Theory of Ultrafast Nonadiabatic Excited-State Processes and their Spectroscopic Detection in Real Time

Differential Shannon Entropies and Mutual Information in a Curve Crossing System: Adiabatic and Diabatic Decompositions

The differential Shannon entropy provides a measure for the localization of a wave function. We regard the vibrational wave packet motion in a curve crossing system and calculate time-dependent entropies. Using a numerical example, we analyze how localization inside diabatic and adiabatic states can be accessed and discuss the differences between these two representations. In order to do so, we extend the usual entropy definition and introduce novel state-selective entropies. These quantities contain information on the form of the nuclear density components on the one hand and on the state population on the other, and it is shown how the contribution of the population can be removed. Having the state-selective entropies at hand, two additional functions derived from these, namely, the conditional entropy and the mutual information, are determined and compared. We find that these quantities relate closely to correlation effects rooted in different electronic properties of the system.

On-the-fly simulation of time-resolved fluorescence spectra and anisotropy

We combine on-the-fly trajectory surface hopping simulations and the doorway-window representation of nonlinear optical response functions to create an efficient protocol for the evaluation of time- and frequency-resolved fluorescence (TFRF) spectra and anisotropies of the realistic polyatomic systems. This approach gives the effective description of the proper (e.g., experimental) pulse envelopes, laser field polarizations, and the proper orientational averaging of TFRF signals directly from the well-established on-the-fly nonadiabatic dynamic simulations without extra computational cost. To discuss the implementation details of the developed protocol, we chose cis-azobenzene as a prototype to simulate the time evolution of the TFRF spectra governed by its nonadiabatic dynamics. The results show that the TFRF is determined by the interplay of several key factors, i.e., decays of excited-state populations, evolution of the transition dipole moments along with the dynamic propagation, and scaling factor of the TFRF signals associated with the cube of emission frequency. This work not only provides an efficient and effective approach to simulate the TFRF and anisotropies of realistic polyatomic systems but also discusses the important relationship between the TFRF signals and the underlining nonadiabatic dynamics.

Parametrically Managed Activation Functions for Improved Global Potential Energy Surfaces for Six Coupled 5A' States and Fourteen Coupled 3A' States of O + O2

We report new potential energy surfaces for six coupled 5A' states and 14 coupled 3A' states of O3. The new surfaces are created by parametrically managed diabatization by deep neural network (PM-DDNN). The PM-DDNN method uses calculated adiabatic potential energy surfaces to discover and fit an underlying adiabatic-equivalent set of diabatic surfaces and their couplings and obtains the fit to the adiabatic surfaces by diagonalization of the diabatic potential energy matrix (DPEM). The procedure yields the adiabatic surfaces and their gradients, as well as the DPEM and its gradient. If desired one can also compute the nonadiabatic coupling due to the transformation. The present work improves on previous work by using a new coordinate to guide the decay of the neural network contribution to the many-body fit to the whole DPEM. The main objective was to obtain smoother potentials than the previous ones with better suitability for dynamics calculations, and this was achieved. Furthermore, we obtained suitably small deviations from the input reference data. For the six coupled 5A' surfaces, the 60,366 data below 10 eV are fit with a mean unsigned error (MUE) of 49 meV, and for the 14 coupled 3A' surfaces, the 76,733 data below 10 eV are fit with an MUE of 28 meV. The data below 5 eV fit even more accurately with MUEs of 37 meV (5A') and 20 meV (3A').

Probing avoided crossings and conical intersections by two-pulse femtosecond stimulated Raman spectroscopy: Theoretical study

This study leverages two-pulse femtosecond stimulated Raman spectroscopy (2FSRS) to characterize molecular systems with avoided crossings (ACs) and conical intersections (CIs) in their low-lying excited electronic states. By simulating 2FSRS spectra of microscopically inspired ACs and CIs models, we demonstrate that 2FSRS not only delivers valuable information on the molecular parameters characterizing ACs and CIs but also helps distinguish between these two systems.

