Kinetic isotope effects model calculation

Solvolytic experiments specifically designed to test Bartell s theory were carried out by Karabatsos et al. (1967), who were primarily interested in an assessment of the relative contributions of hyperconjugation and non-bonded interactions to secondary kinetic isotope effects. Model calculations of the (steric) isotope effect in the reaction 2- 3 were performed, as well as that in the solvolyses of acetyl chloride... 

The chapter starts with a brief review of thermodynamic principles as they apply to the concept of the chemical equilibrium. That section is followed by a short review of the use of statistical thermodynamics for the numerical calculation of thermodynamic equilibrium constants in terms of the chemical potential (often designated as (i). Lastly, this statistical mechanical development is applied to the calculation of isotope effects on equilibrium constants, and then extended to treat kinetic isotope effects using the transition state model. These applications will concentrate on equilibrium constants in the ideal gas phase with the molecules considered in the rigid rotor, harmonic oscillator approximation. 

The value of the kinetic isotope effect method lies mainly in the possibility of making a substitution within tlve reactive center of the molecule, while still retaining the original type of the read ion, thus allowing the cancellation of many poorly defined quantities in the absolute rate equations and permitting a direct comparison between the measured and calculated values of the relative rate constants. Since the magnitude of these latter values depends on the hypothetical transition state model, a diagnostic means is provided by the method for the experimental verification of the nature of tlie transition state in question. 

The decarboxylation of 3-carboxybenzisoxazole (225 R = H, NO2) gives CO2 and (226). This reaction has been studied using 13C and 15N kinetic isotope effects.201 The isotope effects were modelled theoretically at the semiempirical and ab initio levels, but comparison of experimental and theoretical results shows that die former cannot be successfidly predicted by theory at the level of calculation employed. The kinetics of decarboxylation and deamination of DL-leucine by acidic permanganate in die presence of silver ion in moderately concentrated sulfuric acid is a two-stage process.202 The... 

The mechanism of hydrogen evolution has been investigated by impedance measurements [371] and hydrogen-tritium kinetic isotope effects [375]. The effect of halides dissolved in solution has been studied [372, 376] these ions increase the overpotential in the sequence Cl- Adsorption isotherms for halides have been derived. They conform to the Temkin adsorption model with partial charge transfer. The lateral interaction between adsorbed particles has been calculated. It is higher for Br- than for I- and increases with overpotential on account of the weakening in the metal-halide bond. Thus, halides are substantial poisons for hydrogen evolution on iron. Poisons also include metal ions such as Cd2+, Zn2+, and Mn2+ [26]. 

Enthalpies of activation, transition-state geometries, and primary semi-classical (without tunneling) kinetic isotope effects (KIEs) have been calculated for 11 bimolecu-lar identity proton-transfer reactions, four intramolecular proton transfers, four nonidentity proton-transfer reactions, 11 identity hydride transfers, and two 1,2-intramole-cular hydride shifts at the HF/6-311+G, MP2/6-311+G, and B3LYP/6-311+-1-G levels.134 It has been found that the KIEs are systematically smaller for hydride transfers than for proton transfers. The differences between proton and hydride transfers have been rationalized by modeling the central C H- C- unit of a proton-transfer transition state as a four-electron, three-centre (4-e 3-c) system and the same unit of a hydride-transfer transition state as a 2-e 3-c system. 

The rate coefficient of a reactive process is a transport coefficient of interest in chemical physics. It has been shown from linear response theory that this coefficient can be obtained from the reactive flux correlation function of the system of interest. This quantity has been computed extensively in the literature for systems such as proton and electron transfer in solvents as well as clusters [29,32,33,56,71-76], where the use of the QCL formalism has allowed one to consider quantum phenomena such as the kinetic isotope effect in proton transfer [31], Here, we will consider the problem of formulating an expression for a reactive rate coefficient in the framework of the QCL theory. Results from a model calculation will be presented including a comparison to the approximate methods described in Sec. 4. 

The formaldehyde disproportionation has been examined by semi-empirical MO methods (Rzepa and Miller, 1985). With the MNDO procedure, transfer of hydride from hydrate mono-anion to formaldehyde is exothermic by 109 kJ mol-1, and the transition structure [29], corresponding to near symmetrical transfer of hydride, lies 72 kJ mol -1 above the separated reactants. Inclusion of two water molecules, to model solvation effects, stabilizes reactants and transition structures equally. Hydride transfer from the hydrate dianion was found to have a less symmetrical transition structure [30] not unexpected for a more exothermic reaction, but the calculated activation energy, 213 kJ mol-1, is unexpectedly high. Semi-classical primary kinetic isotope effects, kH/kD = 2.864 and 3.941 respectively, have been calculated. Pathways involving electron or atom transfers have also been examined, and these are predicted to be competitive with concerted hydride transfers in reactions of aromatic aldehydes. Experimental evidence for these alternatives is discussed later. 

The work is divided into several parts. Part A in Sec. II briefly sets out the relevant aspects of the RRKM formulation14 for unimolecular reactions. Rather than repeat the derivation of the equations, emphasis is placed upon the present status of the theory, and the best techniques for carrying out computations simply. In Sec. II-B, characteristics of various model hydrocarbon-type molecular species are outlined and are used in Sec. II-C for theoretical calculations that illustrate various aspects of the theory. Some related aspects of kinetic isotope effects are... 

Recently, we have modeled9 intrinsic carbon kinetic isotope effects on the ornithine decarboxylase-catalyzed decarboxylations. Decarboxylations occur from the pyridoxal 5 -phosphate (PLP) - substrate complexes. These reactions provide a good model case since a number of 13C kinetic isotope effects for the wild-type enzyme and its mutants, as well as for physiological and slow substrates, have been reported.10 Using AM1/CHARMM/MD calculations on nearly 18000-atom models... 

Data for the primary kinetic isotope effect, corresponding to the replacement of the simple aldehyde or ketone by the fully tr-deuterated compound, are roughly in agreement with transition state models in which the proton is not far from being half-transferred. For example, the value observed [6.5 (Hine et al., 1972) 6.7 (Toullec and Dubois, 1974)] for fully dissociated acid-catalysed enolisation of acetone are close to the theoretical maximum value which can be calculated for half proton transfer. 

There exist (4, 5, 8, 9, 27) simple direct relations, between isotope effect, structure, and force field, which do not necessarily require a complete knowledge of all molecular parameters and avoid the solution of the secular equation. These relations are, however, approximations restricted to limited ranges of temperature. [Newer approximation methods, based on expansions in Jacobi polynomials, are applicable over wide ranges of temperatures (6, i6).] In the past, before the ready availability of fast digital computers, tests of the validity of these approximations were usually fairly limited in nature, but recent extensive tests on model calculations of kinetic isotope effects have been carried out 23, 28). In addition, extensive tests of power-series approximations (not considered in the present paper) have now been performed (6,16). 

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