Rules for Interpreting Up/Down Wedge Bonds

Yesterday I was reminded of an old anecdote about a maths professor. A professor was lecturing an auditorium and writing down a proof. They proclaim at one part "and obviously x infers y". A student raises their hand and asks, "is it obvious?". The professor then studies the equation for 30 minutes until stating "Yes, it is obvious" and continued on with the proof.

chemists and SMILES experts, is the bridge carbon point towards us, or away from us? FC(F)(F)c1ccc(nc1)O[C@H]1C[C@H](C[C@H]12)C([2H])([2H])N2C(=O)c1cccc(F)c1-c1=Nccc=N1 https://t.co/6WwEvUSbkl (cc @jwmay @cdsouthan) pic.twitter.com/93q8TpZA58

— Egon Willighⓐgen (@egonwillighagen) September 1, 2019

Egon asked is the bridge in the following compound up or down? I replied obviously it's pointing down. Since it might not be obvious to everyone I thought I'd explain the three rules to easily assign up/down wedges to other bonds around a stereocentre in 2D.

The insight actually comes from the algorithm used to assign up/down wedges to a depiction. Since only a handful of people have ever had to write such an algorithm I'm not sure how common knowledge it is (i.e. is it actually obvious?).

Rule 1 (D₄)

A tetrahedral centre with four bonds must have alternating up/down bonds. Therefore no mater what the angle if one bond is labelled as up, we know the bond opposite it must also be up, and the two either side must be down (inverse of up).

Rule 2 (D₃)

For three bonds, when bonds are spaced evenly (i.e. all angles < 180 degrees) then all bonds are the same direction, all up, or all down.

Rule 3 (D₃)

For three bonds, when an angle > 180 exists then think about it like the D₄ case with one neighbour missing. The "outside" bonds are opposite direction to the "middle" one.

Exceptions

Like all rules there are exceptions, a well know ambiguity is when we have three bonds and the angle is exactly 180 degrees:

The problem here is you could move the central atom slightly to apply either Rule 2 or Rule 3. Some chemistry toolkits will refuse to read this others will side on the more likely interpretation (Rule 3).

A bigger and perhaps more common issue is mixing up/down wedges with perspective projection. More precisely MDL (and then SYMYX, Accelrys, now BIOVIA) had something known as the "triangle rule". The idea was if you were looking at a molecule in 3D the lengths of the bond would indicate which way round you were looking at it. They imposed this concept on 2D interpretation.

In practice what the this means is these two structures are read as different enantiomers (by BIOVIA) depending on whether the H is inside or outside the "triangle":

You're unlikely to encounter such cases except when a projection is involved. For example for the bridged system pictured below, perspective has been used and we may end up with the H within the "triangle". Note it's the point stored in the file for the atom not the actual "H" glyph that maters.

This isn't to say projections are bad, only that mixing perspective with up/down wedges can be problematic.