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

A diagrammatic approach for automatically deriving analytical gradients of tensor hyper-contracted electronic structure methods

We introduce a diagrammatic approach to facilitate the automatic derivation of analytical nuclear gradients for tensor hyper-contraction (THC) based electronic structure methods. The automatically derived gradients are guaranteed to have the same scaling in terms of both operation count and memory footprint as the underlying energy calculations, and the computation of a gradient is roughly three times as costly as the underlying energy. The new diagrammatic approach enables the first cubic scaling implementation of nuclear derivatives for THC tensors fitted in molecular orbital basis (MO-THC). Furthermore, application of this new approach to THC-MP2 analytical gradients leads to an implementation, which is at least four times faster than the previously reported, manually derived implementation. Finally, we apply the new approach to the 14 tensor contraction patterns appearing in the supporting subspace formulation of multireference perturbation theory, laying the foundation for developments of analytical nuclear gradients and nonadiabatic coupling vectors for multi-state CASPT2.

Correlated vibration-solvent effects on the non-Condon exciton spectroscopy

Excitation energy transfer is crucially involved in a variety of systems. During the process, the non-Condon vibronic coupling and the surrounding solvent interaction may synergetically play important roles. In this work, we study the correlated vibration-solvent influences on the non-Condon exciton spectroscopy. Statistical analysis is elaborated for the overall vibration-plus-solvent environmental effects. Analytic solutions are derived for the linear absorption of monomer systems. General simulations are accurately carried out via the dissipaton-equation-of-motion approach. The resulted spectra in either the linear absorption or strong field regime clearly demonstrate the coherence enhancement due to the synergetic vibration-solvent correlation.

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.

Ab initio nonadiabatic molecular dynamics of charge carriers in metal halide perovskites

Photoinduced nonequilibrium processes in nanoscale materials play key roles in photovoltaic and photocatalytic applications. This review summarizes recent theoretical investigations of excited state dynamics in metal halide perovskites (MHPs), carried out using a state-of-the-art methodology combining nonadiabatic molecular dynamics with real-time time-dependent density functional theory. The simulations allow one to study evolution of charge carriers at the ab initio level and in the time-domain, in direct connection with time-resolved spectroscopy experiments. Eliminating the need for the common approximations, such as harmonic phonons, a choice of the reaction coordinate, weak electron-phonon coupling, a particular kinetic mechanism, and perturbative calculation of rate constants, we model full-dimensional quantum dynamics of electrons coupled to semiclassical vibrations. We study realistic aspects of material composition and structure and their influence on various nonequilibrium processes, including nonradiative trapping and relaxation of charge carriers, hot carrier cooling and luminescence, Auger-type charge-charge scattering, multiple excitons generation and recombination, charge and energy transfer between donor and acceptor materials, and charge recombination inside individual materials and across donor/acceptor interfaces. These phenomena are illustrated with representative materials and interfaces. Focus is placed on response to external perturbations, formation of point defects and their passivation, mixed stoichiometries, dopants, grain boundaries, and interfaces of MHPs with charge transport layers, and quantum confinement. In addition to bulk materials, perovskite quantum dots and 2D perovskites with different layer and spacer cation structures, edge passivation, and dielectric screening are discussed. The atomistic insights into excited state dynamics under realistic conditions provide the fundamental understanding needed for design of advanced solar energy and optoelectronic devices.

Branching and phase corrected surface hopping: A benchmark of nonadiabatic dynamics in multilevel systems

Since the seminal work of Tully [J. Chem. Phys. 93, 1061 (1990)], two-level scattering models have been extensively adopted as the standard benchmark systems to assess the performance of different trajectory surface hopping methods for nonadiabatic dynamics simulations. Here, we extend the branching and phase corrections to multilevel systems and combine them with both the traditional fewest switches surface hopping (FSSH) and its variant global flux surface hopping (GFSH) algorithms. To get a comprehensive evaluation of the proposed methods, we construct a series of more challenging and diverse three-level and four-level scattering models and use exact quantum solutions as references. Encouragingly, both FSSH and GFSH with the branching and phase corrections produce excellent and nearly identical results in all investigated systems, indicating that the new surface hopping methods are robust to describe multilevel problems and the reliability is insensitive to the definition of self-consistent hopping probabilities in the adiabatic representation. Furthermore, the branching correction is found to be especially important when dealing with strongly repulsive potential energy surfaces, which are common in realistic systems, thus promising for general applications.

A reciprocal-space formulation of mixed quantum-classical dynamics

We derive a formulation of mixed quantum-classical dynamics for modeling electronic carriers interacting with phonons in reciprocal space. For dispersionless phonons, we start by expressing the real-space classical coordinates in terms of complex variables. Taking these variables as a Fourier series then yields the reciprocal-space coordinates. Evaluating the electron-phonon interaction term through Ehrenfest's theorem, we arrive at a reciprocal-space formalism that is equivalent to mean-field mixed quantum-classical dynamics in real space. This equivalence is numerically verified for the Holstein and Peierls models, for which we find the reciprocal-space Hellmann-Feynman forces to involve momentum-derivative contributions in addition to the position-derivative terms commonly seen in real space. To illustrate the advantage of the reciprocal-space formulation, we present a proof of concept for the inexpensive modeling of low-momentum carriers interacting with phonons using a truncated reciprocal-space basis, which is not possible within a real-space formulation.

