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

Triplet State Radical Chemistry: Significance of the Reaction of 3SO2 with HCOOH and HNO3

The triplet excited states of sulfur dioxide can be accessed in the UV region and have a lifetime large enough that they can react with atmospheric trace gases. In this work, we report high level ab initio calculations for the reaction of the a3B1 and b3A2 excited states of SO2 with weak and strong acidic species such as HCOOH and HNO3, aimed to extend the chemistry reported in previous studies with nonacidic H atoms (water and alkanes). The reactions investigated in this work are very versatile and follow different kinds of mechanisms, namely, proton-coupled electron transfer (pcet) and conventional hydrogen atom transfer (hat) mechanisms. The study provides new insights into a general and very important class of excited-state-promoted reactions, opening up interesting chemical perspectives for technological applications of photoinduced H-transfer reactions. It also reveals that atmospheric triplet chemistry is more significant than previously thought.

Non-adiabatic coupling in the potential energy surfaces of SO2 molecule

To investigate the potential energy surfaces and the coupling between the adiabatic states of SO2 molecules, it is necessary to consider the non-adiabatic coupling terms (NACTs), where the Born-Oppenheimer approximation breaks down. In this work, we analyze the conical intersections between 1 1A1 and 1 1B2 states (the A' states in Cs symmetry) and 1 1A2 and 1 1B1 states (the A'' states in Cs symmetry) using NACTs and adiabatic-to-diabatic transformation (ADT) angles. Our results confirm reasonable interaction between 1 1A1 and 1 1B2 states and strong interaction between 1 1A2 and 1 1B1 states.

Effects of Autoionizing Resonances on Wave-Packet Dynamics Studied by Time-Resolved Photoelectron Spectroscopy

We report a combined experimental and theoretical study on the effect of autoionizing resonances in time-resolved photoelectron spectroscopy. The coherent excitation of N_{2} by ∼14.15  eV extreme-ultraviolet photons prepares a superposition of three dominant adjacent vibrational levels (v^{'}=14-16) in the valence b^{'} ^{1}Σ_{u}^{+} state, which are probed by the absorption of two or three near-infrared photons (800 nm). The superposition manifests itself as coherent oscillations in the measured photoelectron spectra. A quantum-mechanical simulation confirms that two autoionizing Rydberg states converging to the excited A ^{2}Π_{u} and B ^{2}Σ_{u}^{+} N_{2}^{+} cores are accessed by the resonant absorption of near-infrared photons. We show that these resonances apply different filters to the observation of the vibrational wave packet, which results in different phases and amplitudes of the oscillating photoelectron signal depending on the nature of the autoionizing resonance. This work clarifies the importance of resonances in time-resolved photoelectron spectroscopy and particularly reveals the phase of vibrational quantum beats as a powerful observable for characterizing the properties of such resonances.

Surface Hopping Dynamics on Vibronic Coupling Models

The simulation of photoinduced non-adiabatic dynamics is of great relevance in many scientific disciplines, ranging from physics and materials science to chemistry and biology. Upon light irradiation, different relaxation processes take place in which electronic and nuclear motion are intimately coupled. These are best described by the time-dependent molecular Schrödinger equation, but its solution poses fundamental practical challenges to contemporary theoretical chemistry. Two widely used and complementary approaches to this problem are multiconfigurational time-dependent Hartree (MCTDH) and trajectory surface hopping (SH). MCTDH is an accurate fully quantum-mechanical technique but often is feasible only in reduced dimensionality, in combination with approximate vibronic coupling (VC) Hamiltonians, or both (i.e., reduced-dimensional VC potentials). In contrast, SH is a quantum–classical technique that neglects most nuclear quantum effects but allows nuclear dynamics in full dimensionality by calculating potential energy surfaces on the fly. If nuclear quantum effects do not play a central role and a linear VC (LVC) Hamiltonian is appropriate—e.g., for stiff molecules that generally keep their conformation in the excited state—then it seems advantageous to combine the efficient LVC and SH techniques. In this Account, we describe how surface hopping based on an LVC Hamiltonian (SH/LVC)—as recently implemented in the SHARC surface hopping package—can provide an economical and automated approach to simulate non-adiabatic dynamics. First, we illustrate the potential of SH/LVC in a number of showcases, including intersystem crossing in SO₂, intra-Rydberg dynamics in acetone, and several photophysical studies on large transition-metal complexes, which would be much more demanding or impossible to perform with other methods. While all of the applications provide very useful insights into light-induced phenomena, they also hint at difficulties faced by the SH/LVC methodology that need to be addressed in the future. Second, we contend that the SH/LVC approach can be useful to benchmark SH itself. By the use of the same (LVC) potentials as MCTDH calculations have employed for decades and by relying on the efficiency of SH/LVC, it is possible to directly compare multiple SH test calculations with a MCTDH reference and ponder the accuracy of various correction algorithms behind the SH methodology, such as decoherence corrections or momentum rescaling schemes. Third, we demonstrate how the efficiency of SH/LVC can also be exploited to identify essential nuclear and electronic degrees of freedom to be employed in more accurate MCTDH calculations. Lastly, we show that SH/LVC is able to advance the development of SH protocols that can describe nuclear dynamics including explicit laser fields—a very challenging endeavor for trajectory-based schemes. To end, this Account compiles the typical costs of contemporary SH simulations, evidencing the great advantages of using parametrized potentials. The LVC model is a sleeping beauty that, kissed by SH, is fueling the field of excited-state molecular dynamics. We hope that this Account will stimulate future research in this direction, leveraging the advantages of the SH/VC schemes to larger extents and extending their applicability to uncharted territories.

