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Most of spectroscopic signals are specified by the nonlinear laser-induced polarization. In recent years, population-detection of signals becomes a trend in femtosecond spectroscopy. Polarization-detected (PD) and population-detected signals are fundamentally different, because they are determined by photoinduced processes acting on disparate time scales. In this work, we consider the fluorescence-detected (FD) N -wave-mixing ( N WM) signal as a representative example of population-detected signals, derive a rigorous expression for this signal, and discuss its approximate variants suitable for numerical simulations. This leads us to the definition of the phenomenological FD (PFD) signal, which contains as a special case all definitions of FD signals available in the literature. Then we formulate and prove the population-polarization equivalence (PPE) theorem, which states that PFD N WM signals produced by (possibly strong) laser pulses can be evaluated as conventional PD signals in which the effective polarization is determined by the PFD transition dipole moment operator. We use the PPE theorem for the construction of the ab initio protocol for the simulation of PFD 4WM signals. As an example, we calculate electronic two-dimensional (2D) PFD spectra of the gas-phase pyrazine and compare them with the corresponding PD 2D spectra.

Two-dimensional (2D) fluorescence-excitation (2D-FLEX) spectroscopy is a recently proposed nonlinear femtosecond technique for the detection of photoinduced dynamics. The method records a time-resolved fluorescence signal in its excitation- and detection-frequency dependence and hence combines the exclusive detection of excited state dynamics (fluorescence) with signals resolved in both excitation and emission frequencies (2D electronic spectroscopy). In this work, we develop an on-the-fly protocol for the simulation of 2D-FLEX spectra of molecular systems, which is based on interfacing the classical doorway-window representation of spectroscopic responses with trajectory surface hopping simulations. Applying this methodology to gas-phase pyrazine, we show that femtosecond 2D-FLEX spectra can deliver detailed information that is otherwise obtainable via attosecond spectroscopy.

A fully quantum, numerically accurate methodology is presented for the simulation of the exciton dynamics and time-resolved fluorescence of cavity-tuned two-dimensional (2D) materials at finite temperatures. This approach was specifically applied to a monolayer WSe2 system. Our methodology enabled us to identify the dynamical and spectroscopic signatures of polaronic and polaritonic effects and to elucidate their characteristic timescales across a range of exciton-cavity couplings. The approach employed can be extended to simulation of various cavity-tuned 2D materials, specifically for exploring finite temperature nonlinear spectroscopic signals.

The efficiency of light-harvesting and energy transfer in multi-chromophore ensembles underpins natural photosynthesis. Dendrimers are highly branched synthetic multi-chromophoric conjugated supra-molecules that mimic these natural processes. After photoexcitation, their repeated units participate in a number of intramolecular electronic energy relaxation and redistribution pathways that ultimately funnel to a sink. Here, a model four-branched dendrimer with a pyrene core is theoretically studied using nonadiabatic molecular dynamics simulations. We evaluate excited-state photoinduced dynamics of the dendrimer, and demonstrate on-the-fly simulations of its transient absorption pump-probe (TA-PP) spectra. We show how the evolutions of the simulated TA-PP spectra monitor in real time photoinduced energy relaxation and redistribution, and provide a detailed microscopic picture of the relevant energy-transfer pathways. To the best of our knowledge, this is the first of this kind of on-the-fly atomistic simulation of TA-PP signals reported for a large molecular system., Competing Interests: There are no conflicts to declare., (This journal is © The Royal Society of Chemistry.)

In recent years, machine learning (ML) surrogate models have emerged as an indispensable tool to accelerate simulations of physical and chemical processes. However, there is still a lack of ML models that can accurately predict molecular vibrational spectra. Here, we present a highly efficient multitask ML surrogate model termed Vibrational Spectra Neural Network (VSpecNN), to accurately calculate infrared (IR) and Raman spectra based on dipole moments and polarizabilities obtained on-the-fly via ML-enhanced molecular dynamics simulations. The methodology is applied to pyrazine, a prototypical polyatomic chromophore. The VSpecNN-predicted energies are well within the chemical accuracy (1 kcal/mol), and the errors for VSpecNN-predicted forces are only half of those obtained from a popular high-performance ML model. Compared to the ab initio reference, the VSpecNN-predicted frequencies of IR and Raman spectra differ only by less than 5.87 cm -1 , and the intensities of IR spectra and the depolarization ratios of Raman spectra are well reproduced. The VSpecNN model developed in this work highlights the importance of constructing highly accurate neural network potentials for predicting molecular vibrational spectra.

