Ultrafast Molecular Frame Quantum Tomography.

We develop and experimentally demonstrate a methodology for a full molecular frame quantum tomography (MFQT) of dynamical polyatomic systems. We exemplify this approach through the complete characterization of an electronically nonadiabatic wave packet in ammonia (NH_{3}). The method exploits both energy and time-domain spectroscopic data, and yields the lab frame density matrix (LFDM) for the system, the elements of which are populations and coherences. The LFDM fully characterizes electronic and nuclear dynamics in the molecular frame, yielding the time- and orientation-angle dependent expectation values of any relevant operator. For example, the time-dependent molecular frame electronic probability density may be constructed, yielding information on electronic dynamics in the molecular frame. In NH_{3}, we observe that electronic coherences are induced by nuclear dynamics which nonadiabatically drive electronic motions (charge migration) in the molecular frame. Here, the nuclear dynamics are rotational and it is nonadiabatic Coriolis coupling which drives the coherences. Interestingly, the nuclear-driven electronic coherence is preserved over longer timescales. In general, MFQT can help quantify entanglement between electronic and nuclear degrees of freedom, and provide new routes to the study of ultrafast molecular dynamics, charge migration, quantum information processing, and optimal control schemes.

A quantum molecular movie: polyad predissociation dynamics in the VUV excited 3pσ2Σu state of NO2.

The optical formation of coherent superposition states, a wavepacket, can allow the study of zeroth-order states, the evolution of which exhibit structural and electronic changes as a function of time: this leads to the notion of a molecular movie. Intramolecular vibrational energy redistribution, due to anharmonic coupling between modes, is the molecular movie considered here. There is no guarantee, however, that the formed superposition will behave semi-classically (e.g. Gaussian wavepacket dynamics) or even as an intuitively useful zeroth-order state. Here we present time-resolved photoelectron spectroscopy (TRPES) studies of an electronically excited triatomic molecule wherein the vibrational dynamics must be treated quantum mechanically and the simple picture of population flow between coupled normal modes fails. Specifically, we report on vibronic wavepacket dynamics in the zeroth-order 3pσ2Σu Rydberg state of NO2. This wavepacket exemplifies two general features of excited state dynamics in polyatomic molecules: anharmonic multimodal vibrational coupling (forming polyads); nonadiabatic coupling between nuclear and electronic coordinates, leading to predissociation. The latter suggests that the polyad vibrational states in the zeroth-order 3p Rydberg manifold are quasi-bound and best understood to be scattering resonances. We observed a rapid dephasing of an initially prepared 'bright' valence state into the relatively long-lived 3p Rydberg state whose multimodal vibrational dynamics and decay we monitor as a function of time. Our quantum simulations, based on an effective spectroscopic Hamiltonian, describe the essential features of the multimodal Fermi resonance-driven vibrational dynamics in the 3p state. We also present evidence of polyad-specificity in the state-dependent predissociation rates, leading to free atomic and molecular fragments. We emphasize that a quantum molecular movie is required to visualize wavepacket dynamics in the 3pσ2Σu Rydberg state of NO2.

VUV excited-state dynamics of cyclic ethers as a function of ring size.

The vacuum ultraviolet (VUV) absorption spectra of cyclic ethers consist primarily of Rydberg ← n transitions. By studying three cyclic ethers of varying ring size (tetrahydropyran, tetrahydrofuran and trimethylene oxide, n = 6-4), we investigated the influence of ring size on the VUV excited-state dynamics of the 3d Rydberg manifold using time-resolved photoelectron spectroscopy (TRPES), time-resolved mass spectroscopy (TRMS) and ab initio electronic structure calculations. Whereas neither the electronic characters nor the term energies of the excited-states are substantially modified when the ring-size is reduced from n = 6 to 5 to 4, the excited-state lifetimes concomitantly decrease five-fold. TRPES and TRMS allow us to attribute the observed dynamics to a Rydberg cascade from the initially excited d-Rydberg manifold via the p-Rydberg manifold to the s-Rydberg state. Cuts through potential energy surfaces along the C-O bond reveal that a nσ* state crossing brings the s-Rydberg state along a path to the ring-opened ground state. The observed difference in excited-state lifetimes is attributed to an increasing slope along the repulsive C-O bond coordinate as ring size decreases.

