Temperature dependence of chemical and biophysical rate processes: Phenomenological approach to deviations from Arrhenius law

The effects of asymmetry in active noises on the efficiency of single colloidal Stirling engines with active noises

Molecular machines, which operate in highly fluctuating environments far from equilibrium, may benefit from their non-equilibrium environments. It is, however, a topic of controversy how the efficiency of the microscopic engines can be enhanced. Recent experiments showed that microscopic Stirling engines in bacterial reservoirs could show high performance beyond the equilibrium thermodynamics. In this work, we perform overdamped Langevin dynamics simulations for microscopic Stirling heat engines in bacterial reservoirs and show that the temperature dependence of the magnitude of active noises should be responsible for such high efficiency. Only when we introduce temperature-dependent active noises, the efficiency of the microscopic Stirling engines is enhanced significantly as in experiments.

Temperature-mediated diffusion of nanoparticles in semidilute polymer solutions

The temperature is often a critical factor affecting the diffusion of nanoparticles in complex physiological media, but its specific effects are still to be fully understood. Here, we constructed a temperature-regulated model of semidilute polymer solution and experimentally investigated the temperature-mediated diffusion of nanoparticles using the particle tracking method. By examining the ensemble-averaged mean square displacements (MSDs), we found that the MSD grows gradually as the temperature increases while the transition time from sublinear to linear stage in MSD decreases. Meanwhile, the temperature-dependent measured diffusivity of the nanoparticles shows an exponential growth. We revealed that these temperature-mediated changes are determined by the composite effect of the macroscale property of polymer solution and the microscale dynamics of polymer chain as well as nanoparticles. Furthermore, the measured non-Gaussian displacement probability distributions were found to exhibit non-Gaussian fat tails, and the tailed distribution is enhanced as the temperature increases. The non-Gaussianity was calculated and found to vary in the same trend with the tailed distribution, suggesting the occurrence of hopping events. This temperature-mediated non-Gaussian feature validates the recent theory of thermally induced activated hopping. Our results highlight the temperature-mediated changes in diffusive transport of nanoparticles in polymer solutions and may provide the possible strategy to improve drug delivery in physiological media.

Model-driven insights into the effects of temperature on metabolism

Temperature affects cellular processes at different spatiotemporal scales, and identifying the genetic and molecular mechanisms underlying temperature responses paves the way to develop approaches for mitigating the effects of future climate scenarios. A systems view of the effects of temperature on cellular physiology can be obtained by focusing on metabolism since: (i) its functions depend on transcription and translation and (ii) its outcomes support organisms' development, growth, and reproduction. Here we provide a systematic review of modelling efforts directed at investigating temperature effects on properties of single biochemical reactions, system-level traits, metabolic subsystems, and whole-cell metabolism across different prokaryotes and eukaryotes. We compare and contrast computational approaches and theories that facilitate modelling of temperature effects on key properties of enzymes and their consideration in constraint-based as well as kinetic models of metabolism. In addition, we provide a summary of insights from computational approaches, facilitating integration of omics data from temperature-modulated experiments with models of metabolic networks, and review the resulting biotechnological applications. Lastly, we provide a perspective on how different types of metabolic modelling can profit from developments in machine learning and models of different cellular layers to improve model-driven insights into the effects of temperature relevant for biotechnological applications.

Enabling forecasts of environmental exposure to chemicals in European agriculture under global change

European agricultural development in the 21st century will be affected by a host of global changes, including climate change, changes in agricultural technologies and practices, and a shift towards a circular economy. The type and quantity of chemicals used, emitted, and cycled through agricultural systems in Europe will change, driven by shifts in the use patterns of pesticides, veterinary pharmaceuticals, reclaimed wastewater used for irrigation, and biosolids. Climate change will also impact the chemical persistence, fate, and transport processes that dictate environmental exposure. Here, we review the literature to identify research that will enable scenario-based forecasting of environmental exposures to organic chemicals in European agriculture under global change. Enabling exposure forecasts requires understanding current and possible future 1.) emissions, 2.) persistence and transformation, and 3.) fate and transport of agricultural chemicals. We discuss current knowledge in these three areas, the impact global change drivers may have on them, and we identify knowledge and data gaps that must be overcome to enable predictive scenario-based forecasts of environmental exposure under global change. Key research gaps identified are: improved understanding of relationships between global change and chemical emissions in agricultural settings; better understanding of environment-microbe interactions in the context of chemical degradation under future conditions; and better methods for downscaling climate change-driven intense precipitation events for chemical fate and transport modelling. We introduce a set of narrative Agricultural Chemical Exposure (ACE) scenarios - augmenting the IPCC's Shared Socio-economic Pathways (SSPs) - as a framework for forecasting chemical exposure in European agriculture. The proposed ACE scenarios cover a plausible range of optimistic to pessimistic 21st century development pathways. Filling the knowledge and data gaps identified within this study and using the ACE scenario approach for chemical exposure forecasting will support stakeholder planning and regulatory intervention strategies to ensure European agricultural practices develop in a sustainable manner.