Ultrafast Fluorescence Depolarization in Conjugated Polymers

We report on large-scale simulations of intrachain exciton dynamics in poly(para-phenylenevinylene). Our theoretical model describes Frenkel exciton coupling to both fast, quantized C-C bond vibrations and slow, classical torsional modes. We also incorporate system-bath interactions. The dynamics is simulated using the time evolution block decimation method, which avoids the failures of the Ehrenfest approximation to describe decoherence processes and nonadiabatic interstate conversion. System-bath interactions are modeled using quantum trajectories and Lindblad quantum jump operators. We find that following photoexcitation, the quantum mechanical entanglement of the exciton and C-C bond phonons causes exciton-site decoherence. Next, system-bath interactions cause the stochastic collapse of high-energy delocalized excitons into chromophores. Finally, torsional relaxation causes additional exciton-density localization. We relate these dynamical processes to the predicted fluorescence depolarization, extract the time scales corresponding to them, and thus interpret the observed sub-ps fluorescence depolarization.

Photoinduced Energy Transfer in Linear Guest-Host Chromophores: A Computational Study

Polymer-based guest-host systems represent a promising class of materials for efficient light-emitting diodes. The energy transfer from the polymer host to the guest is the key process in light generation. Therefore, microscopic descriptions of the different mechanisms involved in the energy transfer can contribute to enlighten the basis of the highly efficient light harvesting observed in this kind of materials. Herein, the nature of intramolecular energy transfer in a dye-end-capped conjugated polymer is explored by using atomistic nonadiabatic excited-state molecular dynamics. Linear perylene end-capped (PEC) polyindenofluorenes (PIF), consisting of n (n = 2, 4, and 6) repeat units, i.e., PEC-PIF_n oligomers, are considered as model systems. After photoexcitation at the oligomer absorption maximum, an initial exciton becomes self-trapped on one of the monomer units (donors). Thereafter, an efficient ultrafast through-space energy transfer from this unit to the perylene acceptor takes place. We observe that this energy transfer occurs equally well from any monomer unit on the chain. Effective specific vibronic couplings between each monomer and the acceptor are identified. These oligomer → end-cap energy transfer steps do not match with the rates predicted by Förster-type energy transfer. The through-space and through-bond mechanisms are two distinct channels of energy transfer. The former dominates the overall process, whereas the through-bond energy transfer between indenofluorene monomer units along the oligomer backbone only makes a minor contribution.

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.

Molecular excited states through a machine learning lens

Theoretical simulations of electronic excitations and associated processes in molecules are indispensable for fundamental research and technological innovations. However, such simulations are notoriously challenging to perform with quantum mechanical methods. Advances in machine learning open many new avenues for assisting molecular excited-state simulations. In this Review, we track such progress, assess the current state of the art and highlight the critical issues to solve in the future. We overview a broad range of machine learning applications in excited-state research, which include the prediction of molecular properties, improvements of quantum mechanical methods for the calculations of excited-state properties and the search for new materials. Machine learning approaches can help us understand hidden factors that influence photo-processes, leading to a better control of such processes and new rules for the design of materials for optoelectronic applications.

Bright Frenkel Excitons in Molecular Crystals: A Survey

We computed the optical properties of a large set of molecular crystals (∼2200 structures) composed of molecules whose lowest excited states are strongly coupled and generate wide excitonic bands. Such bands are classified in terms of their dimensionality (1-, 2-, and 3-dimensional), the position of the optically allowed state in relation with the excitonic density of states, and the presence of Davydov splitting. The survey confirms that one-dimensional aggregates are rare in molecular crystals highlighting the need to go beyond the simple low-dimensional models. Furthermore, this large set of data is used to search for technologically interesting and less common properties. For instance, we considered the largest excitonic bandwidth that is achievable within known molecular crystals and identified materials with strong super-radiant states. Finally, we explored the possibility that strong excitonic coupling can be used to generate emissive states in the near-infrared region in materials formed by molecules with bright visible absorption and we could identify the maximum allowable red shift in this material class. These insights with the associated searchable database provide practical guidelines for designing materials with interesting optical properties.

