Maybe they should call them, “Formal Wins” ?

In April of this year, Braves reliever Luis Avilan came in with a 5-1 lead in the 8th inning. Eight batters later, he’d given up five runs, blowing the lead. Thankfully for him, the Braves came back in the top of the 9th and reliever David Carpenter nailed down the save. The result: Avilan got credit for the win, even though he was the worst pitcher for the Braves that night. Them’s the rules.

Somewhere, Harvey Haddix is shaking his fist, asking “where is the justice?”

A long time ago, people decided that it wasn’t enough to give a win or a loss to a team. They decided to identify the player – well, actually player at a specific position –  most responsible for the victory or defeat, so as to make the assignment of glory or blame an easier task.

The result is that goaltenders, quarterbacks, and pitchers everywhere now ply their trade knowing that no matter how well they perform, there’s always the possibility that their team can play like crap in front of them and they will still get stuck with an “L” next to their name.

Modern statistical techniques in baseball have progressed to the point where some people confidently assert that we can tease out each individual’s contribution to victory. Still, this is largely only of interest to nerds. Who wants to hear the sportscaster say, “Clayton Kershaw earned 0.63 of a victory for the Dodgers in their 4-1 defeat of the Cubs last night”. Not most people.

Assigning team wins and losses to a single player is an act of bookkeeping that sweeps under the rug the difficult task of assigning which players’ partial contributions to victory (or defeat) are greatest.

I suppose by now you’re wondering what exactly  this has to do with organic chemistry? It’s analogous to Formal charge.

You see, any time we’re dealing with a charged species containing more than one atom, we face the same dilemma as the official scorer in baseball. The molecule bears a charge, that is clear. But where on the molecule does the charge reside? Like a “win” in baseball, that charge MUST be assigned to some individual for bookkeeping purposes. There are no such things as “partial wins” in the official scorer’s handbook: same for formal charge. It must be assigned to some atom on the molecule. Like our sportscaster, sometimes we want a simple metric that sweeps all that partial charge stuff under the rug. Injustices be damned!

Hence the rules for formal charge.

Many times, it works very well. Like assigning a win to Bob Gibson in a 1-0 shutout victory [Note 1], what we lose in oversimplification is gained by an intuitive sense that the atom given the charge bears at least most of the responsibility for that charge. We can also make calculations to see how congruent these results are with reality. With the advent of modern computational techniques, we can calculate charge densities extremely well. From these calculations, it’s easy to see where charge is distributed throughout the molecule. For example, ClO- below; oxygen is more electronegative than chlorine, and therefore not only does it bear a formal negative charge, but oxygen is also the atom which bears the bulk of the negative charge, as borne out by the electron density surface. We can satisfy ourselves that the rules of formal charge are in alignment with the electron density. Justice has been done.

And then, like Avilan’s victory, there are times when applying the rules gives us a situation which bears no true resemblance to the reality of the situation. The classic example is H₃O+ . Where’s the positive charge density (blue)? It ain’t on the oxygen!

This is a common source of confusion. Many times introductory students will draw a reaction where a pair of electrons is moving towards the positively charged oxygen in H₃O+ . That formal charge of +1 does not mean oxygen is actually electron deficient (“electrophilic”). It’s just an accident of our sometimes-flawed bookkeeping system of “formal charge”.  The positive charge is actually distributed among the hydrogens, which are less electronegative than oxygen and therefore bear less electron density.

Just like “scorekeepers wins” do not always accurately convey “contribution to victory”, “formal charge” does not always accurately convey electron density.

More in this post – “Watch Out: Formal Charge Can Lie!”.

P.S. Where does this analogy break down? In baseball, a team will have a maximum of one win or loss in a given game.  However, molecules can potentially bear multiple units of charge, including situations where different atoms on the same molecule bear opposite charges (“zwitterions”) but be neutral overall. The advice to proceed with caution in interpreting formal charges still stands, however.

Note 1.  “On another occasion, Gibson won a 1-0 game and in the locker room [catcher Tim] McCarver told him what a hell of a game he had pitched. Gibson absolutely exploded. “Hell of a game my ass – why don’t you guys score some f**king runs!”  “ From “October 1964” by David Halberstam