Time-resolving the UV-initiated photodissociation dynamics of OCS

We present a time-resolved study of the photodissociation dynamics of OCS after UV-photoexcitation at λ = 237 nm. OCS molecules (X1Σ+) were primarily excited to the 11A'' and the 21A' Renner-Teller components of the 1Σ- and 1Δ states. Dissociation into CO and S fragments was observed through time-delayed strong-field ionisation and imaging of the kinetic energy of the resulting CO+ and S+ fragments by intense 790 nm laser pulses. Surprisingly, fast oscillations with a period of ∼100 fs were observed in the S+ channel of the UV dissociation. Based on wavepacket-dynamics simulations coupled with a simple electrostatic-interaction model, these oscillations do not correspond to the known highly-excited rotational motion of the leaving CO(X1Σ+, J ≫ 0) fragments, which has a timescale of ∼140 fs. Instead, we suggest to assign the observed oscillations to the excitation of vibrational wavepackets in the 23A'' or 21A'' states of the molecule that predissociate to form S(3PJ) photoproducts.

Femtosecond Resolving Photodissociation Dynamics of the SO2 Molecule

We experimentally investigate the ultrafast photodissociation dynamics of the SO₂ molecule induced by intense ultrashort laser pulses in a pump-probe scheme. Different three-body fragmentation pathways are discriminated using the time-dependent kinetic energy release spectrum with femtosecond time resolution. A nontrivial three-body fragmentation pathway, denoted as the bonding pathway, is unraveled, in which an intermediate fast rotating O₂ molecule is formed before complete fragmentation. The ultrafast chemical bond rearrangement after electron release is tracked in real time. The bonding pathway generally exists in the three-body fragmentation processes induced by strong laser fields of different wavelengths, which is observed in infrared, ultraviolet, and mixed two-color cases. Our findings are significant for understanding the photon-induced ultrafast processes of the SO₂ molecule in atmospheric chemistry.

Photochemistry from low-lying states of HOSO. J Chem Phys 2020;152:134302. [PMID: 32268736 DOI: 10.1063/5.0001867]

Using configuration interaction ab initio methods, the evolution of the lowest electronic states of singlet and triplet spin multiplicities of HOSO⁺ along the stretching and bending coordinates of is investigated. Equilibrium geometries, rotational constants, and harmonic vibrational frequencies of the lowest electronic states are calculated, i.e., X¹A', 1¹A″, 1³A', and 1³A″. The global minimum of the 1¹A″ state is located below the first dissociation limit and its calculated lifetime is predicted to be 0.40 µs, making it suitable for detection by laser-induced fluorescence. According to the potential energy surfaces, HOSO⁺ should produce SO₂ ⁺ and H after ultraviolet photon absorption to the 2¹A' state. This work opens the door to investigate the branching ratio and the production rates of SO₂ ⁺, SO⁺, and OH from HOSO⁺. These insights can help understand the SO₂ cycle in the earth's atmosphere and its effect on cooling our planet.

