Rate constants of chemical reactions from semiclassical transition state theory in full and one dimension

A Multiconformational Transition State Theory Approach to OH Tropospheric Degradation of Fluorotelomer Aldehydes

Experimental work on the OH-initiated oxidation reactions of fluorotelomer aldehydes (FTALs) strongly suggests that the respective rate coefficients do not depend on the size of the Cx F2x+1 fluoroalkyl chain. FTALs hence represent a challenging test to our multiconformer transition state theory (MC-TST) protocol based on constrained transition state randomization (CTSR), since the calculated rate coefficients should not show significant variations with increasing values of x ${x}$ . In this work we apply the MC-TST/CTSR protocol to thex = 2 , 3 ${x={\rm 2,3}}$ cases and calculate both rate coefficients at 298.15 K with a value ofk = ( 2 . 4 ± 1 . 4 ) × 10 - 12 ${k=(2.4\pm 1.4)\times {10}^{-12}}$  cm3  molecule-1  s-1 , practically coincident with the recommended experimental value of kexp =( 2 . 8 ± 1 . 4 ) × 10 - 12 ${(2.8\pm 1.4)\times {10}^{-12}}$  cm3  molecule-1  s-1 . We also show that the use of tunneling corrections based on improved semiclassical TST is critical in obtaining Arrhenius-Kooij curves with a correct behavior at lower temperatures.

Heavy Atom Tunneling in Organic Reactions at Coupled Cluster Potential Accuracy with a Parallel Implementation of Anharmonic Constant Calculations and Semiclassical Transition State Theory

We describe and test on some organic reactions a parallel implementation strategy to compute anharmonic constants, which are employed in semiclassical transition state theory reaction rate calculations. Our software can interface with any quantum chemistry code capable of a single point energy estimate, and it is suitable for both minimum and transition state geometry calculations. After testing the accuracy and comparing the efficiency of our implementation against other software, we use it to estimate the semiclassical transition state theory (SCTST) rate constant of three reactions of increasing dimensionality, known as examples of heavy atom tunneling. We show how our method is improved in efficiency with respect to other existing implementations. In conclusion, our approach allows SCTST rates and heavy atom tunneling at a high level of electronic structure theory (up to CCSD(T)) to be evaluated. This work shows how crucial the possibility to perform high level ab initio rate evaluations can be.

Entanglement Effect and Angular Momentum Conservation in a Nonseparable Tunneling Treatment

The important, and often dominant, role of tunneling in low temperature kinetics has resulted in numerous theoretical explorations into the methodology for predicting it. Nevertheless, there are still key aspects of the derivations that are lacking, particularly for nonseparable systems in the low temperature regime, and further explorations of the physical factors affecting the tunneling rate are warranted. In this work we obtain a closed-form rate expression for the tunneling rate constant that is a direct analog of the rigid-rotor-harmonic-oscillator expression. This expression introduces a novel "entanglement factor" that modulates the reaction rate. Furthermore, we are able to extend this expression, which is valid for nonseparable systems at low temperatures, to properly account for the conservation of angular momentum. In contrast, previous calculations have considered only vibrational transverse modes and so effectively employ a decoupled rotational partition function for the orientational modes. We also suggest a simple theoretical model to describe the tunneling effects in the vicinity of the crossover temperature (the temperature where tunneling becomes the dominating mechanism). This model allows one to naturally classify, interpret, and predict experimental data. Among other things, it quantitatively explains in simple terms the so-called "quantum bobsled" effect, also known as the negative centrifugal effect, which is related to curvature of the reaction path. Taken together, the expressions obtained here allow one to predict the thermal and E-resolved rate constants over broad ranges of temperatures and energies.

Molecular engineering of cocrystallization process in holt melt extrusion based on kinetics of elementary molecular processes

Continuous co-crystallization in a twin-screw granulator is a promising technology. In order to fundamentally optimize the process flow, it is necessary to investigate the kinetics of molecular interactions within the mixture and the effect of these interactions on co-crystal formation. In this study, the processes governing the co-crystallization of ibuprofen and nicotinamide were considered. Density functional theory calculations employing the Hirshfeld partitioning scheme were used to identify donor-acceptor sites on each molecule. A total of twenty-one different molecular interactions was identified (nine of ibuprofen and nicotinamide (resembling co-crystals), three of ibuprofen and itself (resembling the ibuprofen dimer), and nine of nicotinamide and itself (resembling the nicotinamide dimer)). Each interaction was defined as an artificial reversible reaction and the kinetics were calculated using the transition state theory of chemical reactions, where linear and quadratic synchronous transition methods were utilized to identify transition-state structures; the minimum energy path was determined using the nudged elastic band method. A kinetic Monte Carlo framework was used to study the collective/coupled effect of reactions on the progress of the co-crystallization process. it was found that operating at low temperatures (especially lower or very close to the melting temperature of ibuprofen) for longer residency times creates a safe route for maximizing the presence of ibuprofen and nicotinamide co-crystals. If the proposed route is applied, the purity and properties of the produced co-crystal would be significant, especially its desirable availability within the body.

