Semiclassical Transition State Theory Research Articles

Semiclassical Transition State Theory (SCTST) Rate Coefficients for the Unimolecular Decomposition of the Ethoxy (CH3CH2O) Radical.

The thermal unimolecular decay of ethoxy is important in high-temperature combustion environments where the ethoxy radical is a key reactive intermediate. Two dissociation pathways of ethoxy, including the β-C-C scission to yield CH3 + CH2O and the H-elimination to make H + CH3CHO, were characterized using a high-level coupled-cluster-based composite quantum chemical method (mHEAT-345(QΛ)). The former route is found to be dominant while the latter is insignificant, in agreement with previous experimental and theoretical studies. Thermal rate coefficients are calculated for P = 0.001-658 atm (of air) and T = 300-2500 K using semiclassical transition state theory (SCTST) in combination with a pragmatic two-dimensional E,J-resolved master equation (2DME). The effects of tunneling and anharmonicity on the calculated rate constants are also examined. The tunneling factor is found to be inversely dependent on pressure, contrary to previous observations of pressure-dependent tunneling in entrance channels.

A Perspective on the Investigation of Spectroscopy and Kinetics of Complex Molecular Systems with Semiclassical Approaches.

In this Perspective we show that semiclassical methods provide a rigorous hierarchical way to study the vibrational spectroscopy and kinetics of complex molecular systems. The time averaged approach to spectroscopy and the semiclassical transition state theory for kinetics, which have been first adopted and then further developed in our group, provide accurate quantum results on rigorous physical grounds and can be applied even when dealing with a large number of degrees of freedom. In spectroscopy, the multiple coherent, divide-and-conquer, and adiabatically switched semiclassical approaches have practically permitted overcoming issues related to the convergence of results. In this Perspective we demonstrate the possibility of studying the semiclassical vibrational spectroscopy of a molecule adsorbed on an anatase (101) surface, a system made of 51 atoms. In kinetics, the semiclassical transition state theory is able to account for anharmonicity and the coupling between the reactive and bound modes. Our group has developed this technique for practical applications involving the study of phenomena like kinetic isotope effect, heavy atom tunneling, and elusive conformer lifetimes. Here, we show that our multidimensional anharmonic quantum approach is able to tackle on-the-fly the thermal kinetic rate constant of a 135 degree-of-freedom system. Overall, semiclassical methods open up the possibility to describe at the quantum mechanical level systems characterized by hundreds of degrees of freedom leading to the accurate spectroscopic and kinetic description of biomolecules and complex molecular systems.

Elucidating Heavy-Atom-Tunneling Kinetics in the Cope Rearrangement of Semibullvalene.

In this work, we characterize the temperature dependence of kinetic properties in heavy atom tunneling reactions by means of molecular dynamics simulations, including nuclear quantum effects (NQEs) via Path Integral theory. To this end, we consider the prototypical Cope rearrangement of semibullvalene. The reaction was studied in the 25-300 K temperature range observing that the inclusion of NQEs modifies the temperature behavior of both free energy barriers and dynamical recrossing factors with respect to classical dynamics. Notably, while in classical simulations the activation free energy shows a very weak temperature dependence, it becomes strongly dependent on temperature when NQEs are included. This temperature behavior shows a transition from a regime where the quantum effects are limited and can mainly be traced back to zero point energy, to a low temperature regime where tunneling plays a dominant role. In this regime, the free energy curve tunnels below the potential energy barrier along the reaction coordinate, allowing much faster reaction rates. Finally, the temperature dependence of the rate constants obtained from molecular dynamics simulations was compared with available experimental data and with semi-classical transition state theory calculations, showing comparable behaviors and similar transition temperatures from thermal to (deep) tunneling regime.

Reconciling Imbalanced and Nonadiabatic Reactivity in Transition Metal-Oxo-Mediated Concerted Proton Electron Transfer (CPET).

