Excited-state Molecular Dynamics Simulations Research Articles

Nonadiabatic Molecular Dynamics with Fermionic Subspace-Expansion Algorithms on Quantum Computers.

We introduce a novel computational framework for excited-state molecular quantum dynamics simulations driven by quantum-computing-based electronic-structure calculations. This framework leverages the fewest-switches surface-hopping method for simulating the nuclear dynamics and calculates the required excited-state transition properties with different flavors of the quantum subspace expansion and quantum equation-of-motion algorithms. We apply our method to simulate the collision reaction between a hydrogen atom and a hydrogen molecule. For this system, we critically compare the accuracy and efficiency of different quantum subspace expansion and equation-of-motion algorithms and show that only methods that can capture both weak and strong electron correlation effects can properly describe the nonadiabatic effects that tune the reactive event.

A detailed theoretical investigation on intramolecular charge transfer mechanism of primary, secondary, and tertiary p-amino substituted benzaldehyde

This article reports a detailed theoretical investigation on dual fluorescence properties of p-amino substituted benzaldehyde molecules by taking specifically p-N,N-dimethylaminobenzaldehyde (3° PABA), p-N-methylaminobenzaldehyde (2° PABA), and p-aminobenzaldehyde (1° PABA) molecules. The calculations are performed in gas phase as well as in butanol (BuOH) and dichloromethane (DCM) solvents. Twisted intramolecular charge transfer emission property is particularly looked at by scanning the potential energy curves as a function of -NR2 (R = H/CH3) rotation (twisting) angle. The results suggest that there are dual emission possibilities for 3° and 2° PABA molecules. Experimental validation is available for the former but not for the latter. 1° PABA, on the other hand, does not show any possibility of dual fluorescence except in BuOH. The theoretical absorption and emission spectra are also calculated and compared with experiment where it is available, and they are in close correlation. Excited state molecular dynamics simulations show that for 3° PABA, the molecule reaches to the 90° twisting angle and stays there with a probability higher than the same probability for 2° PABA. 1° PABA, on the other hand, had showed variations in the twisting angle from 0° to above 100°, but no evidence of this molecule to have considerable lifetime at 90° twisting angle.

SpaiNN: equivariant message passing for excited-state nonadiabatic molecular dynamics.

Excited-state molecular dynamics simulations are crucial for understanding processes like photosynthesis, vision, and radiation damage. However, the computational complexity of quantum chemical calculations restricts their scope. Machine learning offers a solution by delivering high-accuracy properties at lower computational costs. We present SpaiNN, an open-source Python software for ML-driven surface hopping nonadiabatic molecular dynamics simulations. SpaiNN combines the invariant and equivariant neural network architectures of SchNetPack with SHARC for surface hopping dynamics. Its modular design allows users to implement and adapt modules easily. We compare rotationally-invariant and equivariant representations in fitting potential energy surfaces of multiple electronic states and properties arising from the interaction of two electronic states. Simulations of the methyleneimmonium cation and various alkenes demonstrate the superior performance of equivariant SpaiNN models, improving accuracy, generalization, and efficiency in both training and inference.

Simulating Non-Adiabatic Dynamics of Photoexcited Phenyl Azide: Investigating Electronic and Structural Relaxation en Route to the Formation of Phenyl Nitrene.

Excited state molecular dynamics simulations of the photoexcited phenyl azide have been performed. The semi-classical surface hopping approximation has enabled an unconstrained analysis of the electronic and nuclear degrees of freedom which contribute to the molecular dissociation of phenyl azide into phenyl nitrene and molecular nitrogen. The significance of the second singlet excited state in leading the photodissociation has been established through electronic structure calculations, based on multi-configurational schemes, and state population dynamics. The investigations on the structural dynamics have revealed the N-N bond separation to be accompanied by synchronous changes in the azide N-N-N bond angle. The 100 fs simulation results in a nitrene fragment that is electronically excited in the singlet manifold.

Excited-State Dynamics Simulations of a Light-Driven Molecular Motor in Solution.

Molecular motors, where light can be transformed into motion, are promising in the design of nanomechanical devices. For applications, however, finding relationships between molecular motion and the environment is important. Here, we report the study of excited-state dynamics of an overcrowded alkene in solution using a hybrid quantum mechanics/molecular mechanics (QM/MM) approach combined with excited-state molecular dynamics simulations. Using QM/MM surface-hopping trajectories, we calculated time-resolved emission and transient absorption spectra. These show the rise of a short-lived Franck-Condon state, followed by the formation of a dark state in the first 150 fs before the molecular motor relaxes to the ground state in about 1 ps. From the analysis of radial distribution functions, we infer that the orientation of the solvent with respect to the molecular motor in the electronic excited state is similar to that in the ground state during the photoisomerization.