Velocity Adjustment in Surface Hopping: Ethylene as a Case Study of the Maximum Error Caused by Direction Choice

The most common surface hopping dynamics algorithms require velocity adjustment after hopping to ensure total-energy conservation. Based on the semiclassical analysis, this adjustment must be made parallel to the nonadiabatic coupling vector's direction. Nevertheless, this direction is not always known, and the common practice has been to adjust the velocity in either the linear momentum or velocity directions. This paper benchmarks surface hopping dynamics of photoexcited ethylene with velocity adjustment in several directions, including those of the nonadiabatic coupling vector, the momentum, and the energy gradient difference. It is shown that differences in time constants and structural evolution fall within the statistical uncertainty of the method considering up to 500 trajectories in each dynamics set, rendering the three approaches statistically equivalent. For larger ensembles beyond 1000 trajectories, significant differences between the results arise, limiting the validity of adjustment in alternative directions. Other possible adjustment directions (velocity, single-state gradients, angular momentum) are evaluated as well. Given the small size of ethylene, the results reported in this paper should be considered an upper limit for the error caused by the choice of the velocity-adjustment direction on surface hopping dynamics.

"Dividing and Conquering" and "Caching" in Molecular Modeling

Molecular modeling is widely utilized in subjects including but not limited to physics, chemistry, biology, materials science and engineering. Impressive progress has been made in development of theories, algorithms and software packages. To divide and conquer, and to cache intermediate results have been long standing principles in development of algorithms. Not surprisingly, most important methodological advancements in more than half century of molecular modeling are various implementations of these two fundamental principles. In the mainstream classical computational molecular science, tremendous efforts have been invested on two lines of algorithm development. The first is coarse graining, which is to represent multiple basic particles in higher resolution modeling as a single larger and softer particle in lower resolution counterpart, with resulting force fields of partial transferability at the expense of some information loss. The second is enhanced sampling, which realizes "dividing and conquering" and/or "caching" in configurational space with focus either on reaction coordinates and collective variables as in metadynamics and related algorithms, or on the transition matrix and state discretization as in Markov state models. For this line of algorithms, spatial resolution is maintained but results are not transferable. Deep learning has been utilized to realize more efficient and accurate ways of "dividing and conquering" and "caching" along these two lines of algorithmic research. We proposed and demonstrated the local free energy landscape approach, a new framework for classical computational molecular science. This framework is based on a third class of algorithm that facilitates molecular modeling through partially transferable in resolution "caching" of distributions for local clusters of molecular degrees of freedom. Differences, connections and potential interactions among these three algorithmic directions are discussed, with the hope to stimulate development of more elegant, efficient and reliable formulations and algorithms for "dividing and conquering" and "caching" in complex molecular systems.

Ultrafast Transfer and Transient Entrapment of Photoexcited Mg Electron in Mg@C_{60}

Electron relaxation is studied in endofullerene Mg@C_{60} after an initial localized photoexcitation in Mg by nonadiabatic molecular dynamics simulations. Two approaches to the electronic structure of the excited electronic states are used: (i) an independent particle approximation based on a density-functional theory description of molecular orbitals and (ii) a configuration-interaction description of the many-body effects. Both methods exhibit similar relaxation times, leading to an ultrafast decay and charge transfer from Mg to C_{60} within tens of femtoseconds. Method (i) further elicits a transient trap of the transferred electron that can delay the electron-hole recombination. Results shall motivate experiments to probe these ultrafast processes by two-photon transient absorption or photoelectron spectroscopy in gas phase, in solution, or as thin films.

Multi-replica biased sampling for photoswitchable π-conjugated polymers

In recent years, π-conjugated polymers are attracting considerable interest in view of their light-dependent torsional reorganization around the π-conjugated backbone, which determines peculiar light-emitting properties. Motivated by the interest in designing conjugated polymers with tunable photoswitchable pathways, we devised a computational framework to enhance the sampling of the torsional conformational space and, at the same time, estimate ground- to excited-state free-energy differences. This scheme is based on a combination of Hamiltonian Replica Exchange Method (REM), parallel bias metadynamics, and free-energy perturbation theory. In our scheme, each REM samples an intermediate unphysical state between the ground and the first two excited states, which are characterized by time-dependent density functional theory simulations at the B3LYP/6-31G^* level of theory. We applied the method to a 5-mer of 9,9-dioctylfluorene and found that upon irradiation, this system can undergo a dihedral inversion from -155° to 155°, crossing a barrier that decreases from 0.1 eV in the ground state (S₀) to 0.05 eV and 0.04 eV in the first (S₁) and second (S₂) excited states. Furthermore, S₁ and even more S₂ were predicted to stabilize coplanar dihedrals, with a local free-energy minimum located at ±44°. The presence of a free-energy barrier of 0.08 eV for the S₁ state and 0.12 eV for the S₂ state can trap this conformation in a basin far from the global free-energy minimum located at 155°. The simulation results were compared with the experimental emission spectrum, showing a quantitative agreement with the predictions provided by our framework.