On the pseudo-hyperbolic behavior of charge transfer resistance-temperature dependence in corrosion behavior of Nickel based glass alloy

Temperature plays an important role in promoting the corrosion of metals. The Arrhenius plot can interpret the corrosion rate-temperature dependence, where the Arrhenius behavior gives a geometrical meaning and makes explicit a positive or negative linear dependence of charge transitivity and temperature. In addition, according to the Arrhenius interpretation, it represents the energy that the molecule in the initial state of the process must acquire before it can take part in the reaction, whether it is a physical, or a chemical process. Taking into account the deviation from the linearity, we have extended the Arrhenius-type expression by one term in 1/T² and we have given some physical meaning to the new related coefficients for which it is found that they depend closely on the number of acid hydrogen atoms in the polyacid for the corrosion and passivation of the Nickel based metallic glass alloy of the composition Ni_82.3Cr₇Fe₃Si_4.5B_3.2. Moreover, we can consider that the deviation to the Arrhenius linear behavior as a super-Arrhenius behavior In addition, a mathematical analysis of the trend of experimental scatter points of the charge transfer resistance with temperature permits us to reveal an interesting homographic behavior which leads us to suggest an original empirical model with only two optimal adjustable parameters, as well as a new pseudo-power dependence of the number of hydrogen atoms in the polyacid.

Depletion Induced Demixing and Crystallization in Binary Colloids Subjected to an External Potential Barrier

Depletion interaction plays an important role in determining the structural and dynamical properties of binary colloidal mixtures. We have investigated the effect of the attractive depletion interaction between an external potential barrier and larger species in the binary mixture on the phase behavior of a binary colloidal mixture using canonical-isokinetic ensemble molecular dynamics simulations. The demixing of the binary mixture due to this depletion interaction increases as the volume fraction increases, and a pure phase of larger particles forms in the region of the potential barrier. The local density of this pure phase is high enough that a face centered cubic crystalline domain is formed at this region. This crystalline phase diffuses perpendicular to the external potential barrier, indicating that moving crystals can be obtained in an equilibrium system. The temperature dependence of diffusivity of larger particles is non-Arrhenius and changes from sub-Arrhenius to super-Arrhenius as the volume fraction increases. This crossover from sub-Arrhenius to super-Arrhenius diffusion coincides with the crystalline formation near the potential barrier.

Aqueous picloram degradation by hydroxyl radicals: Unveiling mechanism, kinetics, and ecotoxicity through experimental and theoretical approaches

Pesticides are chemical compounds widely used to combat pests in crops, and they thus play a key role in agricultural production. However, due to their persistence in aquatic environments, even at low concentrations, their use has been considered an environmental problem and caused concern regarding the adverse effects on human health. This paper reports, for the first time, the mechanisms, kinetics, and an evaluation of the toxicity of picloram degradation initiated by OH radicals in the aqueous environment using quantum chemistry and computational toxicology calculations. The rate constants are calculated using a combination of formulations derived from the Transition State Theory in a realistic temperature range (250-310 K). The results indicate that the two favorable pathways (R1 and R5) of OH -based reactions occur by addition to the pyridine ring. The calculated rate constant at 298 K is compared with the overall second-order reaction rate constant, quantified herein experimentally via the competition kinetics method and data available in the literature showing an excellent agreement. The toxicity assessment and a photolysis study provide important information: i) picloram and the majority of degradation products are estimated as harmful; however, ii) these compounds can suffer photolysis in sunlight. The results of the present study can help understand the mechanism of picloram, also providing important clues regarding risk assessment in aquatic environments as well as novel experimental information.

Topography of the free energy landscape of Claisen-Schmidt condensation: solvent and temperature effects on the rate-controlling step

Recent studies have found that hydroxide elimination and the C[double bond, length as m-dash]C bond formation step in base-promoted aldol condensation have a strong influence on the overall rate of the reaction, in contrast to the well-accepted first enolization or C-C bond formation step. Here, applying theoretical models to the prototypical reaction of chalcone formation, the complete free energy profile of Claisen-Schmidt condensation is assessed, revealing how a protic solvent and a slight increase in temperature can induce the second enolization as the rate-controlling step (RCS). It is also observed: i) the nonexistence of a step with a much higher energetic barrier than the others, making the concept of RCS debatable; and ii) that the overall inverse kinetic isotopic effect does not exclude second enolization as a RCS in protic continuum medium. We expect that these results can expand the understanding of the decisive role of physicochemical factors on the choose of the RCS in the aldol condensation.

Optimal proteome allocation and the temperature dependence of microbial growth laws

Although the effect of temperature on microbial growth has been widely studied, the role of proteome allocation in bringing about temperature-induced changes remains elusive. To tackle this problem, we propose a coarse-grained model of microbial growth, including the processes of temperature-sensitive protein unfolding and chaperone-assisted (re)folding. We determine the proteome sector allocation that maximizes balanced growth rate as a function of nutrient limitation and temperature. Calibrated with quantitative proteomic data for Escherichia coli, the model allows us to clarify general principles of temperature-dependent proteome allocation and formulate generalized growth laws. The same activation energy for metabolic enzymes and ribosomes leads to an Arrhenius increase in growth rate at constant proteome composition over a large range of temperatures, whereas at extreme temperatures resources are diverted away from growth to chaperone-mediated stress responses. Our approach points at risks and possible remedies for the use of ribosome content to characterize complex ecosystems with temperature variation.

Temperature-Dependent Activity of Motor Proteins: Energetics and Their Implications for Collective Behavior

Molecular motor proteins are an extremely important component of the cellular transport system that harness chemical energy derived from ATP hydrolysis to carry out directed mechanical motion inside the cells. Transport properties of these motors such as processivity, velocity, and their load dependence have been well established through single-molecule experiments. Temperature dependent biophysical properties of molecular motors are now being probed using single-molecule experiments. Additionally, the temperature dependent biochemical properties of motors (ATPase activity) are probed to understand the underlying mechanisms and their possible implications on the enzymatic activity of motor proteins. These experiments in turn have revealed their activation energies and how they compare with the thermal energy available from the surrounding medium. In this review, we summarize such temperature dependent biophysical and biochemical properties of linear and rotary motor proteins and their implications for collective function during intracellular transport and cellular movement, respectively.

