Exploring Reaction Energy Profiles Using the Molecules-in-Molecules Fragmentation-Based Approach
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The Molecules-in-Molecules (MIM) fragmentation-based approach has been successfully used in previous studies to obtain the energies, optimized geometries, and spectroscopic properties of large molecular systems. The present work delineates a protocol to study the potential energy profiles for multistep chemical reactions using the MIM methodology. In a complex multistep chemical reaction, the fragmentation scheme needs to be changed as the reacting species transition into a new reaction step, resulting in a discontinuity in the potential energy curve of the reaction. In our approach, the fragmentation scheme for a particular step in a reaction is chosen on the basis of the nature of the bonding changes associated with that step. Thus, the reactant, transition state, and product are treated consistently throughout the reaction step, leading to an accurate energy barrier for that step. The discontinuity now occurs in describing the energies of reaction intermediates at the transition point between two reaction steps that are treated by two different fragmentation schemes. To address this issue, we propose a systematic procedure for obtaining continuous potential energy curves that are least shifted from their initial positions. The corrected MIM potential energy curves are continuous with activation energies preserved. Following this approach, energy profiles of complex reactions involving large molecular species can be obtained at high levels of theory with a reasonable computational cost.Keywords:
Fragmentation
Transition state
Energy profile
Reaction dynamics
Discontinuity (linguistics)
Transition state theory
Reaction path methods provide a powerful tool for bridging the gap between electronic structure and chemical dynamics. Classical mechanical reaction paths may usually be understood in terms of the force field in the vicinity of a minimum energy path (MEP). When there is a significant component of hydrogenic motion along the MEP and a barrier much higher than the average energy of reactants, quantal tunneling paths must be considered, and these tend to be located on the corner-cutting side of the MEP. As the curvature of the MEP in mass-scaled coordinates is increased, the quantal reaction paths may deviate considerably from the classical ones, and the force field must be mapped out over a wider region, called the reaction swath. The required force fields may be represented by global or semiglobal analytic functions, or the dynamics may be computed "directly" from the electronic structure results without the intermediacy of potential energy functions. Applications to atom and diatom reactions in the gas phase and at gas-solid interfaces and to reactions of polyatomic molecules in the gas phase, in clusters, and in aqueous solution are discussed as examples.
Reaction dynamics
Force Field
Energy profile
Reaction
Reaction coordinate
Polyatomic ion
Potential field
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Recent guided ion beam experiments have revealed interesting reaction dynamics of the HBr+ + CO2 → HOCO+ + Br· reaction under different conditions. The hypothesis is that the predominant reaction mechanism depends on the collision energy between two reactants, the angular momentum of HBr+, and the spin-orbit coupling state of the system. The potential energy profile of the HBr+ + CO2 → HOCO+ + Br· reaction is studied in this research to lay the groundwork for an ab initio molecular dynamics simulation. First, a benchmark potential energy profile of this reaction is identified using coupled-cluster theory extrapolated to the complete basis set limit. A transition state connecting the previously reported intermediates is found, making the potential energy surface of the HBr+ + CO2 → HOCO+ + Br· reaction double-welled. Second, various single reference ab initio methods are compared with the benchmark potential energy profile to search for the most suitable ab initio method for the dynamics simulation. Two combinations of double-ζ basis sets (with effective core potentials) with MP2 and density functional theory have been identified to accurately represent the potential energy profile of this reaction.
Potential energy surface
Energy profile
Coupled cluster
Reaction dynamics
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Isodesmic reaction
Transition state theory
Transition state
Thermochemistry
Hydrogen atom abstraction
Potential energy surface
Reactivity
Hydrogen atom
Reaction coordinate
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Transition state theory
Hydrogen atom abstraction
Transition state
Reaction coordinate
Energy profile
Potential energy surface
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Trajectory calculations run on global potential energy surfaces have shown that the topology of the entrance channel has strong implications on the dynamics of the title reactions. This may explain why huge differences are observed between the rate constants calculated from global dynamical methods and those obtained from local methods that employ the same potential energy surfaces but ignore such topological details. Local dynamics approaches such as transition state-based theories should then be used with caution for fine-tuning potential energy surfaces, especially for fast reactions with polyatomic species since the key statistical assumptions of the theory may not be valid for all degrees of freedom.
