Excited-State Molecular Dynamics Triggered by Light Pulses—Ab Initio Multiple Spawning vs Trajectory Surface Hopping

Angular Momentum Transfer between a Molecular System and a Continuous Circularly Polarized Light Field within a Semiclassical Born-Oppenheimer Surface Hopping Framework

We simulate semiclassically angular momentum transfer for a molecular system subject to a circularly polarized light (CPL) field either moving along a single Born-Oppenheimer (BO) surface or moving along multiple BO surfaces. Both sets of simulations are able to conserve the total angular momentum around the propagation direction of the CPL field, the former requiring a Berry force and the latter requiring a surface parametrized by both nuclear position and momentum (a so-called phase-space approach). Our results provide new insight into the nature of semiclassical nonadiabatic dynamics methods and further demonstrate the power of such methods to capture angular momentum transfer between different media, highlighting the need for accurate algorithms that conserve the total angular momentum.

An Exhaustive Quantum-Classical Study of C6F6+ Using the Newly Formulated Parallel TDDVR Method

We recently implemented our parallelized quantum-classical dynamical approach, known as the Time-Dependent Discrete Variable Representation (TDDVR) method, which is applied to the spectroscopically important hexafluorobenzene (HFBz) radical cation, where several conical intersections exist in their seven lowest excited electronic states (S11B2u, S21E1g, S31B1u, S41E1u, and S51A2u) considering degeneracy among potential energy surfaces (PESs), to demonstrate their various dynamical aspects. This new parallel version shows almost linear scalability with increasing number of computing processors. To get photoelectron (PE) spectra, Mass-Analyzed Threshold Ionization (MATI) spectra, population dynamics, and many other dynamical observables, the first-principles dynamics is applied at the state-of-the-art level to the corresponding Hamiltonian, where the Jahn-Teller (JT) and pseudo-Jahn-Teller (PJT) type interactions are involved in those coupled seven electronic states. The quantum-classical method is used to thoroughly analyze the effects of these couplings on the nuclear dynamics of the involved electronic states, and the findings are compared with those observables obtained from experiments. Intrinsic dynamical properties are explained using the reduced densities of the wave packet (WP) in a coupled electronic manifold. The PE and MATI spectra of HFBz computed using TDDVR are found to be in good agreement with earlier experimental data and other theoretically simulated spectra.

Organoboron Complexes as Thermally Activated Delayed Fluorescence (TADF) Materials for Organic Light-Emitting Diodes (OLEDs): A Computational Study

We report on organoboron complexes characterized by very small energy gaps (ΔEST) between their singlet and triplet states, which allow for highly efficient harvesting of triplet excitons into singlet states for working as thermally activated delayed fluorescence (TADF) devices. Energy gaps ranging between 0.01 and 0.06 eV with dihedral angles of ca. 90° were registered. The spin-orbit couplings between the lowest excited S1 and T1 states yielded reversed intersystem crossing rate constants (KRISC) of an average of 105 s-1. This setup accomplished radiative decay rates of ca. 106 s-1, indicating highly potent electroluminescent devices, and hence, being suitable for application as organic light-emitting diodes.

Probing the sensitivity of ab initio multiple spawning to its parameters

Full multiple spawning (FMS) offers a strategy to simulate the nonadiabatic dynamics of molecular systems by describing their nuclear wavefunctions by a linear combination of coupled trajectory basis functions (TBFs). Applying a series of controlled approximations to the full multiple spawning (FMS) equations leads to the ab initio multiple spawning (AIMS), which is compatible with an on-the-fly propagation of the TBFs and an accurate description of nonadiabatic processes. The AIMS strategy and its numerical implementations, however, rely on a series of user-defined parameters. Herein, we investigate the influence of these parameters on the electronic-state population of two molecular systems- trans-azomethane and a two-dimensional model of the butatriene cation. This work highlights the stability of AIMS with respect to most of its parameters, underlines the specific parameters that require particular attention from the user of the method, and offers prescriptions for an informed selection of their value.

Supplementary Information

The online version contains supplementary material available at 10.1007/s00214-023-03004-w.

