How to Solve 'Draw Curved Arrow' Problems

First, it is important to understand the rules for the use of curved arrow symbols.

If you are familiar with these rules skip ahead to the strategy for solving the problems.

Rules for the use of curved arrows

1. The key feature of chemical reactions is that they involve changes in bonding.  For that reason, chemists are primarily interested in tracking the breaking of exisiting bonds and the formation of new bonds in the course of the reactions.  Bonding changes involve the movement of electrons, so it is essential to know where the electrons are in atoms and molecules.

2. In almost all organic compounds, we can safely assume that lines representing covalent bonds are an alternative way of depicting shared pairs of electrons, shared between the two atoms involved (or two pairs in a double bond, etc.).  Atoms may also have 'non-bonding' electrons that are 'localised' on that atom (not shared with others), and are represented by dots.  Non-bonding electrons generally occur as pairs ('lone pairs'), but they may occur singly, in radicals.

   

3. Curved arrows are added to the starting material(s) to depict the electron movements that give rise to the new bonding arrangements in the product(s).  Note that they are used to represent the movement of electrons, not the movement of atoms.

   

4. The number of 'barbs' on the arrowhead is used to indicate the number of electrons involved in the movement; 'single-headed' or 'fish-hook' arrows represent movement of one electron, and 'double-headed' arrows represent movement of a pair of electrons.  Compare the examples above and below.

   

   It is simpler to discuss these two possibilities separately, and we will first describe the use of double-headed arrows, representing the movement of pairs of electrons.

5. Generally, the start of a curved (double-headed) arrow represents the initial position of the pair of electrons (in the starting materials), and the end of the arrow represents the final position of that pair (in the products), though we will have to modify that statement significantly in point 7 below.  From this and point 2, it follows that curved arrows must start at either a bond (a shared pair of electrons) or at an atom (at a lone pair) and, likewise, must end at a bond or at an atom (indicating the formation of a new lone pair on that atom).

   

6. If an arrow starts at an atom, it is good practice to explicitly show the lone pair that is moving.  However it is often acceptable, as a shorthand, to show the arrow starting at the atom symbol.

7. If a new bond is being formed, the arrow 'should' point towards the postion of that bond, i.e. to a point roughly midway between the two atoms that are becoming bonded to each other.  However, it has become almost universal practice to draw the arrow pointing to the atom to which the new bond is being formed, rather than to the midpoint of the incipient bond.

   

   In this situation (formation of a new bond to an atom), I recommend that you think of an arrow pointing to an atom as a 'shorthand' for an arrow pointing to the middle of the new (incipient) bond to that atom.  That way, the rule in point 5 is always obeyed, arrows start at the initial position of the electron pair and point to its final position.

8. Another complication arises if a new bond is formed using a shared pair of electrons from an existing (single or double or triple) bond; how do we show which of the two atoms of the bond that is breaking is involved in formation of the new bond?  The most common way of doing this is simply to position the other atom to which the new bond is being formed closer to whichever atom in the 'donor' bond will become bonded to it.

   

   In these ChemInteractive problems, the atom that reacts with the existing bond is always positioned appropriately , so you don't have to worry about this issue.

Strategy for solving the problems

Following on from Rules 2 and 3 above, drawing curved arrows for a reaction step entails identifying movements of shared pairs and lone pairs of electrons.  This process can be broken into two phases, (i) identifying the the atoms and bonds that have gained or lost electron pairs and (ii) drawing the curved arrows to represent the electron pair movements.  Both phases involves several steps, as described in detail below.
The procedure may appear quite long and complex, but as you become more proficient, you will be able to carry out some of these steps very quickly and easily.

When you try the problems, your answers will be analysed by checking that you have performed each the steps shown below, and the feedback will be structured to help you learn the strategy.

If it is a multi-step mechanism, apply the strategy to each step in turn, and add curved arrows to the starting material(s) and to each of the intermediates.

1. 'Map' the structures of the starting material(s) onto the structures of the product(s).  It may be helpful to number (some of) the atoms in the starting material(s) and add the same numbers to the corresponding atoms in the product(s) (see examples below).

2. Identify all bonds of the starter(s) that undergo changes in bond order, i.e. changes in the number of shared pairs, as a result of movements of pairs of electrons.

   1. If a bond undergoes a decrease in bond order, including one that breaks (single to 'zero-order'), it is 'losing' a shared pair so it is an electron pair 'origin' and an arrow should start at it (red in examples).

   2. If a bond undergoes an increase in bond order, it is 'gaining' a shared pair, so it is an electron pair 'destination' and an arrow should end at it (blue in examples).

   3. Include any new bonds that are formed, i.e. ones that are present in the product(s) but not in the starting material(s).  Think of these as 'zero order' bonds being converted into single bonds by 'gaining' a shared pair.  For clarity, new bonds are shown as dashed lines in some of the examples, but these lines are not included in the problems.

3. Identify all atoms of the starter(s) that undergo changes in the number of lone pairs as a result of movements of pairs of electrons.

