Classical Transition State Theory Research Articles

Robust Gaussian Process Regression Method for Efficient Tunneling Pathway Optimization: Application to Surface Processes.

Simulation of surface processes is a key part of computational chemistry that offers atomic-scale insights into mechanisms of heterogeneous catalysis, diffusion dynamics, and quantum tunneling phenomena. The most common theoretical approaches involve optimization of reaction pathways, including semiclassical tunneling pathways (called instantons). The computational effort can be demanding, especially for instanton optimizations with an ab initio electronic structure. Recently, machine learning has been applied to accelerate reaction-pathway optimization, showing great potential for a wide range of applications. However, previous methods still suffer from numerical and efficiency issues and were not designed for condensed-phase reactions. We propose an improved framework based on Gaussian process regression for general transformed coordinates, which has improved efficiency and numerical stability, and we propose a descriptor that combines internal and Cartesian coordinates suitable for modeling surface processes. We demonstrate with 11 instanton optimizations in three representative systems that the improved approach makes ab initio instanton optimization significantly cheaper, such that it becomes not much more expensive than a classical transition-state theory rate calculation.

Inducing in situ M2 macrophage polarization to promote the repair of bone defects via scaffold-mediated sustained delivery of luteolin

Immunoregulation mediated bone tissue engineering (BTE) has demonstrated huge potential in promoting repair of critical-size bone defects (CSBDs). The trade-off between stable immunoregulation function and extended immunoregulation period has posed a great challenge to this strategy. Here, we reported a 3D porous biodegradable Poly(HEMA-co-3APBA)/LUT scaffold, in which reversible boronic acid ester bond was formed between the 3APBA moiety and the catechol moiety of luteolin (LUT). The boronic acid ester bond not only protected the bioactivity of LUT but also extended the release period of LUT. The rationale behind the phenomenon of sustained LUT release was explained using a classical transition state theory. In vitro/in vivo assays proved the immunoregulation function of the scaffold in inducing M2 polarization of both M0 and M1 Mφ. The crosstalk between the scaffold treated Raw 264.7 and BMSCs were also investigated through the in vitro co-culture assay. The results demonstrated that the scaffold could induce immunoregulation mediated osteogenic differentiation of BMSCs. In addition, CSBDs model of SD rats was also applied, and the corresponding data proved that the scaffold could accelerate new bone formation, therefore promoting repair of CSBDs. The as-prepared scaffold might be a promising candidate for repair of CSBDs in the future.

Diffusional Isotope Effect Based on the Transition-State Theory of Interstitial Mechanism in Solids

It is important to be able to interpret the rapidly growing isotopic diffusion data in mineral grains that are measured using high spatial resolution. Based on previous works, the classical transition-state theory, and quantum statistical mechanics, an atomic theory to evaluate the diffusion coefficient (D) and the kinetic isotope effect (β factor) for the interstitial diffusion mechanism is developed with the unified equations for theoretical calculations. Taking helium diffusion in forsterite as an example, the D and β (4He/3He) were calculated at certain upper mantle conditions (0–20 GPa, 0–1500 °C) based on the developed equations. All parameters needed in our theory were obtained by first-principles calculations. Our calculated results for D at 0 GPa show reasonable agreement with most experimental results, indicating acceptable validity of the developed theory and methods. Meanwhile, possible causes for slight differences between calculations and experimental results at ambient pressure were also explored. We find that the β increases with the increase of temperature, but its pressure dependence is quite limited at least in the case of interstitial helium diffusion in forsterite. Additionally, we confirmed that current widely used simulation protocols with a fixed lattice for diffusion fail to accurately estimate the D values under high pressures due to the neglection of the activation volume. However, we also find that such protocols have almost negligible effects on the β factors for isotope fractionations during diffusion. Finally, potential effects of various approximations and calculation protocols involved in previous studies were carefully evaluated, and we find that some commonly used approximations and techniques are oversimplified and probably lead to significant loss of accuracy, especially at low temperatures (≤∼600 °C). However, it is still quite safe to continue adopting these protocols when dealing with high-temperature problems (e.g., ≥1000 °C).