Super-Arrhenius diffusion in a binary colloidal mixture at low volume fraction: an effect of depletion interaction due to an asymmetric barrier

We report results from the molecular dynamics simulations of a binary colloidal mixture subjected to an external potential barrier along one of the spatial directions at low volume fraction, ϕ = 0.2. The variations in the asymmetry of the external potential barrier do not change the dynamics of the smaller particles, showing Arrhenius diffusion. However, the dynamics of the larger particles shows a crossover from sub-Arrhenius to super-Arrhenius diffusion with the asymmetry in the external potential at the low temperatures and low volume fraction. Super-Arrhenius diffusion is generally observed in the high density systems where the transient cages are present due to dense packing, e.g., supercooled liquids, jammed systems, diffusion through porous membranes, dynamics within the cellular environment, etc. This model can be applied to study the molecular transport across cell membranes, nano-, and micro-channels which are characterized by spatially asymmetric potentials.

Temperature effect on water dynamics in tetramer phosphofructokinase matrix and the super-arrhenius respiration rate

Advances in understanding the temperature effect on water dynamics in cellular respiration are important for the modeling of integrated energy processes and metabolic rates. For more than half a century, experimental studies have contributed to the understanding of the catalytic role of water in respiration combustion, yet the detailed water dynamics remains elusive. We combine a super-Arrhenius model that links the temperature-dependent exponential growth rate of a population of plant cells to respiration, and an experiment on isotope labeled ¹⁸O₂ uptake to H₂¹⁸O transport role and to a rate-limiting step of cellular respiration. We use Phosphofructokinase (PFK-1) as a prototype because this enzyme is known to be a pacemaker (a rate-limiting enzyme) in the glycolysis process of respiration. The characterization shows that PFK-1 water matrix dynamics are crucial for examining how respiration (PFK-1 tetramer complex breathing) rates respond to temperature change through a water and nano-channel network created by the enzyme folding surfaces, at both short and long (evolutionary) timescales. We not only reveal the nano-channel water network of PFK-1 tetramer hydration topography but also clarify how temperature drives the underlying respiration rates by mapping the channels of water diffusion with distinct dynamics in space and time. The results show that the PFK-1 assembly tetramer possesses a sustainable capacity in the regulation of the water network toward metabolic rates. The implications and limitations of the reciprocal-activation-reciprocal-temperature relationship for interpreting PFK-1 tetramer mechanisms are briefly discussed.

Understanding the Dependence of Micropollutant Biotransformation Rates on Short-Term Temperature Shifts

Temperature is a key factor that influences chemical biotransformation potential and rates, on which exposure and fate models rely to predict the environmental (micro)pollutant fate. Arrhenius-based models are currently implemented in environmental exposure assessment to adapt biotransformation rates to actual temperatures, assuming validity in the 0-30 °C range. However, evidence on how temperature shifts affect the physicochemical and microbial features in biological systems is scarce, questioning the validity of the existing modeling approaches. In this work, laboratory-scale batch assays were designed to investigate how a mixed microbial community responds to short-term temperature shifts, and how this impacts its ability to biotransform a range of structurally diverse micropollutants. Our results revealed three distinct kinetic responses at temperatures above 20 °C, mostly deviating from the classic Arrhenius-type behavior. Micropollutants with similar temperature responses appeared to undergo mostly similar initial biotransformation reactions, with substitution-type reactions maintaining Arrhenius-type behavior up to higher temperatures than oxidation-type reactions. Above 20 °C, the microbial community also showed marked shifts in both composition and activity, which mostly correlated with the observed deviations from Arrhenius-type behavior, with compositional changes becoming a more relevant factor in biotransformations catalyzed by more specific enzymes (e.g., oxidation reactions). Our findings underline the need to re-examine and further develop current environmental fate models by integrating biological aspects, to improve accuracy in predicting the environmental fate of micropollutants.

Deciphering the Dynamics of Organic Nanoaggregates with AIEE Effect and Excited States: Lipophilic Benzothiadiazole Derivatives as Selective Cell Imaging Probes

An aggregation-induced emission enhancement (AIEE) effect in fluorescent lipophilic 2,1,3-benzothiadiazole (BTD) derivatives and their organic nanoaggregates were studied. A set of techniques such as single-crystal X-ray, dynamic light scattering (DLS), electron paramagnetic resonance (EPR), UV-vis, fluorescence, and density functional theory (DFT) calculations have been used to decipher the formation/break (kinetics), properties, and dynamics of the organic nanoaggregates of three BTD small organic molecules. An in-depth study of the excited-state also revealed the preferential relaxation emissive pathways for the BTD derivatives and the dynamics associated with it. The results described herein, for the first time, explain the formation of fluorescent BTD nanoaggregate derivatives and allow for the understanding of their dynamics in solution as well as the ruling forces of both aggregation and break processes along with the involved equilibrium. One of the developed dyes could be used at a nanomolar concentration to selectively stain lipid droplets emitting an intense and bright fluorescence at the red channel. The other two BTDs could also stain lipid droplets at very low concentrations and were visualized preferentially at the blue channel.

