent exciton-vibrational dynamics due to non-adiabatic transitions, which is universal across multiple molecular systems. The observed relationships between electronic wavefunctions and the resulting functionalities allows us to understand, and potentially manipulate, excited state dynamics and energy transfer in molecular materials.

Detailed balance, internal consistency, and energy conservation in fragment orbital-based surface hopping

We have recently introduced an efficient semi-empirical non-adiabatic molecular dynamics method for the simulation of charge transfer/transport in molecules and molecular materials, denoted fragment orbital-based surface hopping (FOB-SH) [J. Spencer et al., J. Chem. Phys. 145, 064102 (2016)]. In this method, the charge carrier wavefunction is expanded in a set of charge localized, diabatic electronic states and propagated in the time-dependent potential due to classical nuclear motion. Here we derive and implement an exact expression for the non-adiabatic coupling vectors between the adiabatic electronic states in terms of nuclear gradients of the diabatic electronic states. With the non-adiabatic coupling vectors (NACVs) available, we investigate how different flavours of fewest switches surface hopping affect detailed balance, internal consistency, and total energy conservation for electron hole transfer in a molecular dimer with two electronic states. We find that FOB-SH satisfies detailed balance across a wide range of diabatic electronic coupling strengths provided that the velocities are adjusted along the direction of the NACV to satisfy total energy conservation upon a surface hop. This criterion produces the right fraction of energy-forbidden (frustrated) hops, which is essential for correct population of excited states, especially when diabatic couplings are on the order of the thermal energy or larger, as in organic semiconductors and DNA. Furthermore, we find that FOB-SH is internally consistent, that is, the electronic surface population matches the average quantum amplitudes, but only in the limit of small diabatic couplings. For large diabatic couplings, inconsistencies are observed as the decrease in excited state population due to frustrated hops is not matched by a corresponding decrease in quantum amplitudes. The derivation provided here for the NACV should be generally applicable to any electronic structure approach where the electronic Hamiltonian is constructed in a diabatic electronic state basis.