Nonadiabatic dynamics: The SHARC approach

Nonadiabatic Dynamics in a Laser Field: Using Floquet Fewest Switches Surface Hopping To Calculate Electronic Populations for Slow Nuclear Velocities

We investigate two well-known approaches for extending the fewest switches surface hopping (FSSH) algorithm to periodic time-dependent couplings. The first formalism acts as if the instantaneous adiabatic electronic states were standard adiabatic states, which just happen to evolve in time. The second formalism replaces the role of the usual adiabatic states by the time-independent adiabatic Floquet states. For a set of modified Tully model problems, the Floquet FSSH (F-FSSH) formalism gives a better estimate for both transmission and reflection probabilities than the instantaneous adiabatic FSSH (IA-FSSH) formalism, especially for slow nuclear velocities. More importantly, only F-FSSH predicts the correct final scattering momentum. Finally, in order to use Floquet theory accurately, we find that it is crucial to account for the interference between wavepackets on different Floquet states. Our results should be of interest to all those interested in laser-induced molecular dynamics.

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.

TD-DFT spin-adiabats with analytic nonadiabatic derivative couplings

We present an algorithm for efficient calculation of analytic nonadiabatic derivative couplings between spin-adiabatic, time-dependent density functional theory states within the Tamm-Dancoff approximation. Our derivation is based on the direct differentiation of the Kohn-Sham pseudowavefunction using the framework of Ou et al. Our implementation is limited to the case of a system with an even number of electrons in a closed shell ground state, and we validate our algorithm against finite difference at an S1/T2 crossing of benzaldehyde. Through the introduction of a magnetic field spin-coupling operator, we break time-reversal symmetry to generate complex valued nonadiabatic derivative couplings. Although the nonadiabatic derivative couplings are complex valued, we find that a phase rotation can generate an almost entirely real-valued derivative coupling vector for the case of benzaldehyde.

Stimulated X-ray Raman Imaging of Conical Intersections

The conical intersection dynamics of thiophenol is studied theoretically using the stimulated X-ray Raman imaging (SXRI) technique. SXRI employs a hard X-ray narrowband/broadband hybrid probe field and provides a real-time and real-space image of the passage through conical intersections. The signal, calculated using the minimal-coupling radiation/matter Hamiltonian, carries the phase information, and the real-space image of the transition charge density can be reconstructed by its Fourier transform. The two conical intersections (S₂/S₁ (1¹ππ*/¹πσ*) and S₁/S₀ (¹πσ*/S₀)) can be distinguished and identified by the diffraction patterns in the level crossing regimes.

A molecular perspective on Tully models for nonadiabatic dynamics

We present a series of standardized molecular tests for nonadiabatic dynamics, reminiscent of the one-dimensional Tully models proposed in 1990.

Nonadiabatic Molecular Dynamics on Graphics Processing Units: Performance and Application to Rotary Molecular Motors

Nonadiabatic molecular dynamics (NAMD) simulations of molecular systems require the efficient evaluation of excited-state properties, such as energies, gradients, and nonadiabatic coupling vectors. Here, we investigate the use of graphics processing units (GPUs) in addition to central processing units (CPUs) to efficiently calculate these properties at the time-dependent density functional theory (TDDFT) level of theory. Our implementation in the FermiONs++ program package uses the J-engine and a preselective screening procedure for the calculation of Coulomb and exchange kernels, respectively. We observe good speed-ups for small and large molecular systems (comparable to those observed in ground-state calculations) and reduced (down to sublinear) scaling behavior with respect to the system size (depending on the spatial locality of the investigated excitation). As a first illustrative application, we present efficient NAMD simulations of a series of newly designed light-driven rotary molecular motors and compare their S1 lifetimes. Although all four rotors show different S1 excitation energies, their ability to rotate upon excitation is conserved, making the series an interesting starting point for rotary molecular motors with tunable excitation energies.

