W2X and W3X-L: Cost-Effective Approximations to W2 and W4 with kJ mol–1 Accuracy

Limiting factors in the accuracy of DFT calculation for redox potentials

In the present study, we have investigated factors affecting the accuracy of computational chemistry calculation of redox potentials, namely the gas-phase ionization energy (IE) and electron affinity (EA), and the continuum solvation effect. In general, double-hybrid density functional theory methods yield IEs and EAs that are on average within ~0.1 eV of our high-level W3X-L benchmark, with the best performing method being DSD-BLYP/ma-def2-QZVPP. For lower-cost methods, the average errors are ~0.2-0.3 eV, with ωB97X-3c being the most accurate (~0.15 eV). For the solvation component, essentially all methods have an average error of ~0.3 eV, which shows the limitation of the continuum solvation model. Curiously, the directly calculated redox potentials show errors of ~0.3 eV for all methods. These errors are notably smaller than what can be expected from error propagation with the two components (IE and EA, and solvation effect). Such a discrepancy can be attributed to the cancellation of errors, with the lowest-cost GFN2-xTB method benefiting the most, and the most accurate ωB97X-3c method benefiting the least. For organometallic species, the redox potentials show large deviations exceeding ~0.5 eV even for DSD-BLYP. The large errors are attributed to those for the gas-phase IEs and EAs, which represents a major barrier to the accurate calculation of redox potentials for such systems.

W4Λ: Leveraging Λ Coupled-Cluster for Accurate Computational Thermochemistry Approaches

High-accuracy composite wave function methods like Weizmann-4 (W4) theory, high-accuracy extrapolated ab initio thermochemistry (HEAT), and the Feller-Peterson-Dixon (FPD) approach enable sub-kJ/mol accuracy in gas-phase thermochemical properties. Their biggest computational bottleneck is the evaluation of the valence post-CCSD(T) correction term. We demonstrate here, for the W4-17 thermochemistry benchmark and subsets thereof, that the Λ coupled-cluster expansion converges more rapidly and smoothly than the regular coupled-cluster series. By means of CCSDT(Q)Λ and CCSDTQ(5)Λ, we can considerably (up to an order of magnitude) accelerate W4- and W4.3-type calculations without loss in accuracy, leading to the W4Λ and W4.3Λ computational thermochemistry protocols.

Multireference and Coupled-Cluster Study of Dimethyltetroxide (MeO4Me) Formation and Decomposition

Peroxyl radicals (RO2) are important intermediates in the atmospheric oxidation processes. The RO2 can react with other RO2 to form reactive intermediates known as tetroxides, RO4R. The reaction mechanisms of RO4R formation and its various decomposition channels have been investigated in multiple computational studies, but previous approaches have not been able to provide a unified methodology that is able to connect all relevant reactions together. An apparent difficulty in modeling the RO4R formation and its decomposition is the involvement of open-shell singlet electronic states along the reaction pathway. Modeling such electronic states requires multireference (MR) methods, which we use in the present study to investigate in detail a model reaction of MeO2 + MeO2 → MeO4Me, and its decomposition, MeO4Me → MeO + O2 + MeO, as well as the two-body product complexes MeO···O2 + MeO and MeO···MeO + O2. The used MR methods are benchmarked against relative energies of MeO2 + MeO2, MeO4Me, and MeO + MeO + O2, calculated with CCSD(T)/CBS, W2X, and W3X-L methods. We found that the calculated relative energies of the overall MeO2 + MeO2 → MeO4Me → MeO + O2 + MeO reaction are very sensitive to the chosen MR method and that the CASPT2(22e,14o)-IPEA method is able to reproduce the relative energies obtained by the various coupled-cluster methods. Furthermore, CASPT2(22e,14o)-IPEA and W3X-L results show that the MeO···O2 product complex + MeO is lower in energy than the MeO···MeO complex + O2. The formation of MeO4Me is exothermic, and its decomposition is endothermic, relative to the tetroxide. Both the formation and decomposition reactions appear to follow pathways with no saddle points. According to potential energy surface scans of the decomposition pathway, the concerted cleavage of both MeO···O bonds in MeO4Me is energetically preferred over the corresponding sequential decomposition.

Reactive aldehyde chemistry explains the missing source of hydroxyl radicals

Hydroxyl radicals (OH) determine the tropospheric self-cleansing capacity, thus regulating air quality and climate. However, the state-of-the-art mechanisms still underestimate OH at low nitrogen oxide and high volatile organic compound regimes even considering the latest isoprene chemistry. Here we propose that the reactive aldehyde chemistry, especially the autoxidation of carbonyl organic peroxy radicals (R(CO)O2) derived from higher aldehydes, is a noteworthy OH regeneration mechanism that overwhelms the contribution of the isoprene autoxidation, the latter has been proved to largely contribute to the missing OH source under high isoprene condition. As diagnosed by the quantum chemical calculations, the R(CO)O2 radicals undergo fast H-migration to produce unsaturated hydroperoxyl-carbonyls that generate OH through rapid photolysis. This chemistry could explain almost all unknown OH sources in areas rich in both natural and anthropogenic emissions in the warm seasons, and may increasingly impact the global self-cleansing capacity in a future low nitrogen oxide society under carbon neutrality scenarios.