Stochastic dynamic ultraviolet photofragmentation and high collision energy dissociation mass spectrometric kinetics of triadimenol and sucralose

The major goal of the paper is to provide empirical proof of view that innovative stochastic dynamic mass spectrometric equation D″_SD = 2.6388·10^-17·(< I² >  -  < I > ²) determines the exact analyte concentration in solution via quantifying experimental variable intensity (I) of an analyte ion per any short span of scan time of any measurement, which also appears applicable to quantify laser-induced ultraviolet photofragmentation and high energy collision dissociation mass spectrometric processes. Triadimenol (1) and sucralose (2) using positive and negative polarity are examined. Laser irradiation energy λ_ex = 213 nm is utilized. The issue is of central importance for monitoring organic micro-pollutants in surface, ground, and drinking water as well as tasks of risk assessment for environment and human health from contamination with organics. Despite the significant importance of the topic, answering the question of functional kinetic relations of such processes is by no means straightforward, so far, due to a lack of in-depth knowledge of mechanistic aspects of fragment paths of analytes in environment and foods as well as kinetics of processes under ultraviolet laser irradiation. Although there is truth in the classical theory of first-order reaction kinetics, it does not describe all kinetic data on analytes (1) and (2). A new damped sine wave functional response to a large amount of kinetics is presented. High-resolution mass spectrometric data and chemometrics are used. The study provides empirical evidence for claim that temporal behavior of mass spectrometric variable intensity under negative polarity obeys a certain scientific law written by means of equation above. It is the same for positive and negative soft-ionization mass spectrometric conditions.

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.

A Photochemical Reaction in Different Theoretical Representations

The Born–Oppenheimer picture has forged our representation and interpretation of photochemical processes, from photoexcitation down to the passage through a conical intersection, a funnel connecting different electronic states. In this work, we analyze a full in silico photochemical experiment, from the explicit electronic excitation by a laser pulse to the formation of photoproducts following a nonradiative decay through a conical intersection, by contrasting the picture offered by Born–Oppenheimer and that proposed by the exact factorization. The exact factorization offers an alternative understanding of photochemistry that does not rely on concepts such as electronic states, nonadiabatic couplings, and conical intersections. On the basis of nonadiabatic quantum dynamics performed for a two-state 2D model system, this work allows us to compare Born–Oppenheimer and exact factorization for (i) an explicit photoexcitation with and without the Condon approximation, (ii) the passage of a nuclear wavepacket through a conical intersection, (iii) the formation of excited stationary states in the Franck–Condon region, and (iv) the use of classical and quantum trajectories in the exact factorization picture to capture nonadiabatic processes triggered by a laser pulse.

Solvated Nuclear-Electronic Orbital Structure and Dynamics

Nonadiabatic dynamical processes such as proton-coupled electron transfer and excited state intramolecular proton transfer have been the subject of much research. One of the promising theoretical methods to describe these processes is the nuclear-electronic orbital (NEO) approach. This approach inherently accounts for nuclear quantum effects within quantum chemistry calculations, and it has recently been extended to directly simulate nonadiabatic processes with the development of real-time NEO methods. These processes can also be significantly dependent on the surrounding chemical environment, however, and capturing the effects of the environment is often necessary for analyzing experimentally relevant systems. This work couples the NEO density functional theory and real-time time-dependent density functional theory approaches with solvation through the polarizable continuum model. The effects of this coupling are investigated for ground state properties, solvent-dependent vibrational frequencies, and direct excited state intramolecular proton transfer dynamics.

Dynamics near a conical intersection-A diabolical compromise for the approximations of ab initio multiple spawning