Ultrafast Molecular Frame Quantum Tomography

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

Parameter estimation in ultrafast spectroscopy using probability theory

Ultrafast spectroscopy is a powerful technique that utilizes short pulses on the femtosecond time scale to generate and probe coherent responses in molecular systems. While the specific ultrafast methodologies vary, the most common data analysis tools rely on discrete Fourier transformation for recovering coherences that report on electronic or vibrational states and multi-exponential fitting for probing population dynamics, such as excited-state relaxation. These analysis tools are widely used due to their perceived reliability in estimating frequencies and decay rates. Here, we demonstrate that such "black box" methods for parameter estimation often lead to inaccurate results even in the absence of noise. To address this issue, we propose an alternative approach based on Bayes probability theory that simultaneously accounts for both population and coherence contributions to the signal. This Bayesian inference method offers accurate parameter estimations across a broad range of experimental conditions, including scenarios with high noise and data truncation. In contrast to traditional methods, Bayesian inference incorporates prior information about the measured signal and noise, leading to improved accuracy. Moreover, it provides estimator error bounds, enabling a systematic statistical framework for interpreting confidence in the results. By employing Bayesian inference, all parameters of a realistic model system may be accurately recovered, even in extremely challenging scenarios where Fourier and multi-exponential fitting methods fail. This approach offers a more reliable and comprehensive analysis tool for time-resolved coherent spectroscopy, enhancing our understanding of molecular systems and enabling a better interpretation of experimental data.

Ab initio simulation of peak evolutions and beating maps for electronic two-dimensional signals of a polyatomic chromophore

By employing the doorway-window (DW) on-the-fly simulation protocol, we performed ab initio simulations of peak evolutions and beating maps of electronic two-dimensional (2D) spectra of a polyatomic molecule in the gas phase. As the system under study, we chose pyrazine, which is a paradigmatic example of photodynamics dominated by conical intersections (CIs). From the technical perspective, we demonstrate that the DW protocol is a numerically efficient methodology suitable for simulations of 2D spectra for a wide range of excitation/detection frequencies and population times. From the information content perspective, we show that peak evolutions and beating maps not only reveal timescales of transitions through CIs but also pinpoint the most relevant coupling and tuning modes active at these CIs.

Nonlinear Molecular Electronic Spectroscopy via MCTDH Quantum Dynamics: From Exact to Approximate Expressions

We present an accurate and efficient approach to computing the linear and nonlinear optical spectroscopy of a closed quantum system subject to impulsive interactions with an incident electromagnetic field. It incorporates the effect of ultrafast nonadiabatic dynamics by means of explicit numerical propagation of the nuclear wave packet. The fundamental expressions for the evaluation of first- and higher-order response functions are recast in a general form that can be used with any quantum dynamics code capable of computing the overlap of nuclear wave packets evolving in different states. Here we present the evaluation of these expressions with the multiconfiguration time-dependent Hartree (MCTDH) method. Application is made to pyrene, excited to its lowest bright excited state S₂ which exhibits a sub-100-fs nonadiabatic decay to a dark state S₁. The system is described by a linear vibronic coupling Hamiltonian, parametrized with multiconfiguration electronic structure methods. We show that the ultrafast nonadiabatic dynamics can have a remarkable effect on the spectral line shapes that goes beyond simple lifetime broadening. Furthermore, a widely employed approximate expression based on the time scale separation of dephasing and population relaxation is recast in the same theoretical framework. Application to pyrene shows the range of validity of such approximations.

The hierarchy of Davydov's Ansätze: From guesswork to numerically "exact" many-body wave functions

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansätze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansätze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansätze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrödinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansätze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

Exciton Dynamics and Time-Resolved Fluorescence in Nanocavity-Integrated Monolayers of Transition-Metal Dichalcogenides

We have developed an ab initio-based, fully quantum, numerically accurate methodology for the simulation of the exciton dynamics and time- and frequency-resolved fluorescence spectra of the cavity-controlled two-dimensional materials at finite temperatures and applied this methodology to the single-layer WSe₂ system. Specifically, the multiple Davydov D₂ Ansatz has been employed in combination with the method of thermofield dynamics for the finite-temperature extension of accurate time-dependent variation. This allowed us to establish dynamical and spectroscopic signatures of the polaronic and polaritonic effects as well as uncover their characteristic time scales in the relevant range of temperatures. Our study reveals the pivotal role of multidimensional conical intersections in controlling the many-body dynamics of highly intertwined excitonic, phononic, and photonic modes.