Role of Triplet States in the Photodynamics of Aniline

The dynamics of excited heteroaromatic molecules is a key to understanding the photoprotective properties of many biologically relevant chromophores that dissipate their excitation energy nonreactively and thereby prevent the detrimental effects of ultraviolet radiation. Despite their structural variability, most substituted aromatic compounds share a common feature of a repulsive ¹πσ* potential energy surface. This surface can lead to photoproducts, and it can also facilitate the population transfer back to the ground electronic state by means of a ¹πσ*/S₀ conical intersection. Here, we explore a hidden relaxation route involving the triplet electronic state of aniline, which has recently been discovered by means of time-selected photofragment translational spectroscopy [J. Chem. Phys. 2019, 151, 141101]. By using the recently available analytical gradients for multiconfiguration pair-density functional theory, it is now possible to locate the minimum-energy crossing points between states of different spin and therefore compute the intersystem crossing rates with a multireference method, rather than with the less reliable single-reference methods. Using such calculations, we demonstrate that the population loss of aniline in the T₁(³ππ*) state is dominated by C₆H₅NH₂ → C₆H₅NH· + H· dissociation, and we explain the long nonradiative lifetimes of the T₁(³ππ*) state at the excitation wavelengths of 294-264 nm.

Multiscale Models for Light-Driven Processes

Multiscale models combining quantum mechanical and classical descriptions are a very popular strategy to simulate properties and processes of complex systems. Many alternative formulations have been developed, and they are now available in all of the most widely used quantum chemistry packages. Their application to the study of light-driven processes, however, is more recent, and some methodological and numerical problems have yet to be solved. This is especially the case for the polarizable formulation of these models, the recent advances in which we review here. Specifically, we identify and describe the most important specificities that the polarizable formulation introduces into both the simulation of excited-state dynamics and the modeling of excitation energy and electron transfer processes.

Multi-layer Gaussian-based multi-configuration time-dependent Hartree (ML-GMCTDH) simulations of ultrafast charge separation in a donor-acceptor complex

We report on first applications of the Multi-Layer Gaussian-based Multi-Configuration Time-Dependent Hartree (ML-GMCTDH) method [Römer et al., J. Chem. Phys. 138, 064106 (2013)] beyond its basic two-layer variant. The ML-GMCTDH scheme provides an embedding of a variationally evolving Gaussian wavepacket basis into a hierarchical tensor representation of the wavefunction. A first-principles parameterized model Hamiltonian for ultrafast non-adiabatic dynamics in an oligothiophene-fullerene charge transfer complex is employed, relying on a two-state linear vibronic coupling model that combines a distribution of tuning type modes with an intermolecular coordinate that also modulates the electronic coupling. Efficient ML-GMCTDH simulations are carried out for up to 300 vibrational modes using an implementation within the QUANTICS program. Excellent agreement with reference ML-MCTDH calculations is obtained.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

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.

Ab Initio Surface-Hopping Simulation of Femtosecond Transient-Absorption Pump-Probe Signals of Nonadiabatic Excited-State Dynamics Using the Doorway-Window Representation

An ab initio theoretical framework for the simulation of femtosecond time-resolved transient absorption (TA) pump-probe (PP) spectra with quasi-classical trajectories is presented. The simulations are based on the classical approximation to the doorway-window (DW) representation of third-order four-wave-mixing signals. The DW formula accounts for the finite duration and spectral shape of the pump and probe pulses. In the classical DW formalism, classical trajectories are stochastically sampled from a positive definite doorway distribution, and the signals are evaluated by averaging over a positive definite window distribution. Nonadiabatic excited-state dynamics is described by a stochastic surface-hopping algorithm. The method has been implemented for the pyrazine molecule with the second-order algebraic-diagrammatic construction (ADC(2)) ab initio electronic-structure method. The methodology is illustrated by ab initio simulations of the ground-state bleach, stimulated emission, and excited-state absorption contributions to the TA PP spectrum of gas-phase pyrazine.

Trajectory Surface Hopping Approach to Condensed-Phase Nonradiative Relaxation Dynamics Using Divide-and-Conquer Spin-Flip Time-Dependent Density-Functional Tight Binding

Nonradiative relaxation of excited molecules is central to many crucial issues in photochemistry. Condensed phases are typical contexts in which such problems are considered, and the nonradiative relaxation dynamics are expected to be significantly affected by interactions with the environment, for example, a solvent. We developed a nonadiabatic molecular dynamics simulation technique that can treat the nonradiative relaxation and explicitly include the environment in the calculations without a heavy computational burden. Specifically, we combined trajectory surface hopping with Tully's fewest-switches algorithm, a tight-binding approximated version of spin-flip time-dependent density-functional theory, and divide-and-conquer (DC) spatial fragmentation scheme. Numerical results showed that this method can treat systems with thousands of atoms within reasonable computational resources, and the error arising from DC fragmentation is negligibly small. Using this method, we obtained molecular insights into the solvent dependence of the photoexcited-state dynamics of trans-azobenzene, which demonstrate the importance of the environment for condensed-phase nonradiative relaxation.