Atmospheric degradation mechanisms and kinetics for OH-initiated oxidation of trans-β-ocimene

The reaction mechanisms for OH-initiated oxidation of trans-β-ocimene (TBO) in the atmosphere have been investigated at the CCSD(T)/6-31 + G(d)//BH&HLYP/6-311++G(d,p) levels of theory. Classical transition state theory (CTST) is used to obtain the rate constants of initial reaction pathways over the temperature range of 220–1000K. The calculated results show that in the initial reaction pathways of TBO with OH radical, the reaction is dominated by OH addition to the double bonds, and H-abstraction pathways can be negligible at low to medium temperature. The total rate constant computed is 4.56 × 10−10 cm3 molecule−1 s−1 at 298 K, which is consistent with the experimental data. The Arrhenius equation of the total rate constants can be fitted as in the temperature range of 220–1000 K. In the presence of O2 and NO, the major degradation products of TBO with OH radical are acetone and 4-methyl-3,5-hexadienal, which are in reasonable agreement with the experimental observations. Furthermore, the ozone formation potential of TBO together with the effects of the TBO oxidation products have also been discussed in detail in the paper.

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.

Thermodynamic analysis of dehydration of K2CO3·1.5H2O

This work studied the reversible dehydration of potassium carbonate sesquihydrate (K2CO3·1.5H2O). The study is based on isobaric and isothermal thermogravimetric measurements conducted at a broad range of vapour pressures and temperatures. By controlling both parameters, we examined the influence of both constraints on the reaction kinetics at a wide extent of supersaturations. We have evaluated our experimental findings by employing two thermodynamic theories, classical nucleation theory and transition state theory. By combining both approaches, we were able to establish that: (1) At low supersaturations in a region close to equilibrium, dehydration is limited by nucleation and growth of the anhydrous phase (2) At high supersaturations, dehydration reaches maximum rate and is controlled by the reaction speed. Furthermore, we show that the dehydration of K2CO3·1.5H2O is very sensitive to pressure-temperature conditions and that it does not possess universal activation energy.

Insights into ultrasound-promoted degradation of naphthenic acid compounds in oil sands process affected water. Part II: In silico quantum screening of hydroxyl radical initiated and propagated degradation of benzoic acid

In Part I, we outlined the importance of sustainable sonochemical treatment to intensify oil sands process affected water (OSPW) treatment empirically and hypothesized degradation pathways. Herein, we elucidate the formation of intermediate products with well-defined molecular level solutions. Proposed mechanisms describe hydroxylation, decarboxylation and bond scission which drive the degradation of intermediates towards mineralization. This comprehensive first study on in silico screening of sonochemical degradation investigates quantum methods using density functional theory to explain the postulated degradation mechanisms through a theoretical radical attack approach, based on condensed Fukui reactivity indicators. A nudged elasticity band (NEB) approach is applied to find a minimum energy path (MEP), allowing the determination of intermediate products and energy barriers associated with naphthenic acid degradation. This approach provides structures and energies of the breakdown compounds formed along the reaction pathway enabling the determination of molecular reaction kinetics.In continuation of Part 1, the focus of this study is to evaluate sonochemically-induced hydroxyl radical (OH•) reactions of benzoic acid using density functional theory. Hydroxylation and decarboxylation mechanisms of the model naphthenic acid compound and its intermediates were simulated to determine the prospective pathway to ideal mineralization. DFT was applied to calculate interaction energies, Mulliken charges, Hirshfeld population analysis, dipole moments, frontier orbitals, and polarizability. Electronic properties and frontier orbital trends were also compared to computational work by Riahi et al.[1] to confirm the transition states by Nudged Elastic Band Transition State theory (NEB-TS). In combination with Hirshfeld Population analysis, Fukui indices suggest a more linear degradation pathway narrowed down from earlier experimental work by Singla et al.[2]. The linear free energy relationship for the newly suggested computational benzoic acid degradation can be determined by lnkTST/W=-1.677ΔG-15.41 with a R2 of 0.9997 according to classic transition state theory and Wigner tunneling. This computational method can be used to explore possible degradation pathways of other NAs and bridges molecular-to-macroscale sonochemical degradation of NA’s through a manifestation of molecular solutions.