Microcanonical Tunneling Rates from Density-of-States Instanton Theory

Semiclassical instanton theory is a form of quantum transition-state theory which can be applied to the computation of thermal reaction rates in complex molecular systems including quantum tunneling effects. There have been a number of attempts to extend the theory to treat microcanonical rates. However, the previous formulations are either computationally unfeasible for large systems due to an explicit sum over states or they involve extra approximations, which make them less reliable. We propose a robust and practical microcanonical formulation called density-of-states instanton theory, which avoids the sum over states altogether. In line with the semiclassical approximations inherent to the instanton approach, we employ the stationary-phase approximation to the inverse Laplace transform to obtain the densities of states. This can be evaluated using only post-processing of the data available from a small set of instanton calculations, such that our approach remains computationally efficient. We show that the new formulation predicts results that agree well with quantum scattering theory for an atom-diatom reaction and with experiments for a photoexcited unimolecular hydrogen transfer in a Criegee intermediate. When the thermal rate is evaluated from a Boltzmann average over our new microcanonical formalism, it can overcome some problems of conventional instanton theory. In particular, it predicts a smooth transition at the crossover temperature and is able to describe bimolecular reactions with pre-reactive complexes such as CH₃OH + OH.

Chemical reactivity from the vibrational ground-state level. The role of the tunneling path in the tautomerization of urea and derivatives

Recent developments of low-temperature techniques are providing valuable knowledge about chemical processes that manifest in the quantum regimen. The tunneling effect from the vibrational ground-state is the main mechanism of these reactions, which usually involves the motion or transfer of hydrogen atoms. Theoretical methods can enrich the information supplied by these experimental methods through an insightful analysis of the tunneling process. In this context, canonical variational transition state theory with multidimensional tunneling corrections (CVT/MT) can handle this type of reaction, and it has been applied to several systems within the small-curvature approximation for tunneling (SCT). This method is of proven reliability for polyatomic reactions occurring at room temperature and above, but no tests have been performed to check its performance when only the lowest energy level is populated. In this work, we compare SCT against the least-action tunneling (LAT) method to study the tautomerization and cis-trans interconversion reactions in the enol forms of urea, thiourea, and selenourea. To the best of our knowledge, this is the first time that the LAT method is applied to a polyatomic reaction occurring in the deep-tunneling region. The theoretical results indicate that the reaction mechanisms are controlled by tunneling. The SCT and LAT tautomerization reaction times are in good agreement with the experimental values; however, LAT seems superior to SCT for reactions (tautomerizations) that involve moderate reaction path curvature, whereas the opposite is true for reactions with small curvature (interconversions). These results led us to introduce and recommend the microcanonically optimized tunneling path that selects the tunneling probability as the maximum between the SCT and LAT tunneling probabilities.

Calculations of quantum tunnelling rates for muonium reactions with methane, ethane and propane

Thermal rate constants for Mu + CH₄, Mu + C₂H₆ and Mu + C₃H₈ and their equivalent reactions with H were evaluated with ab initio instanton rate theory. The potential-energy surfaces are fitted using Gaussian process regression to high-level electronic-structure calculations evaluated around the tunnelling pathway. This method was able to successfully reproduce various experimental measurements for the rate constant of these reactions. However, it was not able to reproduce the faster-than-expected rate of Mu + C₃H₈ at 300 K reported by Fleming et al. [Phys. Chem. Chem. Phys., 2015, 17, 19901 and Phys. Chem. Chem. Phys., 2020, 22, 6326]. Analysis of our results indicates that the kinetic isotope effect at this temperature is not significantly influenced by quantum tunnelling. We consider many possible factors for the discrepancy between theory and experiment but conclude that in each case, the instanton approximation is unlikely to be the cause of the error. This is in part based on the good agreement we find between the instanton predictions and new multiconfigurational time-dependent Hartree (MCTDH) calculations for Mu + CH₄ using the same potential-energy surface. Further experiments will therefore be needed to resolve this issue.