Substituent effects on nonadiabatic excited state dynamics: Inertial, steric, and electronic effects in methylated butadienes.

The photochemical dynamics of double-bond-containing hydrocarbons is exemplified by the smallest alkenes, ethylene and butadiene. Chemical substituents can alter both decay timescales and photoproducts through a combination of inertial effects due to substituent mass, steric effects due to substituent size, and electronic (or potential) effects due to perturbative changes to the electronic potential energy surface. Here, we demonstrate the interplay of different substituent effects on 1,3-butadiene and its methylated derivatives using a combination of ab initio simulation of nonadiabatic dynamics and time-resolved photoelectron spectroscopy. The purely inertial effects of methyl substitution are simulated through the use of mass 15 "heavy-hydrogen" atoms. As expected from both inertial and electronic influences, the excited-state dynamics is dominated by pyramidalization at the unsubstituted carbon sites. Although the electronic effects of methyl group substitution are weak, they alter both decay timescales and branching ratios by influencing the initial path taken by the excited wavepacket following photoexcitation.

Directing excited state dynamics via chemical substitution: A systematic study of π-donors and π-acceptors at a carbon-carbon double bond.

Functional group substituents are a ubiquitous tool in ground-state organic chemistry often employed to fine-tune chemical properties and obtain desired chemical reaction outcomes. Their effect on photoexcited electronic states, however, remains poorly understood. To help build an intuition for these effects, we have studied ethylene, substituted with electron acceptor (cyano) and/or electron donor (methoxy) substituents, both theoretically and experimentally: using ab initio quantum molecular dynamics and time-resolved photoelectron spectroscopy. Our results show the consistent trend that photo-induced ethylenic dynamics is primarily localized to the carbon with the greater electron density. For doubly substituted ethylenes, the trend is additive when both substituents are located on opposite carbons, whereas the methoxy group (in concert with steric effects) dominates when both substituents are located on a single carbon atom. These results point to the development of rules for structure-dynamics correlations; in this case, a novel mechanistic ultrafast photochemistry for conjugated carbon chains employing long-established chemical concepts.

Vacuum ultraviolet excited state dynamics of small amides.

Time-resolved photoelectron spectroscopy in combination with ab initio quantum chemistry calculations was used to study ultrafast excited state dynamics in formamide (FOR), N,N-dimethylformamide (DMF), and N,N-dimethylacetamide (DMA) following 160 nm excitation. The particular focus was on internal conversion processes within the excited state Rydberg manifold and on how this behavior in amides compared with previous observations in small amines. All three amides exhibited extremely rapid (<100 fs) evolution from the Franck-Condon region. We argue that this is then followed by dissociation. Our calculations indicate subtle differences in how the excited state dynamics are mediated in DMA/DMF as compared to FOR. We suggest that future studies employing longer pump laser wavelengths will be useful for discerning these differences.

Sequential and direct ionic excitation in the strong-field ionization of 1-butene molecules.

We study the Strong-Field Ionization (SFI) of the hydrocarbon 1-butene as a function of wavelength using photoion-photoelectron covariance and coincidence spectroscopy. We observe a striking transition in the fragment-associated photoelectron spectra: from a single Above Threshold Ionization (ATI) progression for photon energies less than the cation D0-D1 gap to two ATI progressions for a photon energy greater than this gap. For the first case, electronically excited cations are created by SFI populating the ground cationic state D0, followed by sequential post-ionization excitation. For the second case, direct sub-cycle SFI to the D1 excited cation state contributes significantly. Our experiments access ionization dynamics in a regime where strong-field and resonance-enhanced processes can interplay.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. II. Ab initio multiple spawning simulations.

The excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene (BD), has long been the subject of controversy due to its strong coupling, ultrafast time scales and the difficulties that theory faces in describing the relevant electronic states in a balanced fashion. Here we apply Ab Initio Multiple Spawning (AIMS) using state-averaged complete active space multistate second order perturbation theory [SA-3-CAS(4/4)-MSPT2] which describes both static and dynamic electron correlation effects, providing a balanced description of both the initially prepared bright 11Bu (ππ*) state and non-adiabatically coupled dark 21Ag state of BD. Importantly, AIMS allows for on-the-fly calculations of experimental observables. We validate our approach by directly simulating the time resolved photoelectron-photoion coincidence spectroscopy results presented in Paper I [A. E. Boguslavskiy et al., J. Chem. Phys. 148, 164302 (2018)], demonstrating excellent agreement with experiment. Our simulations reveal that the initial excitation to the 11Bu state rapidly evolves via wavepacket dynamics that follow both bright- and dark-state pathways as well as mixtures of these. In order to test the sensitivity of the AIMS results to the relative ordering of states, we considered two hypothetical scenarios biased toward either the bright 1Bu or the dark 21Ag state. In contrast with AIMS/SA-3-CAS(4/4)-MSPT2 simulations, neither of these scenarios yields favorable agreement with experiment. Thus, we conclude that the excited state non-adiabatic dynamics in BD involves both of these ultrafast pathways.

Vacuum ultraviolet excited state dynamics of the smallest ring, cyclopropane. II. Time-resolved photoelectron spectroscopy and ab initio dynamics.

The vacuum-ultraviolet photoinduced dynamics of cyclopropane (C3H6) were studied using time-resolved photoelectron spectroscopy (TRPES) in conjunction with ab initio quantum dynamics simulations. Following excitation at 160.8 nm, and subsequent probing via photoionization at 266.45 nm, the initially prepared wave packet is found to exhibit a fast decay (<100 fs) that is attributed to the rapid dissociation of C3H6 to ethylene (C2H4) and methylene (CH2). The photodissociation process proceeds via concerted ring opening and C-C bond cleavage in the excited state. Ab initio multiple spawning simulations indicate that ring-opening occurs prior to dissociation. The dynamics simulations were subsequently employed to simulate a TRPES spectrum, which was found to be in excellent agreement with the experimental result. On the basis of this agreement, the fitted time constants of 35 ± 20 and 57 ± 35 fs were assigned to prompt (i) dissociation on the lowest-lying excited state, prepared directly by the pump pulse, and (ii) non-adiabatic relaxation from higher-lying excited states that lead to delayed dissociation, respectively.

Excited state non-adiabatic dynamics of the smallest polyene, trans 1,3-butadiene. I. Time-resolved photoelectron-photoion coincidence spectroscopy.

The ultrafast excited state dynamics of the smallest polyene, trans-1,3-butadiene, were studied by femtosecond time-resolved photoelectron-photoion coincidence (TRPEPICO) spectroscopy. The evolution of the excited state wavepacket, created by pumping the bright 1Bu (ππ*) electronic state at its origin of 216 nm, is projected via one- and two-photon ionization at 267 nm onto several ionization continua. The results are interpreted in terms of Koopmans' correlations and Franck-Condon factors for the excited and cationic states involved. The known predissociative character of the cation excited states is utilized to assign photoelectron bands to specific continua using TRPEPICO spectroscopy. This permits us to report the direct observation of the famously elusive S1(21Ag) dark electronic state during the internal conversion of trans 1,3-butadiene. Our phenomenological analysis permits the spectroscopic determination of several important time constants. We report the overall decay lifetimes of the 11Bu and 21Ag states and observe the re-appearance of the hot ground state molecule. We argue that the apparent dephasing time of the S2(11Bu) state, which leads to the extreme breadth of the absorption spectrum, is principally due to large amplitude torsional motion on the 1Bu surface in conjunction with strong non-adiabatic couplings via conical intersections, whereupon nuclear wavepacket revivals to the initial Franck-Condon region become effectively impossible. In Paper II [W. J. Glover et al., J. Chem. Phys. 148, 164303 (2018)], ab initio multiple spawning is used for on-the-fly computations of the excited state non-adiabatic wavepacket dynamics and their associated TRPEPICO observables, allowing for direct comparisons of experiment with theory.

Anisotropy in Time-Resolved Photoelectron Spectroscopy in the Gas Phase.

