Small-curvature Approximation Research Articles

Asymptotically safe f(R)-gravity coupled to matter II: Global solutions

Ultraviolet fixed point functions of the functional renormalisation group equation for f(R)-gravity coupled to matter fields are discussed. The metric is split via the exponential parameterisation into a background metric and a fluctuating part, the former is chosen to be the one of a four-sphere. Also when scalar, fermion and vector fields are included global quadratic solutions exist as in the pure gravity case for discrete sets of values for some endomorphism parameters defining the coarse-graining scheme. The asymptotic, large-curvature behaviour of the fixed point functions is analysed for generic values of these parameters. Examples for global numerical solutions are provided. A special focus is given to the question whether matter fields might destabilise the ultraviolet fixed point function. Similar to a previous analysis of a polynomial, small-curvature approximation to the fixed point functions different classes for such functions are found.

A theoretical study on the dynamics of gas-phase reaction of methyl cation with atomic oxygen

The dynamics and kinetics of the reaction of CH3+ cation with atomic oxygen in its lowest triplet and singlet states in the presence of N2 molecules as the bath gas is theoretically investigated. The potential energies over both surfaces at the CCSD(T)/aug-cc-pVTZ level of theory are explored. Both singlet and triplet surfaces characterize by barrierless initiation step. The entrance channel to form the energized adducts are governed by the capture probability once the centrifugal barrier is surmounted. Multiwell-multichannel mechanisms are found for both singlet and triplet potential energy surfaces. One-dimensional chemical master equation is solved to explore the dynamics and kinetics of the title reaction. The fractional populations of the stationary points as function of time are analyzed to determine the role of the energized intermediates on the dynamics of the title reaction. No significant temperature or pressure dependence for the title reaction was observed over a wide range of temperature (300–3000 K) and pressure (0.1–4.5 atm). The results indicate cis and trans-HCOH+, CH2O+, and H atom are the major products for both surfaces. CVT method was used to explore the importance of tunneling in hydrogen transfer isomerization reactions of CH2O+ to trans-HCOH+ and HOC+ to HCO+ using small-curvature approximation.

Will (CH3)2COO Survive in Humid Conditions?

AbstractCriegee intermediates (CIs) are thought to be important oxidizing agents in the atmosphere; whereas in high humidity conditions, some CIs are quenched by water vapor, while some are immune from it. CIs’ reactivity toward water vapor is strongly dependent on the substituents of the CIs. It was reported previously that syn‐substituted CIs are less reactive toward water vapor than anti‐substituted ones, and this characteristic allows syn‐substituted CIs to survive in high humidity and react with other atmospheric trace gases, for example, SOx, NOx. In this paper, we calculated the rate coefficients of (CH3)2COO+(H2O)n,n=1,2 and compared them with those of syn‐CH3CHOO+(H2O)n,n=1,2 reported in our previous work. We discussed the substituent effect of CIs and the competition between SO2 and water vapor reaction at atmospheric conditions. In addition, we also discussed the tunneling correction with four different methods on these water mediated hydrogen transfer reactions. We calculated the rate coefficients with anharmonic correction for the partition function, with energetic values from our ratio extrapolation strategy, and with tunneling correction by small curvature approximation. At 298K the calculated bimolecular rate coefficients of (CH3)2COO+(H2O)2 and (CH3)2COO+H2O are 7.4×10−15 and 2.3×10−18 cm3sec−1, which are slow enough that (CH3)2COO can survive in high humidity condition, allowing it to possibly play an important role to oxidize SO2.

Multichannel RRKM-TST and CVT Rate Constant Calculations for Reactions of CH2OH or CH3O with HO2

The kinetics and mechanism of the gas-phase reactions between hydroxy methyl radical (CH(2)OH) or methoxy radical (CH(3)O) with hydroproxy radical (HO(2)) have been theoretically investigated on their lowest singlet and triplet surfaces. Our investigations indicate the presence of one deep potential well on the singlet surface of each of these systems that play crucial roles on their kinetics. We have shown that the major products of CH(2)OH + HO(2) system are HCOOH, H(2)O, H(2)O(2), and CH(2)O and for CH(3)O + HO(2) system are CH(3)OH and O(2). Multichannel RRKM-TST calculations have been carried out to calculate the individual rate constants for those channels proceed through the formation of activated adducts on the singlet surfaces. The rate constants for direct hydrogen abstraction reactions on the singlet and triplet surfaces were calculated by means of direct-dynamics canonical variational transition-state theory with small curvature approximation for the tunneling.

