Computational Chemistry of Polyatomic Reaction Kinetics and Dynamics: The Quest for an Accurate CH5 Potential Energy Surface

Current Status of the X + C2H6 [X ≡ H, F(2P), Cl(2P), O(3P), OH] Hydrogen Abstraction Reactions: A Theoretical Review

This paper is a detailed review of the chemistry of medium-size reactive systems using the following hydrogen abstraction reactions with ethane, X + C₂H₆ → HX + C₂H₅; X ≡ H, F(²P), Cl(²P), O(³P) and OH, and focusing attention mainly on the theoretical developments. These bimolecular reactions range from exothermic to endothermic systems and from barrierless to high classical barriers of activation. Thus, the topography of the reactive systems changes from reaction to reaction with the presence or not of stabilized intermediate complexes in the entrance and exit channels. The review begins with some reflections on the inherent problems in the theory/experiment comparison. When one compares kinetics or dynamics theoretical results with experimental measures, one is testing both the potential energy surface describing the nuclei motion and the kinetics or dynamics method used. Discrepancies in the comparison may be due to inaccuracies of the surface, limitations of the kinetics or dynamics methods, and experimental uncertainties that also cannot be ruled out. The paper continues with a detailed review of some bimolecular reactions with ethane, beginning with the reactions with hydrogen atoms. The reactions with halogens present a challenge owing to the presence of stabilized intermediate complexes in the entrance and exit channels and the influence of the spin-orbit states on reactivity. Reactions with O(³P) atoms lead to three surfaces, which is an additional difficulty in the theoretical study. Finally, the reactions with the hydroxyl radical correspond to a reactive system with ten atoms and twenty-four degrees of freedom. Throughout this review, different strategies in the development of analytical potential energy surfaces describing these bimolecular reactions have been critically analyzed, showing their advantages and limitations. These surfaces are fitted to a large number of ab initio calculations, and we found that a huge number of calculations leads to accurate surfaces, but this information does not guarantee that the kinetics and dynamics results match the experimental measurements.

Gas-Phase Preparation of Silyl Cyanide (SiH3CN) via a Radical Substitution Mechanism

The silyl cyanide (SiH₃CN) molecule, the simplest representative of a fully saturated silacyanide, was prepared in the gas phase under single-collision conditions via a radical substitution mechanism. The chemical dynamics were direct and revealed a pronounced backward scattering as a consequence of a transition state with a pentacoordinated silicon atom and almost colinear geometry of the attacking cyano radical and leaving hydrogen. Compared to the isovalent cyano (CN)-methane (CH₄) system, the CN-SiH₄ system dramatically reduces the energy of the transition state to silyl cyanide by nearly 100 kJ mol^-1, which reveals a profound effect on the chemical bonding and reaction mechanism. In extreme high-temperature environments including circumstellar envelopes of IRC +10216, this versatile radical substitution mechanism may synthesize organosilicon molecules via reactions of silane with doublet radicals. Overall, this study provides rare insights into the exotic reaction mechanisms of main-group XIV elements in extreme environments and affords deeper insights into fundamental molecular mass growth processes involving silicon in our universe.

Accurate potential energy surfaces for hydrogen abstraction reactions: A benchmark study on the XYG3 doubly hybrid density functional

The potential energy surface (PES) for the H + CH₄ system has been constructed with the recently developed XYG3 doubly hybrid functional, while those with the standard B3LYP hybrid functional, and the Møller-Plesset perturbation theory up to the second order (MP2) are also presented for comparison. Quantum dynamics studies demonstrated that satisfactory results on the reaction probabilities and the rate coefficients can be obtained on top of the XYG3-PES, as compared to the results based on the highly accurate, yet expensive, CCSD(T)-PES (Li et al., J. Chem. Phys. 2015, 142, 204302). Further investigation suggested that the XYG3 functional is useful in providing accurate rate coefficients for some larger systems involving H atom abstractions. © 2017 Wiley Periodicals, Inc.

