Modeling the kinetics of bimolecular reactions

Calculating Reaction Rates with Partial Hessians: Validation of the Mobile Block Hessian Approach

In an earlier paper, the authors have developed a new method, the mobile block Hessian (MBH), to accurately calculate vibrational modes for partially optimized molecular structures [J. Chem. Phys. 2007, 126 (22), 224102]. The proposed procedure remedies the artifact of imaginary frequencies, occurring in standard frequency calculations, when parts of the molecular system are optimized at different levels of theory. Frequencies are an essential ingredient in predicting reaction rate coefficients due to their input in the vibrational partition functions. The question arises whether the MBH method is able to describe the chemical reaction kinetics in an accurate way in large molecular systems where a full quantum chemical treatment at a reasonably high level of theory is unfeasible due to computational constraints. In this work, such a validation is tested in depth. The MBH method opens a lot of perspectives in predicting accurate kinetic parameters in chemical reactions where the standard full Hessian procedure fails.

Enhancing NMR Prediction for Organic Compounds Using Molecular Dynamics

NMR spectroscopy is a crucial tool in organic chemistry for the routine characterization of small molecules, structural elucidation of natural products, and study of reaction mechanisms. Although there is evidence that thermal motions strongly affect observed resonances, conventional predictions are performed only on stationary structures. Here we show that quasiclassical molecular dynamics provides a highly accurate and broadly applicable method for improving shielding predictions. Gas-phase values of the absolute shieldings of protons and carbons are predicted to nearly within experimental uncertainty, while the chemical shifts of large systems such as natural products are closely reproduced. Importantly, these results are obtained without the use of any empirical corrections. Our analysis suggests that the linear scaling factors currently employed are primarily a correction for vibrational effects. As a result, our method extends the reach of prediction methods to the study of molecules with unusual dynamics such as the iconic and controversial [18]annulene. Our predictions agree closely with experiment at both low and high temperatures and provide strong evidence that the equilibrium structure of [18]annulene is planar and aromatic.

GPU Assisted Simulation Study of Ion-Ion Reactions within Quadrupole Ion Traps

In this study, a gas-phase ion-ion reaction model was developed, and it was integrated into an ion trajectory simulation program. GPU parallel computation techniques were also applied to accelerate the simulation process. With this simulation tool, the dependence of ion-ion reaction rate within 3D quadrupole ion traps on both ion trap operation parameters and the characteristics of reaction pair were investigated. It was found that the m/z values and charge states of ions have significant influences on the reaction rate. Moreover, higher ion-ion reaction rate was achieved under higher trapping voltages and higher buffer gas pressures. Furthermore, secondary reaction and/or neutralization of ETD fragment ions were observed from simulation. The reaction and/or neutralization rate depends on the charge state and m/z of each fragment ion.

Ab initio kinetics and thermal decomposition mechanism of mononitrobiuret and 1,5-dinitrobiuret

Mononitrobiuret (MNB) and 1,5-dinitrobiuret (DNB) are tetrazole-free, nitrogen-rich, energetic compounds. For the first time, a comprehensive ab initio kinetics study on the thermal decomposition mechanisms of MNB and DNB is reported here. In particular, the intramolecular interactions of amine H-atom with electronegative nitro O-atom and carbonyl O-atom have been analyzed for biuret, MNB, and DNB at the M06-2X/aug-cc-pVTZ level of theory. The results show that the MNB and DNB molecules are stabilized through six-member-ring moieties via intramolecular H-bonding with interatomic distances between 1.8 and 2.0 Å, due to electrostatic as well as polarization and dispersion interactions. Furthermore, it was found that the stable molecules in the solid state have the smallest dipole moment amongst all the conformers in the nitrobiuret series of compounds, thus revealing a simple way for evaluating reactivity of fuel conformers. The potential energy surface for thermal decomposition of MNB was characterized by spin restricted coupled cluster theory at the RCCSD(T)/cc-pV∞ Z//M06-2X/aug-cc-pVTZ level. It was found that the thermal decomposition of MNB is initiated by the elimination of HNCO and HNN(O)OH intermediates. Intramolecular transfer of a H-atom, respectively, from the terminal NH2 group to the adjacent carbonyl O-atom via a six-member-ring transition state eliminates HNCO with an energy barrier of 35 kcal/mol and from the central NH group to the adjacent nitro O-atom eliminates HNN(O)OH with an energy barrier of 34 kcal/mol. Elimination of HNN(O)OH is also the primary process involved in the thermal decomposition of DNB, which processes C2v symmetry. The rate coefficients for the primary decomposition channels for MNB and DNB were quantified as functions of temperature and pressure. In addition, the thermal decomposition of HNN(O)OH was analyzed via Rice-Ramsperger-Kassel-Marcus/multi-well master equation simulations, the results of which reveal the formation of (NO2 + H2O) to be the major decomposition path. Furthermore, we provide fundamental interpretations for the experimental results of Klapötke et al. [Combust. Flame 139, 358-366 (2004)] regarding the thermal stability of MNB and DNB, and their decomposition products. Notably, a fundamental understanding of fuel stability, decomposition mechanism, and key reactions leading to ignition is essential in the design and manipulation of molecular systems for the development of new energetic materials for advanced propulsion applications.