The dynamics of the sub-Ohmic spin-boson model under polarized initial conditions at finite temperatures is investigated by employing both analytical tools and the numerically accurate hierarchical equations of motion-tensor train method. By analyzing the features of nonequilibrium dynamics, we discovered a bifurcation phenomenon, which separates two regimes of the dynamics. It is found that before the bifurcation time, increasing temperature slows down the population dynamics, while the opposite effect occurs after the bifurcation time. The dynamics is highly sensitive to both initial preparation of the bath and thermal effects., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Time-resolved spectroscopy is an important tool for unraveling the minute details of structural changes in molecules of biological and technological significance. The nonlinear femtosecond signals detected for such systems must be interpreted, but it is a challenging task for which theoretical simulations are often indispensable. Accurate simulations of transient absorption or two-dimensional electronic spectra are, however, computationally very expensive, prohibiting the wider adoption of existing first-principles methods. Here, we report an artificial-intelligence-enhanced protocol to drastically reduce the computational cost of simulating nonlinear time-resolved electronic spectra, which makes such simulations affordable for polyatomic molecules of increasing size. The protocol is based on the doorway-window approach for the on-the-fly surface-hopping simulations. We show its applicability for the prototypical molecule of pyrazine for which it produces spectra with high precision with respect to ab initio reference while cutting the computational cost by at least 95% compared to pure first-principles simulations.

By employing the numerically accurate multiple Davydov Ansatz (mDA) formalism in combination with the thermo-field dynamics (TFD) representation of quantum mechanics, we systematically explore the influence of three parameters-temperature, photonic-mode detuning, and qubit-phonon coupling-on population dynamics and absorption spectra of the Holstein-Tavis-Cummings (HTC) model. It is found that elevated qubit-phonon couplings and/or temperatures have a similar impact on all dynamic observables: they suppress the amplitudes of Rabi oscillations in photonic populations as well as broaden the peaks and decrease their intensities in the absorption spectra. Our results unequivocally demonstrate that the HTC dynamics is very sensitive to the concerted variation of the three aforementioned parameters, and this finding can be used for fine-tuning polaritonic transport. The developed mDA-TFD methodology can be efficiently applied for modeling, predicting, optimizing, and comprehensively understanding dynamic and spectroscopic responses of actual molecular systems in microcavities., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2024 Author(s). Published under an exclusive license by AIP Publishing.)

Employing the numerically accurate multiple Davydov Ansatz in combination with the thermo-field dynamics approach, we delve into the interplay of the finite-temperature dynamics of holes and magnons in an antiferromagnet, which allows for scrutinizing previous predictions from the self-consistent Born approximation while offering, for the first time, accurate finite-temperature computation of detailed magnon dynamics as a response and a facilitator to the hole motion. The study also uncovers a pronounced temperature dependence of the magnon and hole populations, pointing to the feasibility of potential thermal manipulation and control of hole dynamics. Our methodology can be applied not only to the calculation of steady-state angular-resolved photoemission spectra but also to the simulation of femtosecond terahertz pump-probe and other nonlinear signals for the characterization of antiferromagnetic materials.

The t-J model remains an indispensable construct in high-temperature superconductivity research, bridging the gap between charge dynamics and spin interactions within antiferromagnetic matrices. This study employs the multiple Davydov Ansatz method with thermo-field dynamics to dissect the zero-temperature and finite-temperature behaviors. We uncover the nuanced dependence of hole and spin deviation dynamics on the spin-spin coupling parameter J, revealing a thermally-activated landscape where hole mobilities and spin deviations exhibit a distinct temperature-dependent relationship. This numerically accurate thermal perspective augments our understanding of charge and spin dynamics in an antiferromagnet.