Unconventional two-step spin relaxation dynamics of [Re(CO)3(im)(phen)]+ in aqueous solution

Changes of molecular spin are ubiquitous in chemistry and biology. Among spin flip processes, one of the fastest is intersystem crossing (ISC) in transition metal complexes. Here, we investigate the spin relaxation dynamics and emission spectrum of [Re(CO)3(im)(phen)]+ (im = imidazole, phen = phenanthroline) using extensive full-dimensional excited-state dynamics simulations in explicit aqueous solution. Contrary to what has been observed in other transition metal complexes, the transition from the singlet to triplet states occurs via a two-step process, with clearly separable electronic and nuclear-driven components with two different time scales. The initially excited electronic wave function is a "molecular spin-orbit wave packet" that evolves almost instantaneously, with an 8 fs time constant, into an approximate 25 : 75 singlet-to-triplet equilibrium. Surprisingly, this ISC process is an order of magnitude faster than it was previously documented for this and other rhenium(i) carbonyl diimine complexes from emission spectra. Simulations including explicit laser field interactions evidence that few-cycle UV laser pulses are required to follow the creation and evolution of such molecular spin-orbit wave packets. The analysis of the dynamics also reveals a retarded ISC component, with a time constant of 420 fs, which can be explained invoking intramolecular vibrational energy redistribution. The emission spectrum is shown to be characterized by ISC convoluted with internal conversion and vibrational relaxation. These results provide fundamental understanding of ultrafast intersystem crossing in transition metal complexes.

Quasi-Diabatic Scheme for Nonadiabatic On-the-Fly Simulations

We use the quasi-diabatic (QD) propagation scheme to perform on-the-fly nonadiabatic simulations of the photodynamics of ethylene. The QD scheme enables a seamless interface between accurate diabatic-based quantum dynamics approaches and adiabatic electronic structure calculations, explicitly avoiding any efforts to construct global diabatic states or reformulate the diabatic dynamics approach to the adiabatic representation. Using the partial linearized path-integral approach and the symmetrical quasi-classical approach as the diabatic dynamics methods, the QD propagation scheme enables direct nonadiabatic simulation with complete active space self-consistent field on-the-fly electronic structure calculations. The population dynamics obtained from both approaches are in a close agreement with the quantum wavepacket-based method and outperform the widely used trajectory surface-hopping approach. Further analysis of the ethylene photodeactivation pathways demonstrates the correct predictions of competing processes of nonradiative relaxation mechanism through various conical intersections. This work provides the foundation of using accurate diabatic dynamics approaches and on-the-fly adiabatic electronic structure information to perform ab initio nonadiabatic simulation.

WavePacket: A Matlab package for numerical quantum dynamics. III. Quantum-classical simulations and surface hopping trajectories

WavePacket is an open-source program package for numerical simulations in quantum dynamics. Building on the previous Part I (Schmidt and Lorenz, Comput. Phys. Commun. 2017, 213, 223] and Part II (Schmidt and Hartmann, Comput. Phys. Commun. 2018, 228, 229] which dealt with quantum dynamics of closed and open systems, respectively, the present Part III adds fully classical and mixed quantum-classical propagation techniques to WavePacket. There classical phase-space densities are sampled by trajectories which follow (diabatic or adiabatic) potential energy surfaces. In the vicinity of (genuine or avoided) intersections of those surfaces, trajectories may switch between them. To model these transitions, two classes of stochastic algorithms have been implemented: (1) Tully's fewest switches surface hopping and (2) Landau-Zener-based single switch surface hopping. The latter one offers the advantage of being based on adiabatic energy gaps only, thus not requiring nonadiabatic coupling information any more. The present work describes the MATLAB version of WavePacket 6.1.0, which is essentially an object-oriented rewrite of previous versions, allowing to perform fully classical, quantum-classical and quantum-mechanical simulations on an equal footing, that is, for the same physical system described by the same WavePacket input. The software package is hosted and further developed at the Sourceforge platform, where also extensive Wiki-documentation as well as numerous worked-out demonstration examples with animated graphics are available. © 2019 Wiley Periodicals, Inc.