Hydroxymethyl radical self-recombination in high-temperature water

The self-recombination reaction of (•)CH2OH radicals in neutral aqueous solution has been studied at temperatures up to 300 °C at a pressure of 220 bar using pulse radiolysis and transient absorption. (•)CH2OH species decay by second-order kinetics independent of the applied dose, with a rate constant at 22 °C of 2k = 1.4 ± 0.1 × 10(9) M(-1) s(-1). The recombination follows Arrhenius behavior with the activation energy (E(a)) 12.7 ± 0.9 kJ/mol and pre-exponential factor of 1.9 ± 0.4 × 10(11) M(-1) s(-1). The overall recombination is significantly slower than the diffusion limit at elevated temperature, meaning that both disproportionation and dimerization channels have significant activation barriers. Ab initio calculations support the inference that the dimerization channel has no energy barrier, but has a large negative activation entropy barrier. The disproportionation channel (giving aqueous formaldehyde) almost certainly involves one or more specific water molecules to lower its activation energy relative to the gas phase.

Ozonolysis reactions of monoterpenes: a variational transition state investigation

The O3-initiated oxidation reactions of α-pinene ([1S,5S]-2,6,6-trimethylbicyclo[3.1.1]hept-2-ene), β-pinene ([1R,5R]-6,6-dimethyl-2-methylenebicyclo[3.1.1]heptane), camphene ([1R,4S]-2,2-dimethyl-3-methylenebicyclo[2.2.1]heptane) and sabinene ([1R,5R]-4-methylene-1-(1-methylethyl)bicycle[3.1.0]hexane), four monoterpenes typically emitted into the atmosphere, were studied at the B3LYP/6-31+G(2d,2p) level of theory. The rate coefficients were calculated on the basis of the variational transition state theory for two kinetic models, in order to investigate the reaction mechanism: first assuming a direct bimolecular reaction and the second, assuming the formation of a prebarrier-complex, which further reacts forming the corresponding molozonide. The barrier heights leading to the formation of exo-conformers of the molozonides of α-pinene and camphene are lower than the barrier heights for the formation of the endo-conformers of these molozonides, whereas the inverse trend is observed for β-pinene and sabinene. The canonical variational rate coefficients are found in reasonable agreement with the experimental data, especially when the prebarrier complexes are considered. Microcanonical variational rate coefficients are also calculated, as a final validation test, being found in an expected agreement with the canonical rate coefficients. The best predictions for the rate coefficients at 298 K, based on the microcanonical variational method, for α-pinene, β-pinene, camphene, and sabine are (in units cm(3) molecule(-1) s(-1)): 6.92 × 10(-17), 1.06 × 10(-17), 4.61 × 10(-19), and 4.81 × 10(-17), respectively. Our results suggest that the prebarrier complex is an important specie in the ozone addition mechanism and should be taken into account for the proper description of the overall kinetics.

Cluster-continuum quasichemical theory calculation of the lithium ion solvation in water, acetonitrile and dimethyl sulfoxide: an absolute single-ion solvation free energy scale

A solvation free energy scale excluding the net electrostatic potential inside the solute cavity is presented.

