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The Transition State

A quantitative theory of rate processes has been developed on the assumption that the activated state has a characteristic enthalpy, entropy and free energy the concentration of activated molecules may thus be calculated using statistical mechanical methods. Whilst the theory gives a very plausible treatment of very many rate processes, it suffers from the difficulty of calculating the thermodynamic properties of the transition state. [Pg.402]

Sequences such as the above allow the formulation of rate laws but do not reveal molecular details such as the nature of the transition states involved. Molecular orbital analyses can help, as in Ref. 270 it is expected, for example, that increased strength of the metal—CO bond means decreased C=0 bond strength, which should facilitate process XVIII-55. The complexity of the situation is indicated in Fig. XVIII-24, however, which shows catalytic activity to go through a maximum with increasing heat of chemisorption of CO. Temperature-programmed reaction studies show the presence of more than one kind of site [99,1(K),283], and ESDIAD data show both the location and the orientation of adsorbed CO (on Pt) to vary with coverage [284]. [Pg.732]

It should be emphasized that isomerization is by no means the only process involving chemical reactions in which spectroscopy plays a key role as an experimental probe. A very exciting topic of recent interest is the observation and computation [73, 74] of the spectral properties of the transition state [6]—catching a molecule in the act as it passes the point of no return from reactants to products. Furthennore, it has been discovered from spectroscopic observation [75] that molecules can have motions that are stable for long times even above the barrier to reaction. [Pg.74]

The quasi-equilibrium assumption in the above canonical fonn of the transition state theory usually gives an upper bound to the real rate constant. This is sometimes corrected for by multiplying (A3.4.98) and (A3.4.99) with a transmission coefifiwient 0 < k < 1. [Pg.780]

These equations lead to fomis for the thermal rate constants that are perfectly similar to transition state theory, although the computations of the partition functions are different in detail. As described in figrne A3.4.7 various levels of the theory can be derived by successive approximations in this general state-selected fomr of the transition state theory in the framework of the statistical adiabatic chaimel model. We refer to the literature cited in the diagram for details. [Pg.783]

Evans M G and Polanyi M 1935 Some applications of the transition state method to the calculation of reaction velocities, especially in solution Trans. Faraday Soc. 31 875-94... [Pg.864]

The transition-state spectroscopy experiment based on negative-ion photodetachment described above is well suited to the study of the F + FI2 reaction. The experiment is carried out tln-ough measurement of the photoelectron spectrum of the anion FH,. This species is calculated to be stable with a binding energy of... [Pg.878]

The photoelectron spectrum of FH,is shown in figure A3.7.6 [54]. The spectrum is highly structured, showing a group of closely spaced peaks centred around 1 eV, and a smaller peak at 0.5 eV. We expect to see vibrational structure corresponding to the bound modes of the transition state perpendicular to the reaction coordinate. For this reaction with its entrance chaimel barrier, the reaction coordinate at the transition state is... [Pg.878]

The interplay between favourable reactivity at a collinear geometry and electrostatic forces favouring a T-shaped geometry leads to a bent geometry at the transition state. [Pg.879]

Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle. Figure A3.7.7. Two-dimensional contour plot of the Stark-Wemer potential energy surface for the F + H2 reaction near the transition state. 0 is the F-H-H bend angle.
It is important to recognize that the time-dependent behaviour of tire correlation fimction during the molecular transient time seen in figure A3.8.2 has an important origin [7, 8]. This behaviour is due to trajectories that recross the transition state and, hence, it can be proven [7] that the classical TST approximation to the rate constant is obtained from A3.8.2 in the t —> 0 limit ... [Pg.886]

Chandler D 1978 Statistical mechanics of isomerization dynamics in liquids and the transition state approximation J. Chem. Phys. 68 2959... [Pg.896]

Equation (A3.11.183) is simply a fommla for the number of states energetically accessible at the transition state and equation (A3.11.180) leads to the thenual average of this number. If we imagine that the states of the system fonu a continuum, then PJun, 1 Ican be expressed in tenus of a density of states p as in... [Pg.992]

The inner integral on the right-hand side is just e so equation (A3.11.185) reduces to the transition state partition fiinction (leaving out relative translation) ... [Pg.992]

This is connnonly known as the transition state theory approximation to the rate constant. Note that all one needs to do to evaluate (A3.11.187) is to detennine the partition function of the reagents and transition state, which is a problem in statistical mechanics rather than dynamics. This makes transition state theory a very usefiil approach for many applications. However, what is left out are two potentially important effects, tiiimelling and barrier recrossing, bodi of which lead to CRTs that differ from the sum of step frmctions assumed in (A3.11.1831. [Pg.993]

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. [Pg.1011]

To detemiine k E) from equation (A3.12.9) it is assumed that transition states with positivefomi products. Notmg that / f = p dqf/dt, where p is the reduced mass of the separating fragments, all transition states that lie within and + dq with positive will cross the transition state toward products in the time interval dt = pj dqf p. Inserting this expression into equation (A3.12.9), one finds that the reactant-to-product rate (i.e. flux) through the transition state for momenPim p is... [Pg.1012]