Carotenoid Nuclear Reorganization and Interplay of Bright and Dark Excited States

We report quantum chemical calculations using multireference perturbation theory (MRPT) with the density matrix renormalization group (DMRG) plus photothermal deflection spectroscopy measurements to investigate the manifold of carotenoid excited states and establish their energies relative to the bright state (S₂) as a function of nuclear reorganization. We conclude that the primary photophysics and function of carotenoids are determined by interplay of only the bright (S₂) and lowest-energy dark (S₁) states. The lowest-lying dark state, far from being energetically distinguishable from the lowest-lying bright state along the entire excited-state nuclear reorganization pathway, is instead computed to be either the second or first excited state depending on what equilibrium geometry is considered. This result suggests that, rather than there being a dark intermediate excited state bridging a non-negligible energy gap from the lowest-lying dark state to the lowest-lying bright state, there is in fact no appreciable energy gap to bridge following photoexcitation. Instead, excited-state nuclear reorganization constitutes the bridge from S₂ to S₁, in the sense that these two states attain energetic degeneracy along this pathway.

A combined multi-reference pump-probe simulation method with application to XUV signatures of ultrafast methyl iodide photodissociation

UV pump-XUV/X-ray probe measurements have been successfully applied in the study of photo-induced chemical reactions. Although rich element-specific electronic structure information is accessible within XUV/X-ray (inner-shell) absorption spectra, it can be difficult to interpret the chemistry directly from the spectrum without supporting theoretical simulations. A multireference method to completely simulate UV pump-XUV/X-ray probe measurement has been developed and applied to study the methyl iodide photodissociation process. Multireference, fewest-switches surface hopping (FSSH) trajectories were used to explore the coupled electronic and ionic dynamics upon photoexcitation of methyl iodide. Interpretation of previous measurements is provided by associated multireference, restricted active space, inner-shell spectral simulations. This combination of multireference FSSH trajectories and XUV spectra provides an interpretation of transient features appearing in previous measurements within the first 100 fs after photoexcitation and validates the significant branching ratio in the final excited-state population. This methodology should prove useful for interpretation of the increasing number of inner-shell probe studies of molecular excited states or for directing new experiments toward interesting regions of the potential energy landscape.

Machine learning enables long time scale molecular photodynamics simulations

Photo-induced processes are fundamental in nature but accurate simulations of their dynamics are seriously limited by the cost of the underlying quantum chemical calculations, hampering their application for long time scales. Here we introduce a method based on machine learning to overcome this bottleneck and enable accurate photodynamics on nanosecond time scales, which are otherwise out of reach with contemporary approaches. Instead of expensive quantum chemistry during molecular dynamics simulations, we use deep neural networks to learn the relationship between a molecular geometry and its high-dimensional electronic properties. As an example, the time evolution of the methylenimmonium cation for one nanosecond is used to demonstrate that machine learning algorithms can outperform standard excited-state molecular dynamics approaches in their computational efficiency while delivering the same accuracy.

Nonadiabatic Dynamics Simulation Predict Intersystem Crossing in Nitroaromatic Molecules on a Picosecond Time Scale

Previous time-resolved spectroscopic experiments and static quantum-chemical calculations attributed nitronaphthalene derivatives one of the fastest time scales for intersystem crossing within organic molecules, reaching the 100 fs mark. Nonadiabatic dynamics simulations on three nitronaphthalene derivatives challenge this view, showing that the experimentally observed ∼100 fs process corresponds to internal conversion in the singlet manifolds. Intersystem crossing, instead, takes place on a longer time scale of ∼1 ps. The dynamics simulations further reveal that the spin transitions occur via two distinct pathways with different contribution for the three systems, which are determined by electronic factors and the torsion of the nitro group. This study, therefore, indicates that the existence of sub-picosecond intersystem crossing in other nitroaromatic molecules should be questioned.