Rapid Atmospheric Reactions between Criegee Intermediates and Hypochlorous Acid

Hypochlorous acid (HOCl) is a paramount compound in the atmosphere due to its significant contribution to both tropospheric oxidation capacity and ozone depletion. The main removal routes for HOCl are photolysis and the reaction with OH during the daytime, while these processes are unimportant during the nighttime. Here, we report the rapid reactions of Criegee intermediates (CH2OO and anti/syn-CH3CHOO) with HOCl by using high-level quantum chemical methods as the benchmark; their accuracy is close to coupled cluster theory with single, double, and triple excitations and quasiperturbative connected quadruple excitations with a complete basis limit by extrapolation [CCSDT(Q)/CBS]. Their rate constants have been calculated by using a dual-level strategy; this combines conventional transition state theory calculated at the benchmark level with variational transition state theory with small-curvature tunneling by a validated density functional method. We find that the introduction of the methyl group into Criegee intermediates not only affects their reactivities but also exerts a remarkable influence on anharmonicity. The calculated results uncover that anharmonicity increases the rate constants of CH2OO + HOCl by a factor of 18-5, while it is of minor importance in the anti/syn-CH3CHOO + HOCl reaction at 190-350 K. The present findings reveal that the loose transition state for anti-CH3CHOO and HOCl is a rate-determining step at 190-350 K. We also find that the reaction of Criegee intermediates with HOCl contributes significantly to the sink of HOCl during the nighttime in the atmosphere.

Polysulfides in Magnesium-Sulfur Batteries

Mg-S batteries hold great promise as a potential alternative to Li-based technologies. Their further development hinges on solving a few key challenges, including the lower capacity and poorer cycling performance when compared to Li counterparts. At the heart of the issues is the lack of knowledge on polysulfide chemical behaviors in the Mg-S battery environment. In this Review, a comprehensive overview of the current understanding of polysulfide behaviors in Mg-S batteries is provided. First, a systematic summary of experimental and computational techniques for polysulfide characterization is provided. Next, conversion pathways for Mg polysulfide species within the battery environment are discussed, highlighting the important role of polysulfide solubility in determining reaction kinetics and overall battery performance. The focus then shifts to the negative effects of polysulfide shuttling on Mg-S batteries. The authors outline various strategies for achieving an optimal balance between polysulfide solubility and shuttling, including the use of electrolyte additives, polysulfide-trapping materials, and dual-functional catalysts. Based on the current understanding, the directions for further advancing knowledge of Mg polysulfide chemistry are identified, emphasizing the integration of experiment with computation as a powerful approach to accelerate the development of Mg-S battery technology.

DAPD Set of Pd-Containing Diatomic Molecules: Accurate Molecular Properties and the Great Lengths to Obtain Them

In the present study, we obtained reliable bond energy, bond length, and zero-point vibrational frequency for a set of diatomic Pd species (the DAPD set). It includes PdH, Pd2, and PdX (X = B, C, N, O, F, Al, Si, P, S, and Cl). Our highest-level protocol (W4X-L) represents scalar and spin-orbit relativistic, valence- and inner-valence correlated, extrapolated CCSDTQ(5) energy. The DAPD set of molecules is challenging for computational chemistry methods in different manners; for Pd2, the spin-orbit contribution to the bond energy is fairly large, whereas for PdC and PdSi, the post-CCSD(T) correlation components are considerable. The diverse range of requirements represents a significant challenge for lower-level methods. While density functional theory (DFT) methods generally yield good agreements for bond lengths and vibrational frequencies, large deviations are found for bond energies. In general, hybrid DFT methods are more accurate than nonhybrid functionals, but the agreement in individual cases varies. This illustrates the critical role that new high-quality reference data would play in the continual development of lower-cost methods.

Quantitative kinetics of the atmospheric reaction between isocyanic acid and hydroxyl radicals: post-CCSD(T) contribution, anharmonicity, recrossing effects, torsional anharmonicity, and tunneling

Hydroxyl radicals (OH) are the most important atmospheric oxidant, initiating atmospheric reactions for the chemical transformation of volatile organic compounds. Here, we choose the HNCO + OH reaction as a prototype reaction because it contains the fundamental reaction processes for OH radicals: H-abstraction reaction by OH and OH addition reaction. However, its kinetics are unknown under atmospheric conditions. We investigate the reaction of HNCO with OH by using the GMM(P).L method close to the accuracy of single, double, triple, and quadruple excitations and noniterative quintuple excitations with a complete basis set (CCSDTQ(P)/CBS) as benchmark results and a dual-level strategy for kinetics calculations. The calculated rate constant of HNCO + OH is in good agreement with the experimental data available at the temperatures between 620 and 2500 K. We find that the rate constant cannot be correctly obtained by using experimental data to extrapolate the atmospheric temperature ranges. We find that the post-CCSD(T) contribution is very large for the barrier height with the value of -0.85 kcal mol-1 for the H-abstraction reaction, while the previous investigations were done up to the CCSD(T) level. Moreover, we also find that recrossing effects, tunneling, torsional anharmonicity, and anharmonicity are important for obtaining quantitative kinetics in the OH + HNCO reaction.