The temperature dependence of kinesin motor-protein mechanochemistry

Biophysical studies of the mechanochemical cycle of kinesin motors are essential for understanding the mechanism of energy conversion. Here, we report a systematic study of the impact of temperature on velocity and run length of homodimeric Drosophila kinesin-1, homodimeric C. elegans OSM-3 and heterodimeric C. elegans kinesin-II motor proteins using in vitro single-molecule motility assays. Under saturated ATP conditions, kinesin-1 and OSM-3 are fast and processive motors compared to kinesin-II. From in vitro motility assays employing single-molecule fluorescence microscopy, we extracted single-motor velocities and run lengths in a temperature range from 15 °C to 35 °C. Both parameters showed a non-Arrhenius temperature dependence for all three motors, which could be quantitatively modeled using a simplified, two-state kinetic model of the mechanochemistry of the three motors, providing new insights in the temperature dependence of their mechanochemistry.

Non-invasive and Time-dependent Blood-sugar Monitoring via Breath-derived CO2 Correlation Using Gas Chromatograph with a Milli-whistle Gas Analyzer

A clear and positive correlation between the CO₂ concentration and the blood-sugar level has been observed via a non-invasive and time-dependent monitoring of CO₂ concentration from human breath, which is carried out by using a home-made gas chromatography (GC)/milli-whistle compact analyzer. The time-dependent sampling of the CO₂ concentration correlated between 5.0 to 5.6% (1% = 10⁴ ppm) in accordance with blood-sugar level variations of 80 to 110 mg/dL. The analytical method results in a rapid, continuous and non-invasive determination of blood-sugar level via measurement of the CO₂ concentration exhaled from the lungs.

From the Kinetic Theory of Gases to the Kinetics of Rate Processes: On the Verge of the Thermodynamic and Kinetic Limits

A variety of current experiments and molecular dynamics computations are expanding our understanding of rate processes occurring in extreme environments, especially at low temperatures, where deviations from linearity of Arrhenius plots are revealed. The thermodynamic behavior of molecular systems is determined at a specific temperature within conditions on large volume and number of particles at a given density (the thermodynamic limit): on the other side, kinetic features are intuitively perceived as defined in a range between the extreme temperatures, which limit the existence of each specific phase. In this paper, extending the statistical mechanics approach due to Fowler and collaborators, ensembles and partition functions are defined to evaluate initial state averages and activation energies involved in the kinetics of rate processes. A key step is delayed access to the thermodynamic limit when conditions on a large volume and number of particles are not fulfilled: the involved mathematical analysis requires consideration of the role of the succession for the exponential function due to Euler, precursor to the Poisson and Boltzmann classical distributions, recently discussed. Arguments are presented to demonstrate that a universal feature emerges: Convex Arrhenius plots (super-Arrhenius behavior) as temperature decreases are amply documented in progressively wider contexts, such as viscosity and glass transitions, biological processes, enzymatic catalysis, plasma catalysis, geochemical fluidity, and chemical reactions involving collective phenomena. The treatment expands the classical Tolman’s theorem formulated quantally by Fowler and Guggenheim: the activation energy of processes is related to the averages of microscopic energies. We previously introduced the concept of “transitivity”, a function that compactly accounts for the development of heuristic formulas and suggests the search for universal behavior. The velocity distribution function far from the thermodynamic limit is illustrated; the fraction of molecules with energy in excess of a certain threshold for the description of the kinetics of low-temperature transitions and of non-equilibrium reaction rates is derived. Uniform extension beyond the classical case to include quantum tunneling (leading to the concavity of plots, sub-Arrhenius behavior) and to Fermi and Bose statistics has been considered elsewhere. A companion paper presents a computational code permitting applications to a variety of phenomena and provides further examples.

Unexpected Thiocyanate Adsorption onto Ferrihydrite Under Prebiotic Chemistry Conditions

The most crucial role played by minerals was in the preconcentration of biomolecules or precursors of biomolecules in prebiotic seas. If this step had not occurred, molecular evolution would not have occurred. Thiocyanate is an important molecule in the formation of biomolecules as well as a catalyst for prebiotic reactions. The adsorption of thiocyanate onto ferrihydrite was carried out under pH and ion composition conditions in seawater that resembled those of prebiotic Earth. The seawater used in this work had high Mg²⁺, Ca²⁺ and SO₄^2- concentrations. The most important result of this work was that ferrihydrite adsorbed thiocyanateata pH value (7.2 ± 0.2) that usually does not adsorb thiocyanate. The high adsorptivity of Mg²⁺, Ca²⁺ and SO₄^2-onto ferrihydrite showed that seawater ions can act as carriers of thiocyanate to the ferrihydrite surface, creating a huge outer-sphere complex. Kinetic adsorption and isotherm experiments showed the best fit for the pseudo-second-order model and an activation energy of 23.8 kJ mol^-1forthe Langmuir-Freundlich model, respectively. Thermodynamic data showed positive ΔG values, which apparently contradict the adsorption isotherm data and kinetic data that was obtained. The adsorption of thiocyanate onto ferrihydrite could be explained by coupling with the exergonic SO₄^2- adsorption onto ferrihydrite. The FTIR spectra showed no difference between the C≡N stretching peaks of adsorbed thiocyanate and free thiocyanate, corroborating the formation of an outer-sphere complex. All the results demonstrated the importance of the artificial seawater composition for the adsorption of thiocyanate and for understanding prebiotic chemistry.

