Deuterium nuclear spin

As in the case of hydrogen and tritium, deuterium exhibits nuclear spin isomerism (see Magnetic spin resonance) (14). However, the spin of the deuteron [12597-73-8] is 1 instead of S as in the case of hydrogen and tritium. As a consequence, and in contrast to hydrogen, the ortho form of deuterium is more stable than the para form at low temperatures, and at normal temperatures the ratio of ortho- to para-deuterium is 2 1 in contrast to the 3 1 ratio for hydrogen. 

Similar principles apply to ortho- and para-deuterium except that, as the nuclear spin quantum number of the deuteron is 1 rather than as for the proton, the system is described by Bose-Einstein statistics rather than the more familiar Eermi-Dirac statistics. Eor this reason, the stable low-temperature form is orriio-deuterium and at high temperatures the statistical weights are 6 ortho 3 para leading to an upper equilibrium concentration of 33.3% para-deuterium above about 190K as shown in Eig. 3.1. Tritium (spin 5) resembles H2 rather than D2. 

If deuterio acids are used then ij -HD complexes are formed these are particularly useful in establishing the retention of substantive H-H bonding in the coordinated ligand by observation of a 1 1 1 triplet in the proton nmr spectrum (the proton signal being split by coupling to deuterium with nuclear spin 7 = 1). 

Isotopes of hydrogen. Three isotopes of hydrogen are known H, 2H (deuterium or D), 3H (tritium or T). Isotope effects are greater for hydrogen than for any other elements (and this may by a justification for the different names), but practically the chemical properties of H, D and T are nearly identical except in matters such as rates and equilibrium constants of reactions (see Tables 5.1a and 5.1b). Molecular H2 and D2 have two forms, ortho and para forms in which the nuclear spins are aligned or opposed, respectively. This results in very slight differences in bulk physical properties the two forms can be separated by gas chromatography. 

Notice from Equation 4.113 for I = 1 (deuterium) it is the combination of the symmetric nuclear spin with the symmetric rotational functions which has the higher statistical weight. At high temperature (ortho/para)DEUTERiuM = 2/1, and at low temperature the ortho form predominates. 

It is a fundamental property of atomic particles, such as electrons, protons, and neutrons, to have spins. Spins can be classified as + or spin. For example, a deuterium atom, H, has one unpaired electron, one unpaired proton, and one unpaired neutron. The total nuclear spin = j (from the proton) + j (from the neutron) = 1. Hence, the nuclear spins are paired and result in no net spin for the nucleus. For atoms such as H,... 

Now consider D2. The nuclear spin of a deuteron is 1, and we can have 7=0, 1, or 2. The T— 2 and r=0 nuclear spin functions are symmetric and the T— 1 functions are antisymmetric (Problem 4.24). The ground electronic state must be 2+ (as in H2), and the nuclei are bosons. Hence the 7=0 and T=2 spin functions go with the 7=0,2,4,... rotational levels. Cooling D2 to low temperature in the presence of a paramagnetic catalyst gives molecules with 7=0 and T=0 and 2. Warming this gas in the absence of catalyst gives 7 = 0,2,4,... molecules this modification of D2 is called ortho deuterium. (The convention is to use ortho for the modification with symmetric nuclear spin functions.)... 

When one considers scattering by more than one atom there is the additional complication that the quantity denoted here by b is different for different isotopes and that nuclear spin is also involved in the process. So far as isotope effects are concerned, we will only be concerned with systems where the different isotopes, hydrogen and deuterium, are in predictable positions and so there is no need to analyse the effects of their random distribution in detail. However, in the case of both hydrogen and deuterium, the nuclear spins of the different atoms are, under normal circumstances, randomly arranged. Now the proton has spin and so does the neutron. Thus the combined system can be in a triplet or in a singlet state and the effective value of b is different for the two cases. 

In the case of deuterium, the nuclear spin is 1 and the combined spins of the neutron and the nucleus can be Vi or V. Using an argument analogous to the one given above for hydrogen, one arrives at... 

Figure 4.20 19F NMR spectrum of 4.44- (n-Bu)4N+F 0.5 1 after heating at 150 °C for 1 h in DMSO-c/6 followed by storage at 25 °C for 10 d. The resonances from left to right correspond to anion cryptates with respectively 0, 1, 2, 3, 4, 5 and 6 NH protons replaced by deuterium. The observed multiplicity follows the standard formula multiplicity = 2n/+ 1 where n is the number of H nuclei remaining and /is the nuclear spin quantum number of H, i.e. xh. (Reproduced with permission from [38] 2004 American Chemical Society).

Here and M are the masses of the muon and the nucleus, and p are their magnetic moments, and I is the nuclear spin (1/2 for hydrogen and 1 for deuterium). The reduced mass factor is... 

Figures 1.9a and b demonstrate the effect of proton broadband decoupling in the 13C NMR spectrum of a mixture of ethanol and hexadeuterioethanol. The CH3 and CH2 signals of ethanol appear as intense singlets upon proton broadband decoupling while the CD3 and CD2 resonances of the deuteriated compound still display their septet and quintet fine structure deuterium nuclei are not affected by lH decoupling because their Larmor frequencies are far removed from those of protons further, the nuclear spin quantum number of deuterium is ID = 1 in keeping with the general multiplicity rule (2 nxh+ 1, Section 1.4), triplets, quintets and septets are observed for CD, CD2 and CD3 groups, respectively. The relative intensities in these multiplets do not follow Pascal s triangle (1 1 1 triplet for CD 1 3 4 3 1 quintet for CD2 1 3 6 7 6 3 1 septet for CD3).

