Monitoring the Evolution of Relative Product Populations at Early Times during a Photochemical Reaction.

Identifying multiple rival reaction products and transient species formed during ultrafast photochemical reactions and determining their time-evolving relative populations are key steps toward understanding and predicting photochemical outcomes. Yet, most contemporary ultrafast studies struggle with clearly identifying and quantifying competing molecular structures/species among the emerging reaction products. Here, we show that mega-electronvolt ultrafast electron diffraction in combination with ab initio molecular dynamics calculations offer a powerful route to determining time-resolved populations of the various isomeric products formed after UV (266 nm) excitation of the five-membered heterocyclic molecule 2(5H)-thiophenone. This strategy provides experimental validation of the predicted high (∼50%) yield of an episulfide isomer containing a strained three-membered ring within ∼1 ps of photoexcitation and highlights the rapidity of interconversion between the rival highly vibrationally excited photoproducts in their ground electronic state.

Synthesis, Photophysical and Electronic Properties of a D-π-A Julolidine-Like Pyrenyl-o-Carborane.

We synthesized 2-(1-1,2-dicarbadodecaboranyl(12))-6,6,12,12-tetramethyl-7,8,11,12-tetrahydro-6H,10H-phenaleno[1,9-fg]pyrido[3,2,1-ij]quinoline (4), a julolidine-like pyrenyl-o-carborane, with pyrene substituted at the 2,7-positions on the HOMO/LUMO nodal plane. Using solid state molecular structures, photophysical data, cyclic voltammetry, DFT and LR-TDDFT calculations, we compare o-carborane and B(Mes)2 (Mes=2,4,6-Me3C6H2) as acceptor groups. Whereas the π-acceptor strength of B(Mes)2 is sufficient to drop the pyrene LUMO+1 below the LUMO, the carborane does not do this. We confirm the π-donor strength of the julolidine-like moiety, however, which raises the pyrene HOMO-1 above the HOMO. In contrast to the analogous pyrene-2-yl-o-carborane, 2-(1-1,2-dicarbadodecaboranyl(12))-pyrene VI, which exhibits dual fluorescence, because the rate of internal conversion between locally-excited (LE) and charge transfer (CT) (from the pyrene to the carborane) states is faster than the radiative decay rate, leading to a thermodynamic equilibrium between the 2 states, 4 shows only single fluorescence, as the CT state involving the carborane as the acceptor moiety in not kinetically accessible, so a more localized CT emission involving the julolidine-like pyrene moiety is observed.

A Theoretical Perspective on the Photochemistry of Boron-Nitrogen Lewis Adducts.

Boron-Nitrogen (B-N) Lewis adducts form a versatile family of compounds with numerous applications in functional molecules. Despite the growing interest in this family of compounds for optoelectronic applications, little is currently known about their photophysics and photochemistry. Even the electronic absorption spectrum of ammonia borane, the textbook example of a B-N Lewis adduct, is unavailable. Given the versatility of the light-induced processes exhibited by these molecules, we propose in this work a detailed theoretical study of the photochemistry and photophysics of simple B-N Lewis adducts. We used advanced techniques in computational photochemistry to identify and characterize the possible photochemical pathways followed by ammonia borane and extended this knowledge to the substituted B-N Lewis adducts pyridine-borane and pyridine-boric acid. The photochemistry observed for this series of molecules allows us to extract qualitative rules to rationalize the light-induced behavior of more complex B-N-containing molecules.

On the Topological Phase around Conical Intersections with Tamm-Dancoff Linear-Response Time-Dependent Density Functional Theory.