Atmospheric Chemistry of NH2SO3H in Polluted Areas: An Unexpected Isomerization of NH2SO3H in Acid-Polluted Regions

NH2SO3H is an effective nucleation agent for the formation of atmospheric aerosols and cloud particles. So, the ammonolysis of SO3 to form NH2SO3H without and with neutral (H2O) and basic (NH3) trace gases has been extensively investigated. However, the acidic trace gas X (X = H2SO4 and CH3SO3H)-assisted ammonolysis of SO3 is still up for debate. In this work, a comprehensive theoretical investigation of X-assisted ammonolysis of SO3 and its reverse reaction (the isomerization of NH2SO3H to form SO3-···NH3+) was carried out in the gas phase and at the air-water interface. The gas-phase results show that X-assisted isomerization of NH2SO3H to form SO3-···NH3+ is more energetically and kinetically favorable than its reverse reaction and the isomerization of NH2SO3H in the presence of H2O and NH3. Such unexpected findings revealed that gas-phase NH2SO3H is highly reactive in the presence of acidic trace gas in contrast to the high stability of NH2SO3H in neutral and basic conditions. At the air-water interface, the X-assisted isomerization reaction of NH2SO3H involves multiple water molecules. The loop structure of the reaction center (X···NH2SO3H···3H2O) promotes the transfer of protons in the water molecules to form the SO3-···NH3+ ion pair, which can then interact with several interfacial water molecules to form ammonium bisulfate. These interfacial reaction channels follow a stepwise mechanism and proceed at the picosecond time-scale. The findings of this study will contribute to a better understanding of the atmospheric behavior of NH2SO3H in polluted acidic trace gases.

Kinetics of Sulfur Trioxide Reaction with Water Vapor to Form Atmospheric Sulfuric Acid

Although experimental methods can be used to obtain the quantitative kinetics of atmospheric reactions, experimental data are often limited to a narrow temperature range. The reaction of SO3 with water vapor is important for elucidating the formation of sulfuric acid in the atmosphere; however, the kinetics is uncertain at low temperatures. Here, we calculate rate constants for reactions of sulfur trioxide with two water molecules. We consider two mechanisms: the SO3···H2O + H2O reaction and the SO3 + (H2O)2 reaction. We find that beyond-CCSD(T) contributions to the barrier heights are very large, and multidimensional tunneling, unusually large anharmonicity of high-frequency modes, and torsional anharmonicity are important for obtaining quantitative kinetics. We find that at lower temperatures, the formation of the termolecular precursor complexes, which is often neglected, is rate-limiting compared to passage through the tight transition states. Our calculations show that the SO3···H2O + H2O mechanism is more important than the SO3 + (H2O)2 mechanism at 5-50 km altitudes. We find that the rate ratio between SO3···H2O + H2O and SO3 + (H2O)2 is greater than 20 at altitudes between 10 and 35 km, where the concentration of SO3 is very high.

Unimolecular Reactions of E-Glycolaldehyde Oxide and Its Reactions with One and Two Water Molecules

The kinetics of Criegee intermediates are important for atmospheric modeling. However, the quantitative kinetics of Criegee intermediates are still very limited, especially for those with hydroxy groups. Here, we calculate rate constants for the unimolecular reaction of E-glycolaldehyde oxide [E-hydroxyethanal oxide, E-(CH₂OH)CHOO], for its reactions with H₂O and (H₂O)₂, and for the reaction of the E-(CH₂OH)CHOO…H₂O complex with H₂O. For the highest level of electronic structure, we use W3X-L//CCSD(T)-F12a/cc-pVDZ-F12 for the unimolecular reaction and the reaction with water and W3X-L//DF-CCSD(T)-F12b/jun-cc-pVDZ for the reaction with 2 water molecules. For the dynamics, we use a dual-level strategy that combines conventional transition state theory with the highest level of electronic structure and multistructural canonical variational transition state theory with small-curvature tunneling with a validated density functional for the electronic structure. This dynamical treatment includes high-frequency anharmonicity, torsional anharmonicity, recrossing effects, and tunneling. We find that the unimolecular reaction of E-(CH₂OH)CHOO depends on both temperature and pressure. The calculated results show that E-(CH₂OH)CHOO…H₂O + H₂O is the dominant entrance channel, while previous investigations only considered Criegee intermediates + (H₂O)₂. In addition, we find that the atmospheric lifetime of E-(CH₂OH)CHOO with respect to 2 water molecules is particularly short with a value of 1.71 × 10^-6 s at 0 km, which is about 2 orders of magnitude shorter than those usually assumed for Criegee intermediate reactions with water dimer. We also find that the OH group in E-(CH₂OH)CHOO enhances its reactivity.

Is DFT Accurate Enough to Calculate Regioselectivity? The Case of 1,3-Dipolar Cycloaddition of Azide to Alkynes and Alkenes

The importance of regioselectivity in 1,3-dipolar cycloadditions (DCs) makes it surprising that no benchmarking study on this problem has appeared. We investigated whether DFT calculations are an accurate tool to predict the regioselectivity of uncatalyzed thermal azide 1,3-DCs. We considered the reaction between HN3 and 12 dipolarophiles, comprising ethynes HC≡C-R and ethenes H2 C=CH-R (R=F, OH, NH2 , Me, CN, CHO), which cover a broad range of electron demand and conjugation ability. We established benchmark data by the W3X protocol [complete-basis-set-extrapolated CCSD(T)-F12 energy with T-(T) and (Q) corrections and MP2-calculated core/valence and relativistic effects] and showed that core/valence effects and high-order excitations are important for accurate regioselectivity. Regioselectivities calculated using an extensive set of density functional approximations (DFAs) were compared with benchmark data. Range-separated and meta-GGA hybrids gave the best results. Good treatment of self-interaction and electron exchange are the key features for accurate regioselectivity. Dispersion correction slightly improves agreement with W3X results. The best DFAs provide the isomeric TS energy difference with an expected error ≈0.7 mh and errors ≈2 mh can occur. The isomer yield provided by the best DFA has an expected error of ±5 %, though errors up to 20 % are not rare. At present, an accuracy of 1-2 % is unfeasible but it seems that we are not far from achieving this goal.

