Coherent Motion Reveals Non-Ergodic Nature of Internal Conversion between Excited States

Ultrafast photochemistry and electron diffraction for cyclobutanone in the S2 state: Surface hopping with time-dependent density functional theory

We simulate the photodynamics of gas-phase cyclobutanone excited to the S2 state using fewest switches surface hopping (FSSH) dynamics powered by time-dependent density functional theory (TDDFT). We predict a total photoproduct yield of 8%, with a C3:C2 product ratio of 0 trajectories to 8 trajectories. One primary S2 → S1 conical intersection is identified involving the compression of an α-carbon-carbon-hydrogen bond angle. Excited state lifetimes computed with respect to electronic state populations were found to be 3.96 ps (S2 → S1) and 498 fs (S1 → S0). We also generate time-resolved difference pair distribution functions (ΔPDFs) from our TDDFT-FSSH dynamics results in order to generate direct comparisons with ultrafast electron diffraction experiment observables. Global and target analysis of time-resolved ΔPDFs produced a distinct set of lifetimes: (i) a 0.548 ps decay and (ii) a 1.69 ps decay, both resembling the S2 minimum, as well as (iii) a long decay that resembles the S1 minimum geometry and the fully separated C2 products. Finally, we contextualize our results by considering the impact of the most likely sources of significant errors.

Prediction of photodynamics of 200 nm excited cyclobutanone with linear response electronic structure and ab initio multiple spawning

Simulations of photochemical reaction dynamics have been a challenge to the theoretical chemistry community for some time. In an effort to determine the predictive character of current approaches, we predict the results of an upcoming ultrafast diffraction experiment on the photodynamics of cyclobutanone after excitation to the lowest lying Rydberg state (S2). A picosecond of nonadiabatic dynamics is described with ab initio multiple spawning. We use both time dependent density functional theory (TDDFT) and equation-of-motion coupled cluster singles and doubles (EOM-CCSD) theory for the underlying electronic structure theory. We find that the lifetime of the S2 state is more than a picosecond (with both TDDFT and EOM-CCSD). The predicted ultrafast electron diffraction spectrum exhibits numerous structural features, but weak time dependence over the course of the simulations.

The photodissociation dynamics and ultrafast electron diffraction image of cyclobutanone from the surface hopping dynamics simulation

The comprehension of nonadiabatic dynamics in polyatomic systems relies heavily on the simultaneous advancements in theoretical and experimental domains. The gas-phase ultrafast electron diffraction (UED) technique has attracted significant attention as a unique tool for monitoring photochemical and photophysical processes at the all-atomic level with high temporal and spatial resolutions. In this work, we simulate the UED spectra of cyclobutanone using the trajectory surface hopping method at the extended multi-state complete active space second order perturbation theory (XMS-CASPT2) level and thereby predict the results of the upcoming UED experiments in the Stanford Linear Accelerator Laboratory. The simulated results demonstrate that a few pathways, including the C2 and C3 dissociation channels, as well as the ring opening channel, play important roles in the nonadiabatic reactions of cyclobutanone. We demonstrate that the simulated UED signal can be directly interpreted in terms of atomic motions, which provides a unique way of monitoring the evolution of the molecular structure in real time. Our work not only provides numerical data that help to determine the accuracy of the well-known surface hopping dynamics at the high XMS-CASPT2 electronic-structure level but also facilitates the understanding of the microscopic mechanisms of the photoinduced reactions in cyclobutanone.

Using a multistate mapping approach to surface hopping to predict the ultrafast electron diffraction signal of gas-phase cyclobutanone

Using the recently developed multistate mapping approach to surface hopping (multistate MASH) method combined with SA(3)-CASSCF(12,12)/aug-cc-pVDZ electronic structure calculations, the gas-phase isotropic ultrafast electron diffraction (UED) of cyclobutanone is predicted and analyzed. After excitation into the n-3s Rydberg state (S2), cyclobutanone can relax through two S2/S1 conical intersections, one characterized by compression of the CO bond and the other by dissociation of the α-CC bond. Subsequent transfer into the ground state (S0) is then achieved via two additional S1/S0 conical intersections that lead to three reaction pathways: α ring-opening, ethene/ketene production, and CO liberation. The isotropic gas-phase UED signal is predicted from the multistate MASH simulations, allowing for a direct comparison to the experimental data. This work, which is a contribution to the cyclobutanone prediction challenge, facilitates the identification of the main photoproducts in the UED signal and thereby emphasizes the importance of dynamics simulations for the interpretation of ultrafast experiments.