Regions of nuclear-configuration space away from the Franck-Condon geometry can prove problematic for some electronic structure methods, given the propensity of such regions to possess conical intersections, i.e., (highly connected) points of degeneracy between potential energy surfaces. With the likelihood (perhaps even inevitability) for nonadiabatic dynamics simulations to explore molecular geometries in close proximity to conical intersections, it is vital that the performance of electronic structure methods is routinely examined in this context. In a recent paper [Taylor, J. T. J. Chem. Phys. 2023, 159, 214115.], the ability of linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) to provide a proper description of conical intersections, in terms of their topology and topography, was investigated, with particular attention paid to conical intersections between two excited electronic states. For the same prototypical molecules, protonated formaldimine and pyrazine, we herein consider whether AA LR-TDDFT can correctly reproduce the topological phase accumulated by the adiabatic electronic wave function upon traversing a closed path around an excited-to-excited state conical intersection despite not using the appropriate quadratic-response nonadiabatic coupling vectors. Equally, we probe the ability of the ground-to-excited state intersection ring exhibited by AA LR-TDDFT in protonated formaldimine to give rise to a similar topological phase in spite of its incorrect dimensionality.

Predicting the photodynamics of cyclobutanone triggered by a laser pulse at 200 nm and its MeV-UED signals-A trajectory surface hopping and XMS-CASPT2 perspective.

This work is part of a prediction challenge that invited theoretical/computational chemists to predict the photochemistry of cyclobutanone in the gas phase, excited at 200 nm by a laser pulse, and the expected signal that will be recorded during a time-resolved megaelectronvolt ultrafast electron diffraction (MeV-UED). We present here our theoretical predictions based on a combination of trajectory surface hopping with XMS-CASPT2 (for the nonadiabatic molecular dynamics) and Born-Oppenheimer molecular dynamics with MP2 (for the athermal ground-state dynamics following internal conversion), coined (NA+BO)MD. The initial conditions were sampled from Born-Oppenheimer molecular dynamics coupled to a quantum thermostat. Our simulations indicate that the main photoproducts after 2 ps of dynamics are CO + cyclopropane (50%), CO + propene (10%), and ethene and ketene (34%). The photoexcited cyclobutanone in its second excited electronic state S2 can follow two pathways for its nonradiative decay: (i) a ring-opening in S2 and a subsequent rapid decay to the ground electronic state, where the photoproducts are formed, or (ii) a transfer through a closed-ring conical intersection to S1, where cyclobutanone ring opens and then funnels to the ground state. Lifetimes for the photoproduct and electronic populations were determined. We calculated a stationary MeV-UED signal [difference pair distribution function-ΔPDF(r)] for each (interpolated) pathway as well as a time-resolved signal [ΔPDF(r,t) and ΔI/I(s,t)] for the full swarm of (NA+BO)MD trajectories. Furthermore, our analysis provides time-independent basis functions that can be used to fit the time-dependent experimental UED signals [both ΔPDF(r,t) and ΔI/I(s,t)] and potentially recover the population of photoproducts. We also offer a detailed analysis of the limitations of our model and their potential impact on the predicted experimental signals.

Deciphering the Influence of Ground-State Distributions on the Calculation of Photolysis Observables.

Nonadiabatic molecular dynamics offers a powerful tool for studying the photochemistry of molecular systems. Key to any nonadiabatic molecular dynamics simulation is the definition of its initial conditions (ICs), ideally representing the initial molecular quantum state of the system of interest. In this work, we provide a detailed analysis of how ICs may influence the calculation of experimental observables by focusing on the photochemistry of methylhydroperoxide (MHP), the simplest and most abundant organic peroxide in our atmosphere. We investigate the outcome of trajectory surface hopping simulations for distinct sets of ICs sampled from different approximate quantum distributions, namely harmonic Wigner functions and ab initio molecular dynamics using a quantum thermostat (QT). Calculating photoabsorption cross-sections, quantum yields, and translational kinetic energy maps from the results of these simulations reveals the significant effect of the ICs, in particular when low-frequency (∼ a few hundred cm-1) normal modes are connected to the photophysics of the molecule. Overall, our results indicate that sampling ICs from ab initio molecular dynamics using a QT is preferable for flexible molecules with photoactive low-frequency modes. From a photochemical perspective, our nonadiabatic dynamics simulations offer an explanation for a low-energy tail observed at high excitation energy in the translational kinetic energy map of MHP.