Transition state theory
Polyatomic ion
Reaction dynamics
Energy profile
Potential energy surface
Dynamics
Transition state
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Transition state theory
Transition state
Potential energy surface
Reaction coordinate
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Energy correlation diagrams constructed by means of a Diatomics-in-molecules model, based on the minimum basis of atomic states, indicate some unexpected features of the potential energy surfaces governing the C + + O 2 reaction. Confirmation of the early down-hill character of doublet surfaces and the presence of potential wells in C 2v configurations could rise new aspects of the dynamics and mechanism of the reaction, because it is believed that entrance channel effects are very important in this reaction.
Diatomic molecule
Potential energy surface
Reaction dynamics
Energy profile
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Complex molecules often have many structures (conformations) of the reactants and the transition states, and these structures may be connected by coupled-mode torsions and pseudorotations; some but not all structures may have hydrogen bonds in the transition state or reagents. A quantitative theory of the reaction rates of complex molecules must take account of these structures, their coupled-mode nature, their qualitatively different character, and the possibility of merging reaction paths at high temperature. We have recently developed a coupled-mode theory called multi-structural variational transition state theory (MS-VTST) and an extension, called multi-path variational transition state theory (MP-VTST), that includes a treatment of the differences in the multi-dimensional tunneling paths and their contributions to the reaction rate. The MP-VTST method was presented for unimolecular reactions in the original paper and has now been extended to bimolecular reactions. The MS-VTST and MP-VTST formulations of variational transition state theory include multi-faceted configuration-space dividing surfaces to define the variational transition state. They occupy an intermediate position between single-conformation variational transition state theory (VTST), which has been used successfully for small molecules, and ensemble-averaged variational transition state theory (EA-VTST), which has been used successfully for enzyme kinetics. The theories are illustrated and compared here by application to three thermal rate constants for reactions of ethanol with hydroxyl radical—reactions with 4, 6, and 14 saddle points.
Transition state theory
Transition state
Saddle point
Polyatomic ion
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Classical transition state theory (TST) provides the rigorous basis for the application of molecular dynamics (MD) to infrequent events, i.e., reactions that are slow due to a high energy barrier. The TST rate is simply the equilibrium flux through a surface that divides reactants from products. In order to apply MD to infrequent events, corrections to the TST rate that account for recrossings of the dividing surface are computed by starting trajectories at the dividing surface and integrating them backward and forward in time. Both classical TST and conventional MD invoke the adiabatic approximation, i.e., the assumption that nuclear motion evolves on a single potential energy surface. Many chemical rate processes involve multiple potential energy surfaces, however, and a number of ‘‘surface-hopping’’ MD methods have been developed in order to incorporate nonadiabatic transitions among the potential energy surfaces. In this paper we generalize TST to processes involving multiple potential energy surfaces. This provides the framework for a new method for MD simulation of infrequent events for reactions that evolve on multiple potential energy surfaces. We show how this method can be applied rigorously even in conjunction with phase-coherent surface-hopping methods, where the probability of switching potential energy surfaces depends on the history of the trajectory, so integrating trajectories backward to calculate the recrossing correction is problematic. We illustrate this new method by applying it in conjunction with the ‘‘molecular dynamics with quantum transitions’’ (MDQT) surface-hopping method to a one-dimensional two-state barrier crossing problem.
Surface hopping
Potential energy surface
Transition state theory
Energy profile
Transition state
Rectangular potential barrier
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Theoretical investigations have been performed on the kinetics of bimolecular hydrogen-abstraction reactions of 1,3,5-trioxane and 1,4-dioxane cyclic ethers with OH radicals. Hydrogen abstraction from both axial and equatorial positions of 1,3,5-trioxane and 1,4-dioxane was considered. Optimization of the structures, and the calculation of energies, vibrational frequencies and moments of inertia for all the stationary points including reactants, hydrogen-bonded complexes, transition states and products were carried out using density functional theory at the M06-2X level together with the MG3S basis set. Single-point energy calculations on the optimized points were obtained at the CBS-QB3 level. The calculations show that the title reactions proceed through relatively strong hydrogen-bonded complexes due to the hydrogen bonding between the OH radicals and the oxygen atoms of the cyclic ethers. A two-transition state model (an inner tight transition state and an outer loose transition state) was employed to compute the hydrogen-abstraction rate coefficients. The rate coefficients were also computed using conventional transition state theory considering a tight transition state for the purpose of comparison. It was found that when the reactions proceed via inner transition states with relative energies higher than the reactants, the computed rate coefficients are underestimated by conventional transition state theory.
Hydrogen atom abstraction
Trioxane
Transition state
Transition state theory
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