Recent Developments in Kramers’ Theory of Reaction Rates

In this short review, we provide an update of recent developments in Kramers’ theory of reaction rates. After a brief introduction stressing the importance of this theory initially developed for chemical reactions, we briefly present the main theoretical formalism starting from the generalized Langevin equation and continue by showing the main points of the modern Pollak, Grabert and Hänggi theory. Kramers’ theory is then sketched for quantum and classical surface diffusion. As an illustration the surface diffusion of Na atoms on a Cu(110) surface is discussed showing escape rates, jump distributions and diffusion coefficients as a function of reduced friction. Finally, some very recent applications of turnover theory to different fields such as nanoparticle levitation, microcavity polariton dynamics and simulation of reaction in liquids are presented. We end with several open problems and future challenges faced up by Kramers turnover theory.     

Exact density functional theory for ideal polymer fluids with nearest neighbor bonding constraints

We present a new density functional theory of ideal polymer fluids, assuming nearest-neighbor bonding constraints. The free energy functional is expressed in terms of end site densities of chain segments and thus has a simpler mathematical structure than previously used expressions using multipoint distributions. This work is based on a formalism proposed by Tripathi and Chapman [Phys. Rev. Lett. 94, 087801 (2005)]. Those authors obtain an approximate free energy functional for ideal polymers in terms of monomer site densities. Calculations on both repulsive and attractive surfaces show that their theory is reasonably accurate in some cases, but does differ significantly from the exact result for longer polymers with attractive surfaces. We suggest that segment end site densities, rather than monomer site densities, are the preferred choice of "site functions" for expressing the free energy functional of polymer fluids. We illustrate the application of our theory to derive an expression for the free energy of an ideal fluid of infinitely long polymers.     

Quantum topological resolution of catalyst proficiency

The purpose of this exploratory investigation is to characterize, contrast, and explain the differences between efficient Ni(π‐allyl)₂ and inefficient Pd(π‐allyl)₂ systems in the catalyzed cross‐coupling of alkanes. Within the framework of the quantum theory of atoms in molecules, we have created quantum topology phase diagrams (QTPDs) for nonisomeric species by the creation of aggregate‐isomers; simple sum rules are introduced to ensure that the Poincaré‐Hopf relation is obeyed. We show that the catalyzed reaction cycles can be represented as a directed QTPD where each species of the main reaction cycle forms a closed loop. The topological position of the unwanted side products relative to the main reaction cycle for each catalyst is also considered. We find the more efficient Ni(π‐allyl)₂ catalyst produces a reaction cycle on the QTPD that contains no “missing” topologies, preferentially proceeding to desired product at 94% yield, while avoiding wasteful side‐product pathways, disconnected from the major pathway by “missing” topologies. The converse is true for the less efficient Pd(π‐allyl)₂ catalyst, whose reaction pathway markedly bifurcates to final yields of 56% and 44% for product and side‐product, respectively. We subsequently used our nearest neighbor ring‐critical point approach to show that the species of the main reaction cycle of the efficient Ni(π‐allyl)₂ catalyst facilitates the desired chemical transformation whilst more effectively barring the formation of unwanted side product, with respect to the inefficient Pd(π‐allyl)₂ catalyst. The findings from the QTPD analysis are in agreement with traditional energetic‐barrier interpretations of reaction pathway preference. © 2015 Wiley Periodicals, Inc.     

A computational study of the heats of reaction of substituted monoethanolamine with CO2

Various amines have been considered as materials for chemical capture of CO(2) through liquid-phase reactions to form either carbamate or carbamic acid products. One of the main challenges in these CO(2)-amine reactions lies in tuning the heat of reaction to achieve the correct balance between the extent of reaction and the energy cost for regeneration. In this work, we use a computational approach to study the effect of substitution on the heats of reaction of monoethanolamine (MEA). We use ab initio methods at the MP2/aug-cc-pVDZ level, coupled with geometries generated from B3LYP/6-311++G(d,p) density functional theory along with the conductor-like polarizable continuum model to compute the heats of reaction. We consider two possible reaction products: carbamate, having a 2:1 amine:CO(2) reaction stoichiometry, and carbamic acid, having a 1:1 stoichiometry. We have considered CH(3), NH(2), OH, OCH(3), and F substitution groups at both the α- and β-carbon positions of MEA. We have experimentally measured heats of reaction for MEA and both α- and β-CH(3)-substituted MEA to test the predictions of our model. We find quantitative agreement between the predictions and experiments. We have also computed the relative basicities of the substituted amines and found that the heats of reaction for both carbamate and carbamic acid products are linearly correlated with the computed relative basicities. Weaker basicities result in less exothermic heats of reaction. Heats of reaction for carbamates are much more sensitive to changes in basicity than those for carbamic acids. This leads to a crossover in the heat of reaction so that carbamic acid formation becomes thermodynamically favored over carbamate formation for the weakest basicities. This provides a method for tuning the reaction stoichiometry from 2:1 to 1:1.     

