# Why is the letter J omitted in the spdf... sequence?

Under spherical symmetry, the irreducible representations corresponding to $L = 0, 1, 2, \cdots$ are assigned the letters $\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \cdots$ after which the letters progress in alphabetical order. (The familiar names of the atomic orbitals are also labelled with this sequence of letters.) Therefore, we have:

$$\mathrm{S}, \mathrm{P}, \mathrm{D}, \mathrm{F}, \mathrm{G}, \mathrm{H}, \mathrm{I}, \mathrm{K}, \cdots$$

but as far as I can tell, $\mathrm{J}$ is conspicuously omitted. I am guessing there is a reason behind this - what is it? Is it to avoid confusion with some other $J$, like the total angular momentum quantum number $J$, or is it perhaps based on some typographical argument (J being easily confused with I)?

Omitting j when alphabetically enumerating things has a long tradition.

First of all, the alphabet did not always exist in the form we know it today.

Quoting Wikipedia:

After [...] the 1st century BC, Latin adopted the Greek letters ⟨Y⟩ and ⟨Z⟩ [...] Thus it was during the classical Latin period that the Latin alphabet contained 23 letters:

[no J, V, W]

[...]

It was not until the Middle Ages that the letter ⟨W⟩ [...] was added

[...]

only after the Renaissance did the convention of treating ⟨I⟩ and ⟨U⟩ as vowels, and ⟨J⟩ and ⟨V⟩ as consonants, become established. Prior to that, the former had been merely allographs of the latter.

In some books, this has consequences till today.

The footnotes to the Confession and Catechisms [of the Presbyterian Church], containing the proof texts, are enumerated in the traditional manner, that is, by letters of the alphabet (omitting j and v, as alternative forms for i and u in the Latin alphabet). Source

But even later, long after the letters I and J were considered distinct in terms of proper spelling, their alphabetical order (I preceding J) was not firmly established.

The New General English Dictionary of 1768 had a combined section for I and J, treating both equal with respect to alphabetical order (but not regarding spelling).

Same with Handwörterbuch der allgemeinen Chemie, a German chemistry book printed in 1818.

The latest book, I could find, is the Handwörterbuch der reinen und angewandten Chemie of 1850. This is pretty close to when the letters spdefghik.. must have been defined! (Does anyone know when exactly this was?)

And now, it perfectly makes sense to me. Even if i and j were distinct letters at the time and their order should have been commonly established in the early 20th century, the possibility that some readers could still be confused about what comes first, must have lead to the decision to leave j out.

Update (2017-12)

Concerning the spelling and order of names, I was able to find evidence that is even 100 years younger.

The Berlin telephone book contained a spelling table. The first book of 1890 contained a spelling table that assigned numbers to each letter, omitting the letter J, i.e. I=9 and K=10. That is pretty similar to our orbital labels, isn't it? In the 1903 printing, words were assigned to the letters, but J was still left out. The 1905 printing was the first to include J into the spelling table. (source)

Even the Berlin address book of 1943 did not distinguish between I and J. For instance Jutta is listed before Iwanski. (Interestingly, this book doesn't even use different glyphs for I and J in the Fraktur font.)

Of course, there are many books around that time, and earlier, that sort I before J and that use different glyphs, even if printed in Fraktur (example). Nevertheless, this shows that the convention "I before J", as we know it today, was not firmly established in early 20th century Germany.

• snopes.com/history/american/jstreet.asp Feb 12 '17 at 16:24
• RE: "This is pretty close to when the letters spdefghik.. must have been defined! (Does anyone know when exactly this was?)" I don't see how the spdfghik.. nomenclature could have been worked out before a decent model of the atom was conceived in the early 20th century. I'm sure line spectra were known before then but why certain lines and why the relative intensities varied would have been a mystery. I have no idea what previous nomenclature system might have been used.
– MaxW
Feb 14 '17 at 18:24
• In pretty sure that spectral lines in general go back to the Fraunhofer lines.
– MaxW
Feb 14 '17 at 18:28
• Sorry, just one month late. I spent a long time debating over which answer to accept, and whether I should accept one. Ideally, we would be able to find out when the people who named spdf... named it, and ideally they would have left some written record of why they omitted J. In the (assumed) absence of that, this is the next-best. I think this comes closest to what I was looking for, with all the historical sources. Thanks for sharing! Mar 24 '17 at 22:02

For the azimuthal quantum number (l) of an atom, there is no "j" because some languages do not distinguish between the letters "i" and "j".

