Ortho nuclear spin state

In very pure hydrogen, there can be hardly any permanent chemical change produced by irradiation. However, the ion-molecule reaction (5.1) does occur in the mass spectrometer, and it is believed to be important in radiolysis. The H2 molecule can exist in the ortho (nuclear spin parallel) or para (antiparallel) states. At ordinary temperatures, equilibrium should favor the ortho state by 3 1. However, the rate of equilibration is slow in the absence of catalysts but can be affected by irradiation. Initially, an H atom is produced either by the reaction (5.1) or by the dissociation of an excited molecule. This is followed by the chain reaction (H. Eyring et al, 1936)... 

H2 (the simplest possible compound) also exhibits a well-known S0 0 associated with the ortho para distribution of nuclear spins in the crystalline lattice, arising from the fact that each H nucleus (proton) has intrinsic nuclear spin I = According to the Pauli restriction for identical fermions, the two nuclear spins of diatomic H2 can couple into singlet ( ortho ) or triplet ( para ) spin states in statistical 3 1 proportions. Because the nuclear spin couplings are essentially independent of the electronic interactions that lead to formation of molecules and crystals, the ortho and para nuclear spin states distribute randomly throughout the H2 lattice, leading to conspicuous S0 7 0. 

The requirement set by the exclusion principle, given in equation (6.235), restricts the nuclear spin states which can combine with a rotational level of a given parity. They can be either symmettic or antisymmettic with respect to Pu. The number of symmetric (ortho) states is always greater than the number of antisymmetric (para) states. For equivalent nuclei with spin I, ... 

The overall symmetry of a given level must be antisymmetric with respect to the permutation P 2 of the two H nuclei to satisfy the Pauli principle. The + and -parity combinations defined by equation (8.202) are antisymmetric and symmetric respectively with respect to P 2 (because the electronic wavefunction has u character, see equation (8.251)). Since the ortho and para nuclear spin states are symmetric and antisymmetric respectively, we see that the + parity states combine with the ortho... 

As the ortho-para conversion involves the forbidden triplet-singlet transition in the nuclear spin state, spontaneous transformation is very slow. Thus, samples of hydrogen that have been cooled exhibit the proportion of the two forms corresponding to the equilibrium composition at room temperature. The conversion of the ortho molecules to para molecules and vice versa requires the simultaneous breaking of both the spin and orbital symmetries, and the equilibrium ratio is therefore established slowly. 

At 0 K, J = 1 for ortho-hydrogen, and 2J + 1 = 3. These three rotational states combine with the three nuclear spin states to yield nine quantum states available to the 0-H2 molecule at 0 K. In normal hydrogen, the f mole fraction of 0-H2 is evenly distributed over all nine of these states. On the other hand, for P-H2 at 0 K, J = 0 and 2J + 1 = 1. This one rotational state combines with the one nuclear spin state to yield a single quantum state that is available to the P-H2 molecule. The entire mole fraction of P-H2 in n-H2 occupies this single quantum state at 0 K. 

Table 5.5 Allowed combinations of nuclear-spin states and rotational states for H2 and D2 molecules and their ortho-para designations. Anti-symmetric is abbreviated by AS and symmetric by S / is the total molecular nuclear spin and J the rotational quantum number and 4>i are the rotationtil tmd nuclear-spin wave functions, respectively. The table is adapted from [96] by permission of the American Physical Society...

Figure 7 The symmetry-based selection rules applied to ZEKE spectroscopy are borne out by the different spectra obtained using the ortho- and para-nuclear spin states of ammonia.

Figure 5.18 Nuclear spin statistical weights (ns stat wts) of rotational states of various diatomic molecules a, antisymmetric s, symmetric o, ortho p, para and rotational, nuclear spin...

For C22H2, the nuclear spin of C12 is zero and contributes a factor of 1 to the nuclear statistical weights. The statistical weights are therefore the same as in H2. For the ground vibronic state, the even J levels are s and have nuclear statistical weight 1, corresponding to the one possible ns the odd J levels are a and have nuclear statistical weight 3. The usual selection rule (4.138) holds for collisions as well as radiative transitions, and we have ortho and para acetylene. The two forms have not been separated. 

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.)... 

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