Probing the dynamics and bottleneck of the key atmospheric SO2 oxidation reaction by the hydroxyl radical

SO2 (Sulfur dioxide) is the major precursor to the production of sulfuric acid (H2SO4), contributing to acid rain and atmospheric aerosols. Sulfuric acid formed from SO2 generates light-reflecting sulfate aerosol particles in the atmosphere. This property has prompted recent geoengineering proposals to inject sulfuric acid or its precursors into the Earth's atmosphere to increase the planetary albedo to counteract global warming. SO2 oxidation in the atmosphere by the hydroxyl radical HO to form HOSO2 is a key rate-limiting step in the mechanism for forming acid rain. However, the dynamics of the HO + SO2 → HOSO2 reaction and its slow rate in the atmosphere are poorly understood to date. Herein, we use photoelectron spectroscopy of cryogenically cooled HOSO2- anion to access the neutral HOSO2 radical near the transition state of the HO + SO2 reaction. Spectroscopic and dynamic calculations are conducted on the first ab initio-based full-dimensional potential energy surface to interpret the photoelectron spectra of HOSO2- and to probe the dynamics of the HO + SO2 reaction. In addition to the finding of a unique pre-reaction complex (HO⋯SO2) directly connected to the transition state, dynamic calculations reveal that the accessible phase space for the HO + SO2 → HOSO2 reaction is extremely narrow, forming a key reaction bottleneck and slowing the reaction rate in the atmosphere, despite the low reaction barrier. This study underlines the importance of understanding the full multidimensional potential energy surface to elucidate the dynamics of complex bimolecular reactions involving polyatomic reactants.

Observing Intramolecular Vibrational Energy Redistribution via the Short-Time Fourier Transform

Intramolecular vibrational energy relaxation (IVR) is important in many problems in chemical physics. Here, we apply the short-time Fourier transform method for analyzing IVR with classical dynamics. Calculating time-dependent Fourier transforms to perform such an analysis requires extending the usual Fourier transform method, and we do that here. The guiding concept behind the generalization is that if there is a shift of vibrational energy from one frequency range to another, we see a difference between the spectrum before the shift and the spectrum after the shift. We use time-window functions to transform the power spectrum of a trajectory into a time-dependent density spectrum of the average kinetic energy. The time-dependent average kinetic energy for each interval of the spectrum becomes an indicator to monitor the extent and nature of the energy transfer into and out of the corresponding modes. We illustrate this method for the H₂O molecule. By analyzing cases with different initial conditions, we show that the short-time Fourier transform method can distinguish trends in IVR that depend on the initial distribution of energy and not just on the total energy.

Spectroscopic detection of gas-phase HOSO2

The HOSO₂ radical was detected by microwave spectroscopy in a discharge plasma of a SO₂/H₂O gas mixture. The observed spectrum shows tunneling splittings due to the OH torsional motion. A least-squares analysis considering interactions between the two torsional sublevels of the ground vibronic state, 0⁺ and 0^-, reproduces the observed transition frequencies with a standard deviation of ca. 3 kHz. The splitting between the two torsional sublevels is accurately determined to be 24.3 MHz for HOSO₂ and 0.08 MHz for DOSO₂. The potential barrier for the OH torsional motion is estimated to be 1150 cm^-1 from a one-dimensional hindered rotor model.

Photochemistry of HOSO2 and SO3 and Implications for the Production of Sulfuric Acid

Sulfur trioxide (SO₃) and the hydroxysulfonyl radical (HOSO₂) are two key intermediates in the production of sulfuric acid (H₂SO₄) on Earth's atmosphere, one of the major components of acid rain. Here, the photochemical properties of these species are determined by means of high-level quantum chemical methodologies, and the potential impact of their light-induced reactivity is assessed within the context of the conventional acid rain generation mechanism. Results reveal that the photodissociation of HOSO₂ occurs primarily in the stratosphere through the ejection of hydroxyl radicals (^•OH) and sulfur dioxide (SO₂). This may decrease the production rate of H₂SO₄ in atmospheric regions with low O₂ concentration. In contrast, the photostability of SO₃ under stratospheric conditions suggests that its removal efficiency, still poorly understood, is key to assess the H₂SO₄ formation in the upper atmosphere.