Multireference Electron Correlation Methods: Journeys along Potential Energy Surfaces

Multireference electron correlation methods describe static and dynamical electron correlation in a balanced way and, therefore, can yield accurate and predictive results even when single-reference methods or multiconfigurational self-consistent field theory fails. One of their most prominent applications in quantum chemistry is the exploration of potential energy surfaces. This includes the optimization of molecular geometries, such as equilibrium geometries and conical intersections and on-the-fly photodynamics simulations, both of which depend heavily on the ability of the method to properly explore the potential energy surface. Because such applications require nuclear gradients and derivative couplings, the availability of analytical nuclear gradients greatly enhances the scope of quantum chemical methods. This review focuses on the developments and advances made in the past two decades. A detailed account of the analytical nuclear gradient and derivative coupling theories is presented. Emphasis is given to the software infrastructure that allows one to make use of these methods. Notable applications of multireference electron correlation methods to chemistry, including geometry optimizations and on-the-fly dynamics, are summarized at the end followed by a discussion of future prospects.

Bayesian Analysis of Femtosecond Pump-Probe Photoelectron-Photoion Coincidence Spectra with Fluctuating Laser Intensities

This paper employs Bayesian probability theory for analyzing data generated in femtosecond pump-probe photoelectron-photoion coincidence (PEPICO) experiments. These experiments allow investigating ultrafast dynamical processes in photoexcited molecules. Bayesian probability theory is consistently applied to data analysis problems occurring in these types of experiments such as background subtraction and false coincidences. We previously demonstrated that the Bayesian formalism has many advantages, amongst which are compensation of false coincidences, no overestimation of pump-only contributions, significantly increased signal-to-noise ratio, and applicability to any experimental situation and noise statistics. Most importantly, by accounting for false coincidences, our approach allows running experiments at higher ionization rates, resulting in an appreciable reduction of data acquisition times. In addition to our previous paper, we include fluctuating laser intensities, of which the straightforward implementation highlights yet another advantage of the Bayesian formalism. Our method is thoroughly scrutinized by challenging mock data, where we find a minor impact of laser fluctuations on false coincidences, yet a noteworthy influence on background subtraction. We apply our algorithm to data obtained in experiments and discuss the impact of laser fluctuations on the data analysis.

Triplet state promoted reaction of SO2 with H2O by competition between proton coupled electron transfer (pcet) and hydrogen atom transfer (hat) processes

The excited triplet electronic state of SO₂ (a³B₁) reacts with water through a proton coupled electron transfer (pcet) mechanism rather than via a conventional hydrogen atom transfer (hat) process.

Highly efficient surface hopping dynamics using a linear vibronic coupling model

We report an implementation of the linear vibronic coupling (LVC) model within the surface hopping dynamics approach and present utilities for parameterizing this model in a blackbox fashion. This results in an extremely efficient method to obtain qualitative and even semi-quantitative information about the photodynamical behavior of a molecule, and provides a new route toward benchmarking the results of surface hopping computations. The merits and applicability of the method are demonstrated in a number of applications. First, the method is applied to the SO2 molecule showing that it is possible to compute its absorption spectrum beyond the Condon approximation, and that all the main features and timescales of previous on-the-fly dynamics simulations of intersystem crossing are reproduced while reducing the computational effort by three orders of magnitude. The dynamics results are benchmarked against exact wavepacket propagations on the same LVC potentials and against a variation of the electronic structure level. Four additional test cases are presented to exemplify the broader applicability of the model. The photodynamics of the isomeric adenine and 2-aminopurine molecules are studied and it is shown that the LVC model correctly predicts ultrafast decay in the former and an extended excited-state lifetime in the latter. Futhermore, the method correctly predicts ultrafast intersystem crossing in the modified nucleobase 2-thiocytosine and its absence in 5-azacytosine while it fails to describe the ultrafast internal conversion to the ground state in the latter.

Nonadiabatic dynamics: The SHARC approach

We review the Surface Hopping including ARbitrary Couplings (SHARC) approach for excited-state nonadiabatic dynamics simulations. As a generalization of the popular surface hopping method, SHARC allows simulating the full-dimensional dynamics of molecules including any type of coupling terms beyond nonadiabatic couplings. Examples of these arbitrary couplings include spin-orbit couplings or dipole moment-laser field couplings, such that SHARC can describe ultrafast internal conversion, intersystem crossing, and radiative processes. The key step of the SHARC approach consists of a diagonalization of the Hamiltonian including these couplings, such that the nuclear dynamics is carried out on potential energy surfaces including the effects of the couplings-this is critical in any applications considering, for example, transition metal complexes or strong laser fields. We also give an overview over the new SHARC2.0 dynamics software package, released under the GNU General Public License, which implements the SHARC approach and several analysis tools. The review closes with a brief survey of applications where SHARC was employed to study the nonadiabatic dynamics of a wide range of molecular systems. This article is categorized under: Theoretical and Physical Chemistry > Reaction Dynamics and KineticsSoftware > Simulation MethodsSoftware > Quantum Chemistry.