   1. To help with this step, I recommend that you add the appropriate number of lone pairs to all the atoms, in both the starting material(s) and the product(s), at which bonds are formed or broken, bearing in mind their formal charges.

   2. If an atom 'loses' a lone pair, its charge will change by +1, and it is an electron pair 'origin' so an arrow should start at it (red in examples).

   3. If an atom 'gains' a lone pair, its charge will change by -1, and it is an electron pair 'destination' so an arrow should end at it (blue in examples).

   

   The set of atoms that 'gain' or 'lose' lone pairs and bonds that 'gain' or 'lose' shared pairs together form the 'Path of Electron Movement' (PoEM).
   Note that some atoms on the PoEM may not gain or lose lone pairs, and curved arrows should not start or end at those atoms.

   CHECK: The PoEM should be one of three types.

   (i) an unbroken linear chain of atoms and bonds (example above)

   (ii) an unbroken cyclic path

   

   (iii) a combination of a cyclic path with a linear or a cyclic path, with the two paths having at least one atom in common.

   

   CHECK: The PoEM should consist of an alternating sequence of atoms/bonds that 'lose' electron pairs ('origins', red) and atoms/bonds that 'gain' them ('destinations', blue).

4. Draw the curved arrow(s) that correspond to the electron movements.  This involves drawing arrows from atoms/bonds that you identified as 'losing' electron pairs ('origins') to those that are 'gaining' pairs ('destinations'), to represent the corresponding movements of the electron pairs.

   1. Use arrows with the appropriate arrowhead: single-barbed (fish-hook) for movement of one electron; double-barbed for movement of a pair of electrons.  See Rule 4 above.

   2. Draw a curved arrow that begins at an atom or bond that 'loses' an electron pair and ends at the next atom or bond along the PoEM that 'gains' an electron pair.  Take care to get the direction of the curved arrow right, i.e. FROM the atom/bond that 'loses' electrons TO the atom/bond that 'gains' the electron pair.

      • Remember that if a new bond is being formed, it is conventional to draw the arrow pointing to the atom with which the new bond is forming rather than pointing to the middle of the new bond (see Rule 7 above).

      • Note that curved arrows must be drawn from an 'origin' atom or bond to the next 'destination' atom or bond along the Path of Electron Movement.

        If the electron pair involved in an electron movement originates on an atom, as a lone pair, it must remain associated with atom, as a bonding pair.
        Similarily, if the electron pair involved in an electron movement originates in a bond, as a shared pair, it must remain associated with one of the atoms of that bond, either as a bonding pair or a lone pair.

        Only three types of electron movements obey this rule, as shown below; the atom with which the electron pair remains associated is shown in blue in each case.  Also shown are some examples of incorrect arrows that violate the rule and never occur in reaction mechanisms.

        

        Put another way, electron pairs 'pivot' around atoms, they are never 'transferred' away from the starting atom or from both of the atoms of the starting bond.

      • If the PoEM is linear you can start anywhere along it but I recommend that you start at the atom or bond at the end of the path that acts as the electron 'source', it can be easily identified because it will have an atom whose formal changes by +1.

        

      • If the PoEM is cyclic, and there are no charges or large partial charges on the atoms of the starting materials, start at any bond that is broken or undergoes a reduction in bond order ('loses' a shared pair) and draw the arrow in either direction around the cyclic path to end at the next atom/bond that 'gains' an electron pair.

        

      • However, if the PoEM is cyclic and includes strongly polarised bonds, so there are large partial charges on the atoms, the direction of electron movement IS important.
        In that case, the arrows representing the formation of new bonds should be drawn so that the pairs of electrons are moving towards atoms that bear partial positive charges.

        

        Drawing the arrows in the other direction would lead to the observed products, but would not be consistent with key concepts of chemical reactivity such as nucleophilicity and electrophilicity.

   3. Draw a curved arrow that begins at the next atom or bond along the PoEM that 'loses' an electron pair, and ends at the next atom/bond that 'gains' a pair.

      • Continue in this way until you reach the end of the PoEM.

      • If the PoEM consists of two paths (which must share one or more atoms), follow this procedure for both paths, in any order.

        

   4. CHECK: You should have drawn one arrow for each electron movement, i.e. one arrow for each bond that is formed or changes to a higher bond order, and one for each newly formed lone pair.

      • If you have drawn fewer arrows that this, one or more atoms on the PoEM will violate the Octet Rule because at least one arrow to show movement of electrons away from those atoms is missing.

      • If you have drawn more arrows that this, you may have drawn arrows to atoms or bonds that are not part of the PoEM, or drawn two arrows to represent one electron movement, see an example in section 4.5.

   5. AVOID COMMON ERRORS: As well as the errors already mentioned (wrong direction, electron pair 'transfer', octet violation due to missing arrows) the following are common errors that arise from incorrect use of curved arrows.

      • Do not draw arrows that start or end at atoms or bonds that are not on the PoEM.
        By definition atoms and bonds of the starting materials that are not