Full multiple spawning (FMS) offers an exciting framework for the development of strategies to simulate the excited-state dynamics of molecular systems. FMS proposes to depict the dynamics of nuclear wavepackets by using a growing set of traveling multidimensional Gaussian functions called trajectory basis functions (TBFs). Perhaps the most recognized method emanating from FMS is the so-called ab initio multiple spawning (AIMS). In AIMS, the couplings between TBFs-in principle exact in FMS-are approximated to allow for the on-the-fly evaluation of required electronic-structure quantities. In addition, AIMS proposes to neglect the so-called second-order nonadiabatic couplings and the diagonal Born-Oppenheimer corrections. While AIMS has been applied successfully to simulate the nonadiabatic dynamics of numerous complex molecules, the direct influence of these missing or approximated terms on the nonadiabatic dynamics when approaching and crossing a conical intersection remains unknown to date. It is also unclear how AIMS could incorporate geometric-phase effects in the vicinity of a conical intersection. In this work, we assess the performance of AIMS in describing the nonadiabatic dynamics through a conical intersection for three two-dimensional, two-state systems that mimic the excited-state dynamics of bis(methylene)adamantyl, butatriene cation, and pyrazine. The population traces and nuclear density dynamics are compared with numerically exact quantum dynamics and trajectory surface hopping results. We find that AIMS offers a qualitatively correct description of the dynamics through a conical intersection for the three model systems. However, any attempt at improving the AIMS results by accounting for the originally neglected second-order nonadiabatic contributions appears to be stymied by the hermiticity requirement of the AIMS Hamiltonian and the independent first-generation approximation.

The Quest to Simulate Excited-State Dynamics of Transition Metal Complexes

This Perspective describes current computational efforts in the field of simulating photodynamics of transition metal complexes. We present the typical workflows and feature the strengths and limitations of the different contemporary approaches. From electronic structure methods suitable to describe transition metal complexes to approaches able to simulate their nuclear dynamics under the effect of light, we give particular attention to build a bridge between theory and experiment by critically discussing the different models commonly adopted in the interpretation of spectroscopic experiments and the simulation of particular observables. Thereby, we review all the studies of excited-state dynamics on transition metal complexes, both in gas phase and in solution from reduced to full dimensionality.

Exploring the effects of quantum decoherence on the excited-state dynamics of molecular systems

Fewest-switches surface hopping (FSSH) is employed in order to investigate the nonadiabatic excited-state dynamics of thiophene and related compounds and hence to establish a connection between the electronic system, the critical points in configuration space and the deactivation dynamics. The potential-energy surfaces of the studied molecules were calculated with complete active space self-consistent field and time-dependent density-functional theory. They are analyzed thoroughly to locate and optimize minimum-energy conical intersections, which are essential to the dynamics of the system. The influence of decoherence on the dynamics is examined by employing different decoherence schemes. We find that irrespective of the employed decoherence algorithm, the population dynamics of thiophene give results which are sound with the expectations grounded on the analysis of the potential-energy surface. A more detailed look at single trajectories as well as on the excited-state lifetimes, however, reveals a substantial dependence on how decoherence is accounted for. In order to connect these findings, we describe how ensemble averaging cures some of the overcoherence problems of uncorrected FSSH. Eventually, we identify carbon–sulfur bond cleavage as a common feature accompanying electronic transitions between different states in the simulations of all thiophene-related compounds studied in this work, which is of interest due to their relevance in organic photovoltaics.

Quantum and semiclassical dynamical studies of nonadiabatic processes in solution: achievements and perspectives

We concisely review the main methodological approaches to model nonadiabatic dynamics in isotropic solutions and their applications. Three general classes of models are identified as the most used to include solvent effects in the simulations. The first model describes the solvent as a set of harmonic collective modes coupled to the solute degrees of freedom, and the second as a continuum, while the third explicitly includes solvent molecules in the calculations. The issues related to the use of these models in semiclassical and quantum dynamical simulations are discussed, as well as the main limitations and perspectives of each approach.

Validating fewest-switches surface hopping in the presence of laser fields

The capability of fewest-switches surface hopping (FSSH) to describe non-adiabatic dynamics under explicit excitation with external fields is evaluated. Different FSSH parameters are benchmarked against multi-configurational time dependent Hartree (MCTDH) reference calculations using SO₂ and 2-thiocytosine as model, yet realistic, molecular systems. Qualitatively, FSSH is able to reproduce the trends in the MCTDH dynamics with (also without) an explicit external field; however, no set of FSSH parameters is ideal. The adequate treatment of the overcoherence in FSSH is revealed as the driving factor to improve the description of the excitation process with respect to the MCTDH reference. Here, two corrections were tested: the augmented-FSSH (AFSSH) correction and the energy-based decoherence correction. A dependence on the employed basis is detected in AFSSH, performing better when spin-orbit and external laser field couplings are treated as off-diagonal elements instead of projecting them onto the diagonal of the Hamilton operator. In the presence of an electric field, the excited state dynamics was found to depend strongly on the vector used to rescale the kinetic energy along after a transition between surfaces. For SO₂, recurrence of the excited wave packet throughout the duration of the applied laser pulse is observed for laser pulses (>100 fs), resulting in additional interferences missed by FSSH and only visible in variational multi-configurational Gaussian when utilizing a large number of Gaussian basis functions. This feature vanishes when going toward larger molecules, such as 2-thiocytosine, where this effect is barely visible in a laser pulse 200 fs long.

