Curved Arrows (for reactions)

Curved Arrows: The Accounting System For Electron Movement

If you think of electrons as the currency of chemistry, reactions are transactions of electrons between atoms.

Just like double entry book keeping was developed to formalize how financial transactions  are recorded, chemists have developed their own convention for showing transactions of electrons between atoms. This is called the curved arrow formalism.

Previously we covered how we apply the curved arrow formalism to drawing resonance forms. Here, we’re going to show how we can extend it to show reactions. The same principles that applied to resonance forms apply here to reactions, except that unlike resonance forms we’re dealing with actual reactions, not components of a resonance hybrid.

Table Of Contents

1. The Purpose Of The Curved Arrow Formalism
2. The Three Legal Moves
3. Curved Arrows Also Represent A Way of Tracking Changes In Formal Charge
4. Example #1: Lone Pair → Bond
5. Example #2: Bond → Lone Pair
6. Example #3: Bond → Bond
7. Using Multiple Curved Arrows
8. Conclusion: Curved Arrows Are The Accounting System of Organic Chemistry

1. The Purpose Of The Curved Arrow Formalism

When learning any new reaction, I think you always have to start with the “what”. As in what bonds are forming, and what bonds are breaking.

After you answer “what”, then you can start asking “where” – as in , “where are the electrons of the reactants?” What areas are electron rich? What areas are electron poor? There’s going to be attractive interactions between electron-rich and electron-poor areas. Then, you can use electronegativity and resonance to figure out the potential reactions.

But even that only gets you so far. The next step is to understand, “How Do The Electrons Move?”. And for this, we bring back an old tool from our previous discussion of resonance: the curved arrow formalism.   [See article: Using Curved Arrows To Interconvert Resonance Forms]

The purpose of the curved arrow is to show movement of electrons from one site to another.

Electrons move from the tail to the head. Most of the arrows you’ll see have a double-barb at the head, representing the movement of a pair of electrons. (note: there are also single-barbed arrows depicting the motion of a single electron; those are covered in detail here [see In Summary: Free Radicals).

2. The Three Legal Moves

There are only three legal moves you can do with curved arrows. These three moves are for depiction of a pair of electrons moving from:

• lone pair → bond
• bond → lone pair
• bond → bond

Other than a few problematic examples, every reaction you will encounter in Org 1/ Org 2 can be described using a combination of these three “moves”!

This is just like the three moves for drawing resonance curved arrows! [See: How to used Curved Arrows to interconvert resonance forms]

However, unlike drawing resonance forms – which only involve changes in π bonds – the bond here in question can be either a single (sigma) bond or a π  bond.

3. Curved Arrows Also Represent A Way of Tracking Changes In Formal Charge

Curved arrows are also a way of tracking changes in formal charge:

• Since a pair of electrons are being donated from the “tail”, the atom at the tail will have a formal “loss” of one electron, making its charge more positive by 1.
• Also, since a pair of electrons are being accepted at the “head”, the atom at the head will have a formal “gain” of one electron, making its charge more negative by 1.

Here are three general examples of each transaction. There’s a second layer of analysis that can be done here (sigma bond versus π  bond) but that can be saved for later.

See post on How To Calculate Formal Charge

4. Example #1: Lone Pair → Bond

A curved arrow can be used to show the donation of a lone pair to form either a sigma bond or a pi bond.

The example below shows the simplified example of a lone pair on a naked hydroxide ion going to hydronium ion (H+).(Note 1). The arrow shows the formation of a bond between O and H, with electrons from the lone pair on the oxygen. Note the changes in formal charge: the “tail” becomes more positive, and the “head” becomes more negative.

5. Example #2: Bond → Lone Pair

We can also perform the reverse operation, which results in the breakage of a bond to give a new lone pair. The bond that  breaks can be a sigma bond or a pi bond:

The example below shows the  dissociation of water to give H+ and hydroxide ion. Here, the arrow shows the breaking of the O-H bond, to end up as a lone pair on oxygen.

Note the changes in formal charge: at the “tail”, hydrogen goes from “sharing” to “lacking”, thus losing an electron. At the “head”, oxygen goes from “sharing” to “owning”, gaining an electron. We adjust the charges accordingly.

(Why does it break this way? Rule of thumb: bonds generally break so as to put the electrons on the atom that will best stabilize them. Oxygen, being more electronegative than hydrogen (3.5 vs. 2.2) will better stabilize the additional electrons. See Evaluating Resonance Forms – Applying Electronegativity).

6. Example #3: Bond → Bond

Finally, an example of a bond breaking to form another bond. For reactions (as opposed to resonance forms) both sigma and pi bonds can be formed / broken in these arrow-pushing steps:

Below, the arrow shows the breaking of a π bond between C1 and C2, and the formation of a new C–H bond between C1 and H.

Again, the atom at the “tail” (C-1) becomes more positive by 1, and the atom at the head (H+) becomes more negative by 1.

There’s a little problem with this type of curved arrow: the identity of the atom that is forming the new bond (C1 in this case) is somewhat ambiguous.

For this reason, some instructors (myself included) occasionally draw an additional “dotted line” to remove the ambiguity. Others have developed a “bouncy arrow” technique.

7. Using Multiple Curved Arrows

As we’ve said, with any given arrow, the source (tail) becomes more positive (by 1), and the destination (head) becomes more negative (by 1).

However… sometimes (often!!) you will need to draw more than one arrow, in sequence. What do we do about the charges then?

It’s pretty simple, actually: you still only ever need to change two charges.

Here’s an example showing the deprotonation of H-Cl by hydroxide ion.

Here, the HO(-) is “giving away” a pair of electrons, so it becomes more positive by 1 (from -1 to 0) . And the Cl is “accepting” a pair of electrons so its charge goes from neutral (0) to negative (-1). Meanwhile, the H in between is both accepting and donating electrons, so its charge remains the same.

Here’s two more examples – an example with three arrows, and an exaggerated (but plausible) example with six (!!!) arrows. Notice that no matter how many arrows are drawn, only two charges change.

Knowing that you’ll only ever change two formal charges will make electron accounting easier. [Note 2]

8. Conclusion: Curved Arrows Are The Accounting System of Organic Chemistry

So to summarize, this “accounting system” lets us not only account for the bonds that are formed and broken during a reaction, it also lets us keep track of the charges. This is really useful! If you’re given a molecule with these “curved arrows” drawn on it, it’s a lot like a computer program. The arrows give you precise directions on what to do in order to obtain the product.

Notes

Note 1.  I say it’s somewhat artificial because in reality, each of these will be accompanied by a “counter ion” of opposite charge).

Note 2. By the way, I can’t claim credit for this trick: I got it from watching Steven (Freelance Teacher) – here’s his (useful) website and a link to his videos.