We formulate a contraction theorem that maps quantum dynamics of a multilevel degenerate system (DS) driven by a time-dependent external field to the dynamics of the corresponding contracted non-degenerate system (CNS) of lower dimension, provided transitions between each pair of degenerate levels in the DS have identical transition dipole moments. The theorem is valid for an external field of any strength and shape, with and without rotating wave approximation in the system-field interaction. It establishes explicit relations between DS and CNS observables, significantly simplifies numerical calculations, and clarifies physical origins of the field-induced DS dynamics., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The effects of thermal light-matter interaction on the dynamics of photo-induced electronic transitions in molecules are investigated using a novel first principles approach based on the thermo-field dynamics description of both the molecular vibrational modes and of the radiation field. The developed approach permits numerically accurate simulations of quantum dynamics of electronic/excitonic systems coupled to nuclear and photonic baths kept at different temperatures. The baths can be described by arbitrary spectral densities and can have any system-bath coupling strengths. In agreement with the results obtained previously by less rigorous methods, we show that the excitation process obtained by the continuous interaction with the suddenly turned-on thermal radiation field creates a mixed ensemble having a nonnegligible component consisting of a superposition of vibronic eigenstates which can sustain coherent oscillations for relatively long times. The results become especially relevant for the dynamics of electronic transitions upon sunlight excitation. Analytical results based on time-dependent perturbation theory support the numerical simulations and provide a simple interpretation of the time evolution of quantum observables.

We propose a novel UV/Vis femtosecond spectroscopic technique, two-dimensional fluorescence-excitation (2D-FLEX) spectroscopy, which combines spectral resolution during the excitation process with exclusive monitoring of the excited-state system dynamics at high time and frequency resolution. We discuss the experimental feasibility and realizability of 2D-FLEX, develop the necessary theoretical framework, and demonstrate the high information content of this technique by simulating the 2D-FLEX spectra of a model four-level system and the Fenna-Matthews-Olson antenna complex. We show that the evolution of 2D-FLEX spectra with population time directly monitors energy transfer dynamics and can thus yield direct qualitative insight into the investigated system. This makes 2D-FLEX a highly efficient instrument for real-time monitoring of photophysical processes in polyatomic molecules and molecular aggregates., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

Transient absorption UV pump X-ray probe spectroscopy has been established as a versatile technique for the exploration of ultrafast photoinduced dynamics in valence-excited states. In this work, an ab initio theoretical framework for the simulation of time-resolved UV pump X-ray probe spectra is presented. The method is based on the description of the radiation-matter interaction in the classical doorway-window approximation and a surface-hopping algorithm for the nonadiabatic nuclear excited-state dynamics. Using the second-order algebraic-diagrammatic construction scheme for excited states, UV pump X-ray probe signals were simulated for the carbon and nitrogen K edges of pyrazine, assuming a duration of 5 fs of the UV pump and X-ray probe pulses. It is predicted that spectra measured at the nitrogen K edge carry much richer information about the ultrafast nonadiabatic dynamics in the valence-excited states of pyrazine than those measured at the carbon K edge.

We investigate the dynamics of Landau-Zener (LZ) transitions in an anisotropic, dissipative three-level LZ model (3-LZM) using the numerically accurate multiple Davydov D2Ansatz in the framework of the time-dependent variational principle. It is demonstrated that a non-monotonic relationship exists between the Landau-Zener transition probability and the phonon coupling strength when the 3-LZM is driven by a linear external field. Under the influence of a periodic driving field, phonon coupling may induce peaks in contour plots of the transition probability when the magnitude of the system anisotropy matches the phonon frequency. The 3-LZM coupled to a super-Ohmic phonon bath and driven by a periodic external field exhibits periodic population dynamics in which the period and amplitude of the oscillations decrease with the bath coupling strength., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

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., (© 2023 Author(s). Published under an exclusive license by AIP Publishing.)

The dynamics of the (sub-)Ohmic spin-boson model under various bath initial conditions is investigated by employing the Dirac-Frenkel time-dependent variational approach with the multiple Davydov D 1 Ansatz in the interaction picture. The validity of our approach is carefully checked by comparing the results with those of the hierarchy equations of motion method. By analyzing the features of nonequilibrium dynamics, we identify the phase diagrams for different bath initial conditions. We find that for the spectral exponent s < s c , there exists a transition from coherent to quasicoherent dynamics with increasing coupling strengths. For s c < s ≤ 1, the coherent to incoherent crossover occurs at a certain coupling strength and the quasicoherent dynamics emerges at much larger couplings. The initial preparation of the bath has a considerable influence on the dynamics.