Recently, there have been several experimental demonstrations of how the rates of concerted proton electron transfer (CPET) are affected by stepwise thermodynamic parameters of only proton (ΔG°PT) or electron (ΔG°ET) transfer. Semiclassical structure-activity relationships have been invoked to rationalize these linear free energy relationships, but it is not clear how they would manifest in a nonadiabatic reaction. Using density functional theory calculations, we demonstrate how a decrease in ΔG°PT can lead to transition state imbalance in a nonadiabatic framework. We then use these calculations to anchor a theoretical model that reproduces experimental trends with ΔG°PT and ΔG°ET. Our results reconcile predictions from semiclassical transition state theory with models that treat proton transfer quantum mechanically in CPET reactivity, make new predictions about the importance of basicity for uphill CPET reactions, and suggest similar treatments may be possible for other nonadiabatic reactions.

Thermal rate of transmission through a barrier: Exact expansion of up to and including terms of order ℏ4

Nine decades after Wigner's formulation of quantum rate theory, his celebrated result was recently generalized to the asymmetric barrier using an exact first-order expansion of the transmission probability in terms of ${\ensuremath{\hbar}}^{2}$. This paper extends the first-order quantum correction to second-order correction of order ${\ensuremath{\hbar}}^{4}$ for the thermally averaged transmission probability through an arbitrary barrier. The derivation employs a systematic expansion of the projection operator onto products and the thermal distribution which involves a Taylor expansion of the potential about the barrier up to eighth order. The resulting exact analytical expression is calibrated with numerical calculations of several model potentials and shows excellent agreement when the ${\ensuremath{\hbar}}^{4}$ term is included. In comparison, the semiclassical transition state theory cannot reproduce the correct ${\ensuremath{\hbar}}^{4}$ terms when the anharmonicity is treated on the level of VPT-4 (vibrational perturbation theory---fourth order) and will potentially need a VPT-6 expansion. Further analysis of the quartic barrier reveals suppressed transmission due to the dominant role of quantum reflection above the barrier. These results not only provide a conceptual framework but can also be applied to heavy atom tunneling and machine learning.

Phosphine Reactivity and Its Implications for Pyrolysis Experiments and Astrochemistry

Despite the importance of phosphorus-bearing molecules for life and their abundance outside Earth, the chemistry of those compounds still is poorly described. The present study investigates phosphine (PH3) decomposition and formation pathways. The reactions studied include phosphine thermal dissociation, conversion into PO(2Π), PN(1Σ+), and reactions in the presence of H2O+. The thermodynamic and rate coefficients of all reactions are calculated in the range of 50-2000 K considering the CCSD(T)/6-311G(3df,3pd)//ωB97xD/6-311G(3df,3pd) electronic structure data. The rate coefficients were calculated by RRKM and semiclassical transition-state theory (SCTST). According to our results, PH3 is stable to thermal decomposition at T < 100 K and can be formed promptly by a reaction network involving PH(3Σ-), PO(2Π), and PN(1Σ+). In the presence of radiation or ions, PH3 is readily decomposed. For this reason, it should be mainly associated with dust grains or icy mantles to be observed under the physical conditions prevailing in the interstellar medium (ISM). The intersystem crossing associated with the dissociation of the isomers PON, NPO, and PNO is accessed by multireference methods, and its importance for the gas-phase PH3 formation/destruction is discussed. Also, the implications of the present outcomes on phosphorus astrochemistry are highlighted.

ℏ2 expansion of the transmission probability through a barrier.