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

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

A general implementation of time-dependent vibrational coupled-cluster theory

The first general excitation level implementation of the time-dependent vibrational coupled cluster (TDVCC) method introduced in a recent publication [J. Chem. Phys. 151, 154116 (2019)] is presented. The general framework developed for time-independent vibrational coupled cluster (VCC) calculations has been extended to the time-dependent context. This results in an efficient implementation of TDVCC with general coupling levels in the cluster operator and Hamiltonian. Thus, the convergence of the TDVCC[k] hierarchy toward the complete-space limit can be studied for any sum-of-product Hamiltonian. Furthermore, a scheme for including selected higher-order excitations for a subset of modes is introduced and studied numerically. Three different definitions of the TDVCC autocorrelation function (ACF) are introduced and analyzed in both theory and numerical experiments. Example calculations are presented for an array of systems including imidazole, formyl fluoride, formaldehyde, and a reduced-dimensionality bithiophene model. The results show that the TDVCC[k] hierarchy converges systematically toward the full-TDVCC limit and that the implementation allows accurate quantum-dynamics simulations of large systems to be performed. Specifically, the intramolecular vibrational-energy redistribution of the 21-dimensional imidazole molecule is studied in terms of the decay of the ACF. Furthermore, the importance of product separability in the definition of the ACF is highlighted when studying non-interacting subsystems.

Time-Dependent Perspective for the Intramolecular Couplings of the N–H Stretches of Protonated Tryptophan

Quasi-classical direct dynamics simulations, performed with the B3LYP-D3/cc-pVDZ electronic structure theory, are reported for vibrational relaxation of the three NH stretches of the −NH₃⁺ group of protonated tryptophan (TrpH⁺), excited to the n = 1 local mode states. The intramolecular vibrational energy relaxation (IVR) rates determined for these states, from the simulations, are in good agreement with the experiment. In accordance with the experiment, IVR for the free NH stretch is slowest, with faster IVR for the remaining two NH stretches which have intermolecular couplings with an O atom and a benzenoid ring. For the free NH and the NH coupled to the benzenoid ring, there are beats (i.e., recurrences) in their relaxations versus time. For the free NH stretch, 50% of the population remained in n = 1 when the trajectories were terminated at 0.4 ps. IVR for the free NH stretch is substantially slower than for the CH stretch in benzene. The agreement found in this study between quasi-classical direct dynamics simulations and experiments indicates the possible applicability of this simulation method to larger biological molecules. Because IVR can drive or inhibit reactions, calculations of IVR time scales are of interest, for example, in unimolecular reactions, mode-specific chemistry, and many photochemical processes.

Exploring the features on the OH + SO2 potential energy surface using theory and testing its accuracy by comparison to experimental data

Ab initio theory has been used to identify the pre-reaction complex in the atmospherically important reaction between OH + SO2, (R1), where the binding energy of the pre-reaction complex was determined to be 7.2 kJ mol-1. Using reaction rate theory, implemented with the master equation package MESMER, the effects of this complex on the kinetics of R1 at temperatures above 250 K have been investigated. From simulations and fitting to the experimental kinetic data, it is clear that the influence of this pre-reaction complex is negligible and that the kinetics are controlled by the inner transition-state that leads to the product, HOSO2. While the effect of this complex on the thermal kinetics is small it potentially provides an efficient route to remove energy from vibrationally excited OH. The fitting to the past experimental data reveals that this inner transition-state is submerged with a barrier -0.25 kJ mol-1 below the entrance channel, which is outside the range predicted from the best theoretical calculations. The data fitting also yielded ΔR1H0K equal to -(109 ± 5.6) kJ mol-11 and a more precise expression for k∞1(T), (5.95 ± 0.83) × 10-13 × (T/298)-0.11±0.27.