Dynamical barrier and isotope effects in the simplest substitution reaction via Walden inversion mechanism

Reactions occurring at a carbon atom through the Walden inversion mechanism are one of the most important and useful classes of reactions in chemistry. Here we report an accurate theoretical study of the simplest reaction of that type: the H+CH4 substitution reaction and its isotope analogues. It is found that the reaction threshold versus collision energy is considerably higher than the barrier height. The reaction exhibits a strong normal secondary isotope effect on the cross-sections measured above the reaction threshold, and a small but reverse secondary kinetic isotope effect at room temperature. Detailed analysis reveals that the reaction proceeds along a path with a higher barrier height instead of the minimum-energy path because the umbrella angle of the non-reacting methyl group cannot change synchronously with the other reaction coordinates during the reaction due to insufficient energy transfer from the translational motion to the umbrella mode.

Variational transition state theory: theoretical framework and recent developments

This article reviews the fundamentals of variational transition state theory (VTST), its recent theoretical development, and some modern applications.

Rate constants for the slow Mu + propane abstraction reaction at 300 K by diamagnetic RF resonance

The rate constant for the slow Mu + propane abstraction reaction has been determined by diamagnetic RF resonance. The curves show simulations of the μSR resonance signal. This study provides an important new test of reaction rate theory for the alkanes.

Quantum mechanical fragment methods based on partitioning atoms or partitioning coordinates

Conspectus The development of more efficient and more accurate ways to represent reactive potential energy surfaces is a requirement for extending the simulation of large systems to more complex systems, longer-time dynamical processes, and more complete statistical mechanical sampling. One way to treat large systems is by direct dynamics fragment methods. Another way is by fitting system-specific analytic potential energy functions with methods adapted to large systems. Here we consider both approaches. First we consider three fragment methods that allow a given monomer to appear in more than one fragment. The first two approaches are the electrostatically embedded many-body (EE-MB) expansion and the electrostatically embedded many-body expansion of the correlation energy (EE-MB-CE), which we have shown to yield quite accurate results even when one restricts the calculations to include only electrostatically embedded dimers. The third fragment method is the electrostatically embedded molecular tailoring approach (EE-MTA), which is more flexible than EE-MB and EE-MB-CE. We show that electrostatic embedding greatly improves the accuracy of these approaches compared with the original unembedded approaches. Quantum mechanical fragment methods share with combined quantum mechanical/molecular mechanical (QM/MM) methods the need to treat a quantum mechanical fragment in the presence of the rest of the system, which is especially challenging for those parts of the rest of the system that are close to the boundary of the quantum mechanical fragment. This is a delicate matter even for fragments that are not covalently bonded to the rest of the system, but it becomes even more difficult when the boundary of the quantum mechanical fragment cuts a bond. We have developed a suite of methods for more realistically treating interactions across such boundaries. These methods include redistributing and balancing the external partial atomic charges and the use of tuned fluorine atoms for capping dangling bonds, and we have shown that they can greatly improve the accuracy. Finally we present a new approach that goes beyond QM/MM by combining the convenience of molecular mechanics with the accuracy of fitting a potential function to electronic structure calculations on a specific system. To make the latter practical for systems with a large number of degrees of freedom, we developed a method to interpolate between local internal-coordinate fits to the potential energy. A key issue for the application to large systems is that rather than assigning the atoms or monomers to fragments, we assign the internal coordinates to reaction, secondary, and tertiary sets. Thus, we make a partition in coordinate space rather than atom space. Fits to the local dependence of the potential energy on tertiary coordinates are arrayed along a preselected reaction coordinate at a sequence of geometries called anchor points; the potential energy function is called an anchor points reactive potential. Electrostatically embedded fragment methods and the anchor points reactive potential, because they are based on treating an entire system by quantum mechanical electronic structure methods but are affordable for large and complex systems, have the potential to open new areas for accurate simulations where combined QM/MM methods are inadequate.