Quasi-Classical Trajectory Study of NH(3∑-) + NH(3∑-) Reactive Collisions

A full-dimension quasi-classical trajectory study of collisions between two NH radicals is presented. Interatomic interactions are represented by a previously reported global six-dimensional potential energy surface for singlet electronic state of the N₂H₂ system. This study suggests that the formation of N₂ from the collision of two NH radicals may occur via a one-step (NH + NH → N₂ + H + H) or two-step (NH + NH → N₂H + H → N₂ + H + H) microscopic reaction mechanism. A fast vibrational energy redistribution is observed in the four-body complex in the latter mechanism. Excitation functions are presented and discussed. A variant of the vibrational energy quantum mechanical threshold method was used to correct the zero-point energy leakage in the classical calculations. The influence of reactant's rotational and vibrational energy on reactivity was investigated by state-specific calculations with one or both reactants excited. Reaction rate constants for the ground and some rotationally excited states are presented using an Arrhenius-Kooij-like functional form.

Characterization of the non-Arrhenius behavior of supercooled liquids by modeling nonadditive stochastic systems

The characterization of the formation mechanisms of amorphous solids is a large avenue for research, since understanding its non-Arrhenius behavior is challenging to overcome. In this context, we present one path toward modeling the diffusive processes in supercooled liquids near glass transition through a class of nonhomogeneous continuity equations, providing a consistent theoretical basis for the physical interpretation of its non-Arrhenius behavior. More precisely, we obtain the generalized drag and diffusion coefficients that allow us to model a wide range of non-Arrhenius processes. This provides a reliable measurement of the degree of fragility of the system and an estimation of the fragile-to-strong transition in glass-forming liquids, as well as a generalized Stokes-Einstein equation, leading to a better understanding of the classical and quantum effects on the dynamics of nonadditive stochastic systems.

"Transitivity": A Code for Computing Kinetic and Related Parameters in Chemical Transformations and Transport Phenomena

The Transitivity function, defined in terms of the reciprocal of the apparent activation energy, measures the propensity for a reaction to proceed and can provide a tool for implementing phenomenological kinetic models. Applications to systems which deviate from the Arrhenius law at low temperature encouraged the development of a user-friendly graphical interface for estimating the kinetic and thermodynamic parameters of physical and chemical processes. Here, we document the Transitivity code, written in Python, a free open-source code compatible with Windows, Linux and macOS platforms. Procedures are made available to evaluate the phenomenology of the temperature dependence of rate constants for processes from the Arrhenius and Transitivity plots. Reaction rate constants can be calculated by the traditional Transition-State Theory using a set of one-dimensional tunneling corrections (Bell (1935), Bell (1958), Skodje and Truhlar and, in particular, the deformed ( d -TST) approach). To account for the solvent effect on reaction rate constant, implementation is given of the Kramers and of Collins-Kimball formulations. An input file generator is provided to run various molecular dynamics approaches in CPMD code. Examples are worked out and made available for testing. The novelty of this code is its general scope and particular exploit of d -formulations to cope with non-Arrhenius behavior at low temperatures, a topic which is the focus of recent intense investigations. We expect that this code serves as a quick and practical tool for data documentation from electronic structure calculations: It presents a very intuitive graphical interface which we believe to provide an excellent working tool for researchers and as courseware to teach statistical thermodynamics, thermochemistry, kinetics, and related areas.

Artificial Intelligence Modelling Approach for the Prediction of CO-Rich Hydrogen Production Rate from Methane Dry Reforming

This study investigates the applicability of the Leven–Marquardt algorithm, Bayesian regularization, and a scaled conjugate gradient algorithm as training algorithms for an artificial neural network (ANN) predictively modeling the rate of CO and H2 production by methane dry reforming over a Co/Pr2O3 catalyst. The dataset employed for the ANN modeling was obtained using a central composite experimental design. The input parameters consisted of CH4 partial pressure, CO2 partial pressure, and reaction temperature, while the target parameters included the rate of CO and H2 production. A neural network architecture of 3 13 2, 3 15 2, and 3 15 2 representing the input layer, hidden neuron layer, and target (output) layer were employed for the Leven–Marquardt, Bayesian regularization, and scaled conjugate gradient training algorithms, respectively. The ANN training with each of the algorithms resulted in an accurate prediction of the rate of CO and H2 production. The best prediction was, however, obtained using the Bayesian regularization algorithm with the lowest standard error of estimates (SEE). The high values of coefficient of determination (R2 > 0.9) obtained from the parity plots are an indication that the predicted rates of CO and H2 production were strongly correlated with the observed values.

Kinetics Of The H + CH2 → CH + H2 Reaction At Low Temperature

A quasiclassical trajectory study of the kinetics of the title astrochemical reaction in a range of temperatures varying from 5 to 1000 K (corresponding to both the outer and the inner regions of the protostar and the circumstellar envelopes) was carried out and a clear dependence of the rate coefficient on the temperature is given, in contrast with the constant value adopted in kinetics astrochemical databases. Levering the massive nature of the performed calculations and of the detailed dynamical investigation of the reactive process, a rationalization of the temperature dependence of the released translational energy and of the rovibrational population of the CH and H₂ diatomic products is also provided. Furthermore, the effect of the initial rovibrational energy of CH₂ on the state-specific rate coefficients and cross sections is analyzed in order to single out the role played by the different regions of the potential energy surface on the dynamical outcomes and on the modeling the temperature dependence of the reactive efficiency of the investigated process. This led to a parametrization of the computed rate in terms of the following double Arrhenius expression (in cm³ s^-1), k(T) = 2.50 × 10^-10 exp(- 1.67/T) + 5.98 × 10^-11 exp(- 280.5/T), alternative to the piecewise formulation into the three subintervals of temperature in which the overall 5-1000 K interval can be divided.