Quantitative Kinetics of HO2 Reactions with Aldehydes in the Atmosphere: High-Order Dynamic Correlation, Anharmonicity, and Falloff Effects Are All Important

Kinetics provides the fundamental parameters for elucidating sources and sinks of key atmospheric species and for atmospheric modeling more generally. Obtaining quantitative kinetics in the laboratory for the full range of atmospheric temperatures and pressures is quite difficult. Here, we use computational chemistry to obtain quantitative rate constants for the reactions of HO₂ with HCHO, CH₃CHO, and CF₃CHO. First, we calculate the high-pressure-limit rate constants by using a dual-level strategy that combines conventional transition state theory using a high level of electronic structure wave function theory with canonical variational transition state theory including small-curvature tunneling using density functional theory. The wave-function level is beyond-CCSD(T) for HCHO and CCSD(T)-F12a (Level-A) for XCHO (X = CH₃, CF₃), and the density functional (Level-B) is specifically validated for these reactions. Then, we calculate the pressure-dependent rate constants by using system-specific quantum RRK theory (SS-QRRK) and also by an energy-grained master equation. The two treatments of the pressure dependence agree well. We find that the Level-A//Level-B method gives good agreement with CCSDTQ(P)/CBS. We also find that anharmonicity is an important factor that increases the rate constants of all three reactions. We find that the HO₂ + HCHO reaction has a significant dependence on pressure, but the HO₂ + CF₃CHO reaction is almost independent of pressure. Our findings show that the HO₂ + HCHO reaction makes important contribution to the sink for HCHO, and the HO₂ + CF₃CHO reaction is the dominant sink for CF₃CHO in the atmosphere.

Assessment of DLPNO-CCSD(T)-F12 and its use for the formulation of the low-cost and reliable L-W1X composite method

In the present study, we have investigated the performance of RIJCOSX DLPNO-CCSD(T)-F12 methods for a wide range of systems. Calculations with a high-accuracy option ["DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12"] extrapolated to the complete-basis-set limit using the maug-cc-pV[D+d,T+d]Z basis sets provides fairly good agreements with the canonical CCSD(T)/CBS reference for a diverse set of thermochemical and kinetic properties [with mean absolute deviations (MADs) of ~1-2 kJ mol^-1 except for atomization energies]. On the other hand, the low-cost "RIJCOSX DLPNO-CCSD(T)-F12D" option leads to substantial deviations for certain properties, notably atomization energies (MADs of up to tens of kJ mol^-1 ). With the high-accuracy CBS approach, we have formulated the L-W1X method, which further includes a low-cost core-valence plus scalar-relativistic term. It shows generally good accuracy. For improved accuracies in specific cases, we advise replacing maug-cc-pV(n+d)Z with jun-cc-pV(n+d)Z for the calculation of electron affinities, and using well-constructed isodesmic-type reactions to obtain atomization energies. For medium-sized systems, DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 calculations are several times faster than the corresponding canonical computation; the use of the local approximations (RIJCOSX and DLPNO) leads to a better scaling than that for the canonical calculation (from ~6-7 down to ~2-4 for our test systems). Thus, the DefGrid3 RIJCOSX DLPNO-CCSD(T₁ )-F12 method, and the L-W1X protocol that based on it, represent a useful means for obtaining accurate thermochemical quantities for larger systems.

High-Level Quantum Chemistry Reference Heats of Formation for a Large Set of C, H, N, and O Species in the NIST Chemistry Webbook and the Identification and Validation of Reliable Protocols for Their Rapid Computation

A recent study has examined the accuracy of NIST heats of formation for a set of C, H, and O-containing species with a proposed low-cost quantum chemistry approach. In the present study, we have used high-level methods such as W1X-2 to obtain these data more rigorously, which we have then used to assess the NIST and the previously computed values. We find that many of these NIST data that are as suggested to be unreliable by the previous study are indeed inconsistent with our high-level reference values. However, we also find substantial deviations for the previously computed values from our benchmark. Thus, we have assessed the performance of alternative low-cost methods. In our assessment, we have additionally examined C, H, N, and O-containing species for which heats of formation are available from the NIST database. We find the ωB97M-V/ma-def2-TZVP, DSD-PBEP86/ma-def2-TZVP, and CCSD(T)-F12b/aug'-cc-pVDZ methods to be adequate for obtaining heats of formation with the atomization approach, once their atomic energies are optimized with our benchmark. Notably, the low-cost ωB97M-V method yields values that agree to be within 10 kJ mol^-1 for more than 90% of the (∼1500) species. A higher 20 kJ mol^-1 threshold captures 98% of the data. The outlier species typically contain many electron-withdrawing (nitro) groups. In these cases, the use of isodesmic-type reactions rather than the atomization approach is more reliable. Our assessment has also identified significant outliers from the NIST database, for which experimental re-determination of the heats of formation would be desirable.

