Exploring Exact-Factorization-Based Trajectories for Low-Energy Dynamics near a Conical Intersection.

We study low-energy dynamics generated by a two-dimensional two-state Jahn-Teller Hamiltonian in the vicinity of a conical intersection using quantum wave packet and trajectory dynamics. Recently, these dynamics were studied by comparing the adiabatic representation and the exact factorization, with the purpose to highlight the different nature of topological-phase and geometric-phase effects arising in the two theoretical representations of the same problem. Here, we employ the exact factorization to understand how to accurately model low-energy dynamics in the vicinity of a conical intersection using an approximate description of the nuclear motion that uses trajectories. We find that since nonadiabatic effects are weak but non-negligible, the trajectory-based description that invokes the classical approximation struggles to capture the correct behavior.

Photofragmentation of cyclobutanone at 200 nm: TDDFT vs CASSCF electron diffraction.

To simulate a 200 nm photoexcitation in cyclobutanone to the n-3s Rydberg state, classical trajectories were excited from a Wigner distribution to the singlet state manifold based on excitation energies and oscillator strengths. Twelve singlet and 12 triplet states are treated using TD-B3LYP-D3/6-31+G** for the electronic structure, and the nuclei are propagated with the Tully surface hopping method. Using time-dependent density functional theory, we are able to predict the bond cleavage that takes place on the S1 surface as well as the ultrafast deactivation from the Rydberg n-3s state to the nπ*. After showing that triplet states and higher-lying singlet states do not play any crucial role during the early dynamics (i.e., the first 300 fs), the SA(6)-CASSCF(8,11)/aug-cc-pVDZ method is used as an electronic structure and the outcome of the non-adiabatic dynamic simulations is recomputed. Gas-phase ultrafast electron diffraction spectra are computed for both electronic structure methods, showing significantly different results.

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.

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.

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.

The 3s Rydberg state as a doorway state in the ultrafast dynamics of 1,1-difluoroethylene.

The deactivation dynamics of 1,1-difluoroethylene after light excitation is studied within the surface hopping formalism in the presence of 3s and 3p Rydberg states using multi-state second order perturbation theory (MS-CASPT2). Due to the proximity of the Rydberg π-3s state with the ππ* state, the states are mixed favoring ultrafast exchange of population via a conical intersection that closely resembles the equilibrium structure. After excitation, it is found that the π-3s state acts as a doorway state, trapping the population and delaying internal conversion to the ππ* state, from which deactivation to the closed-shell ground state takes place. Besides the conical intersection between the π-3s and ππ* states, five additional conical intersections between the ππ* state and the ground state are found, indicating that after the system is excited, it stretches the C[double bond, length as m-dash]C bond before it twists and pyramidalizes at any of the carbon atoms, in the spirit of a hula-twist mechanism.

Investigating the Photodynamics of trans-Azobenzene with Coupled Trajectories.

In this work, we present the first implementation of coupled-trajectory Tully surface hopping (CT-TSH) suitable for applications to molecular systems. We combine CT-TSH with the semiempirical floating occupation molecular orbital-configuration interaction electronic structure method to investigate the photoisomerization dynamics of trans-azobenzene. Our study shows that CT-TSH can capture correctly decoherence effects in this system, yielding consistent electronic and nuclear dynamics in agreement with (standard) decoherence-corrected TSH. Specifically, CT-TSH is derived from the exact factorization and the electronic coefficients' evolution is directly influenced by the coupling of trajectories, resulting in the improvement of internal consistency if compared to standard TSH.

On the Nature of Geometric and Topological Phases in the Presence of Conical Intersections.

The observable nature of topological phases related to conical intersections in molecules is studied. Topological phases should be ubiquitous in molecular processes, but their elusive character has often made them a topic of discussion. To shed some light on this issue, we simulate the dynamics governed by a Jahn-Teller Hamiltonian and analyze it employing two theoretical representations of the molecular wave function: the adiabatic and the exact factorization. We find fundamental differences between effects related to topological phases arising exclusively in the adiabatic representation, and thus not related to any physical observable, and geometric phases within the exact factorization that can be connected to an observable quantity. We stress that while the topological phase of the adiabatic representation is an intrinsic property of the Hamiltonian, the geometric phase of the exact factorization depends on the dynamics that the system undergoes and is connected to the circulation of the nuclear momentum field.

Significance of Energy Conservation in Coupled-Trajectory Approaches to Nonadiabatic Dynamics.

