Typography of Orbitals

Question

For mhchem, I need to decide on a typographical representation of orbitals.

Wikipedia tells me, there are atomic orbitals with letters s, p, d, f and g. In a later table, there is even h. Then, there are molecular orbitals with greek letters. Orbital hybridisation uses the letters s, p and sp, sp², sp³.

The IUPAC green book on (printed) page 32 uses upright characters for 1s, 2s, 2p etc. However, in the footnotes on page 19, ‘orbitals r and s’ are in italic. (r? Wikipedia did not tell me about this.)

That is the only occurrence in an IUPAC document I could find via search. Are there more?

There are other occurences in the Blue Book in italic, but they are stereodescriptors. (1s,3s)-cyclobutane-1,3-diol.

A quick search at Google Books revealed the convention of italic font for orbitals, e.g. Organic Chemistry, 2008 or Essentials of Organic Chemistry, 2006, or Orbital Interactions in Chemistry, 2013, all published by Wiley.

However, there are also Molecular Orbitals and Organic Chemical Reactions, 2011 and Discovering Chemistry With Natural Bond Orbitals, 2012 by the same publisher that use an upright font.

Anyhow, I need to decide for one way or the other. Is there any IUPAC document, I could base my decision on? One, that defines the meaning of the letters and not just uses them.

Second question: I need to distinuish orbitals form other notations. Are my following assumptions correct to reliably detect orbital notations?

• Orbitals are always written as number + lower-case letter
• Letters can be s, p, d, f, g, h.
• There is no element entity in chemical notations with these (lower-case) letters. But there is p for proton.
• The letters for abbreviations for organic structure fragments such as ‘c’, ‘m’, ‘p’, ‘r’, ‘s’, and ‘t’ overlap, but they are never written with a number in front of them.

Disclaimer: I am not a chemist and am not familiar with the meaning of all of this. I am interested in the typography, though.

Answer 1

In guidelines published by the International Union of Pure and Applied Physics or IUPAP$^{[1]}$, upright letters are recommended. Whether these letters are capitalised depends on their use. Lowercase is for quantum numbers of a single particle, and uppercase for describing a system.

A letter symbol indicating a quantum number of a single particle should be printed in lower case upright type. A letter symbol indicating a quantum number of a system should be printed in capital upright type.$^{[1]}$

Almost identical text is found in the IUPAC Green Book.$^{[2]}$

The letters themselves ignoring capitalisation are $\mathrm{s}$ – sharp, $\mathrm{p}$ – principal, $\mathrm{d}$ – diffuse, $\mathrm{f}$ – fundamental, $\mathrm{g}$, $\mathrm{h}\ \ldots$ Continue according to the English alphabet skipping letter j.$^{[1]}$

In summary, for orbital angular momentum quantum numbers$^{[1]}$

\begin{align}\begin{split} l\ =\ &0\ \ &1\ \ &2 \ \ &3\ \ &4\ \ &5 \ \ &6\ \ &7\ \ &8 \ \ &9\ \ &10\ \ &11\ \ldots\\ \text{symbol}\ \ \ \ &\mathrm{s}\ \ &\mathrm{p}\ \ &\mathrm{d}\ \ &\mathrm{f}\ \ &\mathrm{g}\ \ &\mathrm{h}\ \ &\mathrm{i}\ \ &\mathrm{k}\ \ &\mathrm{l}\ \ &\mathrm{m}\ \ &\mathrm{n}\ \ &\mathrm{o}\end{split}\tag{for a single particle}\end{align}

\begin{align}\begin{split} L\ =\ &0\ \ &1\ \ &2 \ \ &3\ \ &4\ \ &5 \ \ &6\ \ &7\ \ &8 \ \ &9\ \ &10\ \ &11\ \ldots\\ \text{symbol}\ \ \ \ &\mathrm{S}\ \ &\mathrm{P}\ \ &\mathrm{D}\ \ &\mathrm{F}\ \ &\mathrm{G}\ \ &\mathrm{H}\ \ &\mathrm{I}\ \ &\mathrm{K}\ \ &\mathrm{L}\ \ &\mathrm{M}\ \ &\mathrm{N}\ \ &\mathrm{O}\end{split}\tag{for a system}\end{align}

As an example, here are two ways$^{[1]\ [2]\ [3]}$ of writing the predicted ground state electronic structure$^{[4]}$ of oganesson, element $118$:

$$\ce{Og: [Rn] {5f^{14}}{6d^{10}}{7s^2}{7p^6}\\ Og: [Rn] (5f)^14(6d)^10(7s)^2(7p)^6}$$

Typography regarding spacing is not explicitly stated, but is clear from the examples provided. Nevertheless, if you prefer to use

$$\ce{Og: [Rn] 5f^14 6d^10 7s^2 7p^6},$$

it should be fine as well.

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$[1]$ E. Richard Cohen, Pierre Giacomo. $(1987)$. Symbols, Units, Nomenclature and Fundamental Constants in Physics. ('IUPAP Red Book'). International Union of Pure and Applied Physics. Commission C2 – Sunamco. ($2010$ reprint) (pp 12$-$13)

$[2]$ E. R. Cohen, T. Cvitas, J. G. Frey, B. Holmström, K. Kuchitsu, R. Marquardt, I. Mills, F. Pavese, M. Quack, J. Stohner, H. L. Strauss, M. Takami, A. J. Thor. ($2007$). Quantities, Units, and Symbols in Physical Chemistry. ('IUPAC Green Book'). Third Edition. International Union of Pure and Applied Chemistry. ($2008$ IUPAC & RSC reprint). ISBN: 978-0-85404-433-7. (p 32)

$[3]$ Anne M. Coghill, Lorrin R. Garson. ($2006$). The ACS Style Guide. Effective Communication of Scientific Information. American Chemical Society. DOI: 10.1021/bk-2006-STYG, ISBN: 9780841239999 (print), 9780841228306 (online). (p 256)

$[4]$ 'The Element Oganesson'. $(2016)$. Steve Gagnon. Thomas Jefferson National Accelerator Facility – Office of Science Education. (February 1, 2017)