Ultrafast electron diffraction of photoexcited gas-phase cyclobutanone predicted by ab initio multiple cloning simulations

We present the result of our calculations of ultrafast electron diffraction (UED) for cyclobutanone excited into the S2 electronic state, which is based on the non-adiabatic dynamics simulations with the Ab Initio Multiple Cloning (AIMC) method with the electronic structure calculated at the SA(3)-CASSCF(12,12)/aug-cc-pVDZ level of theory. The key features in the UED pattern were identified, which can be used to distinguish between the reaction pathways observed in the AIMC dynamics, although there is a significant overlap between representative signals due to the structural similarity of the products. The calculated UED pattern can be compared with the experiment.

Ultrafast photochemistry and electron-diffraction spectra in n → (3s) Rydberg excited cyclobutanone resolved at the multireference perturbative level

We study the ultrafast time evolution of cyclobutanone excited to the singlet n → Rydberg state through non-adiabatic surface-hopping simulationsperformed at extended multi-state complete active space second-order perturbation (XMS-CASPT2) level of theory. These dynamics predict relaxation to the ground-state with a timescale of 822 ± 45 fs with minimal involvement of the triplets. The major relaxation path to the ground-state involves a three-state degeneracy region and leads to a variety of fragmented photoproducts. We simulate the resulting time-resolved electron-diffraction spectra, which track the relaxation of the excited state and the formation of various photoproducts in the ground state.

The photochemistry of Rydberg-excited cyclobutanone: Photoinduced processes and ground state dynamics

Owing to ring strain, cyclic ketones exhibit complex excited state dynamics with multiple competing photochemical channels active on the ultrafast timescale. While the excited state dynamics of cyclobutanone after π* ← n excitation into the lowest-energy excited singlet (S1) state has been extensively studied, the dynamics following 3s ← n excitation into the higher-lying singlet Rydberg (S2) state are less well understood. Herein, we employ fully quantum multiconfigurational time-dependent Hartree (MCTDH) simulations using a model Hamiltonian as well as "on-the-fly" trajectory-based surface-hopping dynamics (TSHD) simulations to study the relaxation dynamics of cyclobutanone following 3s ← n excitation and to predict the ultrafast electron diffraction scattering signature of these relaxation dynamics. Our MCTDH and TSHD simulations indicate that relaxation from the initially-populated singlet Rydberg (S2) state occurs on the timescale of a few hundreds of femtoseconds to a picosecond, consistent with the symmetry-forbidden nature of the state-to-state transition involved. There is no obvious involvement of excited triplet states within the timeframe of our simulations (<2 ps). After non-radiative relaxation to the electronic ground state (S0), vibrationally hot cyclobutanone has sufficient internal energy to form multiple fragmented products including C2H4 + CH2CO (C2; 20%) and C3H6 + CO (C3; 2.5%). We discuss the limitations of our MCTDH and TSHD simulations, how these may influence the excited state dynamics we observe, and-ultimately-the predictive power of the simulated experimental observable.

Prediction Challenge: Simulating Rydberg photoexcited cyclobutanone with surface hopping dynamics based on different electronic structure methods

This research examines the nonadiabatic dynamics of cyclobutanone after excitation into the n → 3s Rydberg S2 state. It stems from our contribution to the Special Topic of the Journal of Chemical Physics to test the predictive capability of computational chemistry against unseen experimental data. Decoherence-corrected fewest-switches surface hopping was used to simulate nonadiabatic dynamics with full and approximated nonadiabatic couplings. Several simulation sets were computed with different electronic structure methods, including a multiconfigurational wavefunction [multiconfigurational self-consistent field (MCSCF)] specially built to describe dissociative channels, multireference semiempirical approach, time-dependent density functional theory, algebraic diagrammatic construction, and coupled cluster. MCSCF dynamics predicts a slow deactivation of the S2 state (10 ps), followed by an ultrafast population transfer from S1 to S0 (<100 fs). CO elimination (C3 channel) dominates over C2H4 formation (C2 channel). These findings radically differ from the other methods, which predicted S2 lifetimes 10-250 times shorter and C2 channel predominance. These results suggest that routine electronic structure methods may hold low predictive power for the outcome of nonadiabatic dynamics.

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.