QM/MM Study of the H2 Formation on the Surface of a Water Ice Grain Doped With Formaldehyde: Molecular Dynamics and Reaction Kinetics

Formaldehyde has been widely observed in the icy mantle of interstellar grains. H2CO may be formed from successive hydrogenations of CO and may further contribute to the chemical complexity of the Interstellar medium (ISM) participating to heterogeneous reactions with colliding gas phase atoms. Within this context, Eley-Rideal and Langmuir-Hinshelwood rate constants of H2 formation on a formaldehyde doped amorphous water ice grain model of the ISM, were computed over a wide temperature range [15–2000 K]. We used classical molecular dynamics (MD) simulations to build the model of the H2CO doped ice surface. Then we studied theoretically by means of hybrid QM/MM ab initio and molecular mechanics methodology (ONIOM) H atoms abstraction from formaldehyde molecules and the H2 formation. Specifically, we investigate the reactivity of the gas phase H atom toward one formaldehyde molecule lying at one of the slab surfaces. The reaction path and the energetics are predicted, the mechanism is found to be exothermic by 14.89 kcal/mol and the barrier is 6.75 kcal/mol at the QM level CBS/DLPNO-CCSD(T)//ONIOM/aug-cc-pVTZ. We employ two approaches that take into account tunnelling and non-classical reflection effects by means of the Zero Curvature Tunnelling (ZCT), and the Small Curvature Tunnelling (SCT) which all provided comparable results to predict the kinetics of the reaction path. The rate constants show important quantum tunnelling effects at low temperatures when compared to rates obtained from the purely classical transition-state theory (TST) and from the canonical variational transition state theory (CVT). Corner cutting effects are highlighted in the SCT calculations by 4 to 5 orders of magnitude with respect to ZCT rate constants at low temperatures.

Machine Learning Quantum Reaction Rate Constants.

The ab initio calculation of exact quantum reaction rate constants comes at a high cost due to the required dynamics of reactants on multidimensional potential energy surfaces. In turn, this impedes the rapid design of the kinetics for large sets of coupled reactions. In an effort to overcome this hurdle, a deep neural network (DNN) was trained to predict the logarithm of quantum reaction rate constants multiplied by their reactant partition function-rate products. The training dataset was generated in-house and contains ∼1.5 million quantum reaction rate constants for single, double, symmetric and asymmetric one-dimensional potentials computed over a broad range of reactant masses and temperatures. The DNN was able to predict the logarithm of the rate product with a relative error of 1.1%. Furthermore, when comparing the difference between the DNN prediction and classical transition state theory at temperatures below 300 K a relative percent error of 31% was found with respect to the exact difference. Systems beyond the test set were also studied, these included the H + H2 reaction, the diffusion of hydrogen on Ni(100), the Menshutkin reaction of pyridine with CH3Br in the gas phase, the reaction of formalcyanohydrin with HS- in water and the F + HCl reaction. For these reactions, the DNN predictions were accurate at high temperatures and in good agreement with the exact rates at lower temperatures. This work shows that one can take advantage of a DNN to gain insight on reactivity in the quantum regime.

Computational study of the thermal decomposition of some oxypropenes.

This work aims at describing the computational study of thermal decomposition reaction of three oxypropenes: 2-(1-methylethoxy)propene, 2-ethoxypropene, and 2-butoxypropene. It was carried out in order to delve into the reaction mechanism proposed in experimental studies. Computational optimization calculations and frequencies of the structures were performed with the M06-2X/6-311+G(d,p) method at different temperatures ranging from 600 to 640K. The rate constants were calculated with the classical transition state theory, and the values obtained are of the same order as the reported experimental values. The results derived from the population partitioning technique indicate that transition states are symmetrical and the mechanism is concerted and highly synchronous.

Simulated kinetics of the atmospheric removal of aniline during daytime

Oxidations of aniline (AN) initiated by OH-radicals are simulated in the temperature range 200–400 K using DFT/M06-2X/6-311++G(2df,2p) and ab initio ROCBS-QB3 levels. Chemical kinetics of such reactions were investigated based on several approaches including classical transition state theory (TST), conical variational transition state theory (CVT), and Rice-Ramsperger-Kassel-Marcus master equation (RRKM-ME) theories. Under atmospheric conditions, the reaction of OH radical with AN and the subsequent reactions with O2 molecules are investigated. The results indicate that the majority of O2 addition goes to the anti-directions with a branching ratio of 97.7% and produces the bicyclic peroxy radicals (BPRs) that can react with NO radical to form bicyclic alkoxy radicals (BARs). The latter compounds can be stabilized either by cyclization or via ring cleavage.