Development of an experimental set-up for low-temperature spectroscopic studies of matrix-isolated molecules and molecular ices using synchrotron radiation

An experimental set-up for studying photophysics and photochemistry of molecules in an inert gas medium (matrix-isolated) and in the ice phase at low temperatures has been developed and commissioned at the Photophysics beamline, Indus-1 synchrotron radiation source. This end-station uses an in-house-developed closed-cycle cryostat for achieving cryo-temperatures (∼10 K). Synchrotron radiation from the Photophysics beamline is used as the source of UV-VUV photons and the system is equipped with a Fourier transform infrared spectrometer for characterization of the molecular species formed at low temperature. Various individual components of the end-station like closed-cycle cryostat, experimental chamber, gas mixing and deposition systems are tested to ascertain that the desired performance criteria are satisfied. The performance of the composite system after integration with the Photophysics beamline is evaluated by recording IR and UV-VUV photoabsorption spectra of sulfur dioxide at low temperatures (10 K), both in the ice phase as well as isolated in argon matrices. Results obtained are in good agreement with earlier literature, thus validating the satisfactory performance of the system. As an off-shoot of the study, the VUV absorption spectrum of matrix-isolated SO₂ in argon matrix up to 10.2 eV is reported here for the first time. This experimental end-station will provide new opportunities to study photon-induced reactions in molecules of environmental, astrochemical and industrial importance. Details of the design, development and initial experimental results obtained are presented.

The Role of Rydberg-Valence Coupling in the Ultrafast Relaxation Dynamics of Acetone

The electronic structure of excited states of acetone is represented by a Rydberg manifold that is coupled to valence states which provide very fast and efficient relaxation pathways. We observe and characterize the transfer of population from photoexcited Rydberg states (6p, 6d, 7s) to a whole series of lower Rydberg states (3p to 4d) and a simultaneous decay of population from these states. We obtain these results with time-resolved photoelectron–photoion coincidence (PEPICO) detection in combination with the application of Bayesian statistics for data analysis. Despite the expectedly complex relaxation behavior, we find that a simple sequential decay model is able to describe the observed PEPICO transients satisfactorily. We obtain a slower decay (∼320 fs) from photoexcited states compared to a faster decay (∼100 fs) of states that are populated by internal conversion, demonstrating that different relaxation dynamics are active. Within the series of Rydberg states populated by internal conversion, the decay dynamics seem to be similar, and a trend of slower decay from lower states indicates an increasingly higher energy barrier along the decay pathway for lower states. The presented results agree all in all with previous relaxation studies within the Rydberg manifold. The state-resolved observation of transient population ranging from 3p to 4d can serve as reference for time-dependent simulations.

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.

Time-resolved photoelectron imaging with a femtosecond vacuum-ultraviolet light source: Dynamics in the A∼/B∼- and F∼-bands of SO2

Time-resolved photoelectron imaging is demonstrated using the third harmonic of a 400-nm femtosecond laser pulse as the ionization source. The resulting 133-nm pulses are combined with 266-nm pulses to study the excited-state dynamics in the A∼/B∼- and F∼-band regions of SO₂. The photoelectron signal from the molecules excited to the A∼/B∼-band does not decay for at least several picoseconds, reflecting the population of bound states. The temporal variation of the photoelectron angular distribution (PAD) reflects the creation of a rotational wave packet in the excited state. In contrast, the photoelectron signal from molecules excited to the F∼-band decays with a time constant of 80 fs. This time constant is attributed to the motion of the excited-state wave packet out of the ionization window. The observed time-dependent PADs are consistent with the F∼ band corresponding to a Rydberg state of dominant s character. These results establish low-order harmonic generation as a promising tool for time-resolved photoelectron imaging of the excited-state dynamics of molecules, simultaneously giving access to low-lying electronic states, as well as Rydberg states, and avoiding the ionization of unexcited molecules.