A Computational Study on the Mechanism for the K_2CO_3-catalyzed Reaction of Carbon Dioxide and 1-Chlo-2-propanol

The microcosmic reaction mechanism of K2CO3-catalyzed 1-chlo-2-propanol and carbon dioxide has been investigated by density functional theory(DFT) at the GGA/PW91/DNP level.We optimize the geometric configurations of reactants,intermediates,transition states,and products.The energy analysis calculation approves the authenticity of intermediates and transition states.According to our calculations,four feasible reaction pathways are found.The main pathway of the reaction is ReA → IMA1 → TSA1 → IMA2 → IMA5 → TSA5 → P.Besides,we also in-vestigate the reaction mechanism of 1-chlo-2-propanol and carbon dioxide without K2CO3-catalyzation by the same theory and level.The computational results indicate that the activation barrier with K2CO3-catalyzed is smaller than the activation barrier without K2CO3-catalyzed.That is to say,K2CO3 can promote the reaction to give the product in a high yield,which is in agreement with the experimental results.     

Asymptotic behaviors of a delay difference system of plankton allelopathy

The main purpose of this paper is to study a general delay difference system of the growth of two species of plankton having competing and allelopathic effects on each other. We first show that the system is permanent under some suitable assumptions. Next, by using the continuous theorem of coincidence degree theory and constructing a Lyapunov function, a set of sufficient conditions which guarantee the existence and global attractivity of positive periodic solutions are obtained. Finally, two examples together with their numerical simulations are presented to illustrate the feasibility of our main results.     

MRCISD studies of the dissociation of vinylhydroperoxide, CH2CHOOH: there is a saddle point

Multireference ab initio methods are used to investigate the dissociation of vinylhydroperoxide CH(2)CHOOH into vinyl oxide and hydroxide radicals. In contrast to some previous studies, which claim the reaction has no saddle point, our calculations confirm that the dissociation is associated with a kinetic barrier (transition state). We further propose the existence of a hitherto undiscovered radical-radical complex on the reaction path. The computed reaction energetics are used to estimate VHP dissociation rates, and the results are discussed in the context of atmospheric ozonolysis pathways. Qualitative aspects of the dissociation of larger, substituted vinylhydroperoxides are also discussed.     

A perturbation molecular orbital theory of gas-phase dissociative electron-transfer rates

Gasphase dissociative electron-transfer (ET) reactions are examined in the light of modern electron-transfer theory and a perturbation molecular orbital (PMO) model for ion-molecule collision rates. Two dissociative ET reactions reported by Knighton and Grimsrud—the reaction of azulene anion with dibromodifluoromethane and with carbon tetrachloride—happened in the inverted region of the relationship between reaction rate and free energy. Carbon-halogen vibration participation in dissociative ET reactions is demonstrated in two reaction series. Carbon-hydrogen stretch (3050 cm^?1) activation of electron transfer happened in the most exothermic reaction series: dissociative capture to form bromide from bromotrichloromethane The reasons for the failure of classical ion-molecule collision theory to give a quantitative account of reactive ion-molecule collision rates are presented in some detail. The fundamental failure is a result of a previously unappreciated change in the polarizability of a molecule when the orbitals on the molecule overlap with those on an adjacent ion. The molecular orbital-based collision model used here avoids the need to evaluate the changes in the polarizability tensor with overlap.     

A theoretical analysis of rate constants and kinetic isotope effects corresponding to different reactant valleys in lactate dehydrogenase

In some enzymatic systems large conformational changes are coupled to the chemical step, in such a way that dispersion of rate constants can be observed in single-molecule experiments, each corresponding to the reaction from a different reactant valley. Under this perspective here we present a computational study of pyruvate to lactate transformation catalyzed by lactate dehydrogenase. The reaction consists of a hydride transfer and a proton transfer that seem to take place concertedly. The degree of asynchronicity and the energy barrier depend on the particular starting reactant valley. In order to estimate rate constants we used a free energy perturbation technique adapted to follow the intrinsic reaction coordinate for several possible reaction paths. Tunneling effects are also obtained with a slightly modified version of the ensemble-averaged variational transition state theory with multidimensional tunneling contributions. According to our results the closure of the active site by means of a flexible loop can lead to the formation of different reactant complexes displaying different features in the disposition of some key residues (such as Arg109), interactions with the substrate and number of water molecules in the active site. The chemical step of the reaction takes place with a different reaction rate from each of these complexes. Finally, primary kinetic isotope effects for replacement of the transferring hydrogen of the cofactor with a deuteride are in good agreement with experimental observations, thus validating our methodology.     