A Theoretical Investigation on the Kinetics and Mechanism of the Reaction of Amidogen with Hydroxyl Radical

The kinetics and mechanism of the reaction between amidogen radical and hydroxyl radical have been theoretically investigated on the lowest singlet and triplet surfaces. The singlet surface consists of two long-lived chemically activated NH(2)OH* and NH(3)O* intermediates with 10 different channels. A hydrogen abstraction channel on the triplet surface proceeds through van der Waals complex in both reactant side and product side to produce NH(3) + O((3)P). The effect of multiple reflections of the van der Waals complexes on the rate constant is investigated. Multichannel RRKM-TST calculations have been carried out to calculate the individual rate constants for the formation of those products that proceed through activated adducts on the singlet surface. The rate constants for direct hydrogen abstraction reactions were calculated by using direct-dynamics canonical variational transition-state theory with small curvature approximation for tunneling.

Multichannel RRKM-TST and Direct-Dynamics VTST Study of the Reaction of Hydroxyl Radical with Furan

The kinetics and mechanism of the reaction of OH with furan have been theoretically studied. The potential energy surface for each possible pathway has been investigated by employing DFT, G3MP2, and CCSD methods. The potential energy surface consists of one hydrogen-bonded complex and two energized intermediates. Three different pathways are suggested to be possible for the title reaction. The most probable channel is the hydroxyl radical addition to the C(2) position on the furan ring to cause the ring-opening process. The two other pathways are hydrogen abstraction from one of the C(2) or C(3) position on furan and hydroxyl radical substitution at the C(2) or C(3) position on furan. Abstraction and substitution channels are minor paths at low temperature, but they become comparable with addition channels at high temperature. Addition and substitution reactions proceed via formation of two energized intermediates, Int(1) and Int(2). Multichannel RRKM-TST calculations have been carried out to calculate the individual and overall rate constants for addition and substitution reactions. Direct-dynamics canonical variational transition-state theory calculations with small curvature approximation for tunneling were carried out to study hydrogen abstraction pathways.

The H2O2+OH→HO2+H2O reaction in aqueous solution from a charge-dependent continuum model of solvation

We applied our recently developed protocol of the conductorlike continuum model of solvation to describe the title reaction in aqueous solution. The model has the unique feature of the molecular cavity being dependent on the atomic charges in the solute and can be extended naturally to transition states and reaction pathways. It was used to calculate the reaction energetics and reaction rate in solution for the title reaction. The rate of reaction calculated using canonical variational transition state theory in the context of the equilibrium solvation path approximation, and including correction for tunneling through the small curvature approximation, was found to be 3.6 x 10(6) M(-1) s(-1), significantly slower than in the gas phase in accord with experiment. These results suggest that the present protocol of the conductorlike continuum model of solvation with the charge-dependent cavity definition captures qualitatively and quantitatively the solvation effects at transition states and allows for quantitative estimates of reaction rates in solutions.

Beam propagation modeling of arbitrarily bent waveguides

A numerical method for computing the wave fields in arbitrarily bent waveguides is developed based on a curvilinear coordinate system and the beam propagation method. Unlike earlier approaches based on the conformal mapping or the polar coordinate system, waveguides with arbitrary bends can be conveniently modeled. The new method is accurate for bends with any curvature, since it avoids the small curvature approximation.