Disentangling Multichannel Photodissociation Dynamics in Acetone by Time-Resolved Photoelectron-Photoion Coincidence Spectroscopy

For the investigation of photoinduced dynamics in molecules with time-resolved pump-probe photoionization spectroscopy, it is essential to obtain unequivocal information about the fragmentation behavior induced by the laser pulses. We present time-resolved photoelectron-photoion coincidence (PEPICO) experiments to investigate the excited-state dynamics of isolated acetone molecules triggered by two-photon (269 nm) excitation. In the complex situation of different relaxation pathways, we unambiguously identify three distinct pump-probe ionization channels. The high selectivity of PEPICO detection allows us to observe the fragmentation behavior and to follow the time evolution of each channel separately. For channels leading to fragment ions, we quantitatively obtain the fragment-to-parent branching ratio and are able to determine experimentally whether dissociation occurs in the neutral molecule or in the parent ion. These results highlight the importance of coincidence detection for the interpretation of time-resolved photochemical relaxation and dissociation studies if multiple pathways are present.

Gas-phase hydrolysis of triplet SO2: A possible direct route to atmospheric acid formation

Sulfur chemistry is of great interest to the atmospheric chemistry of several planets. In the presence of water, oxidized sulfur can lead to new particle formation, influencing climate in significant ways. Observations of sulfur compounds in planetary atmospheres when compared with model results suggest that there are missing chemical mechanisms. Here we propose a novel mechanism for the formation of sulfurous acid, which may act as a seed for new particle formation. In this proposed mechanism, the lowest triplet state of SO₂ (³B₁), which may be accessed by near-UV solar excitation of SO₂ to its excited ¹B₁ state followed by rapid intersystem crossing, reacts directly with water to form H₂SO₃ in the gas phase. For ground state SO₂, this reaction is endothermic and has a very high activation barrier; our quantum chemical calculations point to a facile reaction being possible in the triplet state of SO₂. This hygroscopic H₂SO₃ molecule may act as a condensation nucleus for water, giving rise to facile new particle formation (NPF).

Empirical rules of molecular photophysics in the light of ultrafast spectroscopy

The advent of ultrafast laser spectroscopy has allowed entirely new possibilities for the investigation of the ultrafast photophysics of inorganic metal-based molecular complexes. In this review we show different regimes where non-Kasha behavior shows up. We also demonstrate that while ultrafast intersystem crossing is a common observation in metal complexes, the ISC rates do not scale with the magnitude of the spin-orbit coupling constant. Structural dynamics and density of states play a crucial role in such ultrafast ISC processes, which are not limited to molecules containing heavy atoms.

Ultrafast photophysics of transition metal complexes

The properties of transition metal complexes are interesting not only for their potential applications in solar energy conversion, OLEDs, molecular electronics, biology, photochemistry, etc. but also for their fascinating photophysical properties that call for a rethinking of fundamental concepts. With the advent of ultrafast spectroscopy over 25 years ago and, more particularly, with improvements in the past 10-15 years, a new area of study was opened that has led to insightful observations of the intramolecular relaxation processes such as internal conversion (IC), intersystem crossing (ISC), and intramolecular vibrational redistribution (IVR). Indeed, ultrafast optical spectroscopic tools, such as fluorescence up-conversion, show that in many cases, intramolecular relaxation processes can be extremely fast and even shorter than time scales of vibrations. In addition, more and more examples are appearing showing that ultrafast ISC rates do not scale with the magnitude of the metal spin-orbit coupling constant, that is, that there is no heavy-atom effect on ultrafast time scales. It appears that the structural dynamics of the system and the density of states play a crucial role therein. While optical spectroscopy delivers an insightful picture of electronic relaxation processes involving valence orbitals, the photophysics of metal complexes involves excitations that may be centered on the metal (called metal-centered or MC) or the ligand (called ligand-centered or LC) or involve a transition from one to the other or vice versa (called MLCT or LMCT). These excitations call for an element-specific probe of the photophysics, which is achieved by X-ray absorption spectroscopy. In this case, transitions from core orbitals to valence orbitals or higher allow probing the electronic structure changes induced by the optical excitation of the valence orbitals, while also delivering information about the geometrical rearrangement of the neighbor atoms around the atom of interest. With the emergence of new instruments such as X-ray free electron lasers (XFELs), it is now possible to perform ultrafast laser pump/X-ray emission probe experiments. In this case, one probes the density of occupied states. These core-level spectroscopies and other emerging ones, such as photoelectron spectroscopy of solutions, are delivering a hitherto unseen degree of detail into the photophysics of metal-based molecular complexes. In this Account, we will give examples of applications of the various methods listed above to address specific photophysical processes.