Unraveling the internal conversion process within the Q-bands of a chlorophyll-like-system through surface-hopping molecular dynamics simulations

The non-radiative relaxation process within the Q-bands of chlorophylls represents a crucial preliminary step during the photosynthetic mechanism. Despite several experimental and theoretical efforts performed in order to clarify the complex dynamics characterizing this stage, a complete understanding of this mechanism is still far to be reached. In this study, non-adiabatic excited-state molecular dynamic simulations have been performed to model the non-radiative process within the Q-bands for a model system of chlorophylls. This system has been considered in the gas phase and then, to have a more representative picture of the environment, with implicit and mixed implicit-explicit solvation models. In the first part of this analysis, absorption spectra have been simulated for each model in order to guide the setup for the non-adiabatic excited-state molecular dynamic simulations. Then, non-adiabatic excited-state molecular dynamic simulations have been performed on a large set of independent trajectories and the population of the Q_x and Q_y states has been computed as the average of all the trajectories, estimating the rate constant for the process. Finally, with the aim of investigating the possible role played by the solvent in the Q_x-Q_y crossing mechanism, an essential dynamic analysis has been performed on the generated data, allowing one to find the most important motions during the simulated dynamics.

Quantum Dynamics of Exciton Transport and Dissociation in Multichromophoric Systems

Due to the subtle interplay of site-to-site electronic couplings, exciton delocalization, nonadiabatic effects, and vibronic couplings, quantum dynamical studies are needed to elucidate the details of ultrafast photoinduced energy and charge transfer events in organic multichromophoric systems. In this vein, we review an approach that combines first-principles parameterized lattice Hamiltonians with accurate quantum dynamical simulations using advanced multiconfigurational methods. Focusing on the elementary transfer steps in organic functional materials, we address coherent exciton migration and creation of charge transfer excitons in homopolymers, notably representative of the poly(3-hexylthiophene) material, as well as exciton dissociation at polymer:fullerene heterojunctions. We emphasize the role of coherent transfer, trapping effects due to high-frequency phonon modes, and thermal activation due to low-frequency soft modes that drive a diffusive dynamics.

Effect of varying the TD-lc-DFTB range-separation parameter on charge and energy transfer in a model pentacene/buckminsterfullerene heterojunction

Atomistic modeling of energy and charge transfer at the heterojunction of organic solar cells is an active field with many remaining outstanding questions owing, in part, to the difficulties in performing reliable photodynamics calculations on very large systems. One approach to being able to overcome these difficulties is to design and apply an appropriate simplified method. Density-functional tight binding (DFTB) has become a popular form of approximate density-functional theory based on a minimal valence basis set and neglect of all but two center integrals. We report the results of our tests of a recent long-range correction (lc) [A. Humeniuk and R. Mitrić, J. Chem. Phys. 143, 134120 (2015)] for time-dependent (TD) lc-DFTB by carrying out TD-lc-DFTB fewest switches surface hopping calculations of energy and charge transfer times using the relatively new DFTBABY [A. Humeniuk and R. Mitrić, Comput. Phys. Commun. 221, 174 (2017)] program. An advantage of this method is the ability to run enough trajectories to get meaningful ensemble averages. Our interest in the present work is less in determining exact energy and charge transfer rates than in understanding how the results of these calculations vary with the value of the range-separation parameter (R_lc = 1/μ) for a model organic solar cell heterojunction consisting of a gas-phase van der Waals complex P/F made up of a single pentacene (P) molecule together with a single buckminsterfullerene (F) molecule. The default value of R_lc = 3.03 a₀ is found to be much too small as neither energy nor charge transfer is observed until R_lc ≈ 10 a₀. Tests at a single geometry show that the best agreement with high-quality ab initio spectra is obtained in the limit of no lc (i.e., very large R_lc). A plot of energy and charge transfer rates as a function of R_lc is provided, which suggests that a value of R_lc ≈ 15 a₀ yields the typical literature (condensed-phase) charge transfer time of about 100 fs. However, energy and charge transfer times become as high as ∼300 fs for R_lc ≈ 25 a₀. A closer examination of the charge transfer process P^*/F → P⁺/F^- shows that the initial electron transfer is accompanied by a partial delocalization of the P hole onto F, which then relocalizes back onto P, consistent with a polaron-like picture in which the nuclei relax to stabilize the resultant redistribution of charges.

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.

Ultrafast processes: coordination chemistry and quantum theory

Coordination compounds, characterized by fascinating and tunable electronic properties, are capable of binding easily to proteins, polymers, wires and DNA. Upon irradiation, these molecular systems develop functions finding applications in solar cells, photocatalysis, luminescent and conformational probes, electron transfer triggers and diagnostic or therapeutic tools. The control of these functions is activated by the light wavelength, the metal/ligand cooperation and the environment within the first picoseconds (ps). After a brief summary of the theoretical background, this perspective reviews case studies, from 1st row to 3rd row transition metal complexes, that illustrate how spin-orbit, vibronic coupling and quantum effects drive the photophysics of this class of molecules at the early stage of the photoinduced elementary processes within the fs-ps time scale range.

