I have several times used arrow pushing on these blogs. But since the rules for this convention appear to be largely informal, and there appears to be no definitive statement of them, I thought I would try to produce this for our students. This effort is here shared on my blog. It is what I refer to as the standard version; an advanced version is in preparation. Such formality might come as a surprise to some; arrow-pushing is often regarded as far too approximate to succumb to any definition, although it is of course often examined.
The rules above are terse, and in particular I have not tried to add more than one example, although quite a number are sprinkled throughout this blog.
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Thanks for the analysis, Henry. I discovered how intricate the rules of electron-flow arrows are when I wrote an algorithm for calculating the products of e-flow arrows acting on one or more compounds. The algorithm turned out to be remarkably complex, especially when it had to handle errors that students made in their arrow-drawing, such as an arrow starting at H(+). Here is an alternative analysis from yours.
1. An electron-flow arrow can represent the movement of one or two electrons.
2. An electron-flow arrow can begin at either an atom or a bond, called the electron source. (In the first case, some chemists prefer to show the arrow beginning at an unshared electron or lone pair of the source atom, rather than at the atomic symbol itself, but the two representations have the same meaning.)
3. An electron-flow arrow can end at an atom, an existing bond, or an incipient bond between two atoms, called the electron sink.
4. An electron-flow arrow originating at an atom A can point to another atom B if and only if the two atoms do not already share a bond.
4a. If the electron-flow arrow is a two-electron arrow, then this representation is exactly equivalent to the arrow pointing from A to an incipient A...B bond. (See below.)
4b. If the electron-flow arrow is a one-electron arrow, then this representation indicates an electron transfer from A to B. In this case, the formal charge of A increases by one, and the formal charge of B decreases by one.
5. An electron-flow arrow originating at an atom A can point to an existing bond or an incipient bond if and only if A participates in that bond or incipient bond, i.e., the sink bond or incipient bond is A-B or A...B. If the electron-flow arrow is a two-electron arrow, then the formal charge of A increases by one, and the formal charge of B decreases by one.
6. An electron-flow arrow originating at a bond A-B can point to an atom if and only if that sink atom is A or B. If the electron-flow arrow is a two-electron arrow, then, calling the sink atom A, the formal charge of A decreases by one, and the formal charge of B increases by one.
7. An electron-flow arrow originating at a bond A-B can point to another bond or incipient bond if and only if one of the atoms of the source bond is participating in the sink bond or incipient bond, i.e., the sink bond or incipient bond is B-C or B...C. If the electron-flow arrow is a two-electron arrow, then the formal charge of A increases by one, and the formal charge of C decreases by one.
8. It is improper to show an electron-flow arrow beginning at an atom with no unshared valence electrons. It is also improper to show a two-electron electron-flow arrow beginning at an atom with only one unshared valence electron.
9. It is improper to show an odd number of one-electron electron-flow arrows originating at a bond or pointing to a bond or incipient bond. (Experienced chemists will sometimes violate this rule, omitting the one-electron electron-flow arrows pointing in a particular direction. For example, for the atom abstraction reaction A· + B-C -> A-B + C·, an experienced chemist may draw only the electron-flow arrows from A to A...B and from B-C to C, and omit the one from B-C to A...B. Beginners are strongly encouraged to follow this rule.)
10. If an atom has an octet (duet for H), it is improper to show that atom accepting a new bond (or accepting an increase in the order of an existing bond) unless another bond to that atom is simultaneously broken. (Heavier elements such as P, S, etc. may break this rule.)
I should mention that the MarvinSketch applet by ChemAxon incorporates several of the structures in this scheme, for example, by disallowing an electron-flow arrow from A-B from pointing to a bond C-D.
Wonderful Bob. It is great to hear from others that are exploring arrow pushing in this way!
1. I agree that the convention quantises the electron movement into either 1 or 2 electrons. It is difficult to see how we could cope if that were not true. But juxtaposed onto rule 10, it does eventually cause problems.
10. The convention is that higher main group elements such as P,S be forced by the above rules to accept more electrons and hence violate the octet rule. In reality for those elements, the octet rule is not violated. What actually breaks down is the assumption that electrons move only in packs of two (for closed shell reactions). In something a simple as "P(V)", the bonds in this molecule are not two-electron shared bonds, and so any arrows involved in creating a "P(V)" cannot be either.
But I think we can all see that if we allow any given arrow to deviate from being a pair, any convention using them would get very messy. I guess we have to accept such approximations in the interests of having this convention.
I would also mention that planning for the celebration of the centenary of the shared electron bond, first suggested by G. N. Lewis in 1916, is under way. Look out for a one day conference being organised by myself for March 2016 in London! We have a fantastic set of speakers already lined up, and more to come!
I generally agree with your comment on #10, although when I said, "Heavier elements such as P, S, etc. may break this rule," I was referring to the rule about accepting an additional bond, not the octet rule.
It is important to remember that the electron-flow arrow convention relies on the approximation that all bonds are two-electron, two-atom affairs. We are all aware that this approximation works most of the time, but it breaks down in certain situations (e.g., heavy elements, transition metal complexes [try using electron-flow arrows to describe the reaction of H2O with Cl2Pd(CH2=CH2)], oligomeric organolithium and Grignard reagents). Those are the situations when the electron-flow arrow convention will likewise be insufficient. I think it's unwise for us to try to make the electron-flow arrow convention apply to situations where the underlying assumptions on which it is built don't apply. Having said all that, I will continue to tell my students that we can use electron-flow arrows to describe the reactions of P and S, even though we may superficially violate the octet rule in doing so.
Very useful exercise Henry, thank you. The use of a dotted line to represent a bond being formed is a a really useful convention, especially for students just beginning to learn how to draw curly arrow mechanisms. It is a shame that many textbooks instead show arrows pointing directly at the atom being "attacked". This obscures the bond forming process, and in many cases, such as the addition of hydrogen ions to alkenes, means that the position of the incipient bond is ambiguous.
Bob's contribution is interesting as another illustration of the value of trying to write an algorithm in clarifying the "rules" of the process. I'm engaged in a similar exercise, for an online tutorial site, and Bob's work will be most helpful.
After a long hiatus, I have been doing a little work on an online tutor intended to help students learn to write curly arrow mechanisms (the prototype is here: http://www.ucd.ie/chem/chemint/mechanism.htm). The rules that you and Bob Grossman outlined are interesting in that context. My project does not have a rules-based analysis module at present, but I plan to add one. I have one question. In Rule 5.4 you suggest that a curly arrow can represent movement from a lone pair to a lone pair (albeit very rarely). I have been trying to think of an example of that scenario, but can't . Can you offer an example?
Regards, Mike.
Re I have been trying to think of an example of that scenario, but can’t . Can you offer an example?
I cannot now remember whether I had an example in mind when I wrote that two years ago. Perhaps I had changes (reductions) in metal centres in mind?