Non-Arrhenius Reaction-Diffusion Kinetics for Protein Inactivation over a Large Temperature Range

Understanding protein folding and unfolding has been a long-standing fundamental question and has important applications in manipulating protein activity in biological systems. Experimental investigations of protein unfolding have been predominately conducted by small temperature perturbations (e.g., temperature jump), while molecular simulations are limited to small time scales (microseconds) and high temperatures to observe unfolding. Thus, it remains unclear how fast a protein unfolds irreversibly and loses function (i.e., inactivation) across a large temperature range. In this work, using nanosecond pulsed heating of individual plasmonic nanoparticles to create precise localized heating, we examine the protein inactivation kinetics at extremely high temperatures. Connecting this with protein inactivation measurements at low temperatures, we observe that the kinetics of protein unfolding is less sensitive to temperature change at the higher temperatures, which significantly departs from the Arrhenius behavior extrapolated from low temperatures. To account for this effect, we propose a reaction-diffusion model that modifies the temperature-dependence of protein inactivation by introducing a diffusion limit. Analysis of the reaction-diffusion model provides general guidelines in the behavior of protein inactivation (reaction-limited, transition, diffusion-limited) across a large temperature range from physiological temperature to extremely high temperatures. We further demonstrate that the reaction-diffusion model is particularly useful for designing optimal operating conditions for protein photoinactivation. The experimentally validated reaction-diffusion kinetics of protein unfolding is an important step toward understanding protein-inactivation kinetics over a large temperature range. It has important applications including molecular hyperthermia and calls for future studies to examine this model for other protein molecules.

Nucleophilic substitution vs elimination reaction of bisulfide ions with substituted methanes: exploration of chiral selectivity by stereodirectional first-principles dynamics and transition state theory

Control of molecular orientation is emerging as crucial for the characterization of the stereodynamics of kinetics processes beyond structural stereochemistry. The special role played in chiral discrimination phenomena has been particularly emphasized by Aquilanti and collaborators after their extensive probes of experimental control of molecular alignment and orientation. In this work, the manifestation of the Aquilanti mechanism has been demonstrated for the first time in first-principles molecular dynamics simulations: stationary points characterized on potential energy surfaces have been calculated for the study of chemical reactions occurring between the bisulfide anion HS^- and oriented prototypical chiral molecules CHFXY (where X = CH₃ or CN and Y = Cl or I). The important reaction channels are those corresponding to bimolecular nucleophilic substitution (S_N2) and to bimolecular elimination (E2): their relative role has been assessed and alternative pathways due to the mirror forms of the oriented chiral molecule are revealed by the different reactivity of the two enantiomers of CHFCNI in S_N2 reaction.

Temperature Dependence of Rate Processes Beyond Arrhenius and Eyring: Activation and Transitivity

Advances in the understanding of the dependence of reaction rates from temperature, as motivated from progress in experiments and theoretical tools (e. g., molecular dynamics), are needed for the modeling of extreme environmental conditions (e.g., in astrochemistry and in the chemistry of plasmas). While investigating statistical mechanics perspectives (Aquilanti et al., 2017b, 2018), the concept of transitivity was introduced as a measure for the propensity for a reaction to occur. The Transitivity plot is here defined as the reciprocal of the apparent activation energy vs. reciprocal absolute temperature. Since the transitivity function regulates transit in physicochemical transformations, not necessarily involving reference to transition-state hypothesis of Eyring, an extended version is here proposed to cope with general types of transformations. The transitivity plot permits a representation where deviations from Arrhenius behavior are given a geometrical meaning and make explicit a positive or negative linear dependence of transitivity for sub- and super-Arrhenius cases, respectively. To first-order in reciprocal temperature, the transitivity function models deviations from linearity in Arrhenius plots as originally proposed by Aquilanti and Mundim: when deviations are increasingly larger, other phenomenological formulas, such as Vogel-Fulcher-Tammann, Nakamura-Takayanagi-Sato, and Aquilanti-Sanches-Coutinho-Carvalho are here rediscussed from the transitivity concept perspective and with in a general context. Emphasized is the interest of introducing into this context modifications to a very successful tool of theoretical kinetics, Eyring's Transition-State Theory: considering the behavior of the transitivity function at low temperatures, in order to describe deviation from Arrhenius behavior under the quantum tunneling regime, a "d-TST" formulation was previously introduced (Carvalho-Silva et al., 2017). In this paper, a special attention is dedicated to a derivation of the temperature dependence of viscosity, making explicit reference to feature of the transitivity function, which in this case generally exhibits a super-Arrhenius behavior. This is of relevance also for advantages of using the transitivity function for diffusion-controlled phenomena.

Theoretical Investigation on H2O2-Ng (He, Ne, Ar, Kr, Xe, and Rn) Complexes Suitable for Stereodynamics: Interactions and Thermal Chiral Rate Consequences

Although molecular collisions of noble gases (Ng) can be theoretically used to distinguish between the enantiomers of hydrogen peroxide - H₂O₂ (HP), little is known about the effects of HP-Ng interactions on the chiral rate. In this work, the chiral rate as a function of temperature (CRT) between enantiomeric conformations of HP and Ng (Ng=He, Ne, Ar, Kr, Xe, and Rn) are presented at MP2(full)/aug-cc-pVTZ level of theory through a fully basis set superposition error (BSSE) corrected potential energy surface. The results show that: (a) the CRT is highly affected even at a small decrease in the height of trans-barrier; (b) its smallest values occur with Ne for all temperatures between 100 and 4,000 K; (c) that the decrease of CRT shows an inverse correlation with respect to the average valence electron energy of the Ng and (d) Ne and He may be the noble gases more suitable for study the oriented collision dynamics of HP. In addition to binding energies, the electron density ρ and its Laplacian ∇²ρ topological analyses were also performed within the atoms in molecules (AIM) theory in order to determine the nature of the HP-Ng interactions. The results of this work provide a more complete foundation on experiments to study HP's chirality using Ng in crossed molecular beams without a light source.