Intermolecular conical intersections in molecular aggregates

Conical intersections (CoIns) of multidimensional potential energy surfaces are ubiquitous in nature and control pathways and yields of many photo-initiated intramolecular processes. Such topologies can be potentially involved in the energy transport in aggregated molecules or polymers but are yet to be uncovered. Here, using ultrafast two-dimensional electronic spectroscopy (2DES), we reveal the existence of intermolecular CoIns in molecular aggregates relevant for photovoltaics. Ultrafast, sub-10-fs 2DES tracks the coherent motion of a vibrational wave packet on an optically bright state and its abrupt transition into a dark state via a CoIn after only 40 fs. Non-adiabatic dynamics simulations identify an intermolecular CoIn as the source of these unusual dynamics. Our results indicate that intermolecular CoIns may effectively steer energy pathways in functional nanostructures for optoelectronics.

Nonadiabatic Molecular Quantum Dynamics with Quantum Computers

The theoretical investigation of nonadiabatic processes is hampered by the complexity of the coupled electron-nuclear dynamics beyond the Born-Oppenheimer approximation. Classically, the simulation of such reactions is limited by the unfavorable scaling of the computational resources as a function of the system size. While quantum computing exhibits proven quantum advantage for the simulation of real-time dynamics, the study of quantum algorithms for the description of nonadiabatic phenomena is still unexplored. In this Letter, we propose a quantum algorithm for the simulation of fast nonadiabatic chemical processes together with an initialization scheme for quantum hardware calculations. In particular, we introduce a first-quantization method for the time evolution of a wave packet on two coupled harmonic potential energy surfaces (Marcus model). In our approach, the computational resources scale polynomially in the system dimensions, opening up new avenues for the study of photophysical processes that are classically intractable.

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.

Photoinduced Dynamics with Constrained Vibrational Motion: FrozeNM Algorithm

Ab initio molecular dynamics (AIMD) simulation, analyzed in terms of vibrational normal modes, is a widely used technique that facilitates understanding of complex structural motions and coupling between electronic and nuclear degrees of freedom. Usually, only a subset of vibrations is directly involved in the process of interest. The impact of these vibrations can be evaluated by performing AIMD simulations by selectively freezing certain motions. Herein, we present frozen normal mode (FrozeNM), a new algorithm to apply normal-mode constraints in AIMD simulations, as implemented in the nonadiabatic excited state molecular dynamics code. We further illustrate its capacity by analyzing the impact of normal-mode constraints on the photoinduced energy transfer between polyphenylene ethynylene dendrimer building blocks. Our results show that the electronic relaxation can be significantly slowed down by freezing a well-selected small subset of active normal modes characterized by their contributions in the direction of energy transfer. The application of these constraints reduces the nonadiabatic coupling between electronic excited states during the entire dynamical simulations. Furthermore, we validate reduced dimensionality models by freezing all the vibrations, except a few active modes. Altogether, we consider FrozeNM as a useful tool that can be broadly used to underpin the role of vibrational motion in a studied process and to formulate reduced models that describe essential physical phenomena.

Two-oscillator mapping modification of the Poisson bracket mapping equation formulation of the quantum-classical Liouville equation

Mapping basis solutions provide efficient ways for simulating mixed quantum-classical (MQC) dynamics in complex systems by matching multiple quantum states of interest to some fictitious physical states. Recently, various MQC methods were devised such that two harmonic oscillators are employed to represent each electronic state, showing improvements over one-oscillator-based methods. Here, we introduce and analyze newly modified mapping approximations of the quantum-classical Liouville equation (QCLE) using two oscillators for each electronic state. We design two separate mapping relations that we can adopt toward simulating dynamics and computing expectation values. Through the process, two MQC methods can be constructed, one of which actually reproduces the population dynamics of the forward and backward trajectory solution of QCLE. By applying the methods to spin-boson systems with a range of parameters, we find out that the choice of mapping relations greatly affects the simulation results. We also show that further improvement is possible through using modified identity operator formulations. Our findings may be helpful in constructing improved MQC methods in the future.

Vibrationally Hot and Cold Triplets. Sensitizer-Dependent Dynamics and Localized Vibrational Promotion of a Di-π-methane Rearrangement

Large intramolecular 13C kinetic isotope effects (KIEs) for the di-π-methane rearrangement of benzobarrelene fit with statistical expectations from heavy-atom tunneling when a low-energy sensitizer is employed, but much lower KIEs are observed with higher-energy sensitizers. These results in combination with trajectory studies suggest that the excess vibrational energy available from triplet energy transfer leads to hot and nonstatistical dynamics in the rearrangement.