Transient absorption anisotropy is a well-established technique in time-resolved liquid phase spectroscopy. Here, we show how the technique is applied in the gas phase for time-resolved photoelectron spectroscopy and what type of additional information can be obtained as compared to other techniques. We exemplify its use by presenting results on rotational revivals in pyrazine after excitation at 324 nm and provide new insights into two recent experiments: (i) the difference between Rydberg and valence state excitation after one- and two-photon absorption in butadiene and (ii) excitation to the two lowest lying vibronic modes of the degenerate π3p Rydberg state in 1-azabicyclo[2.2.0]octane. Going forward, we expect the technique to be used on a regular basis, especially with the advent of high harmonic probe sources and liquid beam setups where other techniques to extract polarization-dependent information such as velocity map imaging cannot easily be applied.

Excited state wavepacket dynamics in NO2 probed by strong-field ionization.

We present an experimental femtosecond time-resolved study of the 399 nm excited state dynamics of nitrogen dioxide using channel-resolved above threshold ionization (CRATI) as the probe process. This method relies on photoelectron-photoion coincidence and covariance to correlate the strong-field photoelectron spectrum with ionic fragments, which label the channel. In all ionization channels observed, we report apparent oscillations in the ion and photoelectron yields as a function of pump-probe delay. Further, we observe the presence of a persistent, time-invariant above threshold ionization comb in the photoelectron spectra associated with most ionization channels at long time delays. These observations are interpreted in terms of single-pump-photon excitation to the first excited electronic X̃ 2A1 state and multi-pump-photon excitations to higher-lying states. The short time delay (<100 fs) dynamics in the fragment channels show multi-photon pump signatures of higher-lying neutral state dynamics, in data sets recorded with higher pump intensities. As expected for pumping NO2 at 399 nm, non-adiabatic coupling was seen to rapidly re-populate the ground state following excitation to the first excited electronic state, within 200 fs. Subsequent intramolecular vibrational energy redistribution results in the spreading of the ground state vibrational wavepacket into the asymmetric stretch coordinate, allowing the wavepacket to explore nuclear geometries in the asymptotic region of the ground state potential energy surface. Signatures of the vibrationally "hot" ground state wavepacket were observed in the CRATI spectra at longer time delays. This study highlights the complex and sometimes competing phenomena that can arise in strong-field ionization probing of excited state molecular dynamics.

Substituent effects on dynamics at conical intersections: Allene and methyl allenes.

We report a joint experimental and theoretical study on the ultrafast excited state dynamics of allene and a series of its methylated analogues (1,2-butadiene, 1,1-dimethylallene, and tetramethylallene) in order to elucidate the conical intersection mediated dynamics that give rise to ultrafast relaxation to the ground electronic state. We use femtosecond time-resolved photoelectron spectroscopy (TRPES) to probe the coupled electronic-vibrational dynamics following UV excitation at 200 nm (6.2 eV). Ab initio multiple spawning (AIMS) simulations are employed to determine the mechanistic details of two competing dynamical pathways to the ground electronic state. In all molecules, these pathways are found to involve as follows: (i) twisting about the central allenic C-C-C axis followed by pyramidalization at one of the terminal carbon atoms and (ii) bending of allene moiety. Importantly, the AIMS trajectory data were used for ab initio simulations of the TRPES, permitting direct comparison with experiment. For each molecule, the decay of the TRPES signal is characterized by short (30 fs, 52 fs, 23 fs) and long (1.8 ps, 3.5 ps, [306 fs, 18 ps]) time constants for 1,2-butadiene, 1,1-dimethylallene, and tetramethylallene, respectively. However, AIMS simulations show that these time constants are only loosely related to the evolution of electronic character and actually more closely correlate to large amplitude motions on the electronic excited state, modulating the instantaneous vertical ionization potentials. Furthermore, the fully substituted tetramethylallene is observed to undergo qualitatively different dynamics, as displacements involving the relatively massive methyl groups impede direct access to the conical intersections which give rise to the ultrafast relaxation dynamics observed in the other species. These results show that the branching between the "twisting" and "bending" pathways can be modified via the selective methylation of the terminal carbon atoms of allene. The interplay between inertial and potential effects is a key to understanding these dynamical branching pathways. The good agreement between the simulated and measured TRPES confers additional confidence to the dynamical picture presented here.