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 WSe 2 system. Specifically, the multiple Davydov D 2 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.

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.

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 → TT 1 SF in real time. We demonstrate that SF can proceed directly from the upper state S N , bypassing the lowest excited state, S 1 . We determine the main S N → TT 1 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 S 1 → TT 1 SF. We claim that the S N → TT 1 SF offers novel promising opportunities for engineering SF systems and enhancing SF yields.

A numerically accurate, fully quantum methodology has been developed for the simulation of the dynamics and nonlinear spectroscopic signals of cavity-assisted, conical-intersection-controlled singlet fission systems. The methodology is capable of handling several molecular systems strongly coupled to the photonic mode of the cavity and treats the intrinsic conical intersection and cavity-induced polaritonic conical intersections in a numerically exact manner. Contributions of higher-lying molecular electronic states are accounted for comprehensively. The intriguing process of cavity-modified fission dynamics, including all of its electronic, vibrational, and photonic degrees of freedom, together with its two-dimensional spectroscopic manifestation, is simulated for two rubrene dimers strongly coupled to the cavity mode.

By employing the numerically exact multiple Davydov D 2 ansatz, we study cavity-manipulated singlet fission that is mediated by polaritonic conical intersections for both one- and two-molecule systems. The population evolution of the TT state and the cavity photons is carefully examined in search for a high fission efficiency via cavity engineering. Several interesting mechanisms have been uncovered, such as photon-assisted singlet fission, system localization via a displaced photon state, and collective enhancement of the fission efficiency for the two-molecule system. It is also found that the system localization process in the two-molecule system differs substantially from that in the one-molecule system because of the appearance of a novel central polaritonic conical intersection in the two-molecule system. It has been demonstrated that the cavity-controlled singlet fission process can be switched on and off by controlling the average pumping photon number.

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.

By employing the time-dependent variational principle and the versatile multi-D 2 Davydov trial states, in combination with the Green's function method, we study the dynamics of the Tavis-Cummings model and the Holstein-Tavis-Cummings model in the presence of diagonal disorder and cavity-qubit coupling disorder. For the Tavis-Cummings model, time evolution of the photon population, the optical absorption spectra, and the hetero-entanglement between the qubits and the cavity mode are calculated by using the Green's function method to corroborate numerically exact results of Davydov's Ansätze. For the Holstein-Tavis-Cummings model, only the latter is utilized to simulate effects of disorder on the photon population dynamics and the absorption spectra. We have demonstrated that the complementary employment of analytical and numerical methods permits uncovering a fairly comprehensive picture of a variety of complex behaviors in disordered multidimensional polaritonic cavity quantum electrodynamics systems.

Two-dimensional (2D) electronic spectroscopy is a powerful nonlinear technique which provides spectroscopic information on two frequency axes as well as dynamical information as a function of the so-called waiting time. Herein, an ab initio theoretical framework for the simulation of electronic 2D spectra has been developed. The method is based on the classical approximation to the doorway-window representation of three-pulse photon-echo signals and the description of nuclear motion by classical trajectories. Nonadiabatic effects are taken into account by a trajectory surface-hopping algorithm. 2D electronic spectra were simulated with ab initio on-the-fly trajectory calculations using the ADC(2) electronic-structure method for the pyrazine molecule, which is a benchmark system for ultrafast radiationless decay through conical intersections. It is demonstrated that 2D spectroscopy with subfemtosecond UV pulses can provide unprecedented detailed information on the ultrafast photodynamics of polyatomic molecules.

A long 0.9 ps lifetime of the upper excited singlet state in perylene is resolved by femtosecond pump-probe measurements under ultraviolet (4.96 eV) excitation and further validated by theoretical simulations of transient absorption kinetics. This finding prompts exploration and development of novel perylene-based materials for upper excited state photochemistry applications.