Fast Nonadiabatic Molecular Dynamics via Spin-Flip Time-Dependent Density-Functional Tight-Binding Approach: Application to Nonradiative Relaxation of Tetraphenylethylene with Locked Aromatic Rings

Nonadiabatic dynamics around conical intersections between ground and excited states are crucial to understand excited-state phenomena in complex chemical systems. With this background in mind, we present an approach combining fewest-switches trajectory surface hopping and spin-flip (SF) time-dependent (TD) density-functional tight binding (DFTB), which is a simplified version of SF-TD density functional theory (DFT) with semiempirical parametrizations, for computationally efficient nonadiabatic molecular dynamics simulations. The estimated computational time of the SF-TD-DFTB approach is several orders of magnitude lower than that of SF-TD-DFT. In addition, the proposed method reproduces the time scales and quantum yields in photoisomerization reactions of azobenzene at a level comparable with conventional ab initio approaches, demonstrating reasonable accuracy. Finally, we report a practical application of the developed technique to explore the nonradiative relaxation processes of tetraphenylethylene and its derivative with torsionally locked aromatic rings and discuss the effect of locking the rings on the excited-state lifetime.

Quantum dynamical simulations of intra-chain exciton diffusion in an oligo (para-phenylene vinylene) chain at finite temperature

We report on quantum dynamical simulations of exciton diffusion in an oligo(para-phenylene vinylene) chain segment with 20 repeat units (OPV-20) at finite temperature, complementary to our recent study of the same system at T = 0 K [R. Binder and I. Burghardt, J. Chem. Phys. 152, 204120 (2020)]. Accurate quantum dynamical simulations are performed using the multi-layer multi-configuration time-dependent Hartree method as applied to a site-based Hamiltonian comprising 20 electronic states of Frenkel type and 460 vibrational modes, including site-local quinoid-distortion modes along with site-correlated bond-length alternation (BLA) modes, ring torsional modes, and an explicit harmonic-oscillator bath. A first-principles parameterized Frenkel-Holstein type Hamiltonian is employed, which accounts for correlations between the ring torsional modes and the anharmonically coupled BLA coordinates located at the same junction. Thermally induced fluctuations of the torsional modes are described by a stochastic mean-field approach, and their impact on the excitonic motion is characterized in terms of the exciton mean-squared displacement. A normal diffusion regime is observed under periodic boundary conditions, apart from transient localization features. Even though the polaronic exciton species are comparatively weakly bound, exciton diffusion is found to be a coherent-rather than hopping type-process, driven by the fluctuations of the soft torsional modes. Similar to the previous observations for oligothiophenes, the evolution for the most part exhibits a near-adiabatic dynamics of local exciton ground states (LEGSs) that adjust to the local conformational dynamics. However, a second mechanism, involving resonant transitions between neighboring LEGSs, gains importance at higher temperatures.

Predicting in silico electron ionization mass spectra using quantum chemistry

Compound identification by mass spectrometry needs reference mass spectra. While there are over 102 million compounds in PubChem, less than 300,000 curated electron ionization (EI) mass spectra are available from NIST or MoNA mass spectral databases. Here, we test quantum chemistry methods (QCEIMS) to generate in silico EI mass spectra (MS) by combining molecular dynamics (MD) with statistical methods. To test the accuracy of predictions, in silico mass spectra of 451 small molecules were generated and compared to experimental spectra from the NIST 17 mass spectral library. The compounds covered 43 chemical classes, ranging up to 358 Da. Organic oxygen compounds had a lower matching accuracy, while computation time exponentially increased with molecular size. The parameter space was probed to increase prediction accuracy including initial temperatures, the number of MD trajectories and impact excess energy (IEE). Conformational flexibility was not correlated to the accuracy of predictions. Overall, QCEIMS can predict 70 eV electron ionization spectra of chemicals from first principles. Improved methods to calculate potential energy surfaces (PES) are still needed before QCEIMS mass spectra of novel molecules can be generated at large scale.

Branching Corrected Mean Field Method for Nonadiabatic Dynamics

When nonadiabatic dynamics are described on the basis of trajectories, severe trajectory branching occurs when the nuclear wave packets on some potential energy surfaces are reflected while those on the remaining surfaces are not. As a result, the traditional Ehrenfest mean field (EMF) approximation breaks down. In this study, two versions of the branching corrected mean field (BCMF) method are proposed. Namely, when trajectory branching is identified, BCMF stochastically selects either the reflected or the nonreflected group to build the new mean field trajectory or splits the mean field trajectory into two new trajectories with the corresponding weights. As benchmarked in six standard model systems and an extensive model base with two hundred diverse scattering models, BCMF significantly improves the accuracy while retaining the high efficiency of the traditional EMF. In fact, BCMF closely reproduces the exact quantum dynamics in all investigated systems, thus highlighting the essential role of branching correction in nonadiabatic dynamics simulations of general systems.