Ultrafast Dynamics of o-Nitrophenol: An Experimental and Theoretical Study.

The photolysis of o-nitrophenol (o-NP), a typical push-pull molecule, is of current interest in atmospheric chemistry as a possible source of nitrous acid (HONO). To characterize the largely unknown photolysis mechanism, the dynamics of the lowest lying excited singlet state (S1) of o-NP was investigated by means of femtosecond transient absorption spectroscopy in solution, time-resolved photoelectron spectroscopy (TRPES) in the gas phase and quantum chemical calculations. Evidence of the unstable aci-nitro isomer is provided both in the liquid and in the gas phase. Our results indicate that the S1 state displays strong charge transfer character, which triggers excited state proton transfer from the OH to the NO2 group as evidenced by a temporal shift of 20 fs of the onset of the photoelectron spectrum. The proton transfer itself is found to be coupled to an out-of-plane rotation of the newly formed HONO group, finally leading to a conical intersection between S1 and the ground state S0. In solution, return to S0 within 0.2-0.3 ps was monitored by stimulated emission. As a competitive relaxation channel, ultrafast intersystem crossing to the upper triplet manifold on a subpicosecond time scale occurs both in solution and in the gas phase. Due to the ultrafast singlet dynamics, we conclude that the much discussed HONO split-off is likely to take place in the triplet manifold.

Excited state dynamics in SO2. I. Bound state relaxation studied by time-resolved photoelectron-photoion coincidence spectroscopy.

The excited state dynamics of isolated sulfur dioxide molecules have been investigated using the time-resolved photoelectron spectroscopy and time-resolved photoelectron-photoion coincidence techniques. Excited state wavepackets were prepared in the spectroscopically complex, electronically mixed (B̃)(1)B1/(Ã)(1)A2, Clements manifold following broadband excitation at a range of photon energies between 4.03 eV and 4.28 eV (308 nm and 290 nm, respectively). The resulting wavepacket dynamics were monitored using a multiphoton ionisation probe. The extensive literature associated with the Clements bands has been summarised and a detailed time domain description of the ultrafast relaxation pathways occurring from the optically bright (B̃)(1)B1 diabatic state is presented. Signatures of the oscillatory motion on the (B̃)(1)B1/(Ã)(1)A2 lower adiabatic surface responsible for the Clements band structure were observed. The recorded spectra also indicate that a component of the excited state wavepacket undergoes intersystem crossing from the Clements manifold to the underlying triplet states on a sub-picosecond time scale. Photoelectron signal growth time constants have been predominantly associated with intersystem crossing to the (c̃)(3)B2 state and were measured to vary between 750 and 150 fs over the implemented pump photon energy range. Additionally, pump beam intensity studies were performed. These experiments highlighted parallel relaxation processes that occurred at the one- and two-pump-photon levels of excitation on similar time scales, obscuring the Clements band dynamics when high pump beam intensities were implemented. Hence, the Clements band dynamics may be difficult to disentangle from higher order processes when ultrashort laser pulses and less-differential probe techniques are implemented.

Channel- and angle-resolved above threshold ionization in the molecular frame.

In strong-field ionization (SFI) of polyatomic molecules, the participation of multiple electronic ionization channels is emerging as a key aspect. In the molecular frame, each channel is expected to show a characteristic dependence of the SFI yield on the polarization direction of the ionizing field. We apply a new angle- and channel-resolved SFI technique to the polyatomic molecule 1,3-butadiene and compare these molecular-frame measurements with two leading theoretical models.

Initial processes of proton transfer in salicylideneaniline studied by time-resolved photoelectron spectroscopy.