Prediction challenge: First principles simulation of the ultrafast electron diffraction spectrum of cyclobutanone

Computer simulation has long been an essential partner of ultrafast experiments, allowing the assignment of microscopic mechanistic detail to low-dimensional spectroscopic data. However, the ability of theory to make a priori predictions of ultrafast experimental results is relatively untested. Herein, as a part of a community challenge, we attempt to predict the signal of an upcoming ultrafast photochemical experiment using state-of-the-art theory in the context of preexisting experimental data. Specifically, we employ ab initio Ehrenfest with collapse to a block mixed quantum-classical simulations to describe the real-time evolution of the electrons and nuclei of cyclobutanone following excitation to the 3s Rydberg state. The gas-phase ultrafast electron diffraction (GUED) signal is simulated for direct comparison to an upcoming experiment at the Stanford Linear Accelerator Laboratory. Following initial ring-opening, dissociation via two distinct channels is observed: the C3 dissociation channel, producing cyclopropane and CO, and the C2 channel, producing CH2CO and C2H4. Direct calculations of the GUED signal indicate how the ring-opened intermediate, the C2 products, and the C3 products can be discriminated in the GUED signal. We also report an a priori analysis of anticipated errors in our predictions: without knowledge of the experimental result, which features of the spectrum do we feel confident we have predicted correctly, and which might we have wrong?

A CASSCF/MRCI trajectory surface hopping simulation of the photochemical dynamics and the gas phase ultrafast electron diffraction patterns of cyclobutanone

We present the simulation of the photochemical dynamics of cyclobutanone induced by the excitation of the 3 s Rydberg state. For this purpose, we apply the complete active space self-consistent field method together with the spin-orbit multireference configuration interaction singles treatment, combined with the trajectory surface hopping for the inclusion of nonadiabatic effects. The simulations were performed in the spin-adiabatic representation, including nine electronic states derived from three singlet and two triplet spin-diabatic states. Our simulations reproduce the two previously observed primary dissociation channels: the C2 pathway yielding C2H4 + CH2CO and the C3 pathway producing c-C3H6 + CO. In addition, two secondary products, CH2 + CO from the C2 pathway and C3H6 from the C3 pathway, both of them previously reported, are also observed in our simulation. We determine the ratio of the C3:C2 products to be about 2.8. Our findings show that most of the trajectories reach their electronic ground state within 200 fs, with dissociation events finished after 300 fs. We also identify the minimum energy conical intersections that are responsible for the relaxation and provide an analysis of the photochemical reaction mechanism based on multidimensional scaling. Furthermore, we demonstrate a minimal impact of triplet states on the photodissociation mechanism within the observed timescale. In order to provide a direct link to experiments, we simulate the gas phase ultrafast electron diffraction patterns and connect their features to the underlying structural dynamics.

Electronic state influence on selective bond breaking of core-excited nitrosyl chloride (ClNO)

The potential for selective bond breaking of a small molecule was investigated with electron-spectroscopy and electron-ion coincidence experiments on ClNO. The electron spectra were measured upon direct valence photo-ionization and upon resonant core-excitation at the N 1s- and O 1s-edges followed by emission of resonant Auger (RA) electrons. The RA spectra were analyzed with particular emphasis on the assignment of the participator and spectator states. The latter are of special relevance for investigations of how distinct electronic configurations influence selective bond breaking. The electron-ion coincidence measurements provided branching fractions of the produced ion-fragments as a function of electron binding energy. It explicitly demonstrates the influence of the final electronic states created after the photo-ionization and RA decay, on the fragmentation. In particular, we observe a significantly different branching fraction for spectator states compared with participator states. The bonds broken for the spectator states are also found to correlate with the anti-bonding character of the spectator-electron orbital.

Electronic relaxation and dissociation dynamics in formaldehyde: pump wavelength dependence

The effect of the incident UV pump wavelength on the subsequent excited state dynamics, electronic relaxation, and ultimate dissociation of formaldehyde is studied using first principles simulation and Coulomb explosion imaging (CEI) experiments. Transitions in a vibronic progression in the à ← X̃ absorption band are systematically prepared using a tunable UV source which generates pulses centered at 304, 314, 329, and 337 nm. We find, both via ab initio simulation and experimental results, that the rate of excited state decay and subsequent dissociation displays a prominent dependence on which vibronic transition in the absorption band is prepared by the pump. Our simulations predict that nonadiabatic transition rates and dissociation yields will increase by a factor of >100 as the pump wavelength is decreased from 337 to 304 nm. The experimental results and theoretical simulations are in broad agreement and both indicate that the dissociation rate plateaus rapidly after ≈2 ps following an ultrafast sub-ps rise.

Coherent internal conversion from high lying electronic states to S1 in boron-dipyrromethene derivatives

Internal conversion is the first step after photoexcitation to high lying electronic states, and plays a central role in many photoinduced processes. In this report, we demonstrate a truly ultrafast internal conversion (IC) in large molecules by time-resolved fluorescence (TF). Following photoexcitation to the S_n (n ≥ 2) state, TF of the S₁ state was recorded for two boron-dipyrromethene (BODIPY) derivatives in solution. IC to S₁ takes place nearly instantaneously within 20 fs for both molecules. Abundant nuclear wave packet motions in the S₁ state are manifest in the TF signals, which demonstrates that the IC in these BODIPY molecules is coherent with respect to most of the vibrational modes. Theoretical calculations assuming impulsive IC to S₁ account for the wave packet dynamics accurately.

