Monitoring of singlet fission via two-dimensional photon-echo and transient-absorption spectroscopy: Simulations by multiple Davydov trial states

Making Peace with Random Phases: Ab Initio Conical Intersection Quantum Dynamics in Random Gauges

Ab initio modeling of conical intersection wave packet dynamics is crucial for various photochemical, photophysical, and biological processes. However, adiabatic electronic states obtained from electronic structure computations involve random phases, or more generally, random gauge fixings, which cannot be directly used in the modeling of nonadiabatic wave packet simulations. Here we develop a random-gauge local diabatic representation that allows an exact modeling of conical intersection dynamics directly using the adiabatic electronic states with phases randomly assigned during the electronic structure computations. Its utility is demonstrated by an exact ab initio modeling of the two-dimensional Shin-Metiu model with and without an external magnetic field. Our results provide a simple approach to integrating the electronic structure computations into nonadiabatic quantum dynamics, thus paving the way for ab initio modeling of conical intersection dynamics.

Electronic dynamics through conical intersections via non-Markovian stochastic Schrödinger equation with complex modes

Conical intersections (CIs) play a crucial role in photochemical reactions, offering an efficient channel for ultrafast non-adiabatic relaxation of excited states. This significantly influences the reaction pathways and the resulting products. In this work, we utilize the non-Markovian stochastic Schrödinger equation with complex modes method to explore the dynamics of electronic transitions through conical intersections (CIs) in pyrazine. The linear vibronic coupling model serves as the foundational framework, incorporating both intra-state and inter-state electron-vibrational interactions. The dynamics of the excited electronic transitions are analyzed across varying strengths of system-bath coupling and different bath relaxation times. The accuracy of this method is demonstrated by comparing its predictions with those from the hierarchical equations of motion method.

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.

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.

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.

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.

Accurate Simulation of Spectroscopic Signatures of Cavity-Assisted, Conical-Intersection-Controlled Singlet Fission Processes

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.

Engineering Cavity Singlet Fission in Rubrene

By employing the numerically exact multiple Davydov D₂ 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.

Simulation of Emission Spectra of Transition Metal Dichalcogenide Monolayers with the Multimode Brownian Oscillator Model

The multimode Brownian oscillator model is employed to simulate the emission spectra of transition metal dichalcogenide (TMD) monolayers. Good agreement is obtained between measured and simulated photoluminescence spectra of WSe₂, WS₂, MoSe₂, and MoS₂ at various temperatures. The Huang-Rhys factor extracted from the model can be associated with that from the modified semiempirical Varshni equation at high temperatures. Individual mechanisms leading to the unique temperature-dependent emission spectra of those TMDs are validated by the multimode Brownian oscillator (MBO) fitting, while it is, in turn, confirmed that the MBO analysis is an effective method for studying the optical properties of TMD monolayers. Parameters extracted from the MBO fitting can be used to explore exciton-photon-phonon dynamics of TMDs in a more comprehensive model.

Variational Squeezed Davydov Ansatz for Realistic Chemical Systems with Nonlinear Vibronic Coupling

Chemical systems normally possess strong nonlinear vibronic couplings at both zero and finite temperature. For the lowest-order quadratic couplings, here, we introduce a squeezing operator into a variational coherent-state-based method, Davydov ansatz, to simulate the quantum dynamics and the respective spectroscopy. Two molecular systems, pyrazine and the 2-pyridone dimer, are taken as calculated model systems, both of which involve nontrivial quadratic vibronic couplings in high- and low-frequency regions, respectively. Upon a comparison with the benchmarks, the method manifests its advantage for nonlinear couplings. The squeezed bases are also proven to be applicable for the finite temperature by adapting with the thermofield dynamics.

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.

Simulation of Time- and Frequency-Resolved Four-Wave-Mixing Signals at Finite Temperatures: A Thermo-Field Dynamics Approach

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.

Singlet fission dynamics and optical spectra of pentacene and its derivatives

A multimode Brownian oscillator model is employed to investigate the absorption spectra of pentacene and its derivatives in solution and thin films. Excellent agreement has been obtained between simulated and measured absorption spectra. Furthermore, using parameters obtained from fitting the absorption spectra of these pentacene derivatives, the singlet fission dynamics and two-dimensional electronic spectra of an ab initio Hamiltonian are investigated by Dirac-Frenkel time-dependent variation with multiple Davydov trial states. It is found that the periodic wave packet motion induced in the displaced excited state, and the accompanying vibrational relaxation, can be visualized by two-dimensional electronic spectra at short times.

Efficient simulation of time- and frequency-resolved four-wave-mixing signals with a multiconfigurational Ehrenfest approach

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.

Singlet Fission Dynamics in Tetracene Single Crystals Probed by Polarization-Dependent Two-Dimensional Electronic Spectroscopy

The exact mechanism of endothermic singlet fission in crystalline polyacene remains to be clarified. It has been elusive whether the excess energy of vibrational hot states and the upper branch of Davydov splitting is important for the energy compensation. Here, we probe the excited-state specified singlet fission dynamics in tetracene single crystals by polarization-dependent two-dimensional electronic spectroscopy (2DES). While a major spectral transfer with a characteristic lifetime of 86 ps is observed to be largely independent of the excitation energy due to formation of the spatially separated triplet pairs (¹(T···T)), the excitation-energy dependent subpicosecond dynamics show marked differences for different states probed, implying the possible involvement of a coherently formed triplet pair state (¹(TT)). Analysis of coherent vibrational modes suggests the coupling to high energy modes may offset the energy difference between singlet and triplet pair states. Moreover, the beating map of the low frequency mode indicates a vibrational hot state violating the aggregation behavior of Davydov exciton, which can be explained as a resonance of the ¹(TT) state. These results suggest that the coherent vibronic mixing between local excitation and triplet pair states is essential for the singlet fission dynamics in molecule aggregates.