Deuterium isotope frequency shift

In addition to providing a (not always unambiguous ) identification of the spedes present, the frequency shift of a normal mode upon deuterium substitution can often be used to quickly identify the particular type of atomic displacements constituting the normal mode. An excellent example is a study of NH P-alumina by Bates et alP in which two bands at 168 and 145 cm" were observed in the Raman spectrum. In a similar measurement of a P-alumina crystal containing ND4 ions, the bandcentre of the 168 cm" mode was shifted to 152 cm". If this band were due to a translational mode, the calculated isotopic frequency shift ratio would be... 

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. 

Bigeleisen and Mayer (1947) simplified the reduced partition function by observing that vibrational frequency shifts caused by isotope substitution are relatively small (except when deuterium is substituted for normal hydrogen). When the dimensionless quantity hv/kr is of the order 5 or less (corresponding to a typical 1000 cm vibration at 288 K)—a condition applicable to most geochemical situations. 

For the Fe-S proteins, the frequencies and sulfur Isotope dependence of the Fe-S vibrational inodes can be used to distinguish mononuclear, blnuclear, and tetranuclear clusters. Hydrogen bonding of both Fe-0 and Fe-S clusters can be detected by frequency shifts in deuterium-substituted proteins. 

The introduction of isotopes into a compound alters the coupling pattern and the chemical shifts of the observed spectrum. As shovm in Eigure 1.18, deuterium-induced chemical shift variations have allo ved the estimation of the ratio of isomers 90a-d formed in Eq. (2) vhen R = Ph, R = CHjCOOH, and DCOOD/ Et3N is used for the hydrogen transfer [136]. The three sp -carbons Cl, C2 and C3 each afford a distinct singlet for the four possible isotopomers 90a-d (replacement of by shifts the resonances of the adjacent carbon nuclei to lo ver frequency) [137]. 

For the isotopes of water, the subgroup is Cs, consisting in the identity and mirror-plane operations. The deuterium isotopes can also be used in calculating force constants for simple molecules. However, even for such simple molecules as HCN and DCN, the use of isotopes does not lead to a unique solution of the vibrational problem. It was emphasized23 that a certain chemical intuition and a feel for the relative magnitude of force constants is involved. Additional information could be taken from other isotopes (13C, 15N, I70), and this helps in determination of a unique solution. However, such isotopes cause only small frequency shifts, so that frequency measurements must be extremely precise. It appears, then, that the use of isotopic substitution leads to some uncertainties in determination of force constants. 

Several deuterium isotopic effects are found in solid hydrates, additionally to the frequency shifts on deuteration due to the mass ratio (earlier discussed. Sects. 4.2.6, 4.3, 4.4, 4.5). These isotopic effects are caused by the different vibrational zero point energies, the different tunnelling probabilities, and the differently strong H-bonds of hydrates and deuterohydrates, i.e, stronger bonds for OH A than for OD A interactions . ... 

Wood ( ) analyzed all these results in a semi-theoretical paper in which may be found, at least schematically, the spectral consequences (including deuterium isotope effects) to be expected for linear or bent H-bonded systems having potential functions with single minima, or double minima with either low or high barriers. He Interprets those of his (BPS ) systems which show a splitting of the MU " band as having low-barrier double-minimum potential functions. Wood also shows that the anomolous frequency shift of the 550 cm band on deuteration can be explained on the basis of a well-to-well proton transition occurring in a low-barrier double-minimum potential which is markedly asymmetric. 

Recently, it has also been shown that deuterium isotope effects on chemical shifts can be correlated with OH stretching frequencies calculated in the B3YP/6-31G(d) approximation [60]. 

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