We turn now to the corresponding studies of the isotopic species D2 and HD. The deuterium nucleus has spin Id equal to 1, so that the two equivalent deuterium nuclei in D2 have their spins coupled to give total nuclear spin / equal to 2, 1 or 0. The states with / equal to 2 or 0 correspond to ortho-D2, whilst that with / equal to 1 is known as para-T>2. The molecular beam magnetic resonance studies have been performed on para-D2, in the. 1 = 1 rotational level. Formally, therefore, the effective Hamiltonian is the same as that described above for experimental studies of ortho-H2, also in the J = 1 rotational level. There is one extremely important difference, however, in that the... 

As we shall see, each of these two terms, one for each nucleus, describes a second-rank scalar interaction between the electric field gradient at each nucleus and the nuclear quadrupole moment. De Santis, Lurio, Miller and Freund [44] included two other terms which involve the nuclear spins. One is the direct dipolar coupling of the 14N nuclear magnetic moments, an interaction which we discussed earlier in connection with the magnetic resonance spectrum of D2 its matrix elements were given in equation (8.33). The other is the nuclear spin-rotation interaction, also discussed in connection with H2 and its deuterium isotopes. It is represented by the term... 

Cu isotopes both with nuclear spin I-3/2. The nucle r g-factors of these two isotopes are sufficiently close that no resolution of the two isotopes is typically seen in zeolite matrices. No Jahn-Teller effects have been observed for Cu2+ in zeolites. The spin-lattice relaxation time of cupric ion is sufficiently long that it can be easily observed by GSR at room temperature and below. Thus cupric ion exchanged zeolites have been extensively studied (5,17-26) by ESR, but ESR alone has not typically given unambiguous information about the water coordination of cupric ion or the specific location of cupric ion in the zeolite lattice. This situation can be substantially improved by using electron spin echo modulation spectrometry. The modulation analysis is carried out as described in the previous sections. The number of coordinated deuterated water molecules is determined from deuterium modulation in three pulse electron spin echo spectra. The location in the zeolite lattice is determined partly from aluminum modulation and more quantitatively from cesium modulation. The symmetry of the various copper species is determined from the water coordination number and the characteristics of the ESR spectra. 

Use of H-NMR for membrane studies is based on the fact that deuterium nuclei, with spin 1=1, have an electric quadrupole moment. It originates from the asymmetrical charge distribution in the nucleus. In the presence of an external field gradient, which is almost always the case for (deuterium) atoms in molecules, the different orientations of the nuclear spin experience different interaction energies with the quadrupolar field of the environment. 

Ytterbium atoms have been reacted with thermally generated hydrogen or deuterium atoms, with the resultant formation of YbH and YbD (198). The IR pydh stretching-frequency was observed at 1214.9 cm In addition, Yb atom and YbH absorption and emission spectra were observed. The magnetic parameters of YbH were determined from the esr spectra of the molecules (with Yb nuclear spin 1 = 0 and I = Vi) to be gn = 1.9953, gx = 1.9402, AjCH) = 226 MHz, Ax(H) = 224 MHz, Ax[ Yb (I = Vi)] = 5.266 GHz, A, [ Yb (I = Vi)] = 5.724 GHz. The hyperfine parameters indicated that the spin density is less than 20% on the hydrogen, and that the bonding is largely Yb H. ... 

The ortho forms of both hydrogen and deuterium have a small magnetic moment due to the nuclear spins of the two being of the same sense the para forms have none. Nonetheless, hydrogen is essentially diamagnetic as it is without unpaired electrons, and the magnetic moment of a nucleus is very much less than that of an electron. 

For all diatomic molecules, with the exception of hydrogen below 300 K and of deuterium below 200 K, a considerable simplification is possible for temperatures above the very lowest. In the first place, the nuclear spin factor may be ignored for the present (see, however, 24j), since it is independent of temperature and makes no contribution to the heat capacity. The consequence of the nuclei being identical is then allowed for by introducing a s]rmmetry number a, giving the number of equivalent epatial orienta-turns that a tnolecule can occupy as a result of simple rotation. The value of F is 2 for symmetrical diatomic molecules, and for unsymmetrical molecules... 

It is of importance to note that, except for hydrogen and deuterium molecules, the entropy derived from heat capacity measurements, i.e., the thermal entropy, as it is frequently called, is equivalent to the practical entropy in other words, the nuclear spin contribution is not included in the former. The reason for this is that, down to the lowest temperatures at which measurements have been made, the nuclear spin does not affect the experimental values of the heat capacity used in the determination of entropy by the procedure based on the third law of thermodynamics ( 23b). Presumably if heat capacities could be measured right down to the absolute zero, a temperature would be reached at which the nuclear spin energy began to change and thus made a contribution to the heat capacity. The entropy derived from such data would presumably include the nuclear spin contribution of R In (2i + 1) for each atom. Special circumstances arise with molecular hydrogen and deuterium to which reference will be made below ( 24n). 

The thermal entropy of normal deuterium was found to be 33.90 E.u. mole . Normal deuterium consists of two parts of ortho- to one part of para-molecules at low temperatures the former occupy six and the latter nine closely spaced levels. The spin of each deuterium nucleus is 1 unit. Show that the practical standard entropy of deuterium gas at 25 C is 34.62 e.u. mole" (Add the entropy of mixing to the thermal entropy and subtract the nuclear spin contribution.) Compare the result with the value which would be obtained from statistical calculations, using moment of inertia, etc. in Chapter VI. 

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