Imperial College London

Henry Rzepa

[Curly
arrows](http://www.abdn.ac.uk/curly-arrows/org/history.shtml){target="_blank"
rel="noopener"} are something most students of chemistry meet fairly
early on. They rapidly become hard-wired into the chemists brain. They
are also uncontroversial! Or are they? Consider the following very
simple scheme.

::: {#attachment_2738 .wp-caption .aligncenter style="width: 347px"}
[![](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/10/arrow_pushing.jpg "arrow_pushing"){.size-full
.wp-image-2738 loading="lazy" decoding="async"
aria-describedby="caption-attachment-2738" width="337"
height="304"}](http://www.ch.ic.ac.uk/rzepa/blog/wp-content/uploads/2010/10/arrow_pushing.jpg)

Curly arrow pushing
:::

It represents [protonation of an alkene by an
acid](http://www.ch.imperial.ac.uk/rzepa/blog/?p=4837){target="_blank"
rel="noopener"}. Two products are of course possible, leading to either
a tertiary carbocation as shown in (a), or a primary one (not shown).
Either involves two arrows, but how to illustrate this (important)
difference in the outcome using the arrows. Most textbooks show (a). The
lhs arrow starts at the middle of the bond, and ends at the atom of
hydrogen. This unfortunately leads to an ambiguity. It does not define
which carbon is involved in forming the new C-H bond.

In recognition of this problem an article has recently
appeared\[cite\]10.1021/ed086p1389\[/cite\] which attempts to improve
model (a) by using what they call bouncing arrows, as in (b). The arrow
starts at the mid point of the C=C bond, but then bounces to one end,
before heading off to again to end at the H atom. The idea is that the
direction of bounce informs which of the two possible bonds will be
formed. Leaving aside the (non-trivial) issue of how to persuade *e.g.*
ChemDraw to produce a bouncing arrow, I note that an alternative system
has been in use where I teach for many years; (c).

1.  This starts by addressing the problem of which bond to form by
    immediately drawing a dotted line where you want the bond to go.
2.  The arrow starts as before, at the mid point of a bond, but this
    time it ends at the mid-point of the dotted line. If nothing else,
    Chemdraw has no problem with this notation!
3.  Are there any other advantages? Consider (d). The green dots
    indicate the results of a QTAIM analysis, revealing bond-critical
    points (BCP) in either the reactants or the products. The first
    arrow both starts and ends at such a BCP. The second arrow starts at
    a BCP, and ends at a lone pair (these are not revealed using QTAIM.
    If instead, ELF synaptic basin centroids were to be used, then all
    arrows would start or end at such a basin). This therefore gives
    (c)/(d) some quantum mechanical reality.
4.  Another advantage is that one can formulate *check-sum*rules. By
    this I mean extra rules that can be used to check you have gotten
    things correct. Take a look at the red dots, one on the oxygen,
    another on the bromine. The metaphor is that these can be regarded
    as hinges, about which the bond swivels, the course of the swivel
    following that of the trajectory of the arrow.
    1.  For heterolytic (electron pair) arrow pushing in which none of
        the centres involved changes its valency, the red dots must be
        located on **alternating** atoms.
    2.  For heterolytic (electron pair) arrow pushing in which a valency
        change does occur (e.g. formation of a carbene), two red dots
        must be on **adjacent** atoms.
    3.  In general, no more than one arrow either starts, or ends, at a
        bond. This used to be thought of as a fairly hard rule, but in
        fact its not difficult to come up with reactions which break it.
        For example, [this
        one](http://www.ch.ic.ac.uk/rzepa/blog/?p=1158){target="_blank"
        rel="noopener"}, where as many as **three** arrows either start
        or end at a given bond. And, as a challenge, can you break the
        rule by formulating arrow pushing for the (concerted) reaction
        between an alkyne and a per-acid (avoiding the anti-aromatic
        oxirene, the ring opening of which may conflate with the
        peroxidation).
    4.  One can interrupt the concerted flow of arrows to form
        intermediates along the way. One famous example of such
        interruption is [aromatic electrophilic
        substitution](http://www.ch.ic.ac.uk/rzepa/blog/?p=2423){target="_blank"
        rel="noopener"}, which can however be persuaded to move all of
        its arrows more or less synchronously.
5.  The metaphor now is one of doors opening and closing, rather than
    bouncing arrows.

There must be thousands of tutors around the world, teaching tens of
thousands of students the arcane art of arrow pushing. If anyone has yet
another schema for doing so, I would be delighted to hear from them.

::: {.wp_orcid_field}
[https://orcid.org/0000-0002-8635-8390](https://orcid.org/0000-0002-8635-8390){target="_blank"
rel="author"}
:::


Curly arrows are something most students of chemistry meet fairly early on. They rapidly become hard-wired into the chemists brain. They are also uncontroversial! Or are they? Consider the following very simple scheme. Curly arrow pushing  It represents protonation of an alkene by an acid.

Messaggi di Rogue Scholar

Secrets of a university tutor: (curly) arrow pushing