On the description of conical intersections between excited electronic states with LR-TDDFT and ADC(2).

Conical intersections constitute the conceptual bedrock of our working understanding of ultrafast, nonadiabatic processes within photochemistry (and photophysics). Accurate calculation of potential energy surfaces within the vicinity of conical intersections, however, still poses a serious challenge to many popular electronic structure methods. Multiple works have reported on the deficiency of methods like linear-response time-dependent density functional theory within the adiabatic approximation (AA LR-TDDFT) or algebraic diagrammatic construction to second-order [ADC(2)]-approaches often used in excited-state molecular dynamics simulations-to describe conical intersections between the ground and excited electronic states. In the present study, we focus our attention on conical intersections between excited electronic states and probe the ability of AA LR-TDDFT and ADC(2) to describe their topology and topography, using protonated formaldimine and pyrazine as two exemplar molecules. We also take the opportunity to revisit the performance of these methods in describing conical intersections involving the ground electronic state in protonated formaldimine-highlighting in particular how the intersection ring exhibited by AA LR-TDDFT can be perceived either as a (near-to-linear) seam of intersection or two interpenetrating cones, depending on the magnitude of molecular distortions within the branching space.

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.

Photo-isomerization of the isolated photoactive yellow protein chromophore: what comes before the primary step?

Photoactive proteins typically rely on structural changes in a small chromophore to initiate a biological response. While these changes often involve isomerization as the "primary step", preceding this is an ultrafast relaxation of the molecular framework caused by the sudden change in electronic structure upon photoexcitation. Here, we capture this motion for an isolated model chromophore of the photoactive yellow protein using time-resolved photoelectron imaging. It occurs in <150 fs and is apparent from a spectral shift of ∼70 meV and a change in photoelectron anisotropy. Electronic structure calculations enable the quantitative assignment of the geometric and electronic structure changes to a planar intermediate from which the primary step can then proceed.

A Theoretical Perspective on the Actinic Photochemistry of 2-Hydroperoxypropanal.

The photochemical reactions triggered by the sunlight absorption of transient volatile organic compounds in the troposphere are notoriously difficult to characterize experimentally due to the unstable and short-lived nature of these organic molecules. Some members of this family of compounds are likely to exhibit a rich photochemistry given the diversity of functional groups they can bear. Even more interesting is the photochemical fate of volatile organic compounds bearing more than one functional group that can absorb light─this is the case, for example, of α-hydroperoxycarbonyls, which are formed during the oxidation of isoprene. Experimental observables characterizing the photochemistry of these molecules like photoabsorption cross-sections or photolysis quantum yields are currently missing, and we propose here to leverage a recently developed computational protocol to predict in silico the photochemical fate of 2-hydroperoxypropanal (2-HPP) in the actinic region. We combine different levels of electronic structure methods─SCS-ADC(2) and XMS-CASPT2─with the nuclear ensemble approach and trajectory surface hopping to understand the mechanistic details of the possible nonradiative processes of 2-HPP. In particular, we predict the photoabsorption cross-section and the wavelength-dependent quantum yields for the observed photolytic pathways and combine them to determine in silico photolysis rate constants. The limitations of our protocol and possible future improvements are discussed.

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.

Extended Conjugation Attenuates the Quenching of Aggregation-Induced Emitters by Photocyclization Pathways.