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

Temperature-dependent kinetics of the atmospheric reaction between CH2OO and acetone

Criegee intermediates are important oxidants produced in the ozonolysis of alkenes in the atmosphere. Quantitative kinetics of the reactions of Criegee intermediates are required for atmospheric modeling. However, the experimental studies do not cover the full relevant range of temperature and pressure. Here we report the quantitative kinetics of CH₂OO + CH₃C(O)CH₃ by using our recently developed dual strategy that combines coupled cluster theory with high excitation levels for conventional transition state theory and well validated levels of density functional theory for direct dynamics calculations using canonical variational transition theory including tunneling. We find that the W3X-L//DF-CCSD(T)-F12b/jun-cc-pVDZ electronic structure method can be used to obtain quantitative kinetics of the CH₂OO + CH₃C(O)CH₃ reaction. Whereas previous investigations considered a one-step mechanistic pathway, we find that the CH₂OO + CH₃C(O)CH₃ reaction occurs in a stepwise manner. This has implications for the modeling of Criegee-intermediate reactions with other ketones and with aldehydes. In the kinetics calculations, we show that recrossing effects of the conventional transition state are negligible for determining the rate constant of CH₂OO + CH₃C(O)CH₃. The present findings reveal that the rate ratio between CH₂OO + CH₃C(O)CH₃ and OH + CH₃C(O)CH₃ has a significant negative dependence on temperature such that the CH₂OO + CH₃C(O)CH₃ reaction can contribute as a significant sink for atmospheric CH₃C(O)CH₃ at low temperature. The present findings should have broad implications in understanding the reactions of Criegee intermediates with carbonyl compounds and ketones in the atmosphere.

Reaction of SO3 with HONO2 and Implications for Sulfur Partitioning in the Atmosphere

Sulfur trioxide is a critical intermediate for the sulfur cycle and the formation of sulfuric acid in the atmosphere. The traditional view is that sulfur trioxide is removed by water vapor in the troposphere. However, the concentration of water vapor decreases significantly with increasing altitude, leading to longer atmospheric lifetimes of sulfur trioxide. Here, we utilize a dual-level strategy that combines transition state theory calculated at the W2X//DF-CCSD(T)-F12b/jun'-cc-pVDZ level, with variational transition state theory with small-curvature tunneling from direct dynamics calculations at the M08-HX/MG3S level. We also report the pressure-dependent rate constants calculated using the system-specific quantum Rice-Ramsperger-Kassel (SS-QRRK) theory. The present findings show that falloff effects in the SO₃ + HONO₂ reaction are pronounced below 1 bar. The SO₃ + HONO₂ reaction can be a potential removal reaction for SO₃ in the stratosphere and for HONO₂ in the troposphere, because the reaction can potentially compete well with the SO₃ + 2H₂O reaction between 25 and 35 km, as well as the OH + HONO₂ reaction. The present findings also suggest an unexpected new product from the SO₃ + HONO₂ reaction, which, although very short-lived, would have broad implications for understanding the partitioning of sulfur in the stratosphere and the potential for the SO₃ reaction with organic acids to generate organosulfates without the need for heterogeneous chemistry.

Large Pressure Effects Caused by Internal Rotation in the s-cis-syn-Acrolein Stabilized Criegee Intermediate at Tropospheric Temperature and Pressure

Criegee intermediates are important atmospheric oxidants, and quantitative kinetics for stabilized Criegee intermediates are key parameters for atmospheric modeling but are still limited. Here we report barriers and rate constants for unimolecular reactions of s-cis-syn-acrolein oxide (scsAO), in which the vinyl group makes it a prototype for Criegee intermediates produced in the ozonolysis of isoprene. We find that the MN15-L and M06-2X density functionals have CCSD(T)/CBS accuracy for the unimolecular cyclization and stereoisomerization of scsAO. We calculated high-pressure-limit rate constants by the dual-level strategy that combines (a) high-level wave function-based conventional transition-state theory (which includes coupled-cluster calculations with quasiperturbative inclusion of quadruple excitations because of the strongly multiconfigurational character of the electronic wave function) and (b) canonical variational transition-state theory with small-curvature tunneling based on a validated density functional. We calculated pressure-dependent rate constants both by system-specific quantum Rice-Ramsperger-Kassel theory and by solving the master equation. We report rate constants for unimolecular reactions of scsAO over the full range of atmospheric temperature and pressure. We found that the unimolecular reaction rates of this larger-than-previously studied Criegee intermediate depend significantly on pressure. Particularly, we found that falloff effects decrease the effective unimolecular cyclization rate constant of scsAO by about a factor of 3, but the unimolecular reaction is still the dominant atmospheric sink for scsAO at low altitudes. The large falloff caused by the inclusion of the stereoisomerization channel in the master equation calculations has broad implications for mechanistic analysis of reactions with competitive internal rotations that can produce stable rotamers.