Ninety years ago, Wigner derived the leading order expansion term in ℏ2 for the tunneling rate through a symmetric barrier. His derivation included two contributions: one came from the parabolic barrier, but a second term involved the fourth-order derivative of the potential at the barrier top. He left us with a challenge, which is answered in this paper, to derive the same but for an asymmetric barrier. A crucial element of the derivation is obtaining the ℏ2 expansion term for the projection operator, which appears in the flux-side expression for the rate. It is also reassuring that an analytical calculation of semiclassical transition state theory (TST) reproduces the anharmonic corrections to the leading order of ℏ2. The efficacy of the resulting expression is demonstrated for an Eckart barrier, leading to the conclusion that especially when considering heavy atom tunneling, one should use the expansion derived in this paper, rather than the parabolic barrier approximation. The rate expression derived here reveals how the classical TST limit is approached as a function of ℏ and, thus, provides critical insights to understand the validity of popular approximate theories, such as the classical Wigner, centroid molecular dynamics, and ring polymer molecular dynamics methods.

Evaluating the Atmospheric Loss of H2 by NO3 Radicals: A Theoretical Study

Molecular hydrogen (H2) is now considered among the most prominent substitute for fossil fuels. The environmental impacts of a hydrogen economy have received more attention in the last years, but still, the knowledge is relatively poor. In this work, the reaction of H2 with NO3 radical (the dominant night-time detergent of the atmosphere) is studied for the first time using high-level composite G3B3 and modification of high accuracy extrapolated ab initio thermochemistry (mHEAT) methods in combination with statistical kinetics analysis using non-separable semi-classical transition state theory (SCTST). The reaction mechanism is characterized, and it is found to proceed as a direct H-abstraction process to yield HNO3 plus H atom. The reaction enthalpy is calculated to be 12.8 kJ mol−1, in excellent agreement with a benchmark active thermochemical tables (ATcT) value of 12.2 ± 0.3 kJ mol−1. The energy barrier of the title reaction was calculated to be 74.6 and 76.7 kJ mol−1 with G3B3 and mHEAT methods, respectively. The kinetics calculations with the non-separable SCTST theory give a modified-Arrhenius expression of k(T) = 10−15 × T0.7 × exp(−6120/T) (cm3 s−1) for T = 200–400 K and provide an upper limit value of 10−22 cm3 s−1 at 298 K for the reaction rate coefficient. Therefore, as compared to the main consumption pathway of H2 by OH radicals, the title reaction plays an unimportant role in H2 loss in the Earth’s atmosphere and is a negligible source of HNO3.

First principles DFT analysis on the diffusion kinetics of hydrogen isotopes through bcc iron (Fe): Role of temperature and surface coverage

The diffusion of interstitial H, D, and T in Fe metal at different temperature are evaluated using ab-initio density functional theory and transition state theory. The thermal expansion coefficient, Helmholtz free energy of activation, jump factor of diffusion was determined by use of activation energy and phonon calculations. The calculated diffusion coefficient was well described by a constant activation energy, (D = D0exp (-Ea)/kT)) with Ea = 0.016, 0.041, and 0.050 eV and D0 = 1.042 × 10−7, 0.736 × 10−7 and 0.572x10−7 m2.s−1for H, D, and T, respectively using harmonic transition state theory (hTST) with temperature correction. The calculated permeability and solubility also followed the Arrhenius relation.The earlier experimentally reported higher diffusivity of H atom at lower temperatures than that at higher temperature (200–600 K) was well explained by Wigner + hTST model with temperature correction and semi-classical transition state theory (SC-TST). The present computed results followed the similar trend of experimental findings. Further, the ideal fracture energy was evaluated using the Born-Haber thermodynamic cycle for varied coverage of H, D and T to account for decohesion-based embrittlement. The lighter H atom was seen to cause more decohesion-based embrittlement compared to D and T due to reduced cohesion. Additionally, the effect of temperature on ideal fracture energy was evaluated for H, D and T in Fe. The decohesion-based embrittlement was increased with increase in the temperature for H, D and T up to certain temperature (for H lower than 500 K, for D around 500 K and for T above 500 K) but with further increase in the temperature, the ideal fracture energy was reduced due to decrease in the adsorption energy and increase in the solution enthalpy of H isotopes. Further, the path and kinetics of dissociation and reassociation of H2 molecule were established on Fe (100) surface at 0.5 and 2.0 ML coverage. At lower concentration (0.5 ML), dissociation of H2 molecule on Fe (100) surface was favored, whereas at high concentration (2.0 ML), reassociation of H2 molecule was favored.