Herein, we expose how the antagonistic relationship between solid-state luminescence and photocyclization of oligoaryl alkene chromophores is modulated by the conjugation length of their alkenyl backbones. Heptaaryl cycloheptatriene molecular rotors exhibit aggregation-induced emission characteristics. We show that their emission is turned off upon breaking the conjugation of the cycloheptatriene by epoxide formation. While this modification is deleterious to photoluminescence, it enables formation of extended polycyclic frameworks by Mallory reactions. We exploit this dichotomy (i) to manipulate emission properties in a controlled manner and (ii) as a synthetic tool to link together pairs of phenyl rings in a specific sequence. This method to alter the tendency of oligoaryl alkenes to undergo photocyclization can inform the design of solid-state emitters that avoid this quenching mechanism, while also allowing selective cyclization in syntheses of polycyclic aromatic hydrocarbons.

Caveat when using ADC(2) for studying the photochemistry of carbonyl-containing molecules.

Several electronic-structure methods are available to study the photochemistry and photophysics of organic molecules. Among them, ADC(2) stands as a sweet spot between computational efficiency and accuracy. As a result, ADC(2) has recently seen its number of applications booming, in particular to unravel the deactivation pathways and photodynamics of organic molecules. Despite this growing success, we demonstrate here that care has to be taken when studying the nonradiative pathways of carbonyl-containing molecules, as ADC(2) appears to suffer from a systematic flaw.

Nonadiabatic Kinetics in the Intermediate Coupling Regime: Comparing Molecular Dynamics to an Energy-Grained Master Equation.

We propose and test an extension of the energy-grained master equation (EGME) for treating nonadiabatic (NA) hopping between different potential energy surfaces, which enables us to model the competition between stepwise collisional relaxation and kinetic processes which transfer population between different electronic states of the same spin symmetry. By incorporating Zhu-Nakamura theory into the EGME, we are able to treat NA passages beyond the simple Landau-Zener approximation, along with the corresponding treatments of zero-point energy and tunneling probability. To evaluate the performance of this NA-EGME approach, we carried out detailed studies of the UV photodynamics of the volatile organic compound C6-hydroperoxy aldehyde (C6-HPALD) using on-the-fly ab initio molecular dynamics and trajectory surface hopping. For this multichromophore molecule, we show that the EGME is able to capture important aspects of the dynamics, including kinetic timescales, and diabatic trapping. Such an approach provides a promising and efficient strategy for treating the long-time dynamics of photoexcited molecules in regimes which are difficult to capture using atomistic on-the-fly molecular dynamics.

AIMSWISS-Ab initio multiple spawning with informed stochastic selections.

Ab initio multiple spawning (AIMS) offers a reliable strategy to describe the excited-state dynamics and nonadiabatic processes of molecular systems. AIMS represents nuclear wavefunctions as linear combinations of traveling, coupled Gaussians called trajectory basis functions (TBFs) and uses a spawning algorithm to increase as needed the size of this basis set during nonadiabatic transitions. While the success of AIMS resides in this spawning algorithm, the dramatic increase in TBFs generated by multiple crossings between electronic states can rapidly lead to intractable dynamics. In this Communication, we introduce a new flavor of AIMS, coined ab initio multiple spawning with informed stochastic selections (AIMSWISS), which proposes a parameter-free strategy to beat the growing number of TBFs in an AIMS dynamics while preserving its accurate description of nonadiabatic transitions. The performance of AIMSWISS is validated against the photodynamics of ethylene, cyclopropanone, and fulvene. This technique, built upon the recently developed stochastic-selection AIMS, is intended to serve as a computationally affordable starting point for multiple spawning simulations.

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.

Comparing (stochastic-selection) ab initio multiple spawning with trajectory surface hopping for the photodynamics of cyclopropanone, fulvene, and dithiane.

