Para nuclear spin state

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 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... 

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.

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 second part of this equation follows because the proton is a fermion. Thus for the lowest rotational level with J = 0, the nuclear wave function must be the fourth in equation (6.253) with IT = 0. In the second rotational level, on the other hand, i//ns must be symmetric and so corresponds to the triplet spin function. In general, therefore, rotational levels with even J are associated with the singlet nuclear spin state and are called para-H2 (with the lower nuclear statistical weight of one). Rotational levels with odd J have triplet nuclear spin states and are called o/v/w-Iblwith the higher nuclear statistical weight of three). 

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. 

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...

The form of hydrogen with triplet nuclear spin states and odd values of J is called orthohydrogen and the form with singlet nuclear spin state and even values of J is called para-hydrogen. This terminology can be remembered from the fact that in the para form the nuclear spins point in opposite directions, just as do two groups para to each other on a benzene ring. 

In another class of experiments, hyperpolarized states are generated by spin-sensitive chemical reactions. These include para-hydrogen-induced polarization (PHIP) [3-5] and chemically induced dynamic nuclear polarization (CIDNP) [6-8]. The latter involves non-equilibrium nuclear spin state populations that are produced in chemical reactions that proceed through radical pair intermediates. CIDNP s applicability has been focused towards the study of chemical reactions and the detection of surface exposed residues in proteins [9], but has so far remained limited to specialized chemical systems. 

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...

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)... 

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