C2H5NO Isomers: From Acetamide to 1,2-Oxazetidine and Beyond

This work documents the properties of a number of isomers of molecular formula C₂H₅NO from the most stable, acetamide, through 1,2-oxazetidine and including even higher energy species largely of a dipolar nature. Only two of the isomers have been detected in emissions from the interstellar medium (ISM); possible further candidates are identified, and the likelihood of their being detectable is considered. In general, hardly any of these compounds have been discussed in the existing chemical literature, so this work represents an important contribution extending the canon of chemical bonding which can contribute to machine learning, providing a more exacting test of AI applications. The presence in the ISM of acetamide, CH₃C(O)NH₂, is the subject of current debate with no clear and obvious paths to its formation; it is shown that a 1,3-[H]-transfer from (E,Z)-ethanimidic acid, CH₃C(OH)=NH, is feasible in spite of an energy barrier of 130 kJ mol^–1. It is speculated that imidic acid can itself be formed from abundant precursors, H₂O and CH₃C≡N, in an acid-induced, water addition, autocatalytic reaction on water–ice grains. H₃CC≡NH₃CC≡NH⁺ + H₂OH₃CC(O⁺H₂)=NHH₃CC(OH)=NH + H₃O⁺

A computational study of the HO2 + SO3 → HOSO2 + 3O2 reaction catalyzed by water monomer, water dimer and small clusters of sulfuric acid: kinetics and atmospheric implications

Herein, the reaction mechanisms and kinetics for the HO2 + SO3 → HOSO2 + 3O2 reaction catalyzed by water monomer, water dimer and small clusters of sulfuric acid have been...

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Accurate Thermochemistry for Main-Group Elements up to Xenon with the Wn-P34 Series of Composite Methods

In the present study, we introduce the accurate Wn-P34 quantum chemistry composite methods with applicability to heavy p-block elements up to xenon. For a set of thermochemical properties for prototypical third- and fourth-row species and for a diverse set of small light-main-group species, they show accuracies of ∼3 kJ mol^-1 or better. Overall, the Wn-P34 methods are comparable in accuracy to Wn, with a widened applicability to heavier elements. We have used Wn-P34 to compile the P34 set of accurate thermochemical values for heavy p-block species, and we have applied this set to assess a wide range of lower-cost methods. The results of our assessment show that the G4(MP2)-XK composite method provides adequate treatments for these species, but several widely used double-hybrid density functional theory (DH-DFT) methods show uncharacteristically large deviations. In contrast, we find it presently surprising that some pure and hybrid DFT methods such as TPSS and SCANh perform quite well. We hope that our findings and new tools would facilitate the application of computational chemistry for heavy elements, of which the properties are yet to be broadly explored.

Polycyclic aromatic hydrocarbons: from small molecules through nano-sized species towards bulk graphene

We have examined the use of systematic bond-separation reactions and purposely constructed chemistry-preserving isodesmic reactions for the thermochemical calculation of aromatic hydrocarbon species. The bond-separation approach yields somewhat disappointing accuracy even when the reaction energies are obtained with generally robust composite and double-hybrid (DH) density functional theory (DFT) methods. In contrast, for the purposely constructed reactions, we find a dramatic improvement in the accuracy for energies calculated with all methods examined. Notably, for medium-sized aromatic hydrocarbons, we find that an effective approach for formulating a well-balanced reaction is to split the target species into two halves with an aromatic overlapping region. Overall, the G4(MP2)-XK, MPW2PLYP, MN15, PBE, and DC-DFTB3 methods are reasonable within their respective classes of methods for the calculation of bond-separation as well as chemistry-preserving isodesmic reactions. We have further computed per-carbon atomization energy (AE) for a series of D_6h benzene-type molecules, and thus obtained a formula for extrapolation to the graphene limit [AE_n = 711.5 × (1 - 1/n^0.640) kJ mol^-1, where n = number of carbons]. It suggests that nano-graphene with a length larger than 10 nm would resemble properties of bulk graphene, and conversely, downsizing a nano-graphene beyond this point may lead to considerably altered properties from the bulk.

Atmospheric Kinetics: Bimolecular Reactions of Carbonyl Oxide by a Triple-Level Strategy

Criegee intermediates in the atmosphere serve as oxidizing agents to initiate aerosol formation, which are particularly important for atmospheric modeling, and understanding their kinetics is one of the current outstanding challenges in climate change modeling. Because experimental kinetics are still limited, we must rely on theory for the complete picture, but obtaining absolute rates from theory is a formidable task. Here, we report the bimolecular reaction kinetics of carbonyl oxide with ammonia, hydrogen sulfide, formaldehyde, and water dimer by designing a triple-level strategy that combines (i) benchmark results close to the complete-basis limit of coupled-cluster theory with the single, double, triple, and quadruple excitations (CCSDTQ/CBS), (ii) a new hybrid meta density functional (M06CR) specifically optimized for reactions of Criegee intermediates, and (iii) variational transition-state theory with both variable rection coordinates and optimized reaction paths, with multidimensional tunneling, and with pressure effects. For (i) we have found that quadruple excitations are required to obtain quantitative reaction barriers, and we designed new composite methods and strategies to reach CCSDTQ/CBS accuracy. The present findings show that (i) the CH₂OO + HCHO reaction can make an important contribution to the sink of HCHO under wide atmospheric conditions in the gas phase and that (ii) CH₂OO + (H₂O)₂ dominates over the CH₂OO + H₂O reaction below 10 km.