The tenn (E-E ) is tire sum of states at the transition state for energies from 0 to E-E. Equation (A3.12.15) is the RRKM expression for the imimolecular rate constant. [Pg.1013]

The RRKM rate constant is often expressed as an average classical flux tlirough the transition state [18,19 and 20]. To show that this is the case, first recall that the density of states p( ) for the reactant may be expressed as... [Pg.1014]

The inner multiple integral is the transition state s density of states at energy , and also the numerator in... [Pg.1014]

This expression may be inserted into the numerator of the above equation, without altering the equation. Making the above two changes and noting that 8(qj - q ) specifies the transition state, so that the J superscript to the transition state s coordinates and momenta may be dropped, equation (A3.12.21) becomes... [Pg.1015]

The RRKM rate constant written this way is seen to be an average flux tlirough the transition state. [Pg.1015]


See other pages where The Transition State is mentioned: [Pg.375]    [Pg.402]    [Pg.706]    [Pg.706]    [Pg.31]    [Pg.778]    [Pg.779]    [Pg.779]    [Pg.781]    [Pg.781]    [Pg.781]    [Pg.833]    [Pg.833]    [Pg.834]    [Pg.841]    [Pg.842]    [Pg.858]    [Pg.870]    [Pg.871]    [Pg.874]    [Pg.878]    [Pg.878]    [Pg.879]    [Pg.879]    [Pg.883]    [Pg.894]    [Pg.992]    [Pg.1011]    [Pg.1014]   


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Absolute Rate (Transition State) Theory and the Activated Complex

Advanced Topics The Transition State Ensemble for Folding

Ambivalent Lewis structures the transition-state limit

And the transition state

Assumptions and Derivation of the Basic Transition-State Method Expressions

At The Transition State

Beyond Arrhenius to the Eyring Transition State

Conclusion on the General Features of Solid-State Transitions

Conformations of the transition state

Cyclodextrins and other catalysts, the stabilisation of transition states

Cyclodextrins and other catalysts, the stabilization of transition states

Desorption in the Transition State Theory

Energetics of the transition state

Enhanced polarization of the transition state

Enzyme Active Sites Are Most Complementary to the Transition State Structure

Equilibrium Theory of Reaction Rates The Transition-state Method

Exciting the Transition State

Flow without transition to the solid state

Frontier Orbital Interactions in the Transition States of One-Step -Cycloadditions

Frontier Orbital Interactions in the Transition States of One-Step 1,3-Dipolar Cycloadditions Sustmann Classification

Geometry of the transition state

Glass transition and the glassy state

Mapping of the transition-state wavefunction

Nature of the transition state

Noncrystalline state and the glass transition

Oxidation States of the Transition Elements

Photoselective chemistry access to the transition state region

Position of the transition state

Properties of the potential energy surface relevant to transition state theory

Proton transfers in the transition state

Quantitative antihydrophobic effects in water and the geometries of transition states

Reaction in Solution and the Transition-State Theory

Reactivity and development of the transition state

Recrossing of the transition state

Repulsion in the transition state

Saddle Points on the PES. Transition States

Scheme 38. 4-Centered transition state showing the rearrangement of P-ketosilanes

Secondary a-deuterium kinetic isotope effect and the structure of ferrocenylmethyl carbocation type transition state

Spectroscopic Techniques for Measuring Collision-Induced Transitions in the Electronic Ground State of Molecules

Spectroscopy in the transition state region

Stabilization of the transition state

State Transition Diagrams from the Nonlinear Equations

Structure of the transition state

The Active Site and Transition States

The Aldol Addition of Preformed Enolates - Stereoselectivity and Transition-state Models

The Aromatic Transition State

The Mathematics of Transition State Theory

The Nonmetal Atom Sharing Rule of Low-Barrier Transition States

The Reaction Path Hamiltonian and Variational Transition State Theory

The Transition Current Between Two States

The Transition State Theory of Isotope Effects

The Transition-State Theory

The transition-state approach

Theory of the transition state

Thermodynamic Form of the Rate Transition State Expression

Topology of the State Transition Graph

Transition State Geometric Structure in the Adiabatic PT Picture

Transition State Theory Molecular Nature of the Activated Complex

Transition State Theory in the Treatment of Hydrogen Transfer Reactions

Transition from (A, S) to (Ji,J2) coupling for the 2P 2S separated atom states

Transition state for the Cope rearrangment

Transition state for the Diels-Alder reaction

Transition state theory the rate of barrier crossing

Transition states for the Cope rearrangement

Transition states, the stabilization

Transition states, the stabilization of by cyclodextrins and other catalysts

Transition to the solid state

Transition-state theory and the potential of mean force

Transitions between the nuclear spin quantum states - NMR technique

Unit Variability Due to Different Valence States of the Transition Metal Ions

Where is the transition state

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