Excited-state intramolecular proton transfer (ESIPT) in salicylideneaniline (SA) and selected derivatives substituted in the para position of the anilino group have been investigated by femtosecond time-resolved photoelectron spectroscopy (TRPES) and time-dependent density functional theory (TDDFT). SA has a twisted structure at the energetic minimum of the ground state, but ESIPT is assumed to take place through a planar structure, although this has not been fully established. The TRPES studies revealed that the excited-state dynamics within the S1 band varied significantly with excitation wavelength. At finite temperatures, the ground state was found to sample a broad range of torsional angles, from planar to twisted. At lower photon energies (370 nm), only the planar ground-state molecules were excited, and the excited-state reaction took place within 50 fs. At higher energies (350 and 330 nm), predominantly twisted ground-state molecules were excited: they had to planarize before ESIPT could occur. This process was found to be slower in methylated SA but did not change significantly in the brominated and nitrated SAs. These substitution effects on the decay dynamics can be explained by modifications of the potential barriers, as predicted by the TDDFT calculations, and support the mechanism of a twisting motion of the anilino ring prior to ESIPT. The contribution of another pathway leading to internal conversion within the enol form was found to be minor at the excitation wavelengths considered here.

Substituent effects on dynamics at conical intersections: cycloheptatrienes.

Using selective methyl substitution, we study the effects of vibrational dynamics at conical intersections in unsaturated hydrocarbons. Here, we investigate the excited state nonadiabatic dynamics of cycloheptatriene (CHT) and its relation to dynamics in other polyenes by comparing CHT with 7-methyl CHT, 7-ethyl CHT, and perdeuterated CHT using time-resolved photoelectron spectroscopy and photoelectron anisotropy. Our results suggest that, upon ππ*-excitation to the bright 2A" state, we observe an early intersection with the dark 2A' state close to the Franck-Condon region with evidence of wavepacket bifurcation. This indicates that the wavepacket evolves on both states, likely along a planarization coordinate, with the majority of the flux undergoing nonadiabatic transition via conical intersections within 100 fs following light absorption. In CHT, large amplitude motion along the planarization coordinate improves the intra-ring π-overlap, yielding a delocalized electronic density. However, substitutions in 7 position, chosen to modify the inertia of the planarization motion, did not markedly alter the first step in the sequential kinetic scheme. This suggests that there is a crossing of potential energy surfaces before planarization is achieved and, thus, nonadiabatic transition likely takes place far away from a local minimum.

On the condensed phase ring-closure of vinylheptafulvalene and ring-opening of gaseous dihydroazulene.

Dihydroazulenes are interesting because of their photoswitching behavior. While the ring-opening to vinylheptafulvalene (VHF) is light induced, the back reaction is known to proceed thermally. In the present paper, we show the first gas phase study of the ring-opening reaction of 2-phenyl-1,8a-dihydroazulene-1,1-dicarbonitrile (Ph-DHA) by means of time-resolved photoelectron spectroscopy which permits us to follow the ring-opening process. Moreover, we investigated s-trans-Ph-VHF in a series of transient absorption experiments, supported by ab initio computations, to understand the origin of the absence of light-induced ring-closure. The transient absorption results show a biexponential decay governed by a hitherto unknown state. This state is accessed within 1-2 ps and return to the ground state is probably driven through a cis-trans isomerization about the exocyclic C1═C2 double bond. The rapid decrease in potential energy disfavors internal rotation to s-cis-Ph-VHF, the structure that would precede the ring-closure reaction.

The quantitative determination of laser-induced molecular axis alignment.

Experiments in the gas phase usually involve averaging observables over a random molecular axis alignment distribution. This deleterious averaging limits insights gained by probes of molecular dynamics, but can be overcome by prealigning molecular axes using laser-alignment methods. However, the transformation from the laboratory frame to the molecular frame of reference requires quantitative knowledge of the axis alignment distribution. The latter is often hard to obtain directly from experimental data, particularly for polyatomic molecules. Here we describe a general maximum-likelihood classification procedure for non-adiabatic numerical alignment simulations with free parameters that employs experimental data from an alignment-dependent probe. This method delivers (i) the most probable molecular frame angular dependence of the probe, and (ii) the most likely laboratory frame axis alignment distribution of the sample, each with a confidence interval. This procedure was recently used for studies of angle- and channel-resolved strong field ionization of 1,3-butadiene in the molecular frame [Mikosch et al., Phys. Rev. Lett. 110, 023004 (2013)], used here as an illustrative example.