A theoretical study of the mechanism of the atmospherically relevant reaction of chlorine atoms with methyl nitrate, and calculation of the reaction rate coefficients at temperatures relevant to the troposphere

Computed rate coefficients of the atmospherically important Cl + CH₃ONO₂ → HCl + CH₂ONO₂ reaction reported for the first time.

An experimental and theoretical study of the kinetics of the reaction between 3-hydroxy-3-methyl-2-butanone and OH radicals

Absolute experimental and theoretical rate constants are determined for the first time for the reaction of 3-hydroxy-3-methyl-2-butanone with OH as a function of temperature. The atmospheric implications are discussed.

Towards high-level theoretical studies of large biodiesel molecules: an ONIOM [QCISD(T)/CBS:DFT] study of hydrogen abstraction reactions of CnH2n+1COOCmH2m+1 + H

Recent interest in biodiesel combustion urges the need for the theoretical chemical kinetics of large alkyl ester molecules.

Nanodusty plasma chemistry: a mechanistic and variational transition state theory study of the initial steps of silyl anion–silane and silylene anion–silane polymerization reactions

The aim of the present work is to understand the detailed reaction mechanisms in the growth of nanodusty particles, which is critical in plasma chemistry, physics and engineering.

Influence of the double bond on the hydrogen abstraction reactions of methyl esters with hydrogen radical: an ab initio and chemical kinetic study

This work reports a systematic ab initio and chemical kinetic study of the rate constants for hydrogen atom abstraction reactions by hydrogen radical on the isomers of unsaturated C6 methyl esters.

Cattaneo-type subdiffusion-reaction equation

Subdiffusion in a system in which mobile particles A can chemically react with static particles B according to the rule A+B→B is considered within a persistent random-walk model. This model, which assumes a correlation between successive steps of particles, provides hyperbolic Cattaneo normal diffusion or fractional subdiffusion equations. Starting with the difference equation, which describes a persistent random walk in a system with chemical reactions, using the generating function method and the continuous-time random-walk formalism, we will derive the Cattaneo-type subdiffusion differential equation with fractional time derivatives in which the chemical reactions mentioned above are taken into account. We will also find its solution over a long time limit. Based on the obtained results, we will find the Cattaneo-type subdiffusion-reaction equation in the case in which mobile particles of species A and B can chemically react according to a more complicated rule.

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.

Thermochemical and kinetics studies of the CH3SH+S (3P) hydrogen abstraction and insertion reactions

Sulfur-containing molecules have a significant impact on atmosphere and biosphere. In this work we studied, from the point of view of electronic structure and chemical kinetics methods, the elementary reactions between a methanethiol molecule and a sulfur atom leading to hydrogen abstraction C-S bond cleavage (CH(3)SH+S; R1:→ CH(3)S+SH; R2: → CH(2)SH+SH; R3:→ CH(3)+HS(2)). The geometrical structures of the reactants, products, and saddle points for the three reaction paths were optimized using the BB1K method with the aug-cc-pV(T+d)Z basis set. The thermochemical properties were improved using single point coupled-cluster (CCSD(T)) calculations on the BB1K geometries followed by extrapolation to the complete basis set (CBS) limit. This methodology was previously applied and has given accurate values of thermochemical and kinetics properties when compared to benchmark calculations and experimental data. For each reaction, the thermal rate constants were calculated using the improved canonical variational theory (ICVT) including the zero-curvature (ICVT/ZCT) and small-curvature (ICVT/SCT) tunneling corrections. For comparison, the overall ICVT/SCT reaction rate constant at 300 K obtained with single-point CCSD(T)/CBS calculations for the CH(3)SH+S reaction is approximately 1400 times lower than the isovalent CH(3)SH+O reaction, obtained with CVT/SCT. The reaction path involving the hydrogen abstraction from the thiol group is the most important reactive path in all temperatures.