Ab initio based potential energy surface and kinetics study of the OH + NH3 hydrogen abstraction reaction

A full-dimensional analytical potential energy surface (PES) for the OH + NH3 → H2O + NH2 gas-phase reaction was developed based exclusively on high-level ab initio calculations. This reaction presents a very complicated shape with wells along the reaction path. Using a wide spectrum of properties of the reactive system (equilibrium geometries, vibrational frequencies, and relative energies of the stationary points, topology of the reaction path, and points on the reaction swath) as reference, the resulting analytical PES reproduces reasonably well the input ab initio information obtained at the coupled-cluster single double triple (CCSD(T)) = FULL/aug-cc-pVTZ//CCSD(T) = FC/cc-pVTZ single point level, which represents a severe test of the new surface. As a first application, on this analytical PES we perform an extensive kinetics study using variational transition-state theory with semiclassical transmission coefficients over a wide temperature range, 200-2000 K. The forward rate constants reproduce the experimental measurements, while the reverse ones are slightly underestimated. However, the detailed analysis of the experimental equilibrium constants (from which the reverse rate constants are obtained) permits us to conclude that the experimental reverse rate constants must be re-evaluated. Another severe test of the new surface is the analysis of the kinetic isotope effects (KIEs), which were not included in the fitting procedure. The KIEs reproduce the values obtained from ab initio calculations in the common temperature range, although unfortunately no experimental information is available for comparison.

STEREODYNAMICS STUDY OF THE ABSTRACTION REACTION H + CD4 → HD + CD3

A new London–Eyring–Polanyi–Sato (LEPS) potential energy surface (PES) is employed in this work to study the stereo properties for the abstraction reaction of hydrogen with methane at its rovibrationally ground state using the quasiclassical trajectory method (QCT). A "quasi-triatomic" approximation is used to treat the CD3 group of CD4 as a pseudoatom. The calculated excitation function of the title reaction can give a good agreement to most experimental and theoretical data at collision energies (Ec =1.5 ~ 2.5 eV ). Further investigation of the product HD in reaction H + CD4 (v = 0, j = 0) → HD + CD3 and D + CH4 (v = 0, j = 0) → HD + CH3 shows the dependence of the product rotational polarization on collision energies and mass factor, but P(θr) is not sensitive to both the collision energies and the mass factor.

Constructing Potential Energy Surfaces for Polyatomic Systems: Recent Progress and New Problems

Different methods of constructing potential energy surfaces in polyatomic systems are reviewed, with the emphasis put on fitting, interpolation, and analytical (defined by functional forms) approaches, based on quantum chemistry electronic structure calculations. The different approaches are reviewed first, followed by a comparison using the benchmark H + CH4 and the H + NH3 gas-phase hydrogen abstraction reactions. Different kinetics and dynamics properties are analyzed for these reactions and compared with the available experimental data, which permits one to estimate the advantages and disadvantages of each method. Finally, we analyze different problems with increasing difficulty in the potential energy construction: spin-orbit coupling, molecular size, and more complicated reactions with several maxima and minima, which test the soundness and general applicability of each method. We conclude that, although the field of small systems, typically atom-diatom, is mature, there still remains much work to be done in the field of polyatomic systems.

QCT and QM calculations of the Cl(2P) + NH3 reaction: influence of the reactant well on the dynamics