Grand Canonical Rate Theory for Electrochemical and Electrocatalytic Systems I: General Formulation and Proton-coupled Electron Transfer Reactions

Electrochemical interfaces present a serious challenge for atomistic modelling. Electrochemical thermodynamics are naturally addressed within the grand canonical ensemble (GCE) but the lack of a fixed potential rate theory impedes fundamental understanding and computation of electrochemical rate constants. Herein, a generally valid electrochemical rate theory is developed by extending equilibrium canonical rate theory to the GCE. The extension provides a rigorous framework for addressing classical reactions, nuclear tunneling and other quantum effects, non-adiabaticity etc. from a single unified theoretical framework. The rate expressions can be parametrized directly with self-consistent GCE-DFT methods. These features enable a well-defined first principles route to addressing reaction barriers and prefactors (proton-coupled) electron transfer reactions at fixed potentials. Specific rate equations are derived for adiabatic classical transition state theory and adiabatic GCE empirical valence bond (GCE-EVB) theory resulting in a Marcus-like expression within GCE. From GCE-EVB general free energy relations for electrochemical systems are derived. The GCE-EVB theory is demonstrated by predicting the PCET rates and transition state geometries for the adiabatic Au-catalyzed acidic Volmer reaction using (constrained) GCE-DFT. The work herein provides the theoretical basis and practical computational approaches to electrochemical rates with numerous applications in physical and computational electrochemistry.

Decoupling feldspar dissolution and precipitation rates at near-equilibrium with Si isotope tracers: Implications for modeling silicate weathering

Here we show that the isotope tracer experimental method for kinetic studies, aided by the recent advance and accessibility of multi-collector inductively coupled plasma mass spectrometry (MC-ICP-MS) analysis for non-traditional stable isotopes, can provide unidirectional dissolution rates at near-equilibrium conditions. For a long time, the only rates available at near-equilibrium were net reaction rates—dissolution rates minus precipitation rates. This is because the conventional experimental method of kinetic studies is based on element concentrations and can only provide net rates. The availability of unidirectional rates allows us to re-examine some fundamental concepts and practices of modeling weathering in geochemistry.In this study, we used the 29Si isotope tracer to conduct albite and K-feldspar dissolution experiments at near-equilibrium conditions in near-neutral pH solutions at 50 °C. Results show that the saturation indices (SI) of solutions approached zero with respect to albite and K-feldspar after ∼240–360 h (h), but 29Si/28Si ratios of the experimental solutions indicated continual dissolution for another 720–1440 h. The rates of total Si precipitation were much smaller than the rates of Si dissolution. The experimental solutions were supersaturated with respect to amorphous Al(OH)3, gibbsite, quartz, allophane, imogolite, and kaolinite. The SI of the solutions remained constant with respect to these phases while Al concentrations slightly decreased and Si concentrations slightly increased, indicating the coupled feldspar dissolution and precipitation of secondary phases, such as albite → amorphous Al(OH)3 + quartz or albite → solution + Al-Si phase(s), instead of significant albite and K-feldspar precipitation (the reverse reaction) at 50 °C. Reaction path modeling of the temporal evolution of Si, Al, Na, and pH revealed that albite dissolution (without significant backward reaction) coupled with the precipitation of a secondary phase with a Si:Al ratio of ∼2:1 can successfully match the experimental data.Given the negligible feldspar precipitation reactions in low-temperature systems (e.g., T < 100 °C), we recommend modeling feldspar weathering using unidirectional forward rates together with secondary phase precipitation rates in near-equilibrium, feldspar-undersaturated systems. This can be accomplished with minor modifications in geochemical modeling software or input files. The coupled feldspar dissolution with secondary phase precipitation arrests the system in a near-equilibrium steady state. Using affinity-based rate equations such the classical linear Transition State Theory rate law or the Burch empirical relation together with far-from-equilibrium rate data will predict significant feldspar precipitation in solutions undersaturated but close to equilibrium with respect to feldspars, which is unlikely at near ambient temperatures.

Competitive Nitrogen versus Carbon Tunneling.