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.

Mechanism and kinetics of the reaction CH3 + CH3CHO: Ab initio semiclassical transition state theory study

AbstractThe potential energy profile of the reaction between methyl radicals with acetaldehyde is theoretically investigated at different levels of theory prior to calculating the bimolecular rate constants of this reaction by semiclassical transition state theory (SCTST) and one‐dimensional master equation (1DME) modeling. The stationary points on the potential energy surface of the reaction CH3 + CH3CHO are characterized at the levels MP2/6‐311 + g(2d,2p) and CCD/6‐311 + g(2d,2p). To obtain more satisfying energies, single‐point calculations are performed at CCSD(T)/augh‐cc‐pVTZ+2df. It is shown that the title reaction proceeds via either hydrogen abstraction channels or the addition of methyl radical to acetaldehyde, forming an isopropoxy radical. Then, SCTST and 1DME modeling are used to compare the rate constants of distinct reaction channels. The aldehyde hydrogen atom abstraction by methyl radical producing CH4 + CH3CO is dominant both thermodynamically and kinetically. The calculated SCTST rate constants can be expressed as a function of temperature with cm3molecule−1s−1 (200‐3000 K). Hydrogen/deuterium (H/D) isotopic effects on the kinetics are computed for some specific abstraction channels, showing that tunneling indeed plays a vital role in the hydrogen abstraction process. Pressure dependencies of the addition reaction are followed using master equation calculations, illustrating that the stabilization of the isopropoxy radical is dominant at higher pressures and lower temperatures. In contrast, as pressure decreases and temperature increases, the energized radical prefers decomposing to new bimolecular sets.

Semiclassical transition state theory/master equation kinetics of HO + CO: Performance evaluation

AbstractPreviously, master equation (ME) simulations using semiclassical transition state theory (SCTST) and high‐accuracy extrapolated ab initio thermochemistry (HEAT) predicted rate constants in excellent agreement with published experimental data over a wide range of pressure and temperatures ≳250 K, but the agreement was not as good at lower temperatures. Possible reasons for this reduced performance are investigated by (a) critically evaluating the published experimental data and by investigating; (b) three distinct ME treatments of angular momentum, including one that is exact at the zero‐ and infinite‐pressure limits; (c) a hindered‐rotor model for HOCO that implicitly includes the cis‐ and trans‐conformers; (d) possible empirical adjustments of the thermochemistry; (e) possible empirical adjustments to an imaginary frequency controlling tunneling; (f) including or neglecting the prereaction complex PRC1; and (g) its possible bimolecular reactions. Improvements include better approximations to factors in SCTST and using the Hill and van Vleck treatment of angular momentum coupling. Evaluation of literature data does not reveal any specific shortcomings, but the stated uncertainties may be underestimated. All ME treatments give excellent fits to experimental data at T ≥ 250 K, but the discrepancy at T &lt; 250 K persists. Note that each ME model requires individual empirical energy transfer parameters. Thermochemical adjustments were unable to match the experimental H/D kinetic isotope effects. Adjusting an imaginary frequency can achieve good fits, but the adjustments are unacceptably large. Whether PRC1 and its possible bimolecular reactions are included had little effect. We conclude that none of the adjustments is an improvement over the unadjusted theory. Note that only one set of experimental data exists in the regime of the discrepancy with theory, and data for DO + CO are scanty.

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

Tunnelling controlled chemical reactions are those which preferably proceed through pathways with high but narrow potential energy barriers, via quantum tunnelling, resulting in a product that would be disfavoured classically. These reactions are very sensitive to barrier width, height and temperature and so dynamical theoretical methods are required to describe these processes. Recent experimental work on charge-tagged phenyl pyruvic acid derivatives has found, in contrast to similar systems, no evidence of tunnelling control. Using semiclassical transition state theory, we rationalise these results and find tunnelling is significant in this system.

