Curved Arrows
Additional reading recommendation: You may find Chapter 3
of Pushing Electrons : A Guide for Students of Organic Chemistry, 3/e by Daniel P. Weeks (Harcourt College Publishers;
ISBN 0-03-0206936) to be a useful tool for mastering the fundamentals of
using curved arrows.
Discussion: Chemical reactions are a result of bonding changes. These bonding changes are most easily described by considering the changes in electron sharing between atoms. For example, consider how the collision of two water molecules leads to the ionization of water and the formation of hydroxide and hydronium ion.
In this reaction, the oxygen atom of one water molecule collides with a hydrogen atom of the second water molecule. A lone pair of the oxygen atom becomes the new O-H bond in the hydronium ion. Because a hydrogen atom can only fully bond to one other atom at a time, the old O-H bond is lost. The electron pair of the old O-H bond becomes a lone pair, sole property of the oxygen atom of hydroxide ion.
This very simplistic step-by-step bookkeeping description of all the bonding and electron changes in a reaction is called the reaction mechanism. Study, understanding and prediction of reaction mechanisms is at the very heart of reactions in organic chemistry. Mastering the fundamentals of reaction mechanisms is a crucial survival skill for students of organic chemistry. You will use them every day that you study organic chemistry.
Above, we used several lines of text to describe the bonding changes in a single step of a reaction mechanism. A reaction mechanism might have 10 steps or more, making such descriptions very cumbersome. A shorthand notation that summarizes these changes has thus been developed. This notation, called curved arrow formalism, provides a rapid way of drawing bond and electron changes in a given mechanism step. The notation is also useful for indicating electron changes between a set of contributing resonance structures.
Each double-headed curved arrow
represents
the shift of one electron pair. (Later, we will encounter single-headed
curved arrows that represent the shift of single electrons.) The
curved arrows show the direction of electron flow. The tail shows
the electron origin, and always come from an electron source, usually a
lone pair or bonding pair from an s or p
bond. The head of the arrow indicates the electron pair destination,
either as a new lone pair or a new bond. If the arrowhead points
to another atom, that atom must either have an open octet—and thus be able
to accept the electron pair—or have an electron pair that can be displaced
by the incoming electron pair. Electrons never flow from atoms that
are electron-poor to atoms which are electron-rich, so a curved arrow will
never point from an atom with a positive charge to an atom with a negative
charge.
New bond formed to X:The use of curved arrows for the ionization of water are shown below.
Bonding pair becomes lone pair; bond broken:
The tail of the curved arrow on the right starts at the oxygen lone pair, meaning this curved arrow shows a bonding change for this lone pair. The head of the curved arrow points to the space between the oxygen and hydrogen atoms, meaning the electron pair ends in that space as a bond between the oxygen and the hydrogen. The hydrogen that accepts a new bond to oxygen must give up a pair of electrons because it cannot have more than two valence electrons at a time. Thus, the old O-H bond is displaced by the new electron pair from the other oxygen atom. The curved arrow on the left indicates the electron pair that was the O-H bond becomes a lone pair on the oxygen of the hydroxide ion.
The process of drawing a curved arrow mechanism is also commonly called "electron pushing."
When drawing curved arrows, the starting and stopping points of the arrows are critical. Things that make no difference are where the arrows curve up or down, or whether they start or stop at the top or bottom of an atom. The arrows you draw may therefore look different than the arrows shown in this tutorial.
Note also the changes in formal charge that result from the electron changes. If an atom shares a lone pair that it used to have all to itself, then its charge decreases by one (i.e., a neutral atom becomes +1). If an atom gains a bonding electron pair all to itself as a lone pair, then its charge increases by one unit (i.e., a neutral atom becomes -1). The charge is conserved in this mechanism step. The total charge on the left (zero) is the same as the total charge on the right (-1 +1 = 0). Charge is conserved in all mechanism steps. You should make a habit of checking your work against this point to minimize errors.
Lone pairs are often involved in reaction mechanisms, so you should
be in the habit of drawing all lone pairs. It is also important that
your curved arrows be drawn neatly and precisely, clearly showing the atomic
origin of the electron pair at the tail of the curved arrow and the electron
pair destination at the head of the arrow.
Example 1: Provide the curved arrows for the reaction of hydroxide and hydronium ions to form two molecules of water.
Solution 1: A reasonable approach to an exercise like this is to
analyze the bond changes and then draw the corresponding curved arrows.
The oxygen of hydroxide ion has shared a lone electron pair with the hydrogen
of hydronium ion, forming a new O-H bond. Thus, we draw a curved arrow
with the tail at the hydroxide ion lone pair and ending at the hydronium
ion hydrogen. This hydrogen atom can only have one covalent bond
at a time, so it must sacrifice the bond to the hydronium ion. We
draw a curved arrow to show the bonding electron pair between the hydrogen
and oxygen of the hydronium ion moving to become the sole property of the
oxygen atom. The oxygen of the hydroxide ion is sharing a pair of
electrons that it had all to itself before, so its formal charge drops
by one unit (-1 to neutral). The oxygen of the hydronium ion gains
a lone pair of electrons that is used to share with the hydrogen, so its
formal charge decreases by one unit (neutral to +1).
Example 2: Draw the product(s) of the following mechanism step based upon the curved arrows.
Solution 2: The curved arrow that starts at the carbon-carbon
p
bond and ends at the bromine atom indicates the p
bond electron pair has shifted to become a carbon-bromine bond. The
left-hand carbon of the p bond has lost an electron
pair, so its formal charge becomes one unit more positive (neutral to +1).
The curved arrow on the right indicates that the electron pair of the bromine-bromine
bond is shifting to reside solely on the bromine on the right, resulting
in rupture of the bond and formation of bromine with four lone pairs and
a negative charge.
Exercises:
Provide curved arrows that show how the following mechanism steps might occur.
Provide the product(s) for the following mechanism steps based upon the curved arrows.