Equation-of-Motion Methods for the Calculation of Femtosecond Time-Resolved 4-Wave-Mixing and N-Wave-Mixing Signals

Femtosecond nonlinear spectroscopy is the main tool for the time-resolved detection of photophysical and photochemical processes. Since most systems of chemical interest are rather complex, theoretical support is indispensable for the extraction of the intrinsic system dynamics from the detected spectroscopic responses. There exist two alternative theoretical formalisms for the calculation of spectroscopic signals, the nonlinear response-function (NRF) approach and the spectroscopic equation-of-motion (EOM) approach. In the NRF formalism, the system-field interaction is assumed to be sufficiently weak and is treated in lowest-order perturbation theory for each laser pulse interacting with the sample. The conceptual alternative to the NRF method is the extraction of the spectroscopic signals from the solutions of quantum mechanical, semiclassical, or quasiclassical EOMs which govern the time evolution of the material system interacting with the radiation field of the laser pulses. The NRF formalism and its applications to a broad range of material systems and spectroscopic signals have been comprehensively reviewed in the literature. This article provides a detailed review of the suite of EOM methods, including applications to 4-wave-mixing and N-wave-mixing signals detected with weak or strong fields. Under certain circumstances, the spectroscopic EOM methods may be more efficient than the NRF method for the computation of various nonlinear spectroscopic signals.

Plenty of Room on the Top: Pathways and Spectroscopic Signatures of Singlet Fission from Upper Singlet States

We investigate dynamic signatures of the singlet fission (SF) process triggered by the excitation of a molecular system to an upper singlet state S_N (N > 1) and develop a computational methodology for the simulation of nonlinear spectroscopic signals revealing the S_N → TT₁ SF in real time. We demonstrate that SF can proceed directly from the upper state S_N, bypassing the lowest excited state, S₁. We determine the main S_N → TT₁ reaction pathways and show by computer simulation and spectroscopic measurements that the S_N-initiated SF can be faster and more efficient than the traditionally studied S₁ → TT₁ SF. We claim that the S_N → TT₁ SF offers novel promising opportunities for engineering SF systems and enhancing SF yields.

Time Resolved Raman Scattering of Molecules: A Quantum Mechanics Approach with Stochastic Schroedinger Equation

Raman scattering is a very powerful tool employed to characterize molecular systems. Here we propose a novel theoretical strategy to calculate the Raman cross-section in time domain, by computing the cumulative Raman signal emitted during the molecular evolution in time. Our model is based on a numerical propagation of the vibronic wave function under the effect of a light pulse of arbitrary shape. This approach can therefore tackle a variety of experimental setups. Both resonance and nonresonance Raman scattering can be retrieved, and also the time-dependent fluorescence emission is computed. The model has been applied to porphyrin considering both resonance and nonresonance conditions and varying the incident field duration. Moreover the effect of the vibrational relaxation, which should be taken into account when its time scale is similar to that of the Raman emission, has been included through the stochastic Schroedinger equation approach.

Propagation and Parametric Amplification in Four-Wave Mixing Processes: Intramolecular Coupling and High-Order Effects

A strong pump-power dependence of the four-wave mixing (FWM) signal for an aqueous solution of Malachite green is reported. The characteristics of the pump-power dependence of the nonlinear signal are reproduced by a theoretical model based on the coupling between pump-probe, considering signal fields and propagation effects. The effect of the intramolecular coupling on the nonlinear intensity of the FWM signal is studied using a model molecule consisting of two-coupled harmonic curves of electronic energies with minima displaced in energy and nuclear positions. Two-vibrational states are considered while including non-adiabatic effects for the two-state model. Moreover, the coupling among the field components, as well as the propagation effects, are studied by considering a constant pump-intensity. Our calculation scheme, considering both the intramolecular coupling effects in the description of the molecular structure and the effects produced by the propagation of the FWM signal along the optical length, allows the exponential dependence of the latter, as the intensity of the pumping beam increases. Our treatments do not require the inclusion of other non-resonant processes outside the RWA approximation, due to the consideration of an adiabatic basis.

