How to you show a 3-center 2-electron bond in a Lewis structure?

How would you write $$\ce{PCl5}$$ or other hyper-conjugate molecules as a Lewis structure that indicates 3-center 2-electron bonds?

I have seen depictions [1] for transition metal complexes but not for main group non-metals such as sulfur or phosphorous.

• With dashed lines but in some structures I am puzzled, too. – Alchimista Jun 7 '19 at 14:25
• I started writing an answer, but realized I was rambling, and it was probably better as a comment. My opinion is that Lewis structures are too focused on 2-center-2-electron bonds to easily depict anything else. I feel like in practice, you draw everything as a electron pair and rely on reader experience to detect when things are 3-center-2-electron bonds. – Zhe Jun 7 '19 at 18:58
• I had troubles to convey 3c-2e in TEMPO (in conjunction with a big number of hyperconjugation mesomers) to explain the long life of it in an old threat. And still have them. – Alchimista Jun 8 '19 at 10:41
• @Alchimista - TEMPO? Oh, I see: chemistry.stackexchange.com/a/90993 – Karsten Theis Jun 8 '19 at 10:49
• As a general comment, it's clear that the conventions for Lewis structures that have accumulated over the years are are not internally consistent, but are so well-established that it's too late to change. For example, in second row oxides like $\ce{HNO3}$, octet rule wins over "minimize formal charge", but in the third row, expanded octet is preferred over adding formal charge, as in $\ce{H3PO4}$. For more complex bonding interactions like the two $\pi$ half-bonds in $\ce{O2}$, Lewis structures are completely inadequate. – Andrew Jun 8 '19 at 12:12

What about the probably "not so good" approach might be the bent bond as sometimes seen for diborane?

(source)

The latest recommendation by IUPAC I know, exemplified in rule "GR-1.9 Multi-center bonds":

(Brecher, Pure Appl. Chem., 80, 277-410, 2008; doi 10.1351/pac200880020277, open access)

stating:

"As a matter of convention, any such multi-center character is ignored when producing chemical structure diagrams, and regular bonds connecting pairs of atoms are used instead."

To accommodate Karsten Theis' comment on the initial form of this answer, I would like to add the perspective provided by Robert Grossmann's The Art of Writing Reasonable Organic Reaction Mechanisms. Starting page 270 (2nd edition, 2003) the chapter introducing reactions with transition metals draws attention about "Conventions of Drawing Structures"; highlighting that there are field dependent conventions about what line and dash represent. To quote:

"The conventions for drawing organometallic and inorganic compounds differ in subtle ways from those used to draw “ordinary” organic compounds. The most important difference is the way in which bonds are drawn. In organic compounds, one does not use a line to connect a bond to an atom. In organometallic and inorganic compounds, however, a line sometimes connects an atom and a $$\sigma$$ or $$\pi$$ bond. In this case, the line indicates that the pair of electrons in the $$\sigma$$ or $$\pi$$ bond is shared with the metal also."

(loc. cit. p. 271)

"An even more confusing situation arises in complexes in which the electrons in a $$\pi$$ system spread over three or more atoms are used to make a bond to a metal. In this case, the usual convention is to use a curved line to indicate the $$\pi$$ system and a single line to connect the $$\pi$$ system to the metal, regardless of the number of electrons in the $$\pi$$ system (the organometallic chemists’ convention). However, sometimes the curved line is omitted and single lines are used to connect the metal to each of the atoms in the $$\pi$$ system (the crystallographers’ convention). The representation that would make the most sense to organic chemists, in which a single line represents a two-electron bond and a dative bond is used to show two-electron bonds between each individual $$\ce{C=C}$$ $$\pi$$ bond and the metal, is simply never used."

(loc. cit., p. 271)

"Formal charges are usually omitted in inorganic and organometallic complexes. Only the overall charge on the complex is indicated. For example, formal charges are usually not assigned in Lewis acid–base complexes involving transition metals. The acid–base bond is sometimes indicated by an arrow pointing from the ligand to the metal, but more often it is indicated by an ordinary line."

(loc. cit., p. 271)

This precedes just the section about electron counting (specifically in organometallic compounds with transition metals). I speculate, however, Robert Grossman aiming to highlight differences between "organic" and "organometallic" convention meant does while accidentally deploying does not in the first paragraph.

• For the diborane, if you count 2 electrons per line representing a bond, one structure has the correct electron count and the other (the IUPAC-preferred) doesn't. If you don't expect 2e-3c bonds, this might trip you up. I guess it's the same for coordination compounds. – Karsten Theis Jun 8 '19 at 9:42
• @KarstenTheis Thanks to your comment, the perspective provided by the answer was enlarged. – Buttonwood Jun 8 '19 at 11:21