A detailed dynamics study, using both quasi-classical trajectory (QCT) and reduced-dimensional quantum mechanical (QM) calculations, was carried out to understand the reactivity and mechanism of the Cl((2)P) + NH(3)→ HCl + NH(2) gas-phase reaction, which evolves through deep wells in the entry and exit channels. The calculations were performed on an analytical potential energy surface recently developed by our group, PES-2010 [M. Monge-Palacios, C. Rangel, J. C. Corchado and J. Espinosa-Garcia, Int. J. Quantum. Chem., 2011], together with a simplified model surface, mod-PES, in which the reactant well is removed to analyze its influence. The main finding was that the QCT and QM methods show a change of the reaction probability with collision energy, suggesting a change of the atomic-level mechanism of reaction with energy. This change disappeared when the mod-PES was used, showing that the behaviour at low energies is a direct consequence of the existence of the reactant well. Analysis of the trajectories showed that different mechanisms operate depending on the collision energy. Thus, while at high energies (E(coll) > 5 kcal mol(-1)) practically all trajectories are direct, at low energies (E(coll) < 3 kcal mol(-1)) the trajectories are indirect, i.e., with the mediation of a trapping complex in the entry and/or the exit wells. The reactant complex allows repeated encounters between the reactants, increasing the reaction probability at low energies. The differential cross section results reinforce this change of mechanism, showing also the influence of the reactant well on this reaction. Thus, the PES-2010 surface yields a forward-backward symmetry in the scattering, while when the reactant well is removed with the mod-PES the shape is more isotropic.

Bimolecular reaction rates from ring polymer molecular dynamics: application to H + CH4 → H2 + CH3

In a recent paper, we have developed an efficient implementation of the ring polymer molecular dynamics (RPMD) method for calculating bimolecular chemical reaction rates in the gas phase, and illustrated it with applications to some benchmark atom-diatom reactions. In this paper, we show that the same methodology can readily be used to treat more complex polyatomic reactions in their full dimensionality, such as the hydrogen abstraction reaction from methane, H + CH(4) → H(2) + CH(3). The present calculations were carried out using a modified and recalibrated version of the Jordan-Gilbert potential energy surface. The thermal rate coefficients obtained between 200 and 2000 K are presented and compared with previous results for the same potential energy surface. Throughout the temperature range that is available for comparison, the RPMD approximation gives better agreement with accurate quantum mechanical (multiconfigurational time-dependent Hartree) calculations than do either the centroid density version of quantum transition state theory (QTST) or the quantum instanton (QI) model. The RPMD rate coefficients are within a factor of 2 of the exact quantum mechanical rate coefficients at temperatures in the deep tunneling regime. These results indicate that our previous assessment of the accuracy of the RPMD approximation for atom-diatom reactions remains valid for more complex polyatomic reactions. They also suggest that the sensitivity of the QTST and QI rate coefficients to the choice of the transition state dividing surface becomes more of an issue as the dimensionality of the reaction increases.

Depression of reactivity by the collision energy in the single barrier H + CD4 -> HD + CD3 reaction

Crossed molecular beam experiments and accurate quantum scattering calculations have been carried out for the polyatomic H + CD(4) --> HD + CD(3) reaction. Unprecedented agreement has been achieved between theory and experiments on the energy dependence of the integral cross section in a wide collision energy region that first rises and then falls considerably as the collision energy increases far over the reaction barrier for this simple hydrogen abstraction reaction. Detailed theoretical analysis shows that at collision energies far above the barrier the incoming H-atom moves so quickly that the heavier D-atom on CD(4) cannot concertedly follow it to form the HD product, resulting in the decline of reactivity with the increase of collision energy. We propose that this is also the very mechanism, operating in many abstraction reactions, which causes the differential cross section in the backward direction to decrease substantially or even vanish at collision energies far above the barrier height.

Gradient-based multiconfiguration Shepard interpolation for generating potential energy surfaces for polyatomic reactions