L is the total orbital quantum number in spectroscopic notation and uses capital letters. The nomenclature just follows suit with the suborbital notation and skips J since there is no corresponding j.

• Yes, it is because of what @orthocresol mentioned in his post and what you have written. For what it is worth, I looked over the reference given in Wikipedia (Atkins, Paula, Friedman. (2009). 'Quanta, Matter, and Change' (p 106)), and it checks out. see here Would be interesting to know what kind of modern languages do not differentiate between i and j though. Feb 11 '17 at 22:22
• Huh. I always thought it was because i and j look too similar, and j was skipped to avoid interconfusion, as ortho noted. Feb 11 '17 at 22:55
• Mathematicians worldwide do not have the same issue and happily use indexes i and j. Feb 14 '17 at 16:08

Distinguishing between i and j is, as others have mentioned, a rather recent phenomenon, not unlike the distinction between u and v. Especially in German when typesetting in blackletter, the glyphs for capital I and J would be identical and there are still a few (older) road signs around Germany that use a capital J where the letter is in fact an I going by pronunciation (an example would be Jllertissen, but I can’t remember the actual name of the place I saw it).

Some intelligent OpenType fonts such as UnifrakturMaguntia implement quick switches between the two, so that one may type the ‘correct’ letter but the ‘historically accurate’ glyph is used (one would type Illertissen to get Jllertissen in the example above). The font also includes ‘ready-to-use variant fonts’ differing by century; going by the features activated in the 19th century variant the two capital letters were still considered as one in that age. The English language manual also goes on to say:

In some early fraktur texts, j was used at the beginning of a word for both, i and j, while everywhere else i was used for both. [Typesetting adjusted to antiqua rules.]

In der Kajüte ist jemand → Jn der Kaiüte jst jemand.

While the latter was not implemented in historical variants — indicating that according to the designer’s research it was not really common at any point in the history of German blackletter typing — it was nonetheless sufficiently common to be determined worth integrating.

This may serve as further verification that i and j were historically often simply considered variants of each other.

• Having i-j problem in German around 1910 would make a lot of sense. In English i-j were sorted out long before atomic theory was developed. // PS - knew I was never going to be an organic chemist because I don't know German and couldn't read Bilstein.
– MaxW
Feb 12 '17 at 21:19
• @MaxW Yeah, in English i and j represent completely different sounds as they do in French. In most other continental languages, j is what English uses (consonantal) y for, making i and j much more similar — the full-vowel and half-vowel variants of otherwise practically the same sound.
– Jan
Feb 12 '17 at 21:26
• @MaxW No, the differentiation between i and j was definitely done in German around 1910. While, indeed, I found chemistry books that use a font that does not clearly distinguish I and J (books.google.de/…, Inhaber vs. Jod, but i vs. j is clear), there are also plenty of books in roman/antiqua typeface that show chemists had a clear unterstanding of the difference between I and J (books.google.de/… from 1831, Jod vs. Interesse). Feb 14 '17 at 16:04
• @mhchem Inhaber is a very clear-cut case much like Jodeln. Iod/Jod not so much since it stems from Greek io-eidés and thus should have an i etymologically but was pronounced much more like j. But the important point in both my answer and my comment was that there was only one glyph to represent both capital I and J in blackletter. So much like in the history of u and v it would only be the surrounding letters that distinguish which sound was to be represented.
– Jan
Feb 20 '17 at 10:09

When two s-orbitals form bond, we have σ-bond.
When two p(x,y)-orbitals form bond, we have π-bond.
When two d(...)-orbitals form bond, we have δ-bond.
When two f(...)-orbitals form bond, we have φ-bond.

So, similarly, when two g-orbitals form bond, we have γ-bond, h-orbitals form η-bond, i-orbitals form ι-bond, etc...

But what is the Greek character for "j"? There is none. Hence "j" is skipped.

• This is interesting, although it would be more useful if you could think of some sources that support your idea. Jun 29 '17 at 3:23