Frequency isotope effects

The most isotope sensitive motions in molecules are the vibrations, and many thermodynamic and kinetic isotope effects are determined by isotope effects on vibrational frequencies. For that reason it is essential that we have a thorough understanding of the vibrational properties of molecules and their isotope dependence. To that purpose Sections 3.1.1, 3.1.2 and 3.2 present the essentials required for calculations of vibrational frequencies, isotope effects on vibrational frequencies (and by implication calculation of isotope effects on thermodynamic and kinetic properties). Sections 3.3 and 3.4, and Appendices 3.A1 and 3.A2 treat the polyatomic vibrational problem in more detail. Students interested primarily in the results of vibrational calculations, and not in the details by which those results have been obtained, are advised to give these sections the once-over lightly . 

A kinetic isotope effect that is a result of the breaking of the bond to the isotopic atom is called a primary kinetic isotope effect. Equation (6-88) is, therefore, a very simple and approximate relationship for the maximum primary kinetic isotope effect in a reaction in which only bond cleavage occurs. Table 6-5 shows the results obtained when typical vibrational frequencies are used in Eq. (6-88). Evidently the maximum isotope effect is predicted to be very substantial. 

B synchronously moving away from and toward H the H atom does not move (if A and B are of equal mass). If H does not move in a vibration, its replacement with D will not alter (he vibrational frequency. Therefore, there will be no zero-point energy difference between the H and D transition states, so the difference in activation energies is equal to the difference in initial state zero-point energies, just as calculated with Eq. (6-88). The kinetic isotope effect will therefore have its maximal value for this location of the proton in the transition state. 

If the proton is not equidistant between A and B, it will undergo some movement in the symmetric stretching vibration. Isotopic substitution will, therefore, result in a change in transition state vibrational frequency, with the result that there will be a zero-point energy difference in the transition state. This will reduce the kinetic isotope effect below its maximal possible value. For this type of reaction, therefore, should be a maximum when the proton is midway between A and B in the transition state and should decrease as H lies closer to A or to B. 

Values of kH olki3. o tend to fall in the range 0.5 to 6. The direction of the effect, whether normal or inverse, can often be accounted for by combining a model of the transition state with vibrational frequencies, although quantitative calculation is not reliable. Because of the difficulty in applying rigorous theory to the solvent isotope effect, a phenomenological approach has been developed. We define <[), to be the ratio of D to H in site 1 of a reactant relative to the ratio of D to H in a solvent site. That is. 

Methyl- and 2,6-dimethylpyridine as catalysts with sterically hindered a-com-plexes give greater isotope effects (k2n/k2D up to 10.8). Such values are understandable qualitatively, since the basic center of these pyridine derivatives cannot easily approach the C-H group. The possibility of tunneling can be excluded for these reactions, as the ratio of the frequency factors 4h 4d and the difference in activation energies ED—EU (Arrhenius equation) do not have abnormal values. 

Kinetic isotope effect. Calculate the kie for R-H/R-T and R-D/R-T, taking for a carbon-hydrogen bond a stretching frequency of 2900 cm 1. 

Changes in observed CH (CD) stretching frequencies on going from reactant to product are found to be too small and in the wrong direction to account for the observed kinetic isotope effect, and the effect is suggested to be due to increased force constants for lower frequency vibrations, such as for bending (Kaplan and Thornton, 1967). This is consistent with a steric explanation. 

Due to the large factor group spHtting of about 25 cm the bands of the torsional vibration are well separated (Fig. 5) and the isotope effect on the frequency was calculated to about 0.6 cm [131]. Figure 14 clearly demonstrates the broadening and splitting of the and bi components of Vg as... 

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... 

Because fluorine is relatively sensitive to its environment and has such a large range of chemical shifts, considerable changes in chemical shift can be observed when a nearby atom is replaced by an isotope. For example, replacement of 12C by 13C for the atom to which the fluorine is attached, gives rise to a quite measurable shift, usually to lower frequency. A consequence of this isotope effect is the observation that the 13C satellites in a fluorine spectrum are not symmetrical about the 12C—F resonance. 

Observe that all the mechanisms—that is, the classical indirect mechanism and the two quantum ones—predict a satisfactory isotope effect when the proton of the H bond is substituted by deuterium All the damping mechanisms induce approximately a l/y/2 low-frequency shift of the first moment and a 1 / y/2 narrowing of the breadth, which is roughly in agreement with experiment. As a consequence, the isotope effect does not allow us to distinguish between the two damping mechanisms. 

The empirical peak assignments were My confirmed by DFT calculations of the IR spectra ofXRh(CO)2(PH3)2 (X=H and D) complexes. [29] Isotopic effect is clearly seen in Figure 8, which shows the measured spectra and a schematic representation of the frequencies and intensities computed by these model systems. 

An explanation for the isotope effects was given in terms of differences in the zero-point energies of the transition states and the influence of slight reductions of isotope-dependent frequencies on the state sums. 

The first factor is responsible for normal isotope effects, which arise because the bonds being affected by deuteriation are weakened in the transition state, but the absolute effect is greater on the bonds to deuterium rather than protium because the former have higher vibrational frequencies (typically by a factor of ca 1.37). This factor essentially reflects zero-point energy effects, so it becomes progressively more important at lower internal energies. 

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