Calculations on the unimolecular decomposition of the nerve agent VX

It is very difficult to perform experiments on the physical parameters for the thermal decomposition of chemical nerve agents such as VX and computations, therefore, are useful. The reaction dynamics of the gas-phase pericyclic hydrogen transfer of the nerve agent VX is studied computationally. The geometries of the stationary structures are calculated at M06-2X/jul-cc-pVTZ level of theory. Single point energy calculations are carried out at the CBS/QB3 level to correct the energy barriers. Canonical reaction rate constants are calculated as a function of temperature. The one-dimensional semiclassical transition state theory is used to analyse the quantum tunneling effects. A reduced-dimensional hindered rotor model is proposed, tested, and applied to calculate the vibrational partition functions. It is found that the ester (O-side) and thioester (S-side) side chains of VX undergo pericyclic H-transfer reactions that result in decomposition of the molecule. The S-side reaction is favoured both kinetically and thermodynamically and dominates the pyrolysis over the temperature range from 600 K to 1000 K. It is predicted that VX completely decomposes in 2 s at temperatures above 750 K.

Hydrogen tunnelling in the rearrangements of carbenes: the role of dynamical calculations

A tunnelling controlled reaction is studied with semiclassical transition state theory, rationalising the results of experiment.

Understanding H2 Formation on Hydroxylated Pyroxene Nanoclusters: Ab Initio Study of the Reaction Energetics and Kinetics

The rate constants of H₂ formation on five models of silicate nanoclusters with varying degrees of hydroxylation, (Mg₄Si₄O₁₂)(H₂O)_N, were computed over a wide temperature range [180-2000 K]. We tested nine combinations of density functional methods and basis sets for their suitability for calculating reaction energies and barrier heights, and we computed the minimum energy H + H → H₂ reaction paths on each nanocluster. Subsequently, we computed the rate constants employing three semiclassical approaches that take into account tunneling and nonclassical reflection effects by means of the zero curvature tunneling (ZCT), the small curvature tunneling (SCT), and the one-dimensional semiclassical transition state theory (SCTST) methods, which all provided comparable results. Our investigations show that the H₂ formation process following the Langmuir-Hinshelwood (LH) mechanism is more efficient on the hydroxylated (N = 1-4) nanoclusters than on the bare (N = 0) one due to relatively higher reaction barrier height on the latter. H₂ formation is found to have the smallest barrier and the most exothermic reaction for the moderately hydroxylated (Mg₄Si₄O₁₂)(H₂O)₂ nanocluster for all nine considered methods. Overall, we conclude that all the considered nanoclusters are very efficient catalyzing grains for H₂ formation in the physical conditions of the interstellar medium (ISM) with pyroxene nanosilicates having moderate to high hydroxylation being more efficient than bare nanograins.

Parallel Implementation of Semiclassical Transition State Theory

This paper presents the parsctst code, an efficient parallel implementation of the semiclassical transition state theory (SCTST) for reaction rate constant calculations. Parsctst is developed starting from a previously presented approach for the computation of the vibrational density of states of fully coupled anharmonic molecules ( Nguyen et al. Chem. Phys. Lett. 2010 , 499 , 915 ). The parallel implementation makes it practical to tackle reactions involving more than 100 fully coupled anharmonic vibrational degrees of freedom and also includes multidimensional tunneling effects. After describing the pseudocode and demonstrating its computational efficiency, we apply the new code for estimating the rate constant of the proton transfer isomerization reaction of the 2,4,6-tri- tert-butylphenyl to 3,5-di- tert-butylneophyl. Comparison with both theoretical and experimental results is presented. Parsctst code is user-friendly and provides a significant computational time saving compared to serial calculations. We believe that parsctst can boost the application of SCTST as an alternative to the basic transition state theory for accurate kinetics modeling not only in combustion or atmospheric chemistry, but also in organic synthesis, where bigger reactive systems are encountered.