Ultrafast Internal Conversion Dynamics through the on-the-Fly Simulation of Transient Absorption Pump-Probe Spectra with Different Electronic Structure Methods

An on-the-fly surface-hopping simulation protocol is developed for the evaluation of transient absorption (TA) pump-probe (PP) signals of molecular systems exhibiting internal conversion to the electronic ground state. We study the nonadiabatic dynamics of azomethane and the associating TA PP spectra at three levels of the electronic-structure theory, OM2/MRCI, SA-CASSCF, and XMS-CASPT2. The impact of these methods on the population dynamics and time-resolved TA PP signals is substantially different. This difference is attributed to the strong non-Condon effects that must be taken into account for the proper understanding and interpretation of time-resolved TA PP signals of nonadiabatic polyatomic systems. This shows that the combination of the dynamical and spectral simulations definitely provides more accurate and detailed information on the microscopic mechanisms of photophysical and photochemical processes. Hence the simulation of time-resolved spectroscopic signals provides another important dimension to examine the accuracy of quantum chemistry methods.

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

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

Generalized discrete truncated Wigner approximation for nonadiabatic quantum-classical dynamics

Nonadiabatic molecular dynamics occur in a wide range of chemical reactions and femtochemistry experiments involving electronically excited states. These dynamics are hard to treat numerically as the system's complexity increases, and it is thus desirable to have accurate yet affordable methods for their simulation. Here, we introduce a linearized semiclassical method, the generalized discrete truncated Wigner approximation (GDTWA), which is well-established in the context of quantum spin lattice systems, into the arena of chemical nonadiabatic systems. In contrast to traditional continuous mapping approaches, e.g., the Meyer-Miller-Stock-Thoss and the spin mappings, GDTWA samples the electron degrees of freedom in a discrete phase space and thus forbids an unphysical unbounded growth of electronic state populations. The discrete sampling also accounts for an effective reduced but non-vanishing zero-point energy without an explicit parameter, which makes it possible to treat the identity operator and other operators on an equal footing. As numerical benchmarks on two linear vibronic coupling models and Tully's models show, GDTWA has a satisfactory accuracy in a wide parameter regime, independent of whether the dynamics is dominated by relaxation or by coherent interactions. Our results suggest that the method can be very adequate to treat challenging nonadiabatic dynamics problems in chemistry and related fields.

Simulation of Nonlinear Femtosecond Signals at Finite Temperature via a Thermo Field Dynamics-Tensor Train Method: General Theory and Application to Time- and Frequency-Resolved Fluorescence of the Fenna-Matthews-Olson Complex

Addressing needs of contemporary nonlinear femtosecond optical spectroscopy, we have developed a fully quantum, numerically accurate wave function-based approach for the calculation of third-order spectroscopic signals of polyatomic molecules and molecular aggregates at finite temperature. The systems are described by multimode nonadiabatic vibronic-coupling Hamiltonians, in which diagonal terms are treated in harmonic approximation, while off-diagonal interstate couplings are assumed to be coordinate independent. The approach is based on the Thermo Field Dynamics (TFD) representation of quantum mechanics and tensor-train (TT) machinery for efficient numerical simulation of quantum evolution of systems with many degrees of freedom. The developed TFD-TT approach is applied to the calculation of time- and frequency-resolved fluorescence spectra of the Fenna-Matthews-Olson (FMO) antenna complex at room temperature taking into account finite time-frequency resolution in fluorescence detection, orientational averaging, and static disorder.

Optically Induced Charge Transfer in Organic Mixed-Valence Systems: Wave Packet Dynamics and Femtosecond Transient Spectroscopy

We theoretically study the dynamics of charge transfer induced by femtosecond laser-pulse excitation. Models involving coupled electronic states of symmetrically bridged organic mixed-valence molecules are investigated, where the motion proceeds along two reaction coordinates. Linear absorption spectra of two species that differ in the energetical position of the bridge, relative to acceptor and donor states, are determined and compared to experimental results. From the wave packet dynamics it emerges that relaxation dominates the charge transfer. This behavior is reflected in transient absorption spectra, which are obtained from a directional decomposition of the time-dependent polarization. Due to the nature of the coupled dynamics the extraction of the relevant contributions needs an extension of well-known techniques for the decomposition.

The Efficiency of Photoinduced Intramolecular Charge Separation from the Second Excited State: What Factors Can Control It?

