Curved Arrows


Additional reading recommendation: You may find Chapter 3 of Pushing Electrons by Daniel P. Weeks (Saunders College Publishing; 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 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 can only be 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 fundamental 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 ten 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.  They are also useful to indicate electron changes between a set of contributing resonance structures.

Each curved arrow with two barbs on the headrepresents the shift of one electron pair.  (Later we will encounter single-barbed curved arrows that represent the shift of single electrons.)  The curved arrows shows 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 a 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 which 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:

Bonding pair becomes lone pair; bond broken:

The use of curved arrows for the ionization of water are shown below.

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.

If the arrow starts at a bond between two atoms, then that bond is broken.  If the arrow ends between two atoms, then a new bond is formed between those atoms.  (If the atoms are already bonded, then a double or triple bond results.)

The process of drawing a curved arrow mechanism is also commonly called "electron pushing."

When drawing curved arrows, the start 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., neutral atom become +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 are 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.



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