Vibrational Funnels for Energy Transfer in Organic Chromophores

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

The impact of the chalcogen-substitution element and initial spectroscopic state on excited-state relaxation pathways in nucleobase photosensitizers: a combination of static and dynamic studies.

The substitution of oxygen with chalcogen in carbonyl group(s) of canonical nucleobases gives an impressive triplet generation, enabling their promising applications in medicine and other emerging techniques. The excited-state relaxation S2(ππ*) → S1(nπ*) → T1(ππ*) has been considered the preferred path for triplet generation in these nucleobase derivatives. Here, we demonstrate enhanced quantum efficiency of direct intersystem crossing from S2 to triplet manifold upon substitution with heavier chalcogen elements. The excited-state relaxation dynamics of sulfur/selenium substituted guanines in a vacuum is investigated using a combination of static quantum chemical calculations and on-the-fly excited-state molecular dynamics simulations. We find that in sulfur-substitution the S2 state predominantly decays to the S1 state, while upon selenium-substitution the S2 state deactivation leads to simultaneous population of the S1 and T2,3 states in the same time scale and multi-state quasi-degeneracy region S2/S1/T2,3. Interestingly, the ultrafast deactivation of the spectroscopic S3 state of both studied molecules to the S1 state occurs through a successive S3 → S2 → S1 path involving a multi-state quasi-degeneracy S3/S2/S1. The populated S1 and T2 states will cross the lowest triplet state, and the S1 → T intersystem crossing happens in a multi-state quasi-degeneracy region S1/T2,3/T1 and is accelerated by selenium-substitution. The present study reveals the influence of both the chalcogen substitution element and initial spectroscopic state on the excited-state relaxation mechanism of nucleobase photosensitizers and also highlights the important role of multi-state quasi-degeneracy in mediating the complex relaxation process. These theoretical results provide additional insights into the intrinsic photophysics of nucleobase-based photosensitizers and are helpful for designing novel photo-sensitizers for real applications.

An on-the-fly deep neural network for simulating time-resolved spectroscopy: predicting the ultrafast ring opening dynamics of 1,2-dithiane.

Revolutionary developments in ultrafast light source technology are enabling experimental spectroscopists to probe the structural dynamics of molecules and materials on the femtosecond timescale. The capacity to investigate ultrafast processes afforded by these resources accordingly inspires theoreticians to carry out high-level simulations which facilitate the interpretation of the underlying dynamics probed during these ultrafast experiments. In this Article, we implement a deep neural network (DNN) to convert excited-state molecular dynamics simulations into time-resolved spectroscopic signals. Our DNN is trained on-the-fly from first-principles theoretical data obtained from a set of time-evolving molecular dynamics. The train-test process iterates for each time-step of the dynamics data until the network can predict spectra with sufficient accuracy to replace the computationally intensive quantum chemistry calculations required to produce them, at which point it simulates the time-resolved spectra for longer timescales. The potential of this approach is demonstrated by probing dynamics of the ring opening of 1,2-dithiane using sulphur K-edge X-ray absorption spectroscopy. The benefits of this strategy will be more markedly apparent for simulations of larger systems which will exhibit a more notable computational burden, making this approach applicable to the study of a diverse range of complex chemical dynamics.

Machine learning the Hohenberg-Kohn map for molecular excited states

The Hohenberg-Kohn theorem of density-functional theory establishes the existence of a bijection between the ground-state electron density and the external potential of a many-body system. This guarantees a one-to-one map from the electron density to all observables of interest including electronic excited-state energies. Time-Dependent Density-Functional Theory (TDDFT) provides one framework to resolve this map; however, the approximations inherent in practical TDDFT calculations, together with their computational expense, motivate finding a cheaper, more direct map for electronic excitations. Here, we show that determining density and energy functionals via machine learning allows the equations of TDDFT to be bypassed. The framework we introduce is used to perform the first excited-state molecular dynamics simulations with a machine-learned functional on malonaldehyde and correctly capture the kinetics of its excited-state intramolecular proton transfer, allowing insight into how mechanical constraints can be used to control the proton transfer reaction in this molecule. This development opens the door to using machine-learned functionals for highly efficient excited-state dynamics simulations.