The efficiency of photoinduced charge separation (CS) in electron donor-acceptor compounds is commonly limited due to fast deactivation processes, such as the excited-state internal conversion and ultrafast hot reverse electron transfer to the acceptor, charge recombination (CR). A traditional way to avoid undesired energy losses due to CR is to put the reverse electron transfer into the Marcus inverted region, thus effectively suppressing it. This method, however, is not generally applicable when considering CS from the second locally excited state because the driving force of CR to the first excited state is small, and thus charge recombination is ultrafast and efficient. In this paper, we study the kinetic features of CS/CR from the second locally excited state of the donor using a semiclassical stochastic model of electron transfer. Particular attention is paid to the CS efficiency as well as the influence of the polar environment and intramolecular high-frequency vibrational modes on the kinetics of the charge-separated state. The influence of a number of model parameters on the CS yield and the energy efficiency has been analyzed using the results of numerical simulations. Several simple practical recipes for creating molecular compounds with high CS yields have been suggested. Simulations have also revealed a strong and non-monotonous (double-humped) dependence of both the yield and energy efficiency of CS on the driving force.

Quantum yield and energy efficiency of photoinduced intramolecular charge separation

Kinetics of photoinduced intramolecular charge separation (CS) and the ensuing ultrafast charge recombination (CR) in electron-donor-acceptor dyads are studied numerically, taking into account the excitation of charge-transfer active intramolecular vibrations and multiple relaxation time scales of the surrounding polar solvent. Both energetic and dynamic properties of intramolecular and solvent reorganization are considered, and their influence on the CS/CR kinetics and quantum yield of ultrafast CS is explored. Particular attention is paid to the energy efficiency of CS, as one of the most important parameters indicating the promise of using a molecular compound as a basis for emerging optoelectronic devices. The CS quantum yield and the energy efficiency of CS are shown to depend differently on the key model parameters. Necessary conditions for the highly efficient CS are evaluated using analytic formulae for the electron transfer rates and derived from numerical simulation data. The reasons why low-exergonic CS taking place in the Marcus normal region can be much slower than CR in the deep inverted region are discussed.

Upper Excited State Photophysics of Malachite Green in Solution and Films

Relaxation pathways of upper excited electronic states of malachite green (MG) in ethanol and in films are studied by steady-state and time-resolved spectroscopic techniques. In contrast to ethanol, where MG emits weak short-lived spectrally well separated S₂ and S₁ fluorescence with the lifetimes ∼0.3 and ∼0.9 ps, MG films show a much stronger broadband fluorescence within 430-700 nm, revealing multiexponential kinetics with the characteristic decay times τ₁ ≈ 1 ps, τ₂ ≈ 10 ps, τ₃ ≈ 0.05-0.8 ns, and τ₄ ≈ 2-3 ns. By the analysis of spectroscopic responses of MG in ethanol and in films as well as by theoretical modeling, we demonstrate that significant increase of fluorescence lifetimes and substantial enhancement of fluorescence intensity in MG films are stipulated by the decrease of efficiency of the S₂ → S₁ and S₁ → S₀ internal conversion, which in turn is caused by hindrance of rotation of MG's phenyl rings controlling the S₂/S₁ and S₁/S₀ conical intersections. These findings indicate that MG films may become promising non-Kasha materials (with reasonable S₂ emission) with numerous photophysical and photochemical applications.

Understanding and Designing Thermally Activated Delayed Fluorescence Emitters: Beyond the Energy Gap Approximation

In this article recent progress in the development of molecules exhibiting Thermally Activated Delayed Fluorescence (TADF) is discussed with a particular focus upon their application as emitters in highly efficient organic light emitting diodes (OLEDs). The key aspects controlling the desirable functional properties, e. g. fast intersystem crossing, high radiative rate and unity quantum yield, are introduced with a particular focus upon the competition between the key requirements needed to achieve high performance OLEDs. The design rules required for organic and metal organic materials are discussed, and the correlation between them outlined. Recent progress towards understanding the influence of the interaction between a molecule and its environment are explained as is the role of the mechanism for excited state formation in OLEDs. Finally, all of these aspects are combined to discuss the ability to implement high level design rules for achieving higher quality materials for commercial applications. This article highlights the significant progress that has been made in recent years, but also outlines the significant challenges which persist to achieve a full understanding of the TADF mechanism and improve the stability and performance of these materials.