The time-resolved polarization-sensitive transient-absorption (TA) pump-probe (PP) spectra are simulated using on-the-fly surface-hopping nonadiabatic dynamics and the doorway-window representation of nonlinear spectroscopy. A dendrimer model system composed of two linear phenylene ethynylene units (2-ring and 3-ring) is taken as an example. The ground-state bleach (GSB), stimulated emission (SE), and excited-state absorption (ESA) contributions as well as the total TA PP signals are obtained and carefully analyzed. It is shown that intramolecular excited-state energy transfer from the 2-ring unit to the 3-ring unit can be conveniently identified by employing pump and probe pulses with different polarizations. Our results demonstrate that time-resolved polarization-sensitive TA PP signals provide a powerful tool for the elucidation of excited-state energy-transfer pathways, notably in molecular systems possessing several optically bright nonadiabatically coupled electronic states with different orientations of transition dipole moments.

We present a unified and highly numerically efficient formalism for the simulation of quantum dynamics of complex molecular systems, which takes into account both temperature effects and static disorder. The methodology is based on the thermo-field dynamics formalism, and Gaussian static disorder is included into simulations via auxiliary bosonic operators. This approach, combined with the tensor-train/matrix-product state representation of the thermalized stochastic wave function, is applied to study the effect of dynamic and static disorders in charge-transfer processes in model organic semiconductor chains employing the Su-Schrieffer-Heeger (Holstein-Peierls) model Hamiltonian.

Volatile organic compounds (VOCs) present in human breath not only provide information about the internal chemistry of the body but can also be specific to diseases. Therefore, detection and analysis of specific VOCs can be used for medical diagnostics. However, up until today in spite of several existing VOC-based detection techniques and significant efforts, breath analysis is not a diagnostic method available for clinicians. Infrared absorption spectroscopy is a promising technique to fill this gap, with tens of identified VOCs in breath. Currently, a lack of digital spectral databases and several masking effects make difficult reliable molecular identification of observed absorption features. We demonstrate that calculations of rotational bands of vibrational spectra could serve as a basic method for molecular identification of spectral features observed in experiment. Results of comparison of several known VOCs spectra with the predictions of the theoretical model are presented., Competing Interests: Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper., (Copyright © 2021 Elsevier B.V. All rights reserved.)

A computational protocol for simulating time-resolved photoelectron signals of medium-sized molecules is presented. The procedure is based on a trajectory surface-hopping description of the excited-state dynamics and a combined Dyson orbital and multicenter B-spline approach for the computation of cross sections and asymmetry parameters. The accuracy of the procedure has been illustrated for the case of ultrafast internal conversion of gas-phase pyrazine excited to the 1 B 2 u (ππ*) state. The simulated spectra and the asymmetry map are compared to the experimental data, and a very good agreement was obtained without applying any energy-dependent rescaling or broadening. An interesting side result of this work is the finding that the signature of the 1 A u ( n π*) state is indistinguishable from that of the 1 B 3 u ( n π*) state in the time-resolved photoelectron spectrum. By locating four symmetrically equivalent minima on the lowest-excited (S 1 ) adiabatic potential energy surface of pyrazine, we revealed the strong vibronic coupling of the 1 A u ( n π*) and 1 B 3 u ( n π*) states near the S 1 ← S 0 band origin.

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.

We propose a new approach to simulate four-wave-mixing signals of molecular systems at finite temperatures by combining the multiconfigurational Ehrenfest method with the thermo-field dynamics theory. In our approach, the four-time correlation functions at finite temperatures are mapped onto those at zero temperature in an enlarged Hilbert space with twice the vibrational degrees of freedom. As an illustration, we have simulated three multidimensional spectroscopic signals, time- and frequency-resolved fluorescence spectra, transient-absorption pump-probe spectra, and electronic two-dimensional (2D) spectra at finite temperatures, for a conical intersection-mediated singlet fission model of a rubrene crystal. It is shown that a detailed dynamical picture of the singlet fission process can be extracted from the three spectroscopic signals. An increasing temperature leads to lower intensities of the signals and broadened vibrational peaks, which can be attributed to faster singlet-triplet population transfer and stronger bath-induced electronic dephasing at higher temperatures.