This paper describes and illustrates a way to construct multidimensional representations of reactive potential energy surfaces (PESs) by a multiconfiguration Shepard interpolation (MCSI) method based only on gradient information, that is, without using any Hessian information from electronic structure calculations. MCSI, which is called multiconfiguration molecular mechanics (MCMM) in previous articles, is a semiautomated method designed for constructing full-dimensional PESs for subsequent dynamics calculations (classical trajectories, full quantum dynamics, or variational transition state theory with multidimensional tunneling). The MCSI method is based on Shepard interpolation of Taylor series expansions of the coupling term of a 2 x 2 electronically diabatic Hamiltonian matrix with the diagonal elements representing nonreactive analytical PESs for reactants and products. In contrast to the previously developed method, these expansions are truncated in the present version at the first order, and, therefore, no input of electronic structure Hessians is required. The accuracy of the interpolated energies is evaluated for two test reactions, namely, the reaction OH+H(2)-->H(2)O+H and the hydrogen atom abstraction from a model of alpha-tocopherol by methyl radical. The latter reaction involves 38 atoms and a 108-dimensional PES. The mean unsigned errors averaged over a wide range of representative nuclear configurations (corresponding to an energy range of 19.5 kcal/mol in the former case and 32 kcal/mol in the latter) are found to be within 1 kcal/mol for both reactions, based on 13 gradients in one case and 11 in the other. The gradient-based MCMM method can be applied for efficient representations of multidimensional PESs in cases where analytical electronic structure Hessians are too expensive or unavailable, and it provides new opportunities to employ high-level electronic structure calculations for dynamics at an affordable cost.

Structural analysis of HS(CD(2))(12)(O-CH(2)-CH(2))(6)OCH(3) monolayers on gold by means of polarization modulation infrared reflection absorption spectroscopy. progress of the reaction with bromine

A self-assembled monolayer (SAM) on gold was formed with specifically perdeuterated hexaethylene glycol-terminated alkanethiol HS(CD(2))(12)(O-CH(2)-CH(2))(6)OCH(3) (D-OEG). The structure of the d-alkane and the oligoethylene glycol (OEG) parts of the molecule in a SAM was studied by means of polarization modulation infrared reflection absorption spectroscopy. The D-OEG monolayers are highly ordered and exist in a crystalline phase. The d-alkane chain adopts an all-trans conformation. Both, the d-alkane chain and long axis of the OEG part make an angle of 26.0 degrees +/- 1.5 degrees with respect to the surface normal, a value characteristic for the tilt of solid n-alkane thiols in the SAMs on Au. The positions of nu(as)(COC) and CH(2) wagging and rocking modes indicate a helical arrangement of the OEG chains. The D-OEG SAMs were exposed to 25 muM Br(2) in two ways: (i) by immersion into the Br(2) solution and (ii) in the galvanic cell Au|D-OEG SAM|25 muM Br(2) + 0.1 M Na(2)SO(4)|| 50 muM KBr + 0.1 M Na(2)SO(4)|Au. In the galvanic cell, the oxidant (Br(2)) is scavenged by a heterogeneous electron transfer reaction, slowing the reaction of D-OEG with Br(2). The slow progress of the reaction with Br(2) allowed us to draw conclusions about molecular rearrangements taking place during this reaction. The reaction with Br(2) starts on boundaries and/or defects present in the SAM. First, at the defect place, the alpha-C atom of the OEG chain reacts with Br(2) and the OEG part of the molecule is removed from the monolayer. In consequence an increase in disorder in the OEG part of the SAM is observed. The same mechanism of the reaction with Br(2) is applied for the d-dodecane alkanethiol part of the molecule. This reaction is slow, thus the order and the tilt of the hydrocarbon chain changes only a little during the reaction time.

Dissecting competitive mechanisms: thionation vs. cycloaddition in the reaction of thioisomunchnones with isothiocyanates under microwave irradiation