Theoretical modelling of the dynamics of primary photoprocess of cyclopropanone

Photodecomposition of cyclopropanone is investigated by static quantum chemical calculations and non-adiabatic molecular dynamics (NAMD) simulations.

Coherence in nonradiative transitions: internal conversion in Rydberg-excited N-methyl and N-ethyl morpholine

The survival of coherent wavepacket motion during internal conversions is observed in relatively large molecules, N-methyl morpholine and N-ethyl morpholine, where standard models imply fast decoherence in a statistical limit.

The involvement of triplet receiver states in the ultrafast excited state processes of small esters

The photoinduced processes of methyl formate and methyl acetate have been probed by femtosecond time-resolved mass spectrometry and photoelectron spectroscopy experiments supported by quantum chemical calculations.

The role of novel Rydberg-valence behaviour in the non-adiabatic dynamics of tertiary aliphatic amines

Time-resolved photoelectron imaging was used to study non-adiabatic relaxation dynamics in N,N-dimethylisopropylamine, N,N-dimethylpropylamine and N-methylpyrrolidine following excitation at 200 nm. This series of tertiary aliphatic amines are all of similar chemical makeup, but exhibit differences in their structure - being branched, straight-chain and cyclic, respectively. Our experimental investigation, supported by extensive theoretical calculations, provides considerable new insight into the nature of the internal conversion processes that mediate dynamical evolution between electronic states of predominantly Rydberg character in this important class of model photochemical systems. In particular, the angle-resolved data afforded by the imaging approach (something not previously reported for tertiary aliphatic amines) offers novel and highly-detailed mechanistic information about the overall relaxation pathway. Strikingly, both the experimental and theoretical findings suggest that a critical factor driving the non-adiabatic dynamics is the evolution of valence character along an N-C stretching coordinate within a member of the 3p manifold. This is in stark contrast to primary and secondary amines, as well as many other small hetero-atom containing organic species, where evolution of valence character within the 3s state is now a well-established phenomenon implicated in mediating ultrafast non-adiabatic photochemistry.

The geometrical change and intramolecular energy transfer upon S1←S0 excitation in cyclopentanone

The ultrafast dynamics in vibrationally hot S1 electronic excited state in cyclopentanone molecule was discovered with time resolved spectroscopy. Investigation of the geometry change upon the S1←S0 excitation and D0←S1 ionization has shown that the dihedral angle between the C=O bond and the plane given by the carbonyl and the α-carbons is 180° either in S0 or D0 state and is reduced to 145.8° by out-out-plane deformation of the oxygen in S1 state according to the theoretical calculation. The time domain experiments with femtosecond resolution have given rich insights into the energy transfer of the cyclopentanone molecule. The molecules are excited to the vibrationally hot S1 (n,  π(∗)) state following absorption of one 267-nm photon. It is found that the population of the S1 (n, π(∗)) state undergoes ultrafast internal conversion to the highly vibrationally hot S0 state within 80 fs and nonradiative deactivation by intersystem crossing to triplet T1 (n, π(*)) state occurring in 3.14 ps. Several Rydberg states have worked as stepping stones during the ionization. The available energy was distributed in the symmetric methylene group wagging and the symmetric skeletal ring breathing modes in D0 state.

Coherent Nuclear Wave Packets in Q States by Ultrafast Internal Conversions in Free Base Tetraphenylporphyrin

Persistence of vibrational coherence in electronic transition has been noted especially in biochemical systems. Here, we report the dynamics between electronic excited states in free base tetraphenylporphyrin (H2TPP) by time-resolved fluorescence with high time resolution. Following the photoexcitation of the B state, ultrafast internal conversion occurs to the Qx state directly as well as via the Qy state. Unique and distinct coherent nuclear wave packet motions in the Qx and Qy states are observed through the modulation of the fluorescence intensity in time. The instant, serial internal conversions from the B to the Qy and Qx states generate the coherent wave packets. Theory and experiment show that the observed vibrational modes involve the out-of-plane vibrations of the porphyrin ring that are strongly coupled to the internal conversion of H2TPP.

Ultrafast structural dynamics in Rydberg excited N,N,N′,N′-tetramethylethylenediamine: conformation dependent electron lone pair interaction and charge delocalization

Time-resolved Rydberg fingerprint spectroscopy and quantum calculations reveal the structure dependent electron lone pair interaction and charge delocalization in real time.