For a broad class of quantum models of practical interest, we demonstrate that the Hamiltonian of the system nonlinearly coupled to a harmonic bath through the system and bath coordinates can be equivalently mapped into the Hamiltonian of the system bilinearly coupled to the bath through the system and bath momenta. We show that the Hamiltonian with bilinear system-bath momentum coupling can be treated by the hierarchical equations-of-motion (HEOM) method and present the corresponding proof-of-principle simulations. The developed methodology creates the opportunity to scrutinize a new family of nonlinear quantum systems by the numerically accurate HEOM method.

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.

Confined nanoscale spaces, electric fields, and tunneling currents make the molecular electronic junction an experimental device for the discovery of new out-of-equilibrium chemical reactions. Reaction-rate theory for current-activated chemical reactions is developed by combining the Keldysh nonequilibrium Green's function treatment of electrons, Fokker-Planck description of the reaction coordinate, and Kramers first-passage time calculations. The nonequilibrium Green's functions (NEGF) provide an adiabatic potential as well as a diffusion coefficient and temperature with local dependence on the reaction coordinate. Van Kampen's Fokker-Planck equation, which describes a Brownian particle moving in an external potential in an inhomogeneous medium with a position-dependent friction and diffusion coefficient, is used to obtain an analytic expression for the first-passage time. The theory is applied to several transport scenarios: a molecular junction with a single reaction coordinate dependent molecular orbital and a model diatomic molecular junction. We demonstrate the natural emergence of Landauer's blowtorch effect as a result of the interplay between the configuration dependent viscosity and diffusion coefficients. The resultant localized heating in conjunction with the bond-deformation due to current-induced forces is shown to be the determining factors when considering chemical reaction rates, each of which results from highly tunable parameters within the system.

We have extended the multiconfigurational Ehrenfest approach to the simulation of four-wave-mixing signals of systems involving multiple electronic and vibrational degrees of freedom. As an illustration, we calculate signals of three widely used spectroscopic techniques, time- and frequency-resolved fluorescence spectroscopy, transient absorption spectroscopy, and two-dimensional (2D) electronic spectroscopy, for a two-electronic-state, twenty-four vibrational-mode conical intersection model. It has been shown that all these three spectroscopic signals characterize fast population transfer from the higher excited electronic state to the lower excited electronic state. While the time- and frequency-resolved spectrum maps the wave packet propagation exclusively on the electronically excited states, the transient absorption and 2D electronic spectra reflect the wave packet dynamics on both electronically excited states and the electronic ground state. Combining trajectory-guided Gaussian basis functions and the nonlinear response function formalism, the present approach provides a promising general technique for the applications of various Gaussian basis methods to the calculations of four-wave-mixing spectra of polyatomic molecules.

Experimental measurements of electron transport properties of molecular junctions are often performed in solvents. Solvent-molecule coupling and physical properties of the solvent can be used as the external stimulus to control the electric current through a molecule. In this paper, we propose a model that includes dynamical effects of solvent-molecule interaction in non-equilibrium Green's function calculations of the electric current. The solvent is considered as a macroscopic dipole moment that reorients stochastically and interacts with the electrons tunneling through the molecular junction. The Keldysh-Kadanoff-Baym equations for electronic Green's functions are solved in the time domain with subsequent averaging over random realizations of rotational variables using the Furutsu-Novikov method for the exact closure of infinite hierarchy of stochastic correlation functions. The developed theory requires the use of wideband approximation as well as classical treatment of solvent degrees of freedom. The theory is applied to a model molecular junction. It is demonstrated that not only electrostatic interaction between molecular junction and solvent but also solvent viscosity can be used to control electrical properties of the junction. Alignment of the rotating dipole moment breaks the particle-hole symmetry of the transmission favoring either hole or electron transport channels depending upon the aligning potential.

