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WIREs Comput Mol Sci
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Reaction path Hamiltonian and the unified reaction valley approach

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Abstract One of the major goals of chemistry is to control chemical reactions with the purpose of generating new compounds with useful properties. Control of a chemical reaction implies a detailed understanding of its mechanism as it results from the breaking and forming of chemical bonds. In practice, it is rather difficult to get a detailed mechanistic and dynamical description of even the simplest chemical reactions. This has to do with the fact that apart from reactants, products, and possible stable intermediates, all other molecular forms encountered during a reaction have such a short lifetime that standard experimental means are not sufficient to detect and describe them. Progress in modern laser spectroscopy seems to provide an access to transient species with lifetimes in the pico‐ to femtosecond region; however, computational investigations utilizing state‐of‐the art methods of quantum chemistry, in particular ab initio methods, provide still the major source of knowledge on reaction mechanism and reaction dynamics. The reaction path Hamiltonian model has proven as a powerful tool to derive the dynamics of a chemical reaction by following the reacting species along the reaction path from reactants to products as traced out on the potential energy surface. In this article, the original reaction path Hamiltonian will be reviewed, extensions and applications over the past decades will be summarized, and a new perspective, namely to use it in form of the unified reaction valley approach to derive a deep and systematic insight into the mechanism of a chemical reaction will be introduced. © 2011 John Wiley & Sons, Ltd. WIREs Comput Mol Sci 2011 1 531–556 DOI: 10.1002/wcms.65 This article is categorized under: Electronic Structure Theory > Ab Initio Electronic Structure Methods

Definition of a reaction phase based on the scalar curvature k(s) plotted along the reaction paths. A reaction phase is defined by a curvature peak and the reaction path range given by the flanking curvature minima.

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Curvature diagram of the barrierless reaction CH2(1A1) + H2CCH2 → cyclopropane. Curvature (blue), some of the adiabatic curvature coupling coefficients (green, red, purple), and reaction phases (exception: van der Waals phase) are shown. B3LYP/6‐31G(d,p) calculations.104

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Curvature diagram for a symmetry‐forbidden reaction: The cycloaddition reaction of HF to ethane. The van der Waals phase is not shown. B3LYP/6‐31G(d,p) calculations.107

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Curvature diagram (top; bottom: enlarged) for a symmetry‐allowed reaction: The Diels‐Alder reaction, B3LYP/6‐31G(d,p) calculations.106

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Curvature diagram for the reaction: SC(H)OH → HSC(H)O. The scalar curvature k(s) is given as a black line, the adiabatic curvature coupling coefficients An,s(s) as colored lines. The transition state is located at s = 0 amu1/2 Bohr. B3LYP/6‐311G(d,p) calculations.89

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Decomposition of the scalar reaction path curvature k(s) (bold black line) of CH3 + H2 reaction terms of adiabatic curvature coupling coefficients An,s(s) (colored lines). The curvature k(s) has been shifted by 0.5 units to more positive values to facilitate the distinction between k(s) and An,s(s). K1–K4 denote the curvature peaks. Vertical lines separate the reaction phases. The position of the transition state corresponds to s = 0 amu½ Bohr. UMP2/6‐31G(d,p) calculations.90

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Strategy of an URVA analysis. (a) Study of the reaction complex requires the analysis of 3K‐6 internal coordinates qn(s). (b) The same information is contained in the direction t(s) and the curvature k(s) of the reaction path. Normal modes lμ(s) or lν(s) can couple with curvature k(s) if properly aligned. (c) To obtain this information, the scalar curvature k(s) is calculated. (d) Dissected into adiabatic curvature couplings An,s(s), which identify all important changes of the internal coordinates qn(s) of the reaction complex. Just few (M < K) rather than 3K‐6 internal coordinates have to be analyzed to describe structural changes of the reaction complex.

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Schematic representation of the three normal modes of the water molecule (from left to right): symmetric OH stretching, asymmetric OH stretching, and HOH bending mode (top); adiabatic OH stretching and HOH bending modes (bottom). Displacement arrows are given not to length scale to illustrate atom movements. Dashed arrows indicate movement of H atoms due to adiabatic relaxation.

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