Here’s a paradox of paramount importance: which paradigm is right — parahydrogen or para-hydrogen?

Should a hyphen (-) be used to describe this paranormal spin-isomer of hydrogen with ‘parallel’ nuclear spins?

In this post I’ll review the history of the name, present style guides for the use of a hyphen, and risk ripping the field apart in a debate analogous to the Oxford Comma.

“Astonishing Successes” and “Bitter Disappointment” the history of hydrogen’s specific heat

The discovery of hydrogen’s para- and ortho- nuclear spin isomers was the triumph of Werner Heisenberg’s new quantum theory. So much so that the Nobel Prize committee specifically cited this in his award attribution: “for the creation of quantum mechanics, the application of which has, inter alia, led to the discovery of the allotropic forms of hydrogen.” But, as the title of this section suggests, the road to this discovery and subsequent naming of these hydrogen allotropes was studded with some of the greatest minds in physics of the early 20th century. This history is most excellently reviewed in detail by Clayton Gearhart’s 2009 paper of similar title.

With the quickest apologies for making a long and rich story short and bland, please allow some quick context. Combination of the nuclear, translational, rotational, and vibrational quantum states in the hydrogen molecule leads to parity between the nuclear and rotational quantum numbers. This parity results in two separable nuclear spin isomers denoted with the prefixes para- and ortho-. The lower energy state (at cryogenic temperatures) can only occupy even rotational energy modes J = 0,2,4… and the higher energy state (at cryogenic temperatures) can only occupy odd rotational energy modes J = 1,3,5… Spontaneous transition between forms is forbidden due to quantum mechanics so a catalyst or interaction between magnetic dipoles are required for conversion to occur and requires considerable energy transfer associated with the difference between the rotational states (703 kJ/kg for hydrogen below 40 K). This naming convention subsequently resulted in considerable confusion.

The common misconception is what the para- and ortho- prefixes mean. A common assumption is that they are for parallel versus orthogonal, as in the directions of the nuclear spin states of the respective nuclei in this diatomic molecule. While the para- quantum number is often described as anti-symmetric (⇅, up-down, there is only one way to show the spins and they are aligned but opposite). It is more difficult to visualize the spin states with ortho- as there are three ways to show the quantum number, however the spins are symmetric in the same direction, ⇈. Hence the parallel versus orthogonal assumption begins to break down. Historically, para- and ortho- were chosen simply because one state was paranormal or uncommon ‘para-‘ and the other was normal and common ‘ortho-‘ at the typically observed room temperature. For hydrogen para- is less common at room temperature with even rotational energy modes J = 0,2,4… and ortho- is more common at room temperature with odd rotational energy modes J = 1,3,5…

This same naming convention was subsequently applied to deuterium. However, where hydrogen obeys Fermi-Dirac statistics, deuterium obeys Bose-Einstein statistics. This difference results in the lowest energy state of deuterium at cryogenic temperatures (J = 0,2,4…) also being the most prevalent at room temperature and landing the ‘ortho-‘ prefix. Para- for deuterium (J = 1,3,5…) really is uncommon at all temperatures. To make matters worse, tritium follows Fermi-Dirac statistics and the para- versus ortho- convention is the same as hydrogen. At least one major publication on the specific heats of hydrogen and deuterium made the mistake of assuming para- was also the J = 0,2,4… form for deuterium. Thankfully, the non-isotopic molecules hydrogen-deuteride (HD), hydrogen-tritide (HT) and deuterium-tritide (DT) have no nuclear spin isomers or potential for ortho- versus para- confusion.

If you’re confused you’re not alone. To try to address this inconvenient naming convention and reduce human error, P. Clark Souers chose to replace the para- ortho- prefixes with J = 0,2,4… and J = 1,3,5… in his excellent book, “Hydrogen Properties for Fusion Energy.” While technically correct and more likely to reduce error, the percentage of the population that knows statistical thermodynamics and what J = 0,2,4… means is extremely low. Some things are just hard.

Proper use of hyphenation

Although the historical precedent is to use parahydrogen and orthohydrogen when denoting the spin isomers, a quick literature search of journal publications shows para-hydrogen and ortho-hydrogen increasing with use over the last several decades, particularly in chemistry journals. In chemistry para- and ortho- are often used to describe different molecule arrangements where these prefixes are essential to get right for the sake of geometry. But with hydrogen we’ve already established that the geometry assumption is not appropriate when considering the historical context.

So to resolve this conundrum and determine whether we’re crazy dropping the hyphen or not let’s refer to The American Psychological Association handy style guide for use of hyphenation. In short, a hyphen is used:

  1. If a compound adjective can be misread. Example: Is your heavy metal detector heavy? Or does it detect heavy metals? Correct use of hyphen would be heavy-metal detector.
  2. If a temporary compound is used as an adjective before a noun and can be misread. Example: The compound used a two part separator process. Does the process have two parts or does the separator?
  3. If a compound adjective follows a term, do not use a hyphen, because the relationships are clear without one. Example: t-test results versus results from the t tests.
  4. Write most words formed with prefixes and suffixes as one word, except when the prefix and root end and begin with vowels. Example: paranormal, orthogonal,  etc.
  5. When two or more common modifiers have a common base, this base is sometimes omitted in all but the last modifier but is retained. Example: 2-, 3-, and 10-min trials.

A more rigorous style guide is available here.

So parahydrogen or para-hydrogen?

Applying the above style guide to our current debate it’s clear that principles 1-3 do not apply. Principle 4 says use parahydrogen and orthohydrogen. However, since these are often applied in serial lists the editors of chemistry journals have tended towards Principle 5 and use para- and ortho-hydrogen similar to other chemical compounds. Recall that this use based on molecular geometry should not apply to hydrogen, making this not the common modifier usage we see in chemistry. Why is it that I have to explain to chemists that hydrogen is a terrible base?

In the end, use parahydrogen and orthohydrogen without hyphens when hydrogen is added to the end (rule #4). Use para- and ortho- with a hyphen if hydrogen doesn’t appear after (rule #5). Finally, use para-orthohydrogen and ortho-parahydrogen to convert between the two rules.