Through approximating electron-nuclear correlation terms in the exact factorization approach, trajectory-based methods have been derived and successfully applied to the dynamics of a variety of light-induced molecular processes, capturing quantum (de)coherence effects rigorously. These terms account for the coupling among the trajectories, recovering the nonlocal nature of quantum nuclear dynamics that is completely overlooked in traditional independent-trajectory algorithms. Nevertheless, some of the approximations introduced in the derivation of some of these methods do not conserve the total energy. We analyze energy conservation in the coupled-trajectory mixed quantum-classical (CTMQC) algorithm and explore the performance of a modified algorithm, CTMQC-E, where some of the terms are redefined to restore energy conservation. A set of molecular models is used as a test, namely, 2-cis-penta-2,4-dienimium cation, bis(methylene) adamantyl radical cation, butatriene cation, uracil radical cation, and neutral pyrazine.

Study of the Decoherence Correction Derived from the Exact Factorization Approach for Nonadiabatic Dynamics.

We present a detailed study of the decoherence correction to surface hopping that was recently derived from the exact factorization approach. Ab initio multiple spawning calculations that use the same initial conditions and the same electronic structure method are used as a reference for three molecules: ethylene, the methaniminium cation, and fulvene, for which nonadiabatic dynamics follows a photoexcitation. A comparison with the Granucci-Persico energy-based decoherence correction and the augmented fewest-switches surface-hopping scheme shows that the three decoherence-corrected methods operate on individual trajectories in a qualitatively different way, but the results averaged over trajectories are similar for these systems.

Excimer Intermediates en Route to Long-Lived Charge-Transfer States in Single-Stranded Adenine DNA as Revealed by Nonadiabatic Dynamics.

The ultrafast time evolution of a single-stranded adenine DNA is studied using a hybrid multiscale quantum mechanics/molecular mechanics (QM/MM) scheme coupled to nonadiabatic surface hopping dynamics. As a model, we use (dA)20 where a stacked adenine tetramer is treated quantum chemically. The dynamical simulations combined with on-the-fly quantitative wave function analysis evidence the nature of the long-lived electronically excited states formed upon absorption of UV light. After a rapid decrease of the initially excited excitons, relaxation to monomer-like states and excimers occurs within 100 fs. The former monomeric states then relax into additional excimer states en route to forming stabilized charge-transfer states on a longer timescale of hundreds of femtoseconds. The different electronic-state characters is reflected on the spatial separation between the adenines: excimers and charge-transfer states show a much smaller spatial separation than the monomer-like states and the initially formed excitons.

On the Theoretical Determination of Photolysis Properties for Atmospheric Volatile Organic Compounds.

Volatile organic compounds (VOCs) are ubiquitous atmospheric molecules that generate a complex network of chemical reactions in the troposphere, often triggered by the absorption of sunlight. Understanding the VOC composition of the atmosphere relies on our ability to characterize all of their possible reaction pathways. When considering reactions of (transient) VOCs with sunlight, the availability of photolysis rate constants, utilized in general atmospheric models, is often out of experimental reach due to the unstable nature of these molecules. Here, we show how recent advances in computational photochemistry allow us to calculate in silico the different ingredients of a photolysis rate constant, namely, the photoabsorption cross-section and wavelength-dependent quantum yields. The rich photochemistry of tert-butyl hydroperoxide, for which experimental data are available, is employed to test our protocol and highlight the strengths and weaknesses of different levels of electronic structure and nonadiabatic molecular dynamics to study the photochemistry of (transient) VOCs.

Tracking the ultraviolet-induced photochemistry of thiophenone during and after ultrafast ring opening.

Photoinduced isomerization reactions lie at the heart of many chemical processes in nature. The mechanisms of such reactions are determined by a delicate interplay of coupled electronic and nuclear dynamics occurring on the femtosecond scale, followed by the slower redistribution of energy into different vibrational degrees of freedom. Here we apply time-resolved photoelectron spectroscopy with a seeded extreme ultraviolet free-electron laser to trace the ultrafast ring opening of gas-phase thiophenone molecules following ultraviolet photoexcitation. When combined with ab initio electronic structure and molecular dynamics calculations of the excited- and ground-state molecules, the results provide insights into both the electronic and nuclear dynamics of this fundamental class of reactions. The initial ring opening and non-adiabatic coupling to the electronic ground state are shown to be driven by ballistic S-C bond extension and to be complete within 350 fs. Theory and experiment also enable visualization of the rich ground-state dynamics that involve the formation of, and interconversion between, ring-opened isomers and the cyclic structure, as well as fragmentation over much longer timescales.