Quantum mechanical tunneling (QMT) of heavy atoms like carbon or nitrogen has been considered very unlikely for the longest time, but recent evidence suggests that heavy-atom QMT does occur more frequently than typically assumed. Here we demonstrate that carbon vs nitrogen heavy-atom QMT can even be competitive leading to two different products originating from the same starting material. Amino-substituted benzazirine was generated in solid argon (3-18 K) and found to decay spontaneously in the dark, with a half-life of 210 min, to p-aminophenylnitrene and amino-substituted ketenimine. The reaction rate is independent of the cryogenic temperature, in contradiction to the rules inferred from classical transition state theory. Quantum chemical computations confirm the existence of two competitive carbon vs nitrogen QMT reaction pathways. This discovery emphasizes the quantum nature of atoms and molecules, thereby enabling a much higher level of control and a deeper understanding of the factors that govern chemical reactivity.

Quantum Suppression of Intramolecular Deuterium Kinetic Isotope Effects in a Pericyclic Hydrogen Transfer Reaction.

It is generally accepted that hydrogen tunneling enhances both primary and secondary H/D kinetic isotope effects (KIEs) over what would be expected under the assumptions of classical barrier transition. Previous studies have exclusively shown that the effects of tunneling upon primary H/D KIEs have been much larger than those observed for secondary H/D KIEs. Here we present a series of experimental H/D KIE results associated with the Chugaev elimination of methyl xanthate derived from β-phenylethanol over the temperature range of 180 to 290 °C. Intramolecular H/D KIEs computed according to classical transition state theory (TST) are markedly overestimated relative to experimentally measured values. Experimental intermolecular H/D KIEs and direct dynamic calculations based on canonical variational transition state theory (CVT) with small-curvature tunneling correction (SCT) reveal that this result is largely the consequence of extraordinary tunneling enhancement of the secondary H/D KIE. This unexpected behavior is examined in the context of other similar hydrogen transfer reactions.

The Mechanism of C-H Bond Oxidation by Aqueous Permanganate.

The permanganate ion (MnO4-) has been widely used as a reagent for water treatment for over a century. It is a strong enough oxidant to activate carbon-hydrogen bonds, one of the most important reactions in biological and chemical systems. Our current textbook understanding of the oxidation mechanism in aqueous solution involves an initial, rate-limiting hydride abstraction by permanganate followed by reaction of the carbocation with bulk water to form an alcohol. This mechanism fits well into the classic oxidation sequence of alkane → alcohol → aldehyde → carboxylate, the central paradigm for both abiotic and biotic alkane oxidation in aqueous environments. In this study, we provide three lines of evidence through (1) a broken-symmetry density functional theory approach, (2) isotope labeling experiments, and (3) kinetic network modeling to demonstrate that aqueous permanganate can circumvent prior alcohol formation and produce aldehydes directly via a reaction path that bifurcates after the initial transition state. In contrast to classic transition state theory, the rate-limiting step is found to not determine product distribution, bearing critical implications for pathway and rate predictions. This complex reaction network provides new insights into the oxidation mechanisms of organic compounds involving transition metal complexes as well as enzyme or metal oxide surface active sites.

Rate theory of ion pairing at the water liquid-vapor interface: A case of sodium iodide.

Studies on ion pairing at interfaces have been intensified recently because of their importance in many chemical reactive phenomena, such as ion-ion interactions that are affected by interfaces and their influence on kinetic processes. In this study, we performed simulations to examine the thermodynamics and kinetics of small polarizable sodium iodide ions in the bulk and near the water liquid-vapor interface. Using classical transition state theory, we calculated the dissociation rates and corrected them with transmission coefficients obtained from the reactive flux formalism and Grote-Hynes theory. Our results show that in addition to affecting the free energy of ions in solution, the interfacial environments significantly influence the kinetics of ion pairing. The results on the relaxation time obtained using the reactive flux formalism and Grote-Hynes theory present an unequivocal picture that the interface suppresses ion dissociation. The effects of the use of molecular models on the ion interactions as well as the ion-pair configurations at the interface are also quantified and discussed.

Cis-to- Trans Isomerization of Azobenzene Derivatives Studied with Transition Path Sampling and Quantum Mechanical/Molecular Mechanical Molecular Dynamics.