A deep UV trigger for ground-state ring-opening dynamics of 1,3-cyclohexadiene

We explore the photo-induced kinetics of 1,3-cyclohexadiene upon excitation at 200 nm to the 3p state by ultrafast time-resolved, gas-phase x-ray scattering using the Linac Coherent Light Source. Analysis of the scattering anisotropy reveals that the excitation leads to the 3px and 3py Rydberg electronic states, which relax to the ground state with a time constant of 208 ± 11 fs. In contrast to the well-studied 266 nm excitation, at 200 nm the majority of the molecules (76 ± 3%) relax to vibrationally hot cyclohexadiene in the ground electronic state. A subsequent reaction on the ground electronic state surface leads from the hot cyclohexadiene to 1,3,5-hexatriene, with rates for the forward and backward reactions of 174 ± 13 and 355 ± 45 ps, respectively. The scattering pattern of the final hexatriene product reveals a thermal distribution of rotamers about the carbon-carbon single bonds.

Toward the evaluation of intersystem crossing rates with variational relativistic methods

The change in electronic state from one spin multiplicity to another, known as intersystem crossing, occurs in molecules via the relativistic phenomenon of spin-orbit coupling. Current means of estimating intersystem crossing rates rely on the perturbative evaluation of spin-orbit coupling effects. This perturbative approach, valid in lighter atoms where spin-orbit coupling is weaker, is expected to break down for heavier elements where relativistic effects become dominant. Methods which incorporate spin-orbit effects variationally, such as the exact-two-component (X2C) method, will be necessary to treat this strong-coupling regime. We present a novel procedure which produces a diabatic basis of spin-pure electronic states coupled by spin-orbit terms, generated from fully variational relativistic calculations. This method is implemented within X2C using time-dependent density-functional theory and is compared to results from a perturbative relativistic study in the weak spin-orbit coupling regime. Additional calculations on a more strongly spin-orbit-coupled [UO₂Cl₄]^2- complex further illustrate the strengths of this method. This procedure will be valuable in the estimation of intersystem crossing rates within strongly spin-coupled species.

Grid-Based Ehrenfest Model To Study Electron-Nuclear Processes

The two-dimensional electron-nuclear Schrödinger equation using soft-core Coulomb potentials has been a cornerstone for modeling and predicting the behavior of one-active-electron diatomic molecules, particularly for processes where both bound and continuum states are important. The model, however, is computationally expensive to extend to more electron or nuclear coordinates. Here we propose use of the Ehrenfest approach to treat the nuclear motion, while the electronic motion is still solved by quantum propagation on a grid. In this work, we present results for a one-dimensional treatment of H₂⁺, where the quantum and semiclassical dynamics can be directly compared, showing remarkably good agreement for a variety of situations. The advantage of the Ehrenfest approach is that it can be easily extended to treat as many nuclear degrees of freedom as needed.

Mechanism of Photoinduced Dihydroazulene Ring-Opening Reaction

The photoinduced ring-opening reaction is a key process in the functioning of dihydroazulene/vinylheptafulvene (DHA/VHF) photoswitches. Over the years, the mechanism of this reaction has been extensively debated. Herein, by means of nonadiabatic trajectory dynamics simulations and quantum chemistry calculations, we present the first detailed and comprehensive investigation on the mechanism of the photoinduced ring-opening reaction of DHA. The results show the crucial role of the excited-state ring planarization process for the bond breaking. Our dynamics simulations show that the DHA ring opening is an ultrafast reaction that does not follow exponential kinetics but exhibits ballistic dynamics. Upon photoexcitation, the planarization occurs within 300-500 fs. This leads to the ring-opening reaction and concurrent decay of the molecule to the ground state within 100 fs through an S₁ → S₀ internal conversion process toward forming the VHF isomer. These results are consistent with previous ultrafast time-resolved experiments and lead to a thorough understanding of the DHA/VHF photoconversion.