Ab initio kinetics of the HOSO2 + 3O2 → SO3 + HO2 reaction

The detailed kinetic mechanism of the HOSO₂ + ³O₂ reaction, which plays a pivotal role in the atmospheric oxidation of SO₂, was investigated using accurate electronic structure calculations and novel statistical thermodynamic/kinetic models. Explored using the accurate composite method W1U, the detailed potential energy surface (PES) revealed that the addition of O₂ to a HOSO₂ radical to form the adduct (HOSO₄) proceeds via a transition state with a slightly positive barrier (i.e., 0.7 kcal mol^-1 at 0 K). Such a finding compromises a long-term hypothesis about this channel of being a barrierless process. Moreover, the overall reaction was found to be slightly exothermic by 1.7 kcal mol^-1 at 0 K, which is in good agreement with recent studies. On the newly-constructed PES, the temperature- and pressure-dependent behaviors of the title reaction were characterized in a wide range of conditions (T = 200-1000 K & P = 10-760 Torr) using the integrated deterministic and stochastic master equation/Rice-Ramsperger-Kassel-Marcus (ME/RRKM) rate model in which corrections for hindered internal rotation (HIR) and tunneling treatments were included. The calculated numbers were found to be in excellent agreement with literature data. The sensitivity analyses on the derived rate coefficients with respect to the ab initio input parameters (i.e., barrier height and energy transfer) were also performed to further understand the kinetic behaviors of the title reaction. The detailed kinetic mechanism, consisting of thermodynamic and kinetic data (in NASA polynomial and modified Arrhenius formats, respectively), was also provided at different T & P for further use in the modeling/simulation of any related systems.

Formation of a pre-reaction hydrogen-bonded complex and its significance in the potential energy surface of the OH + SO2→ HOSO2 reaction: A computational study

Using computational calculations, we have revisited the potential energy surface (PES) of the reaction between OH and SO2, which is believed as the rate-limiting step in the atmospheric formation of H2SO4. In this work, we report for the first time the presence of a pre-reaction hydrogen-bonded complex between OH and SO2 in the reaction PES. Based on this finding, it has been shown that the reaction can be considered as a two-step process in which the first step is the formation of the pre-reaction complex and the second step is the transformation of this complex to the product. It was observed that due to the presence of this pre-reaction complex as a potential well in the reaction PES, the barrier height got increased by around two-fold for the second step. Based on this observation, it has been proposed that the kinetics of the reaction is going to be affected. Also based on the analysis of the geometries of this pre-reaction complex and the transition state, it has been argued that the step involving the transformation of this pre-reaction complex to the product via the transition state is going to be the slowest step as this transformation involves large structural changes of the stationary points involved.

Reaction and relaxation at surface hotspots: using molecular dynamics and the energy-grained master equation to describe diamond etching

The extent to which vibrational energy transfer dynamics can impact reaction outcomes beyond the gas phase remains an active research question. Molecular dynamics (MD) simulations are the method of choice for investigating such questions; however, they can be extremely expensive, and therefore it is worth developing cheaper models that are capable of furnishing reasonable results. This paper has two primary aims. First, we investigate the competition between energy relaxation and reaction at 'hotspots' that form on the surface of diamond during the chemical vapour deposition process. To explore this, we developed an efficient reactive potential energy surface by fitting an empirical valence bond model to higher-level ab initio electronic structure theory. We then ran 160 000 NVE trajectories on a large slab of diamond, and the results are in reasonable agreement with experiment: they suggest that energy dissipation from surface hotspots is complete within a few hundred femtoseconds, but that a small fraction of CH₃ does in fact undergo dissociation prior to the onset of thermal equilibrium. Second, we developed and tested a general procedure to formulate and solve the energy-grained master equation (EGME) for surface chemistry problems. The procedure we outline splits the diamond slab into system and bath components, and then evaluates microcanonical transition-state theory rate coefficients in the configuration space of the system atoms. Energy transfer from the system to the bath is estimated using linear response theory from a single long MD trajectory, and used to parametrize an energy transfer function which can be input into the EGME. Despite the number of approximations involved, the surface EGME results are in reasonable agreement with the NVE MD simulations, but considerably cheaper. The results are encouraging, because they offer a computationally tractable strategy for investigating non-equilibrium reaction dynamics at surfaces for a broader range of systems.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

An Experimental Study of the Kinetics of OH/OD(v = 1,2,3) + SO2: The Limiting High-Pressure Rate Coefficients as a Function of Temperature