This paper documents in detail the reaction of 1,3-thiazolium-4-olates (thioisomunchnones) with aryl isothiocyanates. Having demonstrated with a chiral model that thionation occurs under these conditions to provide 1,3-thiazolium-4-thiolates and that this process is actually a stepwise domino reaction (J. Org. Chem. 2009, 74, 3698-3705), we extend this study to monocyclic thioisomunchnones. Herein, competition between thionation and 1,3-dipolar cycloaddition takes place. The process is synthetically disappointing at room temperature requiring prolonged reaction times for completion. The protocol has been subsequently investigated by using both microwave dielectric heating and conventional thermal heating (oil bath) in DMF at 100 degrees C with an accurate internal reaction temperature measurement. Although a slight acceleration was observed for reactions conducted under microwave irradiation, for most cases the observed yields and chemoselectivities were quite similar. Thus one can conclude that, within experimental errors, the reactivity is not related to nonthermal effects in agreement with recent reassessments on this subject, particularly by Kappe and associates (J. Org. Chem. 2008, 73, 36; J. Org. Chem. 2009, 74, 6157). The whole reaction system, which includes numerous heavy atoms, can be computationally modeled with a hybrid ONIOM[B3LYP/6-31G(d):PM3] level. This reproduces well experimental results and suggests a sequential mechanism. To further corroborate the nonconcertedness, the potential energy surface (PES) has been constructed for simplified models, locating the corresponding stationary points. In doing so, we introduce for the first time a useful and convenient mathematical protocol to locate the stationary points along a reaction path. The protocol is quite simple and should convince many organic chemists that certain daunting theoretical treatments can be made easy.

Quasiclassical trajectory study of H+SiH4 reactions in full-dimensionality reveals atomic-level mechanisms

This work elucidates new atomic-level mechanisms that may be common in a range of chemical reactions, and our findings are important for the understanding of the nature of polyatomic abstraction and exchange reactions. A global 12-dimensional ab initio potential energy surface (PES), which describes both H+SiH(4) abstraction and exchange reactions is constructed, based on the modified Shepard interpolation method and UCCSD(T)/cc-pVQZ energy calculations at 4,015 geometries. This PES has a classical barrier height of 5.35 kcal/mol for abstraction (our best estimate is 5.35 +/- 0.15 kcal/mol from extensive ab initio calculations), and an exothermicity of -13.12 kcal/mol, in excellent agreement with experiment. Quasiclassical trajectory calculations on this new PES reveal interesting features of detailed dynamical quantities and underlying new mechanisms. Our calculated product angular distributions for exchange are in the forward hemisphere with a tail sideways, and are attributed to the combination of three mechanisms: inversion, torsion-tilt, and side-inversion. With increase of collision energy our calculated angular distributions for abstraction first peak at backward scattering and then shift toward smaller scattering angles, which is explained by a competition between rebound and stripping mechanisms; here stripping is seen at much lower energies, but is conceptually similar to what was observed in the reaction of H+CD(4) by Zare and coworkers [Camden JP, et al. (2005) J Am Chem Soc 127:11898-11899]. Each of these atomic-level mechanisms is confirmed by direct examination of trajectories, and two of them (torsion-tilt and side-inversion) are proposed and designated in this work.

The hydrogen abstraction reaction H + CH4. I. New analytical potential energy surface based on fitting to ab initio calculations

A new analytical potential energy surface is presented for the reaction of hydrogen abstraction from methane by a hydrogen atom. It is based on an analytical expression proposed by Jordan and Gilbert [J. Chem. Phys. 102, 5669 (1995)], and its fittable parameters were obtained by a multibeginning optimization procedure to reproduce high-level ab initio electronic structure calculations obtained at the CCSD(T)/cc-pVTZ level. The ab initio information employed in the fit includes properties (equilibrium geometries, relative energies, and vibrational frequencies) of the reactants, products, saddle point, points on the reaction path, and points on the reaction swath. No experimental information is used. By comparison with the reference results we show that the resulting surface reproduces well not only the ab initio data used in the fitting but also other thermochemical and kinetic results computed at the same ab initio level, such as equilibrium constants, rate constants, and kinetic isotope effects, which were not used in the fit. In this way we show that the new potential energy surface is correctly fitted and almost as accurate as the CCSD(T)/cc-pVTZ method in describing the kinetics of the reaction. We analyze the limitations of the functional form and the fitting method employed, and suggest some solutions to their drawbacks. In a forthcoming communication, we test the quality of the new surface by comparing its results with experimental values.