Pressure-Dependent Rate Constant Predictions Utilizing the Inverse Laplace Transform: A Victim of Deficient Input Data

k(E) can be calculated either from the Rice-Ramsperger-Kassel-Marcus theory or by inverting macroscopic rate constants k(T). Here, we elaborate the inverse Laplace transform approach for k(E) reconstruction by examining the impact of k(T) data fitting accuracy. For this approach, any inaccuracy in the reconstructed k(E) results from inaccurate/incomplete k(T) description. Therefore, we demonstrate how an improved mathematical description of k(T) data leads to accurate k(E) data. Refitting inaccurate/incomplete k(T), hence, allows for recapturing k(T) information that yields more accurate k(E) reconstructions. The present work suggests that accurate representation of experimental and theoretical k(T) data in a broad temperature range could be used to obtain k(T,p). Thus, purely temperature-dependent kinetic models could be converted into fully temperature- and pressure-dependent kinetic models.

A novel assessment of the role of the methyl radical and water formation channel in the CH3OH + H reaction

A number of experimental and theoretical papers accounted almost exclusively for two channels in the reaction of atomic hydrogen with methanol: H-abstraction from the methyl (R1) and hydroxyl (R2) functional groups. Recently, several astrochemical studies claimed the importance of another channel for this reaction, which is crucial for kinetic simulations related to the abundance of molecular constituents in planetary atmospheres: methyl radical and water formation (R3 channel). Here, motivated by the lack of and uncertainties about the experimental and theoretical kinetic rate constants for the third channel, we developed first-principles Car-Parrinello molecular dynamics thermalized at two significant temperatures - 300 and 2500 K. Furthermore, the kinetic rate constant of all three channels was calculated using a high-level deformed-transition state theory (d-TST) at a benchmark electronic structure level. d-TST is shown to be suitable for describing the overall rate constant for the CH₃OH + H reaction (an archetype of the moderate tunnelling regime) with the precision required for practical applications. Considering the experimental ratios at 1000 K, k_R1/k_R2 ≈ 0.84 and k_R1/k_R3 ≈ 15-40, we provided a better estimate when compared with previous theoretical work: 7.47 and 637, respectively. The combination of these procedures explicitly demonstrates the role of the third channel in a significant range of temperatures and indicates its importance considering the thermodynamic control to estimate methyl radical and water formation. We expect that these results can help to shed new light on the fundamental kinetic rate equations for the CH₃OH + H reaction.

Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces

In this Introduction, we show the basic problems of non-statistical and non-equilibrium phenomena related to the papers collected in this themed issue. Over the past few years, significant advances in both computing power and development of theories have allowed the study of larger systems, increasing the time length of simulations and improving the quality of potential energy surfaces. In particular, the possibility of using quantum chemistry to calculate energies and forces 'on the fly' has paved the way to directly study chemical reactions. This has provided a valuable tool to explore molecular mechanisms at given temperatures and energies and to see whether these reactive trajectories follow statistical laws and/or minimum energy pathways. This themed issue collects different aspects of the problem and gives an overview of recent works and developments in different contexts, from the gas phase to the condensed phase to excited states.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Kinetics of low-temperature transitions and a reaction rate theory from non-equilibrium distributions

This article surveys the empirical information which originated both by laboratory experiments and by computational simulations, and expands previous understanding of the rates of chemical processes in the low-temperature range, where deviations from linearity of Arrhenius plots were revealed. The phenomenological two-parameter Arrhenius equation requires improvement for applications where interpolation or extrapolations are demanded in various areas of modern science. Based on Tolman's theorem, the dependence of the reciprocal of the apparent activation energy as a function of reciprocal absolute temperature permits the introduction of a deviation parameter d covering uniformly a variety of rate processes, from those where quantum mechanical tunnelling is significant and d < 0, to those where d > 0, corresponding to the Pareto-Tsallis statistical weights: these generalize the Boltzmann-Gibbs weight, which is recovered for d = 0. It is shown here how the weights arise, relaxing the thermodynamic equilibrium limit, either for a binomial distribution if d > 0 or for a negative binomial distribution if d < 0, formally corresponding to Fermion-like or Boson-like statistics, respectively. The current status of the phenomenology is illustrated emphasizing case studies; specifically (i) the super-Arrhenius kinetics, where transport phenomena accelerate processes as the temperature increases; (ii) the sub-Arrhenius kinetics, where quantum mechanical tunnelling propitiates low-temperature reactivity; (iii) the anti-Arrhenius kinetics, where processes with no energetic obstacles are rate-limited by molecular reorientation requirements. Particular attention is given for case (i) to the treatment of diffusion and viscosity, for case (ii) to formulation of a transition rate theory for chemical kinetics including quantum mechanical tunnelling, and for case (iii) to the stereodirectional specificity of the dynamics of reactions strongly hindered by the increase of temperature.This article is part of the themed issue 'Theoretical and computational studies of non-equilibrium and non-statistical dynamics in the gas phase, in the condensed phase and at interfaces'.