Dialkylbenzene hydrogenation: Kinetic analysis of rollover mechanism

Kinetic analysis is presented for the so-called rollover mechanism in hydrogenation of dialkylbenzenes. The theory of complex reactions and graph theory are applied for discussing plausible mechanisms. It is demonstrated that mechanisms which involve either desorption-readsorption of some reaction intermediate or some kind of “rollover” of an adsorbed intermediate, result in similar kinetic equations if these steps are reversible.     

Potential energy distribution study of infrared frequencies of methylamine and methylphosphine

Normal mode assignments of the IR frequencies of methylamine and methylphosphine and their deuterated isotopomers are determined based on calculated potential energy distributions. The PED for each frequency is found using Kim’s Correspondence Rules of unified group theory and the program MOLVIB. The predominant motion of each PED is used to name the corresponding vibrational frequency. We compare our results with literature values. Our IR frequency assignments show generally good agreement with experiment and other calculations although there are some differences. We observe no differences in the principal component of normal mode PEDs across different levels of theory with the same basis set. We observe a few differences at the same level of theory with different basis sets.     

Interpretation of the gas-phase solvent deuterium kinetic isotope effects in the S(N)2 reaction mechanism: Comparison of theoretical and experimental results in the reaction of microsolvated fluoride ions with methyl halides

We carried out a comprehensive ab initio calculation and transition-state theory analysis of the solvent and secondary deuterium kinetic isotope effects in the SN2 reactions of microsolvated fluoride ions with methyl halides. Water, methanol, and hydrogen fluoride were used as solvents, and the results are compared with recent experiments. Kinetic isotope effects were dissected into contributions from translations, rotations, and different vibration modes, and the validity of such analysis is also discussed. Excellent agreement was found for some reactions, whereas the agreement was poor for other reactions. We showed that the deviation between theory and experiments is related to the reaction kinetics; a faster reaction produced a kinetic isotope effect that was systematically larger (less inverse) than the calculated value. In addition, we also found that the magnitude of the deviation is proportional to the reaction efficiency. We rationalize the disagreement as a failure of the transition-state theory to model barrierless reactions, and we propose a very simple scheme to interpret these findings and predict the deviation between experimental and theoretical values in those reactions.     

Transport properties of normal liquid helium: comparison of various methodologies

We revisit the problem of self-diffusion in normal liquid helium above the lambda transition. Several different methods are applied to compute the velocity autocorrelation function. Since it is still impossible to determine the exact result for the velocity autocorrelation function from simulation, we appeal to the computation of short-time moments to determine the accuracy of the different approaches at short times. The main conclusion reached from our study is that both the quantum mode-coupling theory and the numerical analytic continuation approach must be regarded as a viable and competitive methods for the computation of dynamical properties of quantum systems.     

Reaction mechanism of monoethanolamine with CO₂ in aqueous solution from molecular modeling

We present a theoretical study of the reaction mechanism of monoethanolamine (MEA) with CO? in an aqueous solution. We have used molecular orbital reaction pathway calculations to compute reaction free energy landscapes for the reaction steps involved in the formation of carbamic acids and carbamates. We have used the conductor-like polarizable continuum model to calculate reactant, product, and transition state geometries and vibrational frequencies within density functional theory (DFT). We have also computed single point energies for all stationary structures using a coupled cluster approach with singles, doubles, and perturbational triple excitations using the DFT geometries. Our calculations indicate that a two-step reaction mechanism that proceeds via a zwitterion intermediate to form carbamate is the most favorable reaction channel. The first step, leading to formation of the zwitterion, is found to be rate-determining, and the activation free energies are 12.0 (10.2) and 11.3 (9.6) kcal/mol using Pauling (Bondi) radii within the CPCM model at the CCSD(T)/6-311++G(d,p) and CCSD(T)/6-311++G(2df,2p) levels of theory, respectively, using geometries and vibrational frequencies obtained at the B3LYP/6-311++G(d,p) level of theory. These results are in reasonable agreement with the experimental value of about 12 kcal/mol. The second step is an acid-base reaction between a zwitterion and MEA. We have developed a microkinetic model to estimate the effective reaction order at intermediate concentrations. Our model predicts an equilibrium concentration for the zwitterion on the order of 10?11 mol/L, which explains why the existence of the zwitterion intermediate has never been detected experimentally. The effective reaction order from our model is close to unity, also in agreement with experiments. Complementary ab initio QM/MM molecular dynamics simulations with umbrella sampling have been carried out to determine the free energy profiles of zwitterion formation and proton transfer in solution; the results confirm that the formation of the zwitterion is rate-determining.     

