The Activated Complex and the Absolute Rate of Chemical Reactions.

Eyring, Henry

doi:10.1021/cr60056a006

Cited by 934 publications

(645 citation statements)

References 4 publications

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“…The rate constants, thus obtained at various temperatures, afforded the free energy of activation DG ‡ or bond rotation by applying the Eyring equation. 33 In all cases investigated, the activation energy DG ‡ was found to be virtually invariant in the given temperature range, thus implying a negligible activation entropy DS ‡ . 34…”

Section: ¢-Isopropyldimethylsilyl-2-(trifluoromethyl)biphenyl (11)mentioning

confidence: 85%

The biphenyl-monitored effective size of unsaturated functional or fluorinated ortho substituents

et al. 2010

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The size of a series of typical substituents has been probed by dynamic NMR measurements of the barriers to aryl-aryl rotation of the corresponding biphenyls. The resulting B values are meaningful because only mono-ortho substituted compounds were investigated and thus the results are not compromised by the non-additivity of multiple steric effects. On the basis of the chosen model system ethynyl and cyano groups were found to be slightly smaller than a phenyl ring. In contrast, vinyl and, in particular, formyl groups proved to be larger than phenyl. The latter difference is due to the loss of conjugation forces at the planar transition state. a-Hydroxyhexafluoroisopropyl is slightly more bulky than tert-butyl. Pentafluorophenyl and trifluoromethoxy exhibit nearly the same effective size as phenyl and methoxy, respectively. Trifluoromethyl is somewhat smaller than isopropyl.

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Section: ¢-Isopropyldimethylsilyl-2-(trifluoromethyl)biphenyl (11)mentioning

confidence: 85%

The biphenyl-monitored effective size of unsaturated functional or fluorinated ortho substituents

et al. 2010

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“…The transmission coefficient κ accounts for dynamical effects that are not included in k TST , such as solvent reorganization kinetics during the dissociation of the metal-water pair (43)(44)(45). Here, we predict κ for each metal isotope using ,…”

mentioning

confidence: 99%

Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems

Hofmann

Bourg

DePaolo

2012

Proc. Natl. Acad. Sci. U.S.A.

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Molecular dynamics simulations show that the desolvation rates of isotopes of Li + , K + , Rb + , Ca 2+ , Sr 2+ , and Ba 2+ may have a relatively strong dependence on the metal cation mass. This inference is based on the observation that the exchange rate constant, k wex , for water molecules in the first hydration shell follows an inverse power-law mass dependence (k wex ∝ m −γ ), where the coefficient γ is 0.05 ± 0.01 on average for all cations studied. Simulated waterexchange rates increase with temperature and decrease with increasing isotopic mass for each element. The magnitude of the water-exchange rate is different for simulations run using different water models [i.e., extended simple point charge (SPC/E) vs. four-site transferrable intermolecular potential (TIP4P)]; however, the value of the mass exponent γ is the same. Reaction rate theory calculations predict mass exponents consistent with those determined via molecular dynamics simulations. The simulation-derived mass dependences imply that solids precipitating from aqueous solution under kinetically controlled conditions should be enriched in the light isotopes of the metal cations relative to the solutions, consistent with measured isotopic signatures in natural materials and laboratory experiments. Desolvation effects are large enough that they may be a primary determinant of the observed isotopic fractionation during precipitation.aqueous geochemistry | kinetic isotope effect | ligand exchange N onequilibrium processes are generally recognized as important influences on isotopic fractionation during mineral precipitation, especially at temperatures below a few hundred degrees Celsius (1, 2). Recent work in "nontraditional" stable isotopes (Li, Mg, Ca, Fe, Cd, Cu, etc.) has confirmed this inference and shown that nonequilibrium fractionation must be accounted for to understand global biogeochemical cycles involving these elements (2-5). A key observation is that light isotopes are preferentially incorporated into precipitating solids (6-8)-the opposite direction of enrichment expected for equilibrium fractionation, which depends on bond energetics (9, 10). The origin of this nonequilibrium light-isotope enrichment is a key unknown in the isotopic geochemistry of mineral growth.Calcite grown from aqueous solutions provides an excellent illustration of light-isotope enrichment during precipitation. Synthetically precipitated and natural samples of calcite and aragonite are fractionated relative to aqueous Ca 2+ such that δ 44/40 Ca in calcite is lower by 0.5-2‰ (7, 11). Equilibrium Ca isotope fractionation between Ca 2+ (aq) and calcite has not been measured in the laboratory, but studies of deep-sea sedimentary pore fluids suggest that the equilibrium fractionation is negligible: ε eq ∼ 0.0 ± 0.1‰ (12). Growth of calcite from seawater-like aqueous solutions is not likely to be diffusion-limited for Ca, so the isotopic effects are inferred to be due to kinetic effects occurring at the solid/fluid interface (11, 13). Diffusion in liquid water can r...

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“…Each transition state is associated with two downhill steepest-descent paths corresponding to positive and negative displacements along the reaction coordinate associated with the unique imaginary normal mode frequency. Following these paths enables us to define the connectivity of the PES in terms of the local minima connected by each transition state, and approximate rate constants can be evaluated for these transitions using statistical rate theory [33][34][35][36].…”

Section: Potential Energy Landscapesmentioning

confidence: 99%

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

Wales

2012

Phil. Trans. R. Soc. A.

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Describing a potential energy surface in terms of local minima and the transition states that connect them provides a conceptual and computational framework for understanding and predicting observable properties. Visualizing the potential energy landscape using disconnectivity graphs supplies a graphical connection between different structure-seeking systems, which can relax efficiently to a particular morphology. Landscapes involving competing morphologies support multiple potential energy funnels, which may exhibit characteristic heat capacity features and relaxation time scales. These connections between the organization of the potential energy landscape and structure, dynamics and thermodynamics are common to all the examples presented, ranging from atomic and molecular clusters to biomolecules and soft and condensed matter. Further connections between motifs in the energy landscape and the interparticle forces can be developed using symmetry considerations and results from catastrophe theory.

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The Activated Complex and the Absolute Rate of Chemical Reactions.

Cited by 934 publications

References 4 publications

The biphenyl-monitored effective size of unsaturated functional or fluorinated ortho substituents

The biphenyl-monitored effective size of unsaturated functional or fluorinated ortho substituents

Ion desolvation as a mechanism for kinetic isotope fractionation in aqueous systems

Decoding the energy landscape: extracting structure, dynamics and thermodynamics

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