Isotopes and transition

In the present discussion we present a brief review of the fundamental equations as well as some of the basic and very important aspects in relation to the Mossbauer isotopes and transitions. Instrumentation and spectral analysis through a routine application of the method, follows in Sect. 7 by some representative applications to inorganic materials. This paper is not intended to be an extensive summary of the literatura data on the problem but aims to indicate what kind of information one can obtain from Mossbauer spectra, especially from those involving Fe, Sn, Te and Sb Mossbauer isotopes. The authors consider the topics discussed here to be of practical interest for chemists and material science engineers. 

The individual experiments are compiled in Table 1, which is arranged in the order of elements and gives the isotopes and transitions that were investigated. A separate column shows the production reactions and the accelerator or reactor facility used for the on-line work. As the most extensive experimental program is concentrated at ISOLDE, the standard setup for these measurements will be outlined in the following. 

Studies of the molar volumes of perdeuteriated organic compounds might be expected to be informative about non-bonded intermolecular forces and their manifestations, and such studies might be considered to obviate the necessity of investigating steric isotope effects in reacting systems. The results from non-reacting systems could then be simply applied to the initial and transition states in order to account for a kinetic steric isotope effect. 

Lubell, D., Jackes, M., Schwarcz, H., Knyf, M. and Meiklejohn, C. 1994 The Mesolithic-Neolithic transition in Portugal isotopic and dental evidence oiAiA.Journal of Archaeological Science 21 201-216. 

Zn) and Ga( Zn) isotopes, the transition to the superconducting state leads to a change of the electron density on the metal sites, above the transition the center shift is determined by SOD, below by the influence of Bose condensation, a correlation between the change in electron density and the temperature of the transition to the superconducting state is found... 

Specifically, following the rate expression of QTST in Eq. (4-1) and assuming the quantum transmission coefficients the dynamic frequency factors are the same, the kinetic isotope effect between two isopotic reactions L and H is rewritten in terms of the ratio of the partial partition functions at the centroid reactant and transition state... 

Deuterium kinetic isotope effects, secondary, and transition state structure, 31,143 Diazo compounds, aliphatic, reactions with acids, 5, 331... 

Secondary Deuterium Kinetic Isotope Effects and Transition State Structure... 

Several monographs2-5 have detailed discussions dealing with heavy-atom and primary and secondary hydrogen-deuterium kinetic isotope effects. The monograph by Melander and Saunders5 covers the entire area particularly well. For this reason, only a brief summary of the theory of kinetic isotope effects as well as their important uses in the determination of reaction mechanism and transition-state geometry will be presented. 

Neither of these vibrations corresponds to stretching vibrations of AH or BH. The antisymmetric vibrational mode represents translational motion in the transition state and has an imaginary force constant. The symmetric transition-state vibration has a real force constant but the vibration may or may not involve motion of the central H(D) atom2,12 13. If the motion is truly symmetric, the central atom will be motionless in the vibration and the frequency of the vibration will not depend on the mass of this atom, i.e. the vibrational frequency will be the same for both isotopically substituted transition states. It is apparent that under such circumstances there will be no zero-point energy difference... 

The partition function ratios needed for the calculation of the isotope effect on the equilibrium constant K will be calculated, as before, in the harmonic-oscillator-rigid-rotor approximation for both reactants and transition states. One obtains in terms of molecular partition functions q... 

It is important to point out once again that explanations (rationalizations) of isotope effects which employ arguments invoking hyperconjugation and/or steric effects are completely equivalent to the standard interpretation of KIE s in terms of isotope independent force constant differences, reactant to transition state. In turn, these force constant differences describe isotope dependent vibrational frequencies and frequency differences which are not the same in reactant and transition states. The vibrational frequencies determine the partition functions and partition function ratios in the two states and thus define KIE. The entire process occurs on an isotope independent potential energy surface. This is not to claim that the... 

If isotope effects arise solely from the difference between isotopic zero-point energy differentials in the reactant state and transition state, with no role of excited vibrational states, then - A5p) = 0 on the Eyring model and Ah = Ad on the Arrhenius model. Thus ... 

Glad, S.S. and Jensen, F. (1997). Kinetic isotope effects and transition state geometries. A theoretical investigation of E2 model systems. J. Org. Chem. 62, 253-260... 

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