Modifying the Nonradiative Decay Dynamics through Conical Intersections via Collective Coupling to a Cavity Mode

The coupling of a molecular ensemble to the confined electromagnetic modes of a microcavity can strongly modify the photophysics and photochemistry of the molecules upon photoexcitation. We investigate here how collective coupling effects lead to modifications of the mechanisms and rates of photochemical processes, in particular, photodissociation and nonradiative decay in NaI and pyrazine, respectively. We show that, after direct excitation into the lower polaritonic states, the lower-energy light-matter hybrid states, the dynamics of the molecular ensemble coupled to light is very similar to the dynamics of the corresponding isolated molecules. Conversely, excitation into the upper polaritonic states results in more complex dynamics that involve as a first step the population transfer toward the manifold of intermediate dark states. These dynamics differ substantially from those of the isolated molecules and may result in measurable time delays for nonradiative decay or excited-state reaction mechanisms. Similarly, we describe how addition of a buffer of nonreactive molecules coupled to the cavity mode can be used to delay the onset of the photochemical processes of the reactive part of the ensemble, where the buffer medium is more effective in inhibiting the reactive process than only reactive molecules in the cavity.

Optically Induced Electron Transfer in Mixed-Valence States: A Model Study on Electronic Transitions, Relaxation Dynamics, and Transient Absorption Spectroscopy

Quantum dynamical model calculations are performed on the optically induced electron transfer in a mixed-valence system interacting with different solvents. The simultaneously occurring processes of population transfer between electronic states and relaxation are studied in detail. Transient absorption traces, as recently recorded in our laboratory, are simulated, and the features of the spectra are related to the dynamics. The agreement with the experiment hints at the fact that the employed one-dimensional models catch the essentials of the photochemistry of the investigated systems and that they can be used for the interpretation of the transient absorption spectra. It is inferred that the ultrafast electron transfer processes take place on a sub-picosecond time scale and afterward relaxation occurs within several picoseconds.

Quantum dynamics and spectroscopy of dihalogens in solid matrices. II. Theoretical aspects and G-MCTDH simulations of time-resolved coherent Raman spectra of Schrödinger cat states of the embedded I2Kr18 cluster

This study presents quantum dynamical simulations, using the Gaussian-based multiconfigurational time-dependent Hartree (G-MCTDH) method, of time-resolved coherent Raman four-wave-mixing spectroscopic experiments for the iodine molecule embedded in a cryogenic crystal krypton matrix [D. Picconi et al., J. Chem. Phys. 150, 064111 (2019)]. These experiments monitor the time-evolving vibrational coherence between two wave packets created in a quantum superposition (i.e., a "Schrödinger cat state") by a pair of pump pulses which induce electronic B Πu30⁺⟵XΣg+1 transitions. A theoretical description of the spectroscopic measurement is developed, which elucidates the connection between the nonlinear signals and the wave packet coherence. The analysis provides an effective means to simulate the spectra for several different optical conditions with a minimum number of quantum dynamical propagations. The G-MCTDH method is used to calculate and interpret the time-resolved coherent Raman spectra of two selected initial superpositions for a I₂Kr₁₈ cluster embedded in a frozen Kr cage. The time- and frequency-dependent signals carry information about the molecular mechanisms of dissipation and decoherence, which involve vibrational energy transfer to the stretching mode of the four "belt" Kr atoms. The details of these processes and the number of active solvent modes depend in a non-trivial way on the specific initial superposition.

Ultrafast dynamics induced by the interaction of molecules with electromagnetic fields: Several quantum, semiclassical, and classical approaches

Several strategies for simulating the ultrafast dynamics of molecules induced by interactions with electromagnetic fields are presented. After a brief overview of the theory of molecule-field interaction, we present several representative examples of quantum, semiclassical, and classical approaches to describe the ultrafast molecular dynamics, including the multiconfiguration time-dependent Hartree method, Bohmian dynamics, local control theory, semiclassical thawed Gaussian approximation, phase averaging, dephasing representation, molecular mechanics with proton transfer, and multipolar force fields. In addition to the general overview, some focus is given to the description of nuclear quantum effects and to the direct dynamics, in which the ab initio energies and forces acting on the nuclei are evaluated on the fly. Several practical applications, performed within the framework of the Swiss National Center of Competence in Research "Molecular Ultrafast Science and Technology," are presented: These include Bohmian dynamics description of the collision of H with H2, local control theory applied to the photoinduced ultrafast intramolecular proton transfer, semiclassical evaluation of vibrationally resolved electronic absorption, emission, photoelectron, and time-resolved stimulated emission spectra, infrared spectroscopy of H-bonding systems, and multipolar force fields applications in the condensed phase.