Spin isomers of hydrogen

Molecular hydrogen occurs in two isomeric forms, one with its two proton nuclear spins aligned parallel (orthohydrogen), the other with its two proton spins aligned antiparallel (parahydrogen). These two forms are often referred to as spin isomers. Molecular hydrogen occurs in two isomeric forms, one with its two proton nuclear spins aligned parallel (orthohydrogen), the other with its two proton spins aligned antiparallel (parahydrogen). These two forms are often referred to as spin isomers. Parahydrogen is in a lower energy state than is orthohydrogen. At room temperature and thermal equilibrium, thermal excitation causes hydrogen to consist of approximately 75% orthohydrogen and 25% parahydrogen. When hydrogen is liquified at low temperature, there is a slow spontaneous transition to a predominantly para ratio, with the released energy having implications for storage. Essentially pure parahydrogen form can be obtained at very low temperatures, but it is not possible to obtain a sample containing more than 75% orthohydrogen by heating. A mixture or 50:50 mixture of ortho- and parahydrogen can be synthesised in the laboratory by passing it over an iron(III) oxide catalyst at liquid nitrogen temperature (77 K) or by storing hydrogen at 77 K for 2-3 hours in the presence of activated charcoal. In the absence of a catalyst, gas phase parahydrogen takes days to relax to normal hydrogen at room temperature while it takes hours to do so in organic solvents. Each hydrogen molecule (H2) consists of two hydrogen atoms linked by a covalent bond. If we neglect the small proportion of deuterium and tritium which may be present, each hydrogen atom consists of one proton and one electron. Each proton has an associated magnetic moment, which is associated with the proton's spin of ½. In the H2 molecule, the spins of the two hydrogen nuclei (protons) couple to form a triplet state known as orthohydrogen, and a singlet state known as parahydrogen. The triplet orthohydrogen state has total nuclear spin I = 1 so that the component along a defined axis can have the three values MI = 1, 0, or −1. The corresponding nuclear spin wavefunctions are | ↑↑ ⟩ , 1 2 ( | ↑↓ ⟩ + | ↓↑ ⟩ ) {displaystyle |uparrow uparrow angle ,{frac {1}{sqrt {2}}}(|uparrow downarrow angle +|downarrow uparrow angle )} and | ↓↓ ⟩ {displaystyle |downarrow downarrow angle } . This uses standard bra–ket notation; the symbol ↑ represents the spin-up wavefunction and the symbol ↓ the spin-down wavefunction, so ↑↓ means that the first nucleus is up and the second down. Each orthohydrogen energy level then has a (nuclear) spin degeneracy of three, meaning that it corresponds to three states of the same energy (in the absence of a magnetic field). The singlet parahydrogen state has nuclear spin quantum numbers I = 0 and MI = 0, with wavefunction 1 2 ( | ↑↓ ⟩ − | ↓↑ ⟩ ) {displaystyle {frac {1}{sqrt {2}}}(|uparrow downarrow angle -|downarrow uparrow angle )} . Since there is only one possibility, each parahydrogen level has a spin degeneracy of one and is said to be non-degenerate. Since protons have spin 1/2, they are fermions and the permutational antisymmetry of the total H2 wavefunction imposes restrictions on the possible rotational states the two forms of H2. Orthohydrogen, with symmetric nuclear spin functions, can only have rotational wavefunctions that are antisymmetric with respect to permutation of the two protons, corresponding to odd values of the rotational quantum number J; conversely, parahydrogen with an antisymmetric nuclear spin function, can only have rotational wavefunctions that are symmetric with respect to permutation of the two protons, corresponding to even J. The para form whose lowest level is J=0 is more stable by 1.06 kJ/mol than the ortho form whose lowest level is J=1. The ratio between numbers of ortho and para molecules is about 3:1 at standard temperature where many rotational energy levels are populated, favoring the ortho form as a result of thermal energy. However at low temperatures only the J=0 level is appreciably populated, so that the para form dominates at low temperatures (approx. 99.8% at 20 K). The heat of vaporization is only 0.904 kJ/mol. As a result, ortho liquid hydrogen equilibrating to the para form releases enough energy to cause significant loss by boiling. Applying the rigid rotor approximation, the energies and degeneracies of the rotational states are given by: E J = J ( J + 1 ) ℏ 2 2 I ;   g J = 2 J + 1 {displaystyle E_{J}={frac {J(J+1)hbar ^{2}}{2I}};{ ext{ }}g_{J}=2J+1} .