Azobenzene-based molecular photoswitches are becoming increasingly important for the development of photoresponsive, functional soft-matter material systems. Upon illumination with light, fast interconversion between a more stable trans and a metastable cis configuration can be established resulting in pronounced changes in conformation, dipole moment or hydrophobicity. A rational design of functional photosensitive molecules with embedded azo moieties requires a thorough understanding of isomerization mechanisms and rates, especially the thermally activated relaxation. For small azo derivatives considered in the gas phase or simple solvents, Eyring's classical transition state theory (TST) approach yields useful predictions for trends in activation energies or corresponding half-life times of the cis isomer. However, TST or improved theories cannot easily be applied when the azo moiety is part of a larger molecular complex or embedded into a heterogeneous environment, where a multitude of possible reaction pathways may exist. In these cases, only the sampling of an ensemble of dynamic reactive trajectories (transition path sampling, TPS) with explicit models of the environment may reveal the nature of the processes involved. In the present work we show how a TPS approach can conveniently be implemented for the phenomenon of relaxation-isomerization of azobenzenes starting with the simple examples of pure azobenzene and a push-pull derivative immersed in a polar (DMSO) and apolar (toluene) solvent. The latter are represented explicitly at a molecular mechanical (MM) and the azo moiety at a quantum mechanical (QM) level. We demonstrate for the push-pull azobenzene that path sampling in combination with the chosen QM/MM scheme produces the expected change in isomerization pathway from inversion to rotation in going from a low to a high permittivity (explicit) solvent model. We discuss the potential of the simulation procedure presented for comparative calculation of reaction rates and an improved understanding of activated states.

Diffusion and interactions of interstitials in hard-sphere interstitial solid solutions.

Using computer simulations, we study the dynamics and interactions of interstitial particles in hard-sphere interstitial solid solutions. We calculate the free-energy barriers associated with their diffusion for a range of size ratios and densities. By applying classical transition state theory to these free-energy barriers, we predict the diffusion coefficients, which we find to be in good agreement with diffusion coefficients as measured using event-driven molecular dynamics simulations. These results highlight that transition state theory can capture the interstitial dynamics in the hard-sphere model system. Additionally, we quantify the interactions between the interstitials. We find that, apart from excluded volume interactions, the interstitial-interstitial interactions are almost ideal in our system. Lastly, we show that the interstitial diffusivity can be inferred from the large-particle fluctuations alone, thus providing an empirical relationship between the large-particle fluctuations and the interstitial diffusivity.

Macromolecular rate theory (MMRT) provides a thermodynamics rationale to underpin the convergent temperature response in plant leaf respiration.

Temperature is a crucial factor in determining the rates of ecosystem processes, for example, leaf respiration (R) - the flux of plant respired CO2 from leaves to the atmosphere. Generally, R increases exponentially with temperature and formulations such as the Arrhenius equationare widely used in earth system models. However, experimental observations have shown a consequential and consistent departure from an exponential increase in R. What are the principles that underlie these observed patterns? Here, we demonstrate that macromolecular rate theory (MMRT), based on transition state theory (TST) for enzyme-catalyzed kinetics, provides a thermodynamic explanation for the observed departure and the convergent temperature response of R using a global database. Three meaningful parameters emerge from MMRT analysis: the temperature at which the rate of respiration would theoretically reach a maximum (the optimum temperature, Topt ), the temperature at which the respiration rate is most sensitive to changes in temperature (the inflection temperature, Tinf ) and the overall curvature of the log(rate) versus temperature plot (the change in heat capacity for the system, ΔCP‡). On average, the highest potential enzyme-catalyzed rates of respiratory enzymes for R are predicted to occur at 67.0±1.2°C and the maximum temperature sensitivity at 41.4±0.7°C from MMRT. The average curvature (average negative ΔCP‡) was -1.2±0.1kJmol-1 K-1 . Interestingly, Topt , Tinf and ΔCP‡ appear insignificantly different across biomes and plant functional types, suggesting that thermal response of respiratory enzymes in leaves could be conserved. The derived parameters from MMRT can serve as thermal traits for plant leaves that represent the collective temperature response of metabolic respiratory enzymes and could be useful to understand regulations of R under a warmer climate. MMRT extends the classic TST to enzyme-catalyzed reactions and provides an accurate and mechanistic model for the short-term temperature response of R around the globe.