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.

Density functional theory thermal rate constant calculation of hydrogen abstraction reactions of trans-cyc-CF2CF2CF2CHFCHF and cyc-CF2CF2CF2CHFCH2 with OH radicals

The bimolecular hydrogen abstraction rate constants of the reactions trans-cyc-CF2CF2CF2CHFCHF + OH and cyc-CF2CF2CF2CHFCH2 + OH are investigated. The stationary points on the potential energy surface of the reaction are found at the KMLYP/6-311+g(d,p). To have more reliable energies obtained, single point calculations are done by the same method along with two distinct basis sets; 6-311++G(3df,2p) and aug-cc-pVTZ. Furthermore, the energies of the stationary points are calculated at the levels M05-2X/6-31+G(d,p)//MG3S and MPWB1K/6-31+G(d,p)//MG3S for the purpose of comparison. The ro-vibrational properties calculated at KMLYP/6-311+G(d,p) are employed in the semiclassical transition state theory to compute the rate constants at the temperature range of 200–2000 K. We found that the rate constants computed via the barrier heights at M05-2X and MPWB1K are in more accordance with the experimental results than the ones at the DFT level KMLYP. The atmospheric lifetime of trans-cyc-CF2CF2CF2CHFCHF and cyc-CF2CF2CF2CHFCH2 are estimated by the level M05-2X to be 1.21 years and 3.59 years, respectively.

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.

Tunnelling in cyclocarbenes: An application of Semiclassical Transition State Theory in reduced dimensions

Methods to calculate rates of chemical reactions ab initio, in reduced dimensions, using Semiclassical Transition State Theory have recently been formulated. Here we further develop its application to unimolecular reactions where the choice of active degrees of freedom is not clear a priori. We describe in more detail a procedure to determine which degrees of freedom must be accounted for explicitly in the reduced dimensionality framework, and illustrate its success on a hydrogen transfer reaction of a cyclocarbene species.

Ring-polymer molecular dynamics studies of thermal rate coefficients for reaction F + H2O → HF + OH

The prototype tetra-atomic reaction F + H2O → HF + OH plays a significant role in both atmospheric and astronomical chemistry. In this work, thermal rate coefficients of this reaction are determined with the ring polymer molecular dynamics (RPMD) method on a full-dimensional potential energy surface (PES). This PES is the most accurate one for the title reaction, as demonstrated by the correct barrier height and reaction energy, compared to the benchmark calculations by the focal point analysis and the high accuracy extrapolated ab initio thermochemistry methods. The RPMD rate coefficients are in excellent agreement with those calculated by the semiclassical transition state theory and a two-dimensional master equation technique, and some experimental measurements. As has been found in many RPMD applications, quantum effects, including tunneling and zero-point energy effects, can be efficiently and effectively captured by the RPMD method. In addition, the convergence of the results with respect to the number of beads is rapid, which is also consistent with previous RPMD applications.

New Developments in Semiclassical Transition-State Theory.

This Feature Article describes some recent developments and applications of the Semiclassical Transition-State Theory (SCTST) for treating quantum tunneling in chemical reactions. A reduced dimensional form of the SCTST is discussed and is shown to be particularly efficient, as the required number of electronic structure calculations is reduced to an absolute minimum. We also describe how an alternative formulation of SCTST developed by Hernandez and Miller [ Chem. Phys. Lett. 1993 , 214 , 129 ], the SCTST-θ, has advantages in allowing for straightforward applications of the SCTST for any form of the potential expansion at the transition state. We also illustrate the power of SCTST in applications to more complex systems. We show how polyatomic modes such as internal rotations and torsions can be treated efficiently in SCTST calculations. We also describe some applications of the method to hydrogen atom tunneling in unimolecular reactions including the degradation of chemical nerve agents and the decay of the atmospherically important Criegee intermediates.

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.