A chemically consistent rate constant for the reaction of nitrogen dioxide with the oxygen atom

In the present study, a chemically consistent rate constant for the reaction between nitrogen dioxide and the oxygen atom has been obtained by combining low-temperature experimental data from the literature and new high-temperature quantum chemical calculations. The expression for our rate constant is kNO2+O=NO+O2= 2.589 × 1015T-1.035 exp(-226/RT) + 4.242 × 1016T-0.861exp(-50 917/RT) cm3 mol-1 s-1, where R = 8.314 J mol-1 K-1, and is valid over the temperature range T = 221 to 3000 K. The effect of the inclusion of the new rate constant on the prediction of three detailed reaction models from the literature has been studied using (i) new experimental oxygen atom profiles obtained in a shock tube during nitrogen dioxide pyrolysis, and (ii) published shock tube and jet-stirred reactor data for H2-NOx mixtures with and without dioxygen. The impact of the new rate constant on the sensitivity coefficients and reaction pathways has also been analyzed under some conditions. Overall, the predictive capability of the reaction models were improved. The present study suggests that our chemically consistent rate constant should be included in detailed reaction models for combustion applications.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Fullerene Thermochemical Stability: Accurate Heats of Formation for Small Fullerenes, the Importance of Structural Deformation on Reactivity, and the Special Stability of C60

We have used quantum chemistry computations, in conjunction with isodesmic-type reactions, to obtain accurate heats of formation (HoFs) for the small fullerenes C₂₀ (2358.2 ± 8.0 kJ mol^-1), C₂₄ (2566.2 ± 7.6), and the lowest-energy isomers of C₃₂ (2461.1 ± 15.4), C₄₂ (2629.0 ± 20.5), and C₅₄ (2686.2 ± 25.3). As part of this endeavor, we have also obtained accurate HoFs for several medium-sized molecules, namely 216.6 ± 1.4 for fulvene, 375.5 ± 1.5 for pentalene, 670.8 ± 2.9 for acepentalene, and 262.7 ± 2.5 for acenaphthylene. We combine the energies of the small fullerenes and previously obtained energies for larger fullerenes (from C₆₀ to C₆₀₀₀) into a full picture of fullerene thermochemical stability. In general, the per-carbon energies can be reasonably approximated by the "R+D" model that we have previously developed [Chan et al. J. Chem. Theory Comput. 2019, 15, 1255-1264], which takes into account Resonance and structural Deformation factors. In a case study on C₅₄, we find that most of the high-deformation-energy atoms correspond to the sites of the C-Cl bond in the experimentally captured C₅₄Cl₈. In another case study, we find that C₆₀ has the lowest value for the maximum local-deformation energy when compared with similar-sized fullerenes, which is consistent with its "special stability". These results are indicative of structural deformation playing an important role in the reactivity of fullerenes.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.

Association of Cl with C2H2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C₂H₂→C₂H₂Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C₂H₂Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C-H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.

New mechanistic pathways for the formation of organosulfates catalyzed by ammonia and carbinolamine formation catalyzed by sulfuric acid in the atmosphere

Sulfuric acid exerts a remarkable catalytic role in the H₂SO₄ + HCHO + NH₃ reaction that leads to the formation of carbinolamine.

Effect of NH3 and HCOOH on the H2O2 + HO → HO2 + H2O reaction in the troposphere: competition between the one-step and stepwise mechanisms

The H₂O₂ + HO → HO₂ + H₂O reaction is an important reservoir for both radicals of HO and HO₂ catalyzing the destruction of O₃. Here, this reaction assisted by NH₃ and HCOOH catalysts was explored using the CCSD(T)-F12a/cc-pVDZ-F12//M06-2X/aug-cc-pVTZ method and canonical variational transition state theory with small curvature tunneling. Two possible sets of mechanisms, (i) one-step routes and (ii) stepwise processes, are possible. Our results show that in the presence of both NH₃ and HCOOH catalysts under relevant atmospheric temperature, mechanism (i) is favored both energetically and kinetically than the corresponding mechanism (ii). At 298 K, the relative rate for mechanism (i) in the presence of NH₃ (10, 2900 ppbv) and HCOOH (10 ppbv) is respectively 3–5 and 2–4 orders of magnitude lower than that of the water-catalyzed reaction. This is due to a comparatively lower concentration of NH₃ and HCOOH than H₂O which indicates the positive water effect under atmospheric conditions. Although NH₃ and HCOOH catalysts play a negligible role in the reservoir for both radicals of HO and HO₂ catalyzing the destruction of O₃, the current study provides a comprehensive example of how acidic and basic catalysts assisted the gas-phase reactions.

The H₂O₂ + HO → HO₂ + H₂O reaction is an important reservoir for both radicals of HO and HO₂ catalyzing the destruction of O₃.