Ab Initio Multiple Spawning (AIMS) simulates the excited-state dynamics of molecular systems by representing nuclear wavepackets in a basis of coupled traveling Gaussian functions, called trajectory basis functions (TBFs). New TBFs are spawned when nuclear wavepackets enter regions of strong nonadiabaticity, permitting the description of non-Born-Oppenheimer processes. The spawning algorithm is simultaneously the blessing and the curse of the AIMS method: it allows for an accurate description of the transfer of nuclear amplitude between different electronic states, but it also dramatically increases the computational cost of the AIMS dynamics as all TBFs are coupled. Recently, a strategy coined stochastic-selection AIMS (SSAIMS) was devised to limit the ever-growing number of TBFs and tested on simple molecules. In this work, we use the photodynamics of three different molecules-cyclopropanone, fulvene, and 1,2-dithiane-to investigate (i) the potential of SSAIMS to reproduce reference AIMS results for challenging nonadiabatic dynamics, (ii) the compromise achieved by SSAIMS in obtaining accurate results while using the smallest average number of TBFs as possible, and (iii) the performance of SSAIMS in comparison to the mixed quantum/classical method trajectory surface hopping (TSH)-both in terms of its accuracy and computational cost. We show that SSAIMS can accurately reproduce the AIMS results for the three molecules considered at a much cheaper computational cost, often close to that of TSH. We deduce from these tests that an overlap-based criterion for the stochastic-selection process leads to the best agreement with the reference AIMS dynamics for the smallest average number of TBFs.

Ab Initio Nonadiabatic Quantum Molecular Dynamics.

The Born-Oppenheimer approximation underlies much of chemical simulation and provides the framework defining the potential energy surfaces that are used for much of our pictorial understanding of chemical phenomena. However, this approximation breaks down when the dynamics of molecules in excited electronic states are considered. Describing dynamics when the Born-Oppenheimer approximation breaks down requires a quantum mechanical description of the nuclei. Chemical reaction dynamics on excited electronic states is critical for many applications in renewable energy, chemical synthesis, and bioimaging. Furthermore, it is necessary in order to connect with many ultrafast pump-probe spectroscopic experiments. In this review, we provide an overview of methods that can describe nonadiabatic dynamics, with emphasis on those that are able to simultaneously address the quantum mechanics of both electrons and nuclei. Such ab initio quantum molecular dynamics methods solve the electronic Schrödinger equation alongside the nuclear dynamics and thereby avoid the need for precalculation of potential energy surfaces and nonadiabatic coupling matrix elements. Two main families of methods are commonly employed to simulate nonadiabatic dynamics in molecules: full quantum dynamics, such as the multiconfigurational time-dependent Hartree method, and classical trajectory-based approaches, such as trajectory surface hopping. In this review, we describe a third class of methods that is intermediate between the two: Gaussian basis set expansions built around trajectories.

A molecular perspective on Tully models for nonadiabatic dynamics.

Over the past decades, an important number of methods have been developed to simulate the nonadiabatic dynamics of molecules, that is, the dynamics of molecules beyond the Born-Oppenheimer approximation. These nonadiabatic methods differ in the way they approximate the dynamics emanating from the time-dependent molecular Schrödinger equation. In 1990, Tully devised a series of three one-dimensional model systems to test the approximations of the method called trajectory surface hopping. The Tully models were designed to probe different scenarios of nonadiabatic processes, such as single and multiple nonadiabatic (re)crossings. These one-dimensional models rapidly became the testbed for any new nonadiabatic dynamics strategy. In this work, we present a molecular perspective to the Tully models by highlighting a correspondence between these simple one-dimensional models and processes happening during the excited-state dynamics of molecules. More importantly, each of these nonadiabatic processes can be connected to a given exemplary molecular system, and we propose here three molecules that could serve as molecular Tully models, reproducing some of the key features of the original models but this time in a high-dimensional space. We compare trajectory surface hopping with the ab initio multiple spawning for the three molecular Tully models and highlight particular features and differences between these methods resulting from their distinct approximations. We also provide all the necessary information - initial conditions and all required parameters for the dynamics as well as the electronic structure - employed in our simulations such that the molecular Tully models can become in the future a unified and standardized test for ab initio nonadiabatic molecular dynamics methods. The molecular Tully models also offer an exciting link between the world of low-dimensional model systems for nonadiabatic dynamics and the excited-state dynamics of molecular systems in their full dimensionality.

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.