Dynamic effects dictate the mechanism and selectivity of dehydration-rearrangement reactions of protonated alcohols [Me2 (R)CCH(OH2 )Me](+) (R=Me, Et, iPr) in the gas phase

The gas-phase dehydration-rearrangement (DR) reactions of protonated alcohols [Me2 (R)CCH(OH2 )Me](+) [R=Me (ME), Et (ET), and iPr (I-PR)] were studied by using static approaches (intrinsic reaction coordinate (IRC), Rice-Ramsperger-Kassel-Marcus theory) and dynamics (quasiclassical trajectory) simulations at the B3LYP/6-31G(d) level of theory. The concerted mechanism involves simultaneous water dissociation and alkyl migration, whereas in the stepwise reaction pathway the dehydration step leads to a secondary carbocation intermediate followed by alkyl migration. Internal rotation (IR) can change the relative position of the migrating alkyl group and the leaving group (water), so distinct products may be obtained: [Me(R)CCH(Me)Me⋅⋅⋅OH2 ](+) and [Me(Me)CCH(R)Me⋅⋅⋅OH2 ](+) . The static approach predicts that these reactions are concerted, with the selectivity towards these different products determined by the proportion of the conformers of the initial protonated alcohols. These selectivities are explained by the DR processes being much faster than IR. These results are in direct contradiction with the dynamics simulations, which indicate a predominantly stepwise mechanism and selectivities that depend on the alkyl groups and dynamics effects. Indeed, despite the lifetimes of the secondary carbocations being short (<0.5 ps), IR can take place and thus provide a rich selectivity. These different selectivities, particularly for ET and I-PR, are amenable to experimental observation and provide evidence for the minor role played by potential-energy surface and the relevance of the dynamics effects (non-IRC pathways, IR) in determining the reaction mechanisms and product distribution (selectivity).

Dynamics of chlorine atom reactions with hydrocarbons: insights from imaging the radical product in crossed beams

We present a comprehensive overview of our ongoing studies applying dc slice imaging in crossed molecular beams to probe the dynamics of chlorine atom reactions with polyatomic hydrocarbons. Our approach consists in measuring the full velocity-flux contour maps of the radical products using vacuum ultraviolet "soft" photoionization at 157 nm. Our overall goal is to extend the range of chemical dynamics investigations from simple triatomic or tetraatomic molecules to systematic investigations of a sequence of isomers or a homologous series of reactants of intermediate size. These experimental investigations are augmented by high-level ab initio calculations which, taken together, reveal trends in product energy and angular momentum partitioning and offer deep insight into the reaction mechanisms as a function of structure, bonding patterns, and kinematics. We explore these issues in alkanes, for which only direct reactive encounters are found, and in unsaturated hydrocarbons, for which an addition-elimination mechanism competes with direct abstraction. The results for alkene addition-elimination in particular suggest a new view of these reactions: The only pathway to HCl elimination is accessed by means of roaming excursions of the Cl atom from the strongly bound adduct.

First principle chemical kinetics in zeolites: the methanol-to-olefin process as a case study

To optimally design next generation catalysts a thorough understanding of the chemical phenomena at the molecular scale is a prerequisite. Apart from qualitative knowledge on the reaction mechanism, it is also essential to be able to predict accurate rate constants. Molecular modeling has become a ubiquitous tool within the field of heterogeneous catalysis. Herein, we review current computational procedures to determine chemical kinetics from first principles, thus by using no experimental input and by modeling the catalyst and reacting species at the molecular level. Therefore, we use the methanol-to-olefin (MTO) process as a case study to illustrate the various theoretical concepts. This process is a showcase example where rational design of the catalyst was for a long time performed on the basis of trial and error, due to insufficient knowledge of the mechanism. For theoreticians the MTO process is particularly challenging as the catalyst has an inherent supramolecular nature, for which not only the Brønsted acidic site is important but also organic species, trapped in the zeolite pores, must be essentially present during active catalyst operation. All these aspects give rise to specific challenges for theoretical modeling. It is shown that present computational techniques have matured to a level where accurate enthalpy barriers and rate constants can be predicted for reactions occurring at a single active site. The comparison with experimental data such as apparent kinetic data for well-defined elementary reactions has become feasible as current computational techniques also allow predicting adsorption enthalpies with reasonable accuracy. Real catalysts are truly heterogeneous in a space- and time-like manner. Future theory developments should focus on extending our view towards phenomena occurring at longer length and time scales and integrating information from various scales towards a unified understanding of the catalyst. Within this respect molecular dynamics methods complemented with additional techniques to simulate rare events are now gradually making their entrance within zeolite catalysis. Recent applications have already given a flavor of the benefit of such techniques to simulate chemical reactions in complex molecular environments.

