Spin isomers of hydrogen

thumb|upright=1.2|right|Spin isomers of molecular hydrogen

Molecular hydrogen occurs in two nuclear isomeric forms, orthohydrogen with the nuclear spins of its two protons aligned parallel to each other, and parahydrogen with its two proton spins aligned antiparallel. These two forms can be called spin isomers or more specifically nuclear spin isomers.

Parahydrogen is in a lower energy state than 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 50:50 mixture of ortho- and parahydrogen can be made 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. 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 (approximately 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.

: <math>E_J = \frac{J(J + 1)\hbar^2}{2I};\quad g_J = 2J + 1</math>.

The rotational partition function is conventionally written as:

: <math>Z_\text{rot} = \sum\limits_{J=0}^\infty{g_J e^{-E_J/k_\text{B} T\;</math>.

However, as long as the two spin isomers are not in equilibrium, it is more useful to write separate partition functions for each:

: <math>\begin{align}

Z_{\text{para &= \sum\limits_{\text{even }J}{(2J + 1)e^\\

Z_{\text{ortho &= 3\sum\limits_{\text{odd }J}{(2J + 1)e^

\end{align}</math>

The factor of 3 in the partition function for orthohydrogen accounts for the spin degeneracy associated with the +1 spin state; when equilibrium between the spin isomers is possible, then a general partition function incorporating this degeneracy difference can be written as:

: <math>Z_\text{equil} = \sum\limits_{J=0}^\infty{\left(2 - (-1)^{J}\right)(2J + 1)e^</math>

The molar rotational energies and heat capacities are derived for any of these cases from:

: <math>\begin{align}

U_\text{rot} &= RT^2 \left( \frac{\partial \ln Z_\text{rot{\partial T} \right) \\

C_{v,\text{ rot &= \frac{\partial U_\text{rot{\partial T}

\end{align}</math>

Plots shown here are molar rotational energies and heat capacities for ortho- and parahydrogen, and the "normal" ortho:para ratio (3:1) and equilibrium mixtures:

thumb|250px|Molar rotational energy ER/R in kelvins, or equivalently mean molecular rotational energy εrot/kB in kelvins

thumb|250px|Molar heat capacities; only rotational and spin contribution is shown. Total value is 1.5R higher due to translational degrees of freedom (rotational degrees were included in the rigid rotor approximation itself).

Because of the antisymmetry-imposed restriction on possible rotational states, orthohydrogen has residual rotational energy at low temperature wherein nearly all the molecules are in the J = 1 state (molecules in the symmetric spin-triplet state cannot fall into the lowest, symmetric rotational state) and possesses nuclear-spin entropy due to the triplet state's threefold degeneracy. The residual energy is significant because the rotational energy levels are relatively widely spaced in ; the gap between the first two levels when expressed in temperature units is twice the characteristic rotational temperature for :

: <math>\frac{E_{J=1} - E_{J=0{k_\text{B = 2\theta_\text{rot} = \frac{\hbar^2}{k_\text{B}I} \approx 174.98\text{ K}</math>.

This is the T = 0 intercept seen in the molar energy of orthohydrogen. Since "normal" room-temperature hydrogen is a 3:1 ortho:para mixture, its molar residual rotational energy at low temperature is (3/4) × 2Rθrot ≈ 1091 J/mol, which is somewhat larger than the enthalpy of vaporization of normal hydrogen, 904 J/mol at the boiling point, Tb ≈ 20.369 K. Notably, the boiling points of parahydrogen and normal (3:1) hydrogen are nearly equal; for parahydrogen ∆Hvap ≈ 898 J/mol at Tb ≈ 20.277 K, and it follows that nearly all the residual rotational energy of orthohydrogen is retained in the liquid state.

However, orthohydrogen is thermodynamically unstable at low temperatures and spontaneously converts into parahydrogen. This process lacks any natural de-excitation radiation mode, so it is slow in the absence of a catalyst which can facilitate interconversion of the singlet and triplet spin states. The two forms of molecular hydrogen were first proposed by Werner Heisenberg and Friedrich Hund in 1927. Taking into account this theoretical framework, pure parahydrogen was first synthesized by Paul Harteck and Karl Friedrich Bonhoeffer in 1929 at the Kaiser Wilhelm Institute for Physical Chemistry and Electrochemistry. When Heisenberg was awarded the 1932 Nobel prize in physics for the creation of quantum mechanics, this discovery of the "allotropic forms of hydrogen" was singled out as its most noteworthy application. Further work on the properties and chemical reactivity of parahydrogen was carried out in the following decade by Elly Schwab-Agallidis and Georg-Maria Schwab.

Uses

In infrared spectroscopy

Isolation of pure parahydrogen uses continuous in-vacuum deposition, resulting in millimeters thick solid parahydrogen (p–) samples which are notable for their excellent optical qualities. Parahydrogen is used as a host for matrix isolation studies: since hydrogen interacts weakly with other molecules, the infrared spectrum of these molecules embedded in parahydrogen films has sharp linewidths.

In NMR and MRI

When an excess of parahydrogen is used during hydrogenation reactions (instead of the normal mixture of orthohydrogen to parahydrogen of 3:1), the resultant product exhibits hyperpolarized signals in proton NMR spectra, an effect termed PHIP (Parahydrogen-induced polarization) or, equivalently, PASADENA (Parahydrogen And Synthesis Allow Dramatically Enhanced Nuclear Alignment); named for first recognition of the effect by Bowers and Weitekamp of Caltech), a phenomenon that has been used to study the mechanism of hydrogenation reactions.

Signal amplification by reversible exchange (SABRE) is a technique to hyperpolarize samples without chemically modifying them. Compared to orthohydrogen or organic molecules, a much greater fraction of the hydrogen nuclei in parahydrogen align with an applied magnetic field. In SABRE, a metal center reversibly binds to both the test molecule and a parahydrogen molecule facilitating the target molecule to pick up the polarization of the parahydrogen. This technique can be improved and utilized for a wide range of organic molecules by using an intermediate "relay" molecule like ammonia. The ammonia efficiently binds to the metal center and picks up the polarization from the parahydrogen. The ammonia then transfers the polarization to other molecules that don't bind as well to the metal catalyst. This enhanced NMR signal allows the rapid analysis of very small amounts of material and has great potential for applications in magnetic resonance imaging.

Deuterium

Diatomic deuterium () has nuclear spin isomers like diatomic hydrogen, but with different populations of the two forms because the deuterium nucleus (deuteron) is a boson with nuclear spin equal to one. There are six possible nuclear spin wave functions which are ortho or symmetric to exchange of the two nuclei, and three which are para or antisymmetric. and methylene (CH2), Their ortho:para ratios differ from that of dihydrogen. The ortho and para forms of water have recently been isolated. Para water was found to be 25% more reactive for a proton-transfer reaction.

Molecular oxygen () also exists in three lower-energy triplet states and one singlet state, as ground-state paramagnetic triplet oxygen and energized highly reactive diamagnetic singlet oxygen. These states arise from the spins of their unpaired electrons, not their protons or nuclei.

Spin isomers of hydrogen

Uses

In infrared spectroscopy

In NMR and MRI

Deuterium

References

Further reading