Theoretical Study of Gas-Phase Unimolecular Decomposition of Simulants of the Nerve Agent VX

In order to further understand and support approaches for the degradation and destruction of toxic chemicals, the thermal decomposition of the nerve agent VX through possible pericyclic hydrogen transfer reactions is investigated using simulant molecules. A total of four simulant molecules are studied. Three of them have only one possible H-transfer site, while the other has two. They are chosen to bring physical insights into individual steps of the pericyclic reaction mechanism as well as the possible existence of competing mechanisms. The unimolecular reaction rate constants at the high-pressure limit are calculated. Geometries of stationary structures on the potential energy surfaces are calculated with the MP2 method as well as the B3LYP and M06-2X functionals and 6-311++G(d,p), jul-cc-pVTZ, and aug-cc-pVTZ basis sets. The barrier heights are corrected using energy values obtained at the CBS/QB3 level of theory. The contribution of the quantum tunneling effect to the reaction rate constants is included using one-dimensional semiclassical transition state theory. Adiabatic barrier heights, reaction rate constants, and branching ratio of the competing mechanisms are reported.

The hydrogen abstraction reaction H + C2H6 → H2(v,j) + C2H5. Part II. Theoretical kinetics and dynamics study

Two important issues motivated the present study: the role of the tunnelling contribution at low temperatures and the role of the alkyl fragment in the dynamics.

Application of one-dimensional semiclassical transition state theory to the CH3OH + H ⇌ CH2OH/CH3O + H2 reactions

The rate constants of the two branches of H-abstractions from CH₃OH by the H-atom and the corresponding reactions in the reverse direction are calculated using the one-dimensional semiclassical transition state theory (1D SCTST). In this method, only the reaction mode vibration of the transition state (TS) is treated anharmonically, while the remaining internal degrees of freedom are treated as they would have been in a standard TS theory calculation. A total of eight ab initio single-point energy calculations are performed in addition to the computational cost of a standard TS theory calculation. This allows a second-order Richardson extrapolation method to be employed to improve the numerical estimation of the third- and fourth-order derivatives, which in turn are used in the calculation of the anharmonic constant. Hindered-rotor (HR) vibrations are identified in the equilibrium states of CH₃OH and CH₂OH, and the TSs of the reactions. The partition function of the HRs are calculated using both a simple harmonic oscillator model and a more sophisticated one-dimensional torsional eigenvalue summation (1D TES) method. The 1D TES method can be easily adapted in 1D SCTST computation. The resulting 1D SCTST with 1D TES rate constants show good agreement to previous theoretical and experimental works. The effects of the HR on rate constants for different reactions are also investigated.This article is part of the theme issue 'Modern theoretical chemistry'.

Spiers Memorial Lecture : Introductory lecture: quantum dynamics of chemical reactions

This Spiers Memorial Lecture discusses quantum effects that can be calculated and observed in the chemical reactions of small molecules.

Catalysis and tunnelling in the unimolecular decay of Criegee intermediates

Semi-classical Transition State theory can be applied to catalysed atmospheric reactions, but reaction mode anharmonicity must be treated carefully.

Ab initio instanton rate theory made efficient using Gaussian process regression

Ab initio instanton rate theory is a computational method for rigorously including tunnelling effects into the calculations of chemical reaction rates based on a potential-energy surface computed on the fly from electronic-structure theory. This approach is necessary to extend conventional transition-state theory into the deep-tunnelling regime, but it is also more computationally expensive as it requires many more ab initio calculations. We propose an approach which uses Gaussian process regression to fit the potential-energy surface locally around the dominant tunnelling pathway. The method can be converged to give the same result as from an on-the-fly ab initio instanton calculation but it requires far fewer electronic-structure calculations. This makes it a practical approach for obtaining accurate rate constants based on high-level electronic-structure methods. We show fast convergence to reproduce benchmark H + CH4 results and evaluate new low-temperature rates of H + C2H6 in full dimensionality at a UCCSD(T)-F12b/cc-pVTZ-F12 level.

A Combined Theoretical and Experimental Study of Sarin (GB) Decomposition at High Temperatures

Theoretical and experimental results are presented for the pyrolytic decomposition of the nerve agent sarin (GB) in the gas phase. High-level quantum chemistry calculations are performed together with a semiclassical transition-state theory for describing quantum mechanical tunneling. The experimental and theoretical results for the temperature dependence of the survival times show very good agreement, as does the calculated and measured activation energy for thermal decomposition. The combined results suggest that the thermal decomposition of GB, for temperature ranging from 350 to 500 °C, goes through a pericyclic reaction mechanism with a transition state consisting of a six-membered ring structure.

Recent advances in quantum scattering calculations on polyatomic bimolecular reactions

This review surveys quantum scattering calculations on chemical reactions of polyatomic molecules in the gas phase published in the last ten years.