Atmospheric chemistry of the self-reaction of HO2 radicals: stepwise mechanism versus one-step process in the presence of (H2O)n (n = 1-3) clusters

The effects of water on radical-radical reactions are of great importance for the elucidation of the atmospheric oxidation process of free radicals. In the present work, the HO2 + HO2 reactions with (H2O)n (n = 1-3) have been investigated using quantum chemical methods and canonical variational transition state theory with small curvature tunneling. We have explored both one-step and stepwise mechanisms, in particular the stepwise mechanism initiated by ring enlargement. The calculated results have revealed that the stepwise mechanism is the dominant one in the HO2 + HO2 reaction that is catalyzed by one water molecule. This is because its pseudo-first-order rate constant (kRWM1') is 3 orders of magnitude larger than that of the corresponding one-step mechanism. Additionally, the value of kRWM1' at 298 K has been found to be 4.3 times larger than that of the rate constant of the HO2 + HO2 reaction (kR1) without catalysts, which is in good agreement with the experimental findings. The calculated results also showed that the stepwise mechanism is still dominant in the (H2O)2 catalyzed reaction due to its higher pseudo-first-order rate constant, which is 3 orders of magnitude larger than that of the corresponding one-step mechanism. On the other hand, the one-step process is much faster than the stepwise mechanism by a factor of 105-106 in the (H2O)3 catalyzed reaction. However, the pseudo-first-order rate constants for the (H2O)2 and (H2O)3-catalyzed reactions are lower than that of the H2O-catalyzed reaction by 3-4 orders of magnitude, which indicates that the water monomer is the most efficient one among all the catalysts of (H2O)n (n = 1-3). The present results have provided a definitive example that water and water clusters have important influences on atmospheric reactions.

The CUAGAU Set of Coupled-Cluster Reference Data for Small Copper, Silver, and Gold Compounds and Assessment of DFT Methods

We have obtained benchmark data for a set of small molecular systems of Cu, Ag, and Au using coupled-cluster methods. Using this collection of reference data (that we termed the CUAGAU set) for assessing DFT-type methods, we find the MN15-L nonhybrid DFT to be cost-effective for geometry optimization [mean absolute deviation (MAD) in bond length = 0.20 Å], with an accuracy that is comparable to that for the double-hybrid (DH) DFT method DSD-PBEP86 (MAD = 0.19 Å). For the computation of thermochemical properties, among "conventional" (non-MP2-based) DFT methods, the best performance is found for the global-hybrid meta-GGA functional MN15, with an MAD of 11.4 kJ mol^-1. We also find the nonhybrid method B97M-rV to have a reasonable performance (MAD = 14.4 kJ mol^-1), and it may serve as a cost-effective means for qualitative study. If we look beyond conventional functionals, we find DSD-PBEP86 (MAD = 7.3 kJ mol^-1) to be more accurate than even MN15. Nonetheless, this level of accuracy is still not sufficient for quantitative studies. In this regard, high-level wave function methods such as composite procedures that are based on coupled cluster are still indispensable for obtaining reliable reference data for transition-metal species.

Rapid unimolecular reaction of stabilized Criegee intermediates and implications for atmospheric chemistry

Elucidating atmospheric oxidation mechanisms is necessary for estimating the lifetimes of atmospheric species and understanding secondary organic aerosol formation and atmospheric oxidation capacity. We report an unexpectedly fast mechanistic pathway for the unimolecular reactions of large stabilized Criegee intermediates, which involves the formation of bicyclic structures from large Criegee intermediates containing an aldehyde group. The barrier heights of the mechanistic pathways are unexpectedly low – about 2–3 kcal/mol – and are at least 10 kcal/mol lower than those of hydrogen shift processes in large syn Criegee intermediates; and the calculated rate constants show that the mechanistic pathways are 10⁵-10⁹ times faster than those of the corresponding hydrogen shift processes. The present findings indicate that analogous low-energy pathways can now also be expected in other large Criegee intermediates and that oxidative capacity of some Criegee intermediates is smaller than would be predicted by existing models.

Criegee intermediates have received much attention in atmospheric chemistry because of their importance in ozonolysis mechanisms. Here, using quantum mechanical kinetics, the authors reveal an unexpectedly fast mechanistic pathway for unimolecular reactions of large stabilized Criegee intermediates.

Ab initio dynamics of hydrogen abstraction from N2H4 by OH radicals: an RRKM-based master equation study

The detailed kinetic mechanism of the N₂H₄ + OH reaction is comprehensively reported for a wide condition range of conditions (i.e., 200–3000 K & 1–7600 Torr) using the CCSD(T)/CBS//M06-2X/6-311++G(3df,2p) level and the RRKM-based master equation rate model.

Extrapolation of high-order correlation energies: the WMS model

We have developed a new composite model chemistry method called WMS (Wuhan-Minnesota scaling method) with three characteristics: (1) a composite scheme to approximate the complete configuration interaction valence energy with the affordability condition of requiring no calculation more expensive than CCSD(T)/jul-cc-pV(T+d)Z, (2) low-cost methods for the inner-shell correlation contribution and scalar relativistic correction, and (3) accuracy comparable to methods with post-CCSD(T) components. The new method is shown to be accurate for the W4-17 database of 200 atomization energies with an average mean unsigned error (averaged with equal weight over strongly correlated and weakly correlated subsets of the data) of 0.45 kcal mol-1, and the performance/cost ratio of these results compares very favorably to previously available methods. We also assess the WMS method against the DBH24-W4 database of diverse barrier heights and the energetics of the reactions of three strongly correlated Criegee intermediates with water. These results demonstrate that higher-order correlation contributions necessary to obtain high accuracy for molecular thermochemistry may be successfully extrapolated from the lower-order components of CCSD(T) calculations, and chemical accuracy can now be obtained for larger and more complex molecules and reactions.