Sub-10-fs observation of bound exciton formation in organic optoelectronic devices

Fundamental mechanisms underlying exciton formation in organic semiconductors are complex and elusive as it occurs on ultrashort sub-100-fs timescales. Some fundamental aspects of this process, such as the evolution of exciton binding energy, have not been resolved in time experimentally. Here, we apply a combination of sub-10-fs Pump-Push-Photocurrent, Pump-Push-Photoluminescence, and Pump-Probe spectroscopies to polyfluorene devices to track the ultrafast formation of excitons. While Pump-Probe is sensitive to the total concentration of excited states, Pump-Push-Photocurrent and Pump-Push-Photoluminescence are sensitive to bound states only, providing access to exciton binding dynamics. We find that excitons created by near-absorption-edge photons are intrinsically bound states, or become such within 10 fs after excitation. Meanwhile, excitons with a modest >0.3 eV excess energy can dissociate spontaneously within 50 fs before acquiring bound character. These conclusions are supported by excited-state molecular dynamics simulations and a global kinetic model which quantitatively reproduce experimental data.

Generalized Formulation of the Density Functional Tight Binding-Based Restricted Ensemble Kohn-Sham Method with Onsite Correction to Long-Range Correction.

We present a generalized formulation for the combination of the density functional tight binding (DFTB) approach and the state-interaction state-average spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS or SSR) method by considering onsite correction (OC) as well as the long-range corrected (LC) functional. The OC contribution provides more accurate energies and analytic gradients for individual microstates, while the multireference character of the SSR provides the correct description for conical intersections. We benchmark the LC-OC-DFTB/SSR method against various DFTB calculation methods for excitation energies and conical intersection structures with π/π* or n/π* characters. Furthermore, we perform excited-state molecular dynamics simulations with a molecular rotary motor with variations of LC-OC-DFTB/SSR approaches. We show that the OC contribution to the LC functional is crucial to obtain the correct geometry of conical intersections.

Exploring far-from-equilibrium ultrafast polarization control in ferroelectric oxides with excited-state neural network quantum molecular dynamics.

Ferroelectric materials exhibit a rich range of complex polar topologies, but their study under far-from-equilibrium optical excitation has been largely unexplored because of the difficulty in modeling the multiple spatiotemporal scales involved quantum-mechanically. To study optical excitation at spatiotemporal scales where these topologies emerge, we have performed multiscale excited-state neural network quantum molecular dynamics simulations that integrate quantum-mechanical description of electronic excitation and billion-atom machine learning molecular dynamics to describe ultrafast polarization control in an archetypal ferroelectric oxide, lead titanate. Far-from-equilibrium quantum simulations reveal a marked photo-induced change in the electronic energy landscape and resulting cross-over from ferroelectric to octahedral tilting topological dynamics within picoseconds. The coupling and frustration of these dynamics, in turn, create topological defects in the form of polar strings. The demonstrated nexus of multiscale quantum simulation and machine learning will boost not only the emerging field of ferroelectric topotronics but also broader optoelectronic applications.

Vibronic Photoexcitation Dynamics of Perylene Diimide: Computational Insights.

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

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

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

Defect Tolerance Mechanism Revealed! Influence of Polaron Occupied Surface Trap States on CsPbBr3 Nanocrystal Photoluminescence: Ab Initio Excited-State Dynamics.

Lead halide perovskite (LHP) nanocrystals (NCs) show exceptional defect tolerance which has been attributed to their unique electronic structure, where defect energy levels are not introduced inside the fundamental bandgap, and the role of polarons in screening charge carriers from defects. Here, we use ab initio atomistic simulations to explore the interplay between various surface chemistries (A = Cs+, R'NH3+; X = Br-, RCOO-) used to passivate a CsPbBr3 NC surface and their impact on the ground-state (GS) and excited-state (ES) photophysical properties. We investigate pristine fully passivated surfaces and A-X vacancy defects that reflect chemical reactions A+ + X- → AX on the surface, which result in ligand desorption. For each surface configuration, calculations are performed in the GS and lowest ES (L-ES) electronic configurations, approximating polaron formation after photoexcitation. For models with A-X surface vacancies, we find that localized electron surface trap (ST) states emerge ∼100-400 meV below the pristine Se band in the L-ES configuration due to polaronic nuclear reorganization. Surprisingly, these trap states contribute relatively bright Sh → ST spectral features. To test if these surface trap states remain bright in a dynamic (thermal) situation we implement excited-state molecular dynamics simulations. It is found that the surface defected model shows an enhanced nonradiative recombination rate which reduces the photoluminescence quantum yield (PLQY) from 95% for the pristine surface to 75%. This is accompanied by an order of magnitude reduction in PL intensity and a red shift of the transition energy. This study provides more evidence of the defect tolerance of LHP NCs along with evidence of surface trap states contributing to efficient photoluminescence. The observation of relatively bright surface trap states could provide insight into photophysical phenomena, such as size-dependent stretched-exponential photoluminescence decay and Stokes shifts.

Quantum-classical nonadiabatic dynamics of Floquet driven systems.

We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing us to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schrödinger equation with the inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.