Quantum-classical nonadiabatic dynamics of Floquet driven systems

We develop a trajectory-based approach for excited-state molecular dynamics simulations of systems subject to an external periodic drive. We combine the exact-factorization formalism, allowing us to treat electron-nuclear systems in nonadiabatic regimes, with the Floquet formalism for time-periodic processes. The theory is developed starting with the molecular time-dependent Schrödinger equation with the inclusion of an external periodic drive that couples to the system dipole moment. With the support of the Floquet formalism, quantum dynamics is approximated by combining classical-like, trajectory-based, nuclear evolution with electronic dynamics represented in the Floquet basis. The resulting algorithm, which is an extension of the coupled-trajectory mixed quantum-classical scheme for periodically driven systems, is applied to a model study, exactly solvable, with different field intensities.

SSAIMS-Stochastic-Selection Ab Initio Multiple Spawning for Efficient Nonadiabatic Molecular Dynamics

Ab initio multiple spawning provides a powerful and accurate way of describing the excited-state dynamics of molecular systems, whose strength resides in the proper description of coherence effects during nonadiabatic processes thanks to the coupling of trajectory basis functions. However, the simultaneous propagation of a large number of trajectory basis functions can be numerically inconvenient. We propose here an elegant and simple solution to this issue, which consists of (i) detecting uncoupled groups of coupled trajectory basis functions and (ii) selecting stochastically one of these groups to continue the ab initio multiple spawning dynamics. We show that this procedure can reproduce the results of full ab initio multiple spawning dynamics in cases where the uncoupled groups of trajectory basis functions stay uncoupled throughout the dynamics (which is often the case in high-dimensional problems). We present and discuss the aforementioned idea in detail and provide simple numerical applications on indole, ethylene, and protonated formaldimine, highlighting the potential of stochastic-selection ab initio multiple spawning.

Real-Time Time-Dependent Nuclear-Electronic Orbital Approach: Dynamics beyond the Born-Oppenheimer Approximation

The quantum mechanical treatment of both electrons and nuclei is crucial in nonadiabatic dynamical processes such as proton-coupled electron transfer. The nuclear-electronic orbital (NEO) method provides an elegant framework for including nuclear quantum effects beyond the Born-Oppenheimer approximation. To enable the study of nonequilibrium properties, we derive and implement a real-time NEO (RT-NEO) approach based on time-dependent Hatree-Fock or density functional theory, in which the electronic and nuclear degrees of freedom are propagated in a time-dependent variational framework. Nuclear and electronic spectral features can be resolved from the time-dependent dipole moment computed using the RT-NEO method. The test cases show the dynamical interplay between the quantum nuclei and the electrons through vibronic coupling. Moreover, vibrational excitation in the RT-NEO approach is demonstrated by applying a resonant driving field, and electronic excitation is demonstrated by simulating excited state intramolecular proton transfer. This work shows that the RT-NEO approach is a promising tool to study nonadiabatic quantum dynamical processes within a time-dependent variational description for the coupled electronic and nuclear degrees of freedom.

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

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

A molecular perspective on Tully models for nonadiabatic dynamics

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

Exact Potential Energy Surface for Molecules in Cavities

We find and analyze the exact time-dependent potential energy surface driving the proton motion for a model of cavity-induced suppression of proton-coupled electron transfer. We show how, in contrast to the polaritonic surfaces, its features directly correlate to the proton dynamics and we discuss cavity modifications of its structure responsible for the suppression. The results highlight the interplay between nonadiabatic effects from coupling to photons and coupling to electrons and suggest caution is needed when applying traditional dynamics methods based on polaritonic surfaces.