Melting and thermal decompositions of solids

This analysis of interface phenomena considers the alternative processes that may result from heating a crystal, particularly including thermal decomposition, involving chemical reactions, and melting, involving loss of long-range structural order. Such comparisons are expected to provide insights into the factors that determine and control the different types of thermal changes of solids. The survey also critically reviews some theoretical concepts that are currently used to describe solid-state thermal reactions and which provides relevant background information to models used in a recently proposed theory of melting. Probable reasons for the current lack of progress in characterizing the factors that control chemical changes and mechanisms of thermal reactions in solids are also discussed. It is concluded that some aspects of the macro properties of reaction interfaces in crystal reactions have been adequately described, including geometric representations of interface advance during nucleation and growth processes. In contrast, relatively very little is known about the detailed (micro) processes occurring within these active, advancing interfacial zones: reactant/product contacts during chemical reactions and crystal/melt contacts during fusion. From the patterns of behaviour distinguished, a correlation scheme, based on relative stabilities of crystal structures and components therein, is proposed, which accounts for the four principal types of thermal changes that occur on heating solids: sublimation, decomposition, crystallographic transformation or melting. Identifications of the reasons for these different consequences of heating are expected to contribute towards increasing our understanding of each of the individual processes mentioned and to advance theory of the thermal chemistry of solids, currently enjoying a prolonged quiescent phase.     

Density functional theory study of beta-hydride elimination of ethyl on flat and stepped Cu surfaces

Plane wave density functional theory calculations have been used to characterize the transition states for beta-hydride elimination of ethyl on Cu(100), Cu(110), Cu(111), and Cu(221). The reaction rates predicted by these calculations have been compared to experiments by including tunneling corrections within harmonic transition state theory. Tunneling corrections are found to be important in describing the peak temperatures observed using temperature programmed desorption experiments on Cu(110), Cu(111), and Cu(221). Once these corrections are included, the effective activation energies obtained from our calculations are in good agreement with previous experimental studies of this reaction on these four Cu surfaces. The transition states determined in our calculations are used to examine two general hypotheses that have been suggested to describe structure sensitivity in metal-catalyzed surface reactions.     

Gas-phase reaction of the isobutenyl anion with N2O from ab initio calculations

Calculations using conventional ab initio theory are performed to investigate the reaction mechanism associated with the gas-phase ion/molecule reaction of isobutenyl anion with N₂O. As a result, our theoretical findings strongly suggest that the main pathway is the reaction pattern of end-N attack and that the corresponding reaction mechanism basically relates to hydrogen migration, which may yield products cis-CH₂(CH₃)CCN ₂ ^? , trans-CH₂(CH₃)CCN ₂ ^? , and H₂O. Those are in good agreement with the experimental observations. Moreover, based on the NBO, Activation Strain model and methyl group effect analysis, we also explored the characters of rate-determining step of the main pathway.     

Traveling wave patterns in nonlinear reaction–diffusion equations

In this paper we study a reaction–diffusion model equation with general nonlinear diffusion and arbitrary kinetic orders in the reaction terms, which appears in the applied biochemical modeling. We carry both analytical and numerical studies of the model equation to show the existence of monotone and oscillatory waves. Our numerical computations are illustrated for a particular case of the equation by using different methods which lead to accurate wave profiles and confirm the analytical results.     

Low temperature CO oxidation over unsupported nanoporous gold

Supported Au nanoclusters are well-known for their unusual properties in catalysis. We describe here that nanostructured porous Au made via dealloying represents a new class of unsupported catalysts with extraordinary activities in important reactions such as CO oxidation. Although nanoporous Au may contain some oxides on the surface, our results demonstrate that it is metallic Au that plays the main role in this catalytic reaction. Furthermore, this material has good low-temperature catalytic stability and is extremely CO tolerant.