Machine Learning-Assisted Excited State Molecular Dynamics with the State-Interaction State-Averaged Spin-Restricted Ensemble-Referenced Kohn-Sham Approach.

We present a machine learning-assisted excited state molecular dynamics (ML-ESMD) based on the ensemble density functional theory framework. Since we represent a diabatic Hamiltonian in terms of generalized valence bond ansatz within the state-interaction state-averaged spin-restricted ensemble-referenced Kohn-Sham (SI-SA-REKS) method, we can avoid singularities near conical intersections, which are crucial in excited state molecular dynamics simulations. We train the diabatic Hamiltonian elements and their analytical gradients with the SchNet architecture to construct machine learning models, while the phase freedom of off-diagonal elements of the Hamiltonian is cured by introducing the phase-less loss function. Our machine learning models show reasonable accuracy with mean absolute errors of ∼0.1 kcal/mol and ∼0.5 kcal/mol/Å for the diabatic Hamiltonian elements and their gradients, respectively, for penta-2,4-dieniminium cation. Moreover, by exploiting the diabatic representation, our models can predict correct conical intersection structures and their topologies. In addition, our ML-ESMD simulations give almost identical result with a direct dynamics at the same level of theory.

Excited State Molecular Dynamics of Photoinduced Proton-Coupled Electron Transfer in Anthracene-Phenol-Pyridine Triads.

Photoinduced proton-coupled electron transfer (PCET) in anthracene-phenol-pyridine triads exhibits inverted region behavior, where the more thermodynamically favorable process is slower. The long-lived transient charge-separated state (CSS) associated with electron transfer from phenol to anthracene and inverted region behavior were only observed experimentally for certain triads. Herein, excited state molecular dynamics simulations were performed on four different triads to simulate the nonequilibrium dynamics following photoexcitation to the locally excited state (LES) of anthracene. These simulations identified two distinct PCET pathways: the triads exhibiting inverted region behavior transitioned from the LES to the CSS, whereas the other triads transitioned to a local electron-proton transfer (LEPT) state within phenol and pyridine. The simulations suggest that PCET to the LEPT state is slower than PCET to the CSS and provides an alternative relaxation pathway. The mechanistic pathways, as well as the time scales of the electron and proton transfers, can be controlled by tuning the substituents.

Electronic Energy Relaxation in a Photoexcited Fully Fused Edge-Sharing Carbon Nanobelt.

Carbon nanobelts are cylindrical molecules composed of fully fused edge-sharing arene rings. Because of their aesthetically appealing structures, they acquire unusual optoelectronic properties that are potentially suitable for a range of applications in nanoelectronics and photonics. Nevertheless, the very limited success of their synthesis has led to their photophysical properties remaining largely unknown. Compared to that of carbon nanorings (arenes linked by single bonds), the strong structural rigidity of nanobelts prevents significant deformations away from the original high-symmetry conformation and, therefore, impacts their photophysical properties. Herein, we study the photoinduced dynamics of a successfully synthesized belt segment of (6,6)CNT (carbon nanotube). Modeling this process with nonadiabatic excited state molecular dynamics simulations uncovers the critical role played by the changes in excited state wave function localization on the different types of carbon atoms. This allows a detailed description of the excited state dynamics and spatial exciton evolution throughout the nanobelt scaffold. Our results provide detailed information about the excited state electronic properties and internal conversion rates that is potentially useful for designing nanobelts for nanoelectronic and photonic applications.

Vibronic Quantum Beating between Electronic Excited States in a Heterodimer.

Energy transfer in multichromophoric molecules can be affected by coherences that are induced by the electronic and vibrational couplings between chromophore units. Coherent electron-vibrational dynamics can persist at the subpicosecond time scale even at room temperature. Furthermore, wave-like localized-delocalized motions of the electronic wave function can be modulated by vibrations that actively participate in the intermolecular energy transfer process. Herein, nonadiabatic excited state molecular dynamics simulations have been performed on a rigid synthetic heterodimer that has been proposed as a simplified model for investigating the role and mechanism of coherent energy transfer in multichromophoric systems. Both surface hopping (SH) and Ehrenfest approaches (EHR) have been considered. After photoexcitation of the system at room temperature, EHR simulations reveal an ultrafast beating of electronic populations between the two lowest electronic states. These oscillations are not observed at low temperature and have vibrational origins. Furthermore, they cannot be reproduced using SH approach. This periodic behavior of electronic populations induces oscillations in the spatial localization of the electronic transition density between monomers. Vibrations whose frequencies are near-resonant with energy difference between the two lowest electronic excited states are in the range of the electronic population beating, and they are the ones that contribute the most to the coherent dynamics of these electronic transitions.