Theoretical reaction kinetics astride the transition between moderate and deep tunneling regimes: the F + HD case

For the reaction between F and HD, giving HF + D and DF + H, the rate constants, obtained from rigorous quantum scattering calculations at temperatures ranging from 350 K down to 100 K, show deviations from the Arrhenius behavior that have been interpreted in terms of tunneling of either H or D atoms through a potential energy barrier. The interval of temperature investigated extends from above to below a crossover value Tc, a transition temperature separating the moderate and deep quantum tunneling regimes. Below Tc, the rate of the H or D exchange reaction is controlled by the prevalence of tunneling over the thermal activation mechanism. In this temperature range, Bell's early treatment of quantum tunneling, based on a semiclassical approximation for the barrier permeability, provides a reliable tool to quantitatively account for the contribution of the tunneling effect. This treatment is here applied for extracting from rate constants properties of the effective tunneling path, such as the activation barrier height and width. We show that this is a way of parametrizing the dependence of the apparent activation energy on temperature useful for both calculated and experimental rate constants in an ample interval of temperature, from above to below Tc, relevant for modelization of astrophysical and in general very low-temperature environments.

Crossing the dividing surface of transition state theory. II. Recrossing times for the atom-diatom interaction

We consider a triatomic system with zero total angular momentum and demonstrate that, no matter how complicated the anharmonic part of the potential energy function, classical dynamics in the vicinity of a saddle point is constrained by symmetry properties. At short times and at not too high energies, recrossing dynamics is largely determined by elementary local structural parameters and thus can be described in configuration space only. Conditions for recrossing are given in the form of inequalities involving structural parameters only. Explicit expressions for recrossing times, valid for microcanonical ensembles, are shown to obey interesting regularities. In a forward reaction, when the transition state is nonlinear and tight enough, one-fourth of the trajectories are expected to recross the plane R = R* (where R* denotes the position of the saddle point) within a short time. Another fourth of them are expected to have previously recrossed at a short negative time, i.e., close to the saddle point. These trajectories do not contribute to the reaction rate. The reactive trajectories that obey the transition state model are to be found in the remaining half. However, no conclusion can be derived for them, except that if recrossings occur, then they must either take place in the distant future or already have taken place in the remote past, i.e., far away from the saddle point. Trajectories that all cross the plane R = R* at time t = 0, with the same positive translational momentum P(R*) can be partitioned into two sets, distinguished by the parity of their initial conditions; both sets have the same average equation of motion up to and including terms cubic in time. Coordination is excellent in the vicinity of the saddle point but fades out at long (positive or negative) times, i.e., far away from the transition state.

Challenges in modelling homogeneous catalysis: new answers from ab initio molecular dynamics to the controversy over the Wacker process

We present here a review of the mechanistic studies of the Wacker process stressing the long controversy about the key reaction steps. We give an overview of the previous experimental and theoretical studies on the topic. Then we describe the importance of the most recent Ab Initio Molecular Dynamics (AIMD) calculations in modelling organometallic reactivity in water. As a prototypical example of homogeneous catalytic reactions, the Wacker process poses serious challenges to modelling. The adequate description of the multiple role of the water solvent is very difficult by using static quantum chemical approaches including cluster and continuum solvent models. In contrast, such reaction systems are suitable for AIMD, and by combining with rare event sampling techniques, the method provides reaction mechanisms and the corresponding free energy profiles. The review also highlights how AIMD has helped to obtain a novel understanding of the mechanism and kinetics of the Wacker process.

Ring-Polymer Molecular Dynamics Rate Coefficient Calculations for Insertion Reactions: X + H2 → HX + H (X = N, O)

The thermal rate constants of two prototypical insertion-type reactions, namely, N/O + H2 → NH/OH + H, are investigated with ring polymer molecular dynamics (RPMD) on full-dimensional potential energy surfaces using recently developed RPMDrate code. It is shown that the unique ability of the RPMD approach among the existing theoretical methods to capture the quantum effects, e.g., tunneling and zero-point energy, as well as recrossing dynamics quantum mechanically with ring-polymer trajectories leads to excellent agreement with rigorous quantum dynamics calculations. The present result is encouraging for future applications of the RPMD method and the RPMDrate code to complex-forming chemical reactions involving polyatomic reactants.