Non-linear van't Hoff behavior in pulmonary surfactant model membranes

Pulmonary surfactant exhibits phase coexistence over a wide range of surface pressure and temperature. Less is known about the effect of temperature on pulmonary surfactant models. Given the lack of studies on this issue, we used electron paramagnetic resonance (EPR) and nonlinear least-squares (NLLS) simulations to investigate the thermotropic phase behavior of the matrix that mimics the pulmonary surfactant lipid complex, i.e., the lipid mixture composed of dipalmitoyl phosphatidylcholine (DPPC), palmitoyl-oleoyl phosphatidylcholine (POPC) and palmitoyl-oleoyl phosphatidylglycerol (POPG). Irrespective of pH, the EPR spectra recorded from 5°C to 25°C in the DPPC/POPC/POPG (4:3:1) model membrane contain two spectral components corresponding to lipids in gel-like and fluid-like phases, indicating a coexistence of two domains in that range. The temperature dependence of the distribution of spin labels between the domains yielded nonlinear van't Hoff plots. The thermodynamic parameters evaluated were markedly different for DPPC and for the ternary DPPC/POPC/POPG (4:3:1) membranes and exhibited a dependence on chemical environment. While enthalpy and entropy changes for DPPC were always positive and presented a quadratic behavior with temperature, those of the ternary mixture were linearly dependent on temperature and changed from negative to positive values. Despite that, enthalpy-entropy compensation takes place in the two systems. The thermotropic process associated with the coexistence of the two domains is entropically-driven in DPPC and either entropically- or enthalpically-driven in the pulmonary surfactant membrane depending on the pH, ionic strength and temperature. The significance of these results to the structure and function of the pulmonary surfactant lipid matrix is discussed.

Deformed transition-state theory: Deviation from Arrhenius behavior and application to bimolecular hydrogen transfer reaction rates in the tunneling regime

A formulation is presented for the application of tools from quantum chemistry and transition-state theory to phenomenologically cover cases where reaction rates deviate from Arrhenius law at low temperatures. A parameter d is introduced to describe the deviation for the systems from reaching the thermodynamic limit and is identified as the linearizing coefficient in the dependence of the inverse activation energy with inverse temperature. Its physical meaning is given and when deviation can be ascribed to quantum mechanical tunneling its value is calculated explicitly. Here, a new derivation is given of the previously established relationship of the parameter d with features of the barrier in the potential energy surface. The proposed variant of transition state theory permits comparison with experiments and tests against alternative formulations. Prescriptions are provided and implemented to three hydrogen transfer reactions: CH₄  + OH → CH₃  + H₂ O, CH₃ Cl + OH → CH₂ Cl + H₂ O and H₂  + CN → H + HCN, widely investigated both experimentally and theoretically. © 2016 Wiley Periodicals, Inc.

Stereodirectional Origin of anti-Arrhenius Kinetics for a Tetraatomic Hydrogen Exchange Reaction: Born-Oppenheimer Molecular Dynamics for OH + HBr

Among four-atom processes, the reaction OH + HBr → H2O + Br is one of the most studied experimentally: its kinetics has manifested an unusual anti-Arrhenius behavior, namely, a marked decrease of the rate constant as the temperature increases, which has intrigued theoreticians for a long time. Recently, salient features of the potential energy surface have been characterized and most kinetic aspects can be considered as satisfactorily reproduced by classical trajectory simulations. Motivation of the work reported in this paper is the investigation of the stereodirectional dynamics of this reaction as the prominent reason for the peculiar kinetics: we started in a previous Letter ( J. Phys. Chem. Lett. 2015 , 6 , 1553 - 1558 ) a first-principles Born-Oppenheimer "canonical" molecular dynamics approach. Trajectories are step-by-step generated on a potential energy surface quantum mechanically calculated on-the-fly and are thermostatically equilibrated to correspond to a specific temperature. Here, refinements of the method permitted a major increase of the number of trajectories and the consideration of four temperatures -50, +200, +350, and +500 K, for which the sampling of initial conditions allowed us to characterize the stereodynamical effect. The role is documented of the adjustment of the reactants' mutual orientation to encounter the entrance into the "cone of acceptance" for reactivity. The aperture angle of this cone is dictated by a range of directions of approach compatible with the formation of the specific HOH angle of the product water molecule; and consistently the adjustment is progressively less effective the higher the kinetic energy. Qualitatively, this emerging picture corroborates experiments on this reaction, involving collisions of aligned and oriented molecular beams, and covering a range of energies higher than the thermal ones. The extraction of thermal rate constants from this molecular dynamics approach is discussed and the systematic sampling of the canonical ensemble is indicated as needed for quantitative comparison with the kinetic experiments.

Nonstatistical dynamics on the caldera

We explore both classical and quantum dynamics of a model potential exhibiting a caldera: that is, a shallow potential well with two pairs of symmetry related index one saddles associated with entrance/exit channels. Classical trajectory simulations at several different energies confirm the existence of the "dynamical matching" phenomenon originally proposed by Carpenter, where the momentum direction associated with an incoming trajectory initiated at a high energy saddle point determines to a considerable extent the outcome of the reaction (passage through the diametrically opposing exit channel). By studying a "stretched" version of the caldera model, we have uncovered a generalized dynamical matching: bundles of trajectories can reflect off a hard potential wall so as to end up exiting predominantly through the transition state opposite the reflection point. We also investigate the effects of dissipation on the classical dynamics. In addition to classical trajectory studies, we examine the dynamics of quantum wave packets on the caldera potential (stretched and unstretched). These computations reveal a quantum mechanical analogue of the "dynamical matching" phenomenon, where the initial expectation value of the momentum direction for the wave packet determines the exit channel through which most of the probability density passes to product.