Finite-temperature dynamics of singlet fission in crystalline rubrene is investigated by utilizing the Dirac-Frenkel time-dependent variational method in combination with multiple Davydov D 2 trial states. To probe temperature effects on the singlet fission process mediated by a conical intersection, the variational method is extended to include number state propagation with thermally averaged Boltzmann distribution as initialization. This allows us to simulate two-dimensional electronic spectroscopic signals of two-mode and three-mode models of crystalline rubrene in the temperature range from 0 K to 300 K. It is demonstrated that an elevated temperature facilitates excitonic population transfer and accelerates the singlet fission process. In addition, increasing temperature leads to dramatic changes in two-dimensional spectra, thanks to temperature-dependent electronic dephasing and to an increased number of system eigenstates amenable to spectroscopic probing.

We studied spectroscopic signatures of the nonadiabatic dynamics at conical intersections formed by the lowest excited singlet states in pyrazine. We considered two ab initio models of conical intersections in the excited states of pyrazine developed by Sala et al. [Phys. Chem. Chem. Phys. 16, 15957 (2014)]: a two-state (B 2u and B 3u ), five-mode model and a three-state (B 2u , B 3u , and A u ), nine-mode model. We simulated the signals of three widely used techniques: time- and frequency-resolved fluorescence spectroscopy, transient absorption pump-probe spectroscopy, and electronic two-dimensional spectroscopy. The signals were calculated through third-order response functions, which, in turn, were evaluated with the numerically accurate multiple Davydov ansatz. We establish spectroscopic signatures of the optically dark A u state and demonstrate that the key features of the photoinduced dynamics, such as electronic/nuclear populations, electronic/nuclear coherences, and electronic/nuclear energy transfer processes, are imprinted in the spectroscopic signals. We show that a fairly complete picture of the nonadiabatic dynamics at conical intersections can be obtained when several spectroscopic techniques are combined. Provided that the time resolution is sufficient, time- and frequency-resolved fluorescence may provide the best visualization of the nonadiabatic dynamics near conical intersections.

The effects of high pulse intensity and chirp on two-dimensional electronic spectroscopy signals are experimentally investigated in the highly non-perturbative regime using atomic rubidium vapor as clean model system. Data analysis is performed based on higher-order Feynman diagrams and non-perturbative numerical simulations of the system response. It is shown that higher-order contributions may lead to a fundamental change of the static appearance and beating-maps of the 2D spectra and that chirped pulses enhance or suppress distinct higher-order pathways. We further give an estimate of the threshold intensity beyond which the high-intensity effects become visible for the system under consideration.

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 S 2 and S 1 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 τ 1 ≈ 1 ps, τ 2 ≈ 10 ps, τ 3 ≈ 0.05-0.8 ns, and τ 4 ≈ 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 S 2 → S 1 and S 1 → S 0 internal conversion, which in turn is caused by hindrance of rotation of MG's phenyl rings controlling the S 2 /S 1 and S 1 /S 0 conical intersections. These findings indicate that MG films may become promising non-Kasha materials (with reasonable S 2 emission) with numerous photophysical and photochemical applications.

We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integrals and exciton-phonon couplings are carefully examined by a detailed comparison with the fully variational multiple Davydov D 2 ansatz. It is found that while the MCE approach and the multi-D 2 ansatz produce almost exactly the same results for a small transfer integral, the results obtained by the multi-D 2 ansatz start to deviate from those by the MCE approach at longer times for a large transfer integral. A large number of coherent state basis functions are required to characterize the delocalized features of the phonon wavefunction in the case of large transfer integral, which becomes computationally too demanding for the multi-D 2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate and efficient simulations of polaron dynamics.

Monitoring of wave packet dynamics at conical intersections by time- and frequency-resolved fluorescence spectroscopy has been investigated theoretically for a three-state two-mode model of a conical intersection coupled to a dissipative environment. The ideal and the actually measurable time- and frequency-gated fluorescence spectra are accurately and efficiently simulated by combining the hierarchy equations-of-motion method for dissipative quantum dynamics with the methodology of the equation-of-motion phase-matching approach for the calculation of spectroscopic signals. It is shown that time- and frequency-resolved fluorescence spectra reveal essential aspects of the wave packet dynamics at conical intersections and the effects of environment-induced dissipation. The results of the present work indicate that fluorescence up-conversion spectroscopy with femtosecond time resolution is an efficient tool for the characterization of ultrafast dynamics at conical intersections.