Ultrafast X-ray scattering reveals vibrational coherence following Rydberg excitation

The coherence and dephasing of vibrational motions of molecules constitute an integral part of chemical dynamics, influence material properties and underpin schemes to control chemical reactions. Considerable progress has been made in understanding vibrational coherence through spectroscopic measurements, but precise, direct measurement of the structure of a vibrating excited-state polyatomic organic molecule has remained unworkable. Here, we measure the time-evolving molecular structure of optically excited N-methylmorpholine through scattering with ultrashort X-ray pulses. The scattering signals are corrected for the differences in electron density in the excited electronic state of the molecule in comparison to the ground state. The experiment maps the evolution of the molecular geometry with femtosecond resolution, showing coherent motion that survives electronic relaxation and seems to persist for longer than previously seen using other methods.

Performance of trajectory surface hopping method in the treatment of ultrafast intersystem crossing dynamics

We carried out extensive studies to examine the performance of the fewest-switches surface hopping method in the description of the ultrafast intersystem crossing dynamic of various singlet-triplet (S-T) models by comparison with the results of the exact full quantum dynamics. Different implementation details and some derivative approaches were examined. As expected, it is better to perform the trajectory surface hopping calculations in the spin-adiabatic representation or by the local diabatization approach, instead of in the spin-diabatic representation. The surface hopping method provides reasonable results for the short-time dynamics in the S-T model with weak spin-orbital coupling (diabatic coupling), although it does not perform well in the models with strong spin-orbital coupling (diabatic coupling). When the system accesses the S-T potential energy crossing with rather high kinetic energy, the trajectory surface hopping method tends to produce a good description of the nonadiabatic intersystem crossing dynamics. The impact of the decoherence correction on the performance of the trajectory surface hopping is system dependent. It improves the result accuracy in many cases, while its influence may also be minor for other cases.

Configuration interaction singles with spin-orbit coupling: Constructing spin-adiabatic states and their analytical nuclear gradients

For future use in modeling photoexcited dynamics and intersystem crossing, we calculate spin-adiabatic states and their analytical nuclear gradients within configuration interaction singles theory. These energies and forces should be immediately useful for surface hopping dynamics, which are natural within an adiabatic framework. The resulting code has been implemented within the Q-Chem software and preliminary results suggest that the additional cost of including spin-orbit coupling within the singles-singles block is not large.

Ultrafast dynamics in polycyclic aromatic hydrocarbons: the key case of conical intersections at higher excited states and their role in the photophysics of phenanthrene monomer

Proper interpretation of phenanthrene's and similar PAHs’ photocycle relies on two higher excited state relaxations due to the simultaneous presence of non-adiabatic and adiabatic transitions.

Finite-temperature Wigner phase-space sampling and temperature effects on the excited-state dynamics of 2-nitronaphthalene

The concept of finite temperature Wigner phase-space sampling allowing the population of vibrationally excited states is introduced and employed to study temperature effects on the absorption spectrum of 2-nitronaphtalene (2NN) and its relaxation dynamics.

Highly efficient surface hopping dynamics using a linear vibronic coupling model

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

Surface Hopping within an Exciton Picture. An Electrostatic Embedding Scheme

We report the development and the implementation of an exciton approach that allows ab initio nonadiabatic dynamics simulations of electronic excitation energy transfer in multichromophoric systems. For the dynamics, a trajectory-based strategy is used within the surface hopping formulation. The approach features a consistent hybrid formulation that allows the construction of potential energy surfaces and gradients by combining quantum mechanics and molecular mechanics within an electrostatic embedding scheme. As an application, the study of a molecular dyad consisting of a covalently bound BODIPY moiety and a tetrathiophene group is presented using time-dependent density functional theory (TDDFT). The results obtained with the exciton model are compared to previously performed full TDDFT dynamics of the same system. Our results show excellent agreement with the full TDDFT results, indicating that the couplings that lead to excitation energy transfer (EET) are dominated by Coulomb interaction terms and that charge-transfer states are not necessary to properly describe the nonadiabatic dynamics of the system. The exciton model also reveals ultrafast coherent oscillations of the excitation between the two units in the dyad, which occur during the first 50 fs.