The kinetics of the reaction OH/OD(v = 1,2,3) + SO₂ were studied using a photolysis/laser-induced fluorescence technique. The rate coefficients OH/OD(v = 1,2,3) + SO₂, k₁, over the temperature range of 295-810 K were used to determine the limiting high-pressure limit k₁^∞. This method is usually applicable if the reaction samples the potential well of the adduct HOSO₂ and if intramolecular vibrational relaxation is fast. In the present case, however, the rate coefficients showed an additional fast removal contribution as evidenced by the increase in k₁ with vibrational level; this behavior together with its temperature dependence is consistent with the existence of a weakly bound complex on the potential energy surface prior to adduct formation. The data were analyzed using a composite mechanism that incoporates energy-transfer mechanisms via both the adduct and the complex, and yielded a value of k₁^∞(295 K) equal to (7.2 ± 3.3) × 10^-13 cm³ molecule^-1 s^-1 (errors at 1σ), a factor of between 2 and 3 smaller than the current recommended IUPAC and JPL values of (2.0_-1.0^+2.0) and (1.6 ± 0.4) × 10^-12 cm³ molecule^-1 s^-1 at 298 K, respectively, although the error bars do overlap. k₁^∞ was observed to only depend weakly on temperature. Further evidence for a smaller k₁^∞ is presented in the companion paper.

Reaction of SO2with OH in the atmosphere

We theoretically investigate the rate constantk(T,p) of the OH + SO₂reaction with experimental accuracy.

Multiconfigurational Ehrenfest approach to quantum coherent dynamics in large molecular systems

This article briefly describes recently developed Multiconfigurational Ehrenfest dynamics method to simulate quantum dynamics in systems with many degrees of freedom. The central idea is to guide the trajectories of basis wave functions by means of the Ehrenfest trajectories. The amplitudes of guided basis functions are coupled through a system of linear equations. The approach has been applied to simulations of nonadiabatic dynamics in Spin-Boson model and in pyrazine molecule. A new application to nonadiabatic dynamics in 24D model of pyrazine, where good spectrum for is obtained with the basis of only 34 basis Ehrenfest configurations is reported. This application provides the ground for future fully quantum direct dynamics. Another new application to the model of sticking to the surface described by the System-Bath Hamiltonian is presented to demonstrate the broadness of the approach, which can be applied to both electronically adiabatic and nonadiabatic dynamics. For all applications the results are in good agreement with those of MCTDH, which is very difficult to achieve with other trajectory-based methods. Therefore MCE can serve as a starting point for future use with "on the fly" direct dynamics. MCE provides an efficient fully quantum method capable of catching coherent dynamics in multidimentional systems, which is a necessary step for developing and understanding coherent control in realistic quantum systems.

Taking Ockham's razor to enzyme dynamics and catalysis

The role of protein dynamics in enzyme catalysis is a matter of intense current debate. Enzyme-catalysed reactions that involve significant quantum tunnelling can give rise to experimental kinetic isotope effects with complex temperature dependences, and it has been suggested that standard statistical rate theories, such as transition-state theory, are inadequate for their explanation. Here we introduce aspects of transition-state theory relevant to the study of enzyme reactivity, taking cues from chemical kinetics and dynamics studies of small molecules in the gas phase and in solution--where breakdowns of statistical theories have received significant attention and their origins are relatively better understood. We discuss recent theoretical approaches to understanding enzyme activity and then show how experimental observations for a number of enzymes may be reproduced using a transition-state-theory framework with physically reasonable parameters. Essential to this simple model is the inclusion of multiple conformations with different reactivity.

Computational studies of the isomerization and hydration reactions of acetaldehyde oxide and methyl vinyl carbonyl oxide

Alkene ozonolysis is a major source of hydroxyl radical (*OH), the most important oxidant in the troposphere. Previous experimental and computational work suggests that for many alkenes the measured *OH yields should be attributed to the combined impact of both chemically activated and thermalized syn-alkyl Criegee intermediates (CIs), even though the thermalized CI should be susceptible to trapping by molecules such as water. We have used RRKM/master equation and variational transition state theory calculations to quantify the competition between unimolecular isomerization and bimolecular hydration reactions for the syn and anti acetaldehyde oxide formed in trans-2-butene ozonolysis and for the CIs formed in isoprene ozonolysis possessing syn-methyl groups. Statistical rate theory calculations were based on quantum chemical data provided by the B3LYP, QCISD, and multicoefficient G3 methods, and thermal rate constants were corrected for tunneling effects using the Eckart method. At tropospheric temperatures and pressures, all thermalized CIs with syn-methyl groups are predicted to undergo 1,4-hydrogen shifts from 2 to 8 orders of magnitude faster than they react with water monomer at its saturation number density. For thermalized anti acetaldehyde oxide, the rates of dioxirane formation and hydration should be comparable.