High Level and Dual Level Direct Dynamics in the Intramolecular Proton Transfer of Hydrogenoxalate Anion. Influence of Tunneling and Isotopic Effect

Direct ab initio dynamics methodology was used to investigate intramolecular proton transfer in hydrogenoxalate anion and its deuterated species. The method used is based on the variational theory of the transition state as modified by introducing semiclassical corrections for the estimation of tunneling on the sole basis of electronic structure calculations. Such calculations, which included energies, gradients, and Hessians, both at stationary points and throughout the reaction path, were done by using the MP2/6-31++G** level with barrier height corrections at QCISD/6-31++G** (4.85 kcal/mol). No variational effects were observed at this fairly high computational level over the temperature range studied. Some of the modes of this reaction are highly coupled to the reaction path, so tunneling may be quite substantial. Within the direct ab initio dynamics we used the small curvature approximation (SCT) to assess tunneling; however, because the particle transferred is a light particle, the problem may call ...

Analysis of certain factors in the direct dynamics method: Variational rate constant of the NH3+OH→NH2+H2O reaction

The minimum energy path for the NH3+OH→NH2+H2O reaction was traced and the coupling between the reaction coordinate and normal modes was analyzed along it. Following the ‘‘direct dynamics’’ methodology, the rate constants were calculated for the temperature range 200–4000 K using the variational transition-state theory with two approximations to calculate the tunneling effect. With respect to the construction of the minimum energy path, the influence of the number of points calculated along this path, the scale factor in the Hessian matrix, and different ways of scaling the potential energy surface were analyzed. As this reaction presents a large reaction-path curvature, the small curvature approximation was not suitable for including the tunneling effect and a fitted Eckart potential was used. The variational effects were concluded to be negligible for this reaction, and good agreement with experimental values was found for T≥300 K when using the PSAC4/A1 curve (scaled by 0.8 and shifted to s=0), the Hessian matrix scaled by 0.9, and the fitted Eckart factor for the tunneling correction.

Reaction-path analysis of the effect of monomer excitation on the tunneling splitting of the hydrogen fluoride dimer

The tunneling splitting of (HF)2 has been calculated by semiclassical adiabatic reaction-path methods, employing a small-curvature approximation for the effective mass along the tunneling path. The calculations include all six vibrational degrees of freedom and are based on the partly ab initio, partly semiempirical potential energy surface proposed recently by the authors and Dykstra. The calculations are carried out for both unexcited and excited monomer vibrations, and they correctly predict that excitation of either monomer lowers the tunneling splitting, but they do not explain why the lower-energy monomer stretch is equally as effective as the higher-energy one.

POLYRATE: A general computer program for variational transition state theory and semiclassical tunneling calculations of chemical reaction rates

We present a computer program for calculating rate constants of gas-phase chemical reactions involving one or two reactants with a total of three to ten atoms. The program accepts information about the potential energy surface in the form of either an analytic potential energy function or a sequence of geometries, energies, gradients and second (or higher) derivative matrices at points along the reaction path. In the former case the program itself calculates the reaction pathe and the sequence of derivative matrices. From this information the program calculates the rate constant for quantized internal degrees of freedom and classical reaction-path motion by variational transition state theory (VTST). The probabilities for tunneling and nonclassical reflection are estimated by semiclassical methods and incorporated by a transmission coefficient, which for thermal reactions is based on the ground state. There are several options for including the effects of anharmonicity in the independent-normal-mode approximation, and the reaction-path curvature may be included in the tunneling calculation by the small-curvature approximation. The article also presents test calculations illustrating the use of new reaction-path interpolation and extrapolation procedures which should be useful in conjunction with VTST calculations based on ab initio gradients and Hessian calculations.

A general small-curvature approximation for transition-state-theory transmission coefficients

ADVERTISEMENT RETURN TO ISSUEArticleNEXTA general small-curvature approximation for transition-state-theory transmission coefficientsRex T. Skodje, Donald G. Truhlar, and Bruce C. GarrettCite this: J. Phys. Chem. 1981, 85, 21, 3019–3023Publication Date (Print):October 1, 1981Publication History Published online1 May 2002Published inissue 1 October 1981https://doi.org/10.1021/j150621a001RIGHTS & PERMISSIONSArticle Views1116Altmetric-Citations292LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InReddit PDF (598 KB) Get e-Alerts