Analysis of Photosynthetic Systems and Their Applications with Mathematical and Computational Models

In biological and life science applications, photosynthesis is an important process that involves the absorption and transformation of sunlight into chemical energy. During the photosynthesis process, the light photons are captured by the green chlorophyll pigments in their photosynthetic antennae and further funneled to the reaction center. One of the most important light harvesting complexes that are highly important in the study of photosynthesis is the membrane-attached Fenna–Matthews–Olson (FMO) complex found in the green sulfur bacteria. In this review, we discuss the mathematical formulations and computational modeling of some of the light harvesting complexes including FMO. The most recent research developments in the photosynthetic light harvesting complexes are thoroughly discussed. The theoretical background related to the spectral density, quantum coherence and density functional theory has been elaborated. Furthermore, details about the transfer and excitation of energy in different sites of the FMO complex along with other vital photosynthetic light harvesting complexes have also been provided. Finally, we conclude this review by providing the current and potential applications in environmental science, energy, health and medicine, where such mathematical and computational studies of the photosynthesis and the light harvesting complexes can be readily integrated.

Modeling nonlocal electron-phonon coupling in organic crystals using interpolative maps: The spectroscopy of crystalline pentacene and 7,8,15,16-tetraazaterrylene

Electron-phonon coupling plays a central role in the transport properties and photophysics of organic crystals. Successful models describing charge- and energy-transport in these systems routinely include these effects. Most models for describing photophysics, on the other hand, only incorporate local electron-phonon coupling to intramolecular vibrational modes, while nonlocal electron-phonon coupling is neglected. One might expect nonlocal coupling to have an important effect on the photophysics of organic crystals because it gives rise to large fluctuation in the charge-transfer couplings, and charge-transfer couplings play an important role in the spectroscopy of many organic crystals. Here, we study the effects of nonlocal coupling on the absorption spectrum of crystalline pentacene and 7,8,15,16-tetraazaterrylene. To this end, we develop a new mixed quantum-classical approach for including nonlocal coupling into spectroscopic and transport models for organic crystals. Importantly, our approach does not assume that the nonlocal coupling is linear, in contrast to most modern charge-transport models. We find that the nonlocal coupling broadens the absorption spectrum non-uniformly across the absorption line shape. In pentacene, for example, our model predicts that the lower Davydov component broadens considerably more than the upper Davydov component, explaining the origin of this experimental observation for the first time. By studying a simple dimer model, we are able to attribute this selective broadening to correlations between the fluctuations of the charge-transfer couplings. Overall, our method incorporates nonlocal electron-phonon coupling into spectroscopic and transport models with computational efficiency, generalizability to a wide range of organic crystals, and without any assumption of linearity.

Elucidating the Magnitude of Internal Reorganization Energy of Molecular Excited States from the Perspective of Transition Density

Quantifying vibronic couplings in molecular excited states is crucial for the elucidation of a broad range of photophysical phenomena. In this study, we compare different theoretical approaches for the calculation of reorganization energy, a measure of vibronic coupling strength, and provide a rigorous derivation to show that molecular transition density characterizing electron-hole excitation could be used to quantify the magnitude of reorganization energy. The theory enables a descriptor based on molecular-orbital coefficients and atomic transition densities to quantify the magnitude of reorganization energies in molecular excited states. Applying the approach to low-lying excited states of polyacenes, we demonstrate that transition density distribution explains the difference in the magnitude of the reorganization energy of different excited states. Furthermore, to clarify the applicability of the transition density descriptor in molecular design for small-reorganization energy molecules, we investigate a broad range of molecular chromophores to show the effectiveness of the proposed theory. With this perspective on the relationship between reorganization energy and transition density, we successfully provide a quantitative rule to identify π-conjugated systems with small reorganization energy in the excited state, which should be useful for the development of novel optoelectronic materials.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

Nonadiabatic dynamics in multidimensional complex potential energy surfaces

Despite the continuous development of theoretical methodologies for describing nonadiabatic dynamics of molecular systems, there is a lack of approaches for processes where the norm of the wave function is not conserved, i.e., when an imaginary potential accounts for some irreversible decaying mechanism. Current approaches rely on building potential energy surfaces of reduced dimensionality, which is not optimal for more involving and realistic multidimensional problems. Here, we present a novel methodology for describing the dynamics of complex-valued molecular Hamiltonians, which is a generalisation of the trajectory surface hopping method. As a first application, the complex surface fewest switches surface hopping (CS-FSSH) method was employed to survey the relaxation mechanisms of the shape resonant anions of iodoethene. We have provided the first detailed and dynamical picture of the π*/σ* mechanism of dissociative electron attachment in halogenated unsaturated compounds, which is believed to underlie electron-induced reactions of several molecules of interest. Electron capture into the π* orbital promotes C Created by potrace 1.16, written by Peter Selinger 2001-2019 ]]> C stretching and out-of-plane vibrations, followed by charge transfer from the double bond into the σ* orbital at the C–I bond, and, finally, release of the iodine ion, all within only 15 fs. On-the-fly dynamics simulations of a vast class of processes can be envisioned with the CS-FSSH methodology, including autoionisation from transient anions, core-ionised and superexcited states, Auger and interatomic coulombic decay, and time-dependent luminescence.

Despite the continuous development of methods for describing nonadiabatic dynamics, there is a lack of multidimensional approaches for processes where the wave function norm is not conserved. A new surface hopping variant closes this knowledge gap.