Non-linear transition states

Primary isotope effects in non-linear transition states If the transition state is nonlinear, the vibration corresponding to the symmetric stretch looks like 33. Now even for the symmetrical case, the H (D) moves with relatively high... 

Attempts to calculate theoretical values for the isotope effects and their temperature dependence were made using a linear activated complex model and a Sato potential energy surface. Various tunneling corrections were applied but only the Bell model ° predicts the curvature observed in log (fcio/ ii) versus l/T. Similar theoretical isotope effect predictions were found using a non-linear transition state model. 

An insight into the nature of the transition state was provided by deuterium kinetic isotope effect studies in which 1 /1 for conversion of 5-methyl-CPD to 1-methyl-CPD using the perdeuterio compound was used to determine A . Here, log /l = -1.0 - 2450/2.3RT, which indicates hydrogen, and not deuterium, tunneling although the large temperature dependence was also attributed to a non-linear transition state with nearly complete loss of one C-H bending mode (Scheme 6.2). ... 

When the molecular entity involved is a transition state, one of its normal coordinates is the reaction coordinate, motion along which is not opposed by a restoring force. The transition state is situated at a saddle point on the potential energy surface [25, Chap. 5] [26, pp. 101-107], at which A, the force constant for motion along the reaction coordinate is negative and is consequently imaginary, so a non-linear transition state can have no more than... 

Isotope Effects for Linear vs. Non-Linear Transition States... 

More O Ferrall, R. A. "Model Calculations of Hydrogen Isotope Effects for Non-linear Transition States." J. Chem. Soc. B, 785 (1970). 

Non-linear transition states. The operation of the Westheimer effect depends on the transition state being linear. If it is not, the balance of forces that leads to isotopic insensitivity for the real stretching vibration in a symmetrical transition state cannot occur. An obvious... 

Stretching modes of linear and non-linear transition states... 

The proposal that low isotope effects may be associated with bent transition states was made before Westheimer s treatment of linear transition states became available [93]. Nonetheless experimental confirmation would clearly provide evidence in its support. In fact there are a number of reactions, most notably 1,2-hyride rearrangements and carbene and nitrene insertions, for which the consistent observation of small isotope effects can reasonably be ascribed to non-linear transition states [90]. On the other hand the mechanisms of the reactions have not always been entirely clear and it may perhaps be questioned whether a definite and general conclusion can yet be drawn. 

Mechanisms have been suggested for the N-bromosuccinimide (NBS) oxidation of cyclopentanol and cyclohexanol, catalysed by iridium(III) chloride,120 of ethanolamine, diethanolamine, and triethanolamine in alkaline medium,121 and for ruthenium(III)-catalysed and uncatalysed oxidation of ethylamine and benzylamine.122 A suitable mechanism has been suggested to explain the break in the Hammett plot observed in the oxidation of substituted acetophenone oximes by NBS in acidic solution.123 Oxidation of substituted benhydrols with NBS showed a C-H/C-D primary kinetic isotope effect and a linear correlation with er+ values with p = —0.69. A cyclic transition state in the absence of mineral acid and a non-cyclic transition state in the presence of the acid are proposed.124 Sulfides are selectively oxidized to sulfoxides with NBS, catalysed by ft-cyclodextrin, in water. This reaction proceeds without over-oxidation to sulfones under mild conditions.125... 

For an Sn2 reaction, a radical and non-radical can therefore orientate themselves to give a linear transition state which maximizes the interaction of the radical orbitals and the vacant a-orbital of the bond which is broken. These may, however, be difficult for very bulky molecules, where steric hindrance can prevent the orbitals from becoming close enough for efficient overlap (Scheme 2.4). 

This is the first observed behaviour of the type for Vaska s compound, and the higher A 2 values for the less basic phosphines are also unusual and a consequence of the L dissociation mechanism. The linear free-energy relation between and the Hammett polar transition state such as (16). 

The use of this model leads to derived rate constants which exceed the diffusion-controlled limit. Further n.m.r. studies and a reconsideration of earlier published experimental data lead to a new proposal of an associative mechanism for iodide exchange, in which iodide attacks at one end of the tri-iodide. It is possible, from the observed kinetic pattern, that the I so generated has a sufficient lifetime to be considered an intermediate rather than a transition state. A transfer diffusion investigation of the same reaction also culminates in the proposal of an associative mechanism, with a linear transition state. Allowing for the non-spherical nature of the tri-iodide, it is possible to calculate a diffusion-controlled rate constant, which turns out to be the same as the experimentally determined (by this method or from n.m.r.) second-order rate constant. Some calculations on the transition state have been made in connection with this transfer diffusion study of the iodide-tri-iodide exchange reaction. Further study of the iodide-thiocyanate reaction has resulted in an estimate of the association constant for the initial rapid association of the reactants to give the intermediate charge-transfer complex la.SCN-. ... 

Steady-state voltage regulation Acceptable transitent voltage variation Non-linearity characteristics of load current Percentage distortion in voltage Frequency tolerance Power factor of load Inmsh upon switch-on... 

Conjugated polymers are centrosymmetric systems where excited states have definite parity of even (A,) or odd (B ) and electric dipole transitions are allowed only between states of opposite parity. The ground state of conjugated polymers is an even parity singlet state, written as the 1A... PM spectroscopy is a linear technique probing dipole allowed one-photon transitions. Non linear spectroscopies complement these measurements as they can couple to dipole-forbidden trail-... 

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