Employing the Dirac-Frenkel time dependent variational method, the nonlinear spectra monitoring the singlet fission process mediated by a conical intersection (CI) of the two lowest excited electronic states are investigated for different optical dephasings. The simulated two-dimensional spectra at different population times follow ultrafast population transfer through the CI and exhibit spectral features related to the tuning mode. The anticorrelated oscillations of cross peaks located at symmetric positions with respect to the main diagonal are clearly identified after the stimulated-emission contribution quenches. The simulated transient absorption signals show a fast decay of the first excited singlet state and exhibit multiple peaks revealing the tuning mode. These findings could be regarded as signatures of the CI in the singlet fission process.

We study the effect of a dissipative environment on the orientational relaxation of a three-dimensional quantum linear rotor. We provide a derivation of the Hamiltonian of a linear rotor coupled to a harmonic bath from first principles, confirming earlier conjectures. The dynamics generated by this Hamiltonian is investigated by the hierarchical equations-of-motion method assuming a Drude spectral density of the bath. We perform numerically accurate simulations and analyze the behavior of orientational correlation functions and the rotational structures of infrared absorption and Raman scattering spectra. We explore the features of orientational correlation functions and their spectra for a wide range of system-bath couplings, bath memory times, and temperatures. We discuss the signatures of the orientational relaxation in the underdamped regime, the strongly damped regime, and the librational regime. We show that the behavior of orientational correlation functions and their spectra can conveniently be analyzed in terms of three characteristic times, which are explicitly expressed in terms of the parameters of the Hamiltonian.

Unraveling the many facets of coherent and incoherent exciton motion in an ensemble of chromophores is an inherently complex quantum mechanical problem that has triggered a vivid debate on the role of quantum effects in molecular materials and biophysical systems. Here the dynamics of a statistical ensemble of molecular aggregates consisting of identical chromophores is investigated within a new theoretical framework. Taking account of intrinsic properties of the system, the Hamiltonian of the aggregate is partitioned into two mutually commuting vibrational and vibronic operators. This representation paves the way for an analysis that reveals the role of static disorder in ensembles of aggregates. Using analytical methods, it is demonstrated that after a critical time τ D ≃ 2π/σ (σ being the dispersion of the disorder) any dynamic variable of the aggregate exhibits purely vibrational dynamics. This result is confirmed by exact numerical calculations of the time-dependent site populations of the aggregate. These findings may be useful for the interpretation of recent femtosecond spectroscopic experiments on molecular aggregates.

We introduce and analyze the concept of the "ideal" time and frequency resolved transient-absorption pump-probe (PP) signal. The ideal signal provides the most direct link between the "real" (measurable) PP signal and the material system dynamics. The simulation of PP signals involves two steps. (i) The ideal signal, which exhibits perfect time and frequency resolution, is calculated. For this purpose, the probe pulse is replaced by an auxiliary continuous-wave pulse. (ii) The real signal is obtained by the convolution of the ideal signal with the appropriate time- and frequency-gate function, which depends on the envelope of the actual probe pulse. This concept has been used to simulate integral and dispersed PP signals for a model system exhibiting nonadiabatic and dissipative dynamics. The ideal signal is computed with the two-pulse equation-of-motion phase-matching approach which has been extended to take excited-state absorption into account. We demonstrate how the ideal signal, an object exhibiting the features of moving wave packets as well as stationary spectra, is related to real signals detected with short (good temporal resolution) or long (good frequency resolution) probe pulses.

The ultrafast nonadiabatic dynamics of a two-electronic-state four-vibrational-mode conical intersection coupled to a finite bath with up to 20 harmonic oscillators has been investigated by employing the multiple Davydov D 2 ansatz . It is demonstrated, using the multi-configuration time-dependent Hartree method as a benchmark, that this approach provides an efficient and robust description of the internal conversion process at multimode conical intersections. Thanks to the Gaussian nature of the Davydov ansatz , it allows for numerically accurate simulations of time-dependent diabatic and (for the first time for a 24-mode system) adiabatic populations of the electronic states and reduced probability densities of the tuning and coupling modes. The obtained adiabatic populations and wave packets can be used as benchmarks for the testing of various simulation methods, in particular, surface-hopping methods.