Finite-Temperature, Anharmonicity, and Duschinsky Effects on the Two-Dimensional Electronic Spectra from Ab Initio Thermo-Field Gaussian Wavepacket Dynamics

Artificial-Intelligence-Enhanced On-the-Fly Simulation of Nonlinear Time-Resolved Spectra

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.

Finite-temperature vibronic spectra from the split-operator coherence thermofield dynamics

We present a numerically exact approach for evaluating vibrationally resolved electronic spectra at finite temperatures using the coherence thermofield dynamics. In this method, which avoids implementing an algorithm for solving the von Neumann equation for coherence, the thermal vibrational ensemble is first mapped to a pure-state wavepacket in an augmented space, and this wavepacket is then propagated by solving the standard, zero-temperature Schrödinger equation with the split-operator Fourier method. We show that the finite-temperature spectra obtained with the coherence thermofield dynamics in a Morse potential agree exactly with those computed by Boltzmann-averaging the spectra of individual vibrational levels. Because the split-operator thermofield dynamics on a full tensor-product grid is restricted to low-dimensional systems, we briefly discuss how the accessible dimensionality can be increased by various techniques developed for the zero-temperature split-operator Fourier method.

Prediction of fluorescence quantum yields using the extended thawed Gaussian approximation

Spontaneous emission and internal conversion rates are calculated within harmonic approximations and compared to the results obtained within the semi-classical extended thawed Gaussian approximation (ETGA). This is the first application of the ETGA in the calculation of internal conversion and emission rates for real molecular systems, namely, formaldehyde, fluorobenzene, azulene, and a dicyano-squaraine dye. The viability of the models as black-box tools for prediction of spontaneous emission and internal conversion rates is assessed. All calculations were done using a consistent protocol in order to investigate how different methods perform without previous experimental knowledge using density functional theory (DFT) and time-dependent DFT (TD-DFT) with B3LYP, PBE0, ωB97XD, and CAM-B3LYP functionals. Contrasting the results with experimental data shows that there are further improvements required before theoretical predictions of emission and internal conversion rates can be used as reliable indicators for the photo-luminescence properties of molecules. We find that the ETGA performs rather similar to the vertical harmonical model. Including anharmonicities in the calculation of internal conversion rates has a moderate effect on the quantitative results in the studied systems. The emission rates are fairly stable with respect to computational parameters, but the internal conversion rate reveals itself to be highly dependent on the choice of the spectral line shape function, particularly the width of the Lorentzian function, associated with homogeneous broadening.

Anharmonic Assignment of the Water Octamer Spectrum in the OH Stretch Region

We interface the quasi-classical trajectory approach with an ab initio potential energy surface for water to assign the vibrational spectroscopical features of the OH stretch region of the water octamer cluster, which is considered to be a precursor of ice. An attempt by Li et al. to assign their recent reference experiment involved lower-level calculations based on an ad hoc scaled harmonic approach. Differently from the conclusions of this previous assignment, which invoked the contribution of 5 conformers and a solvated form of the water heptamer in the spectrum, we find out that the spectroscopic features can be related to the 4 conformers of the octamer lying lower in energy.

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.

Vibrational spectroscopy simulation of solvation effects on a G-quadruplex

It is commonly believed that solvation effects on the vibrational properties of a solute are easily accounted for by simple rules of thumbs, that is, solvating a polar molecule in a polar medium has the only effect of red shifting all its spectroscopical features and, similarly, solvating a polar molecule in a nonpolar medium has the opposite effect. In this work, we use theoretical vibrational spectroscopy at quasi-classical and quantum approximate semiclassical level to gain atomistic insights about solvent-solute interactions for 2'-deoxyguanosine and the G-quadruplex. We employ the quasi-classical trajectory method to include full anharmonicity into our calculated spectra, and then introduce quantum nuclear effects by means of divide-and-conquer semiclassical spectroscopy calculations. Solvation is treated explicitly leading to a good reproducibility of the available experimental data and reliable predictions when an experimental reference is missing.Communicated by Ramaswamy H. Sarma.

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.

Semiclassical and VSCF/VCI Calculations of the Vibrational Energies of trans- and gauche-Ethanol Using a CCSD(T) Potential Energy Surface

A recent full-dimensional Δ-Machine learning potential energy surface (PES) for ethanol is employed in semiclassical and vibrational self-consistent field (VSCF) and virtual-state configuration interaction (VCI) calculations, using MULTIMODE, to determine the anharmonic vibrational frequencies of vibration for both the trans and gauche conformers of ethanol. Both semiclassical and VSCF/VCI energies agree well with the experimental data. We find significant mixing between the VSCF basis states due to Fermi resonances between bending and stretching modes. The same effects are also accurately described by the full-dimensional semiclassical calculations. These are the first high-level anharmonic calculations using a PES, in particular a "gold-standard" CCSD(T) one.

Characterizing Mode Anharmonicity and Huang-Rhys Factors Using Models of Femtosecond Coherence Spectra

Femtosecond laser pulses readily produce coherent quantum beats in transient-absorption spectra. These oscillatory signals often arise from molecular vibrations and therefore may contain information about the excited-state potential energy surface near the Franck-Condon region. Here, by fitting the measured spectra of two laser dyes to microscopic models of femtosecond coherence spectra (FCS) arising from molecular vibrations, we classify coherent quantum-beat signals as fundamentals or overtones and quantify their Huang-Rhys factors and anharmonicity values. We discuss the extracted Huang-Rhys factors in the context of quantum-chemical computations. This work solidifies the use of FCS for analysis of coherent quantum beats arising from molecular vibrations, which will aid studies of molecular aggregates and photosynthetic proteins.

Applicability of the Thawed Gaussian Wavepacket Dynamics to the Calculation of Vibronic Spectra of Molecules with Double-Well Potential Energy Surfaces

Simulating vibrationally resolved electronic spectra of anharmonic systems, especially those involving double-well potential energy surfaces, often requires expensive quantum dynamics methods. Here, we explore the applicability and limitations of the recently proposed single-Hessian thawed Gaussian approximation for the simulation of spectra of systems with double-well potentials, including 1,2,4,5-tetrafluorobenzene, ammonia, phosphine, and arsine. This semiclassical wavepacket approach is shown to be more robust and to provide more accurate spectra than the conventional harmonic approximation. Specifically, we identify two cases in which the Gaussian wavepacket method is especially useful due to the breakdown of the harmonic approximation: (i) when the nuclear wavepacket is initially at the top of the potential barrier but delocalized over both wells, e.g., along a low-frequency mode, and (ii) when the wavepacket has enough energy to classically go over the low potential energy barrier connecting the two wells. The method is efficient and requires only a single classical ab initio molecular dynamics trajectory, in addition to the data required to compute the harmonic spectra. We also present an improved algorithm for computing the wavepacket autocorrelation function, which guarantees that the evaluated correlation function is continuous for arbitrary size of the time step.

Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics

Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.

Calculating Multidimensional Optical Spectra from Classical Trajectories

Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra.

Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

Ab Initio Quasiclassical Simulation of Femtosecond Time-Resolved Two-Dimensional Electronic Spectra of Pyrazine

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 thermofield-based multilayer multiconfigurational time-dependent Hartree approach to non-adiabatic quantum dynamics at finite temperature

We introduce a thermofield-based formulation of the multilayer multiconfigurational time-dependent Hartree (MCTDH) method to study finite temperature effects on non-adiabatic quantum dynamics from a non-stochastic, wave function perspective. Our approach is based on the formal equivalence of bosonic many-body theory at zero temperature with a doubled number of degrees of freedom and the thermal quasi-particle representation of bosonic thermofield dynamics (TFD). This equivalence allows for a transfer of bosonic many-body MCTDH as introduced by Wang and Thoss to the finite temperature framework of thermal quasi-particle TFD. As an application, we study temperature effects on the ultrafast internal conversion dynamics in pyrazine. We show that finite temperature effects can be efficiently accounted for in the construction of multilayer expansions of thermofield states in the framework presented herein. Furthermore, we find our results to agree well with existing studies on the pyrazine model based on the ρMCTDH method.

Multi-state harmonic models with globally shared bath for nonadiabatic dynamics in the condensed phase

Model Hamiltonians constructed from quantum chemistry calculations and molecular dynamics simulations are widely used for simulating nonadiabatic dynamics in the condensed phase. The most popular two-state spin-boson model could be built by mapping the all-atom anharmonic Hamiltonian onto a two-level system bilinearly coupled to a harmonic bath using the energy gap time correlation function. However, for more than two states, there lacks a general strategy to construct multi-state harmonic (MSH) models since the energy gaps between different pairs of electronic states are not entirely independent and need to be considered consistently. In this paper, we extend the previously proposed approach for building three-state harmonic models for photoinduced charge transfer to the arbitrary number of electronic states with a globally shared bath and the system-bath couplings are scaled differently according to the reorganization energies between each pair of states. We demonstrate the MSH model construction for an organic photovoltaic carotenoid-porphyrin-C₆₀ molecular triad dissolved in explicit tetrahydrofuran solvent. Nonadiabatic dynamics was simulated using mixed quantum-classical techniques, including the linearized semiclassical and symmetrical quasiclassical dynamics with the mapping Hamiltonians, mean-field Ehrenfest, and mixed quantum-classical Liouville dynamics in two-state, three-state, and four-state harmonic models of the triad system. The MSH models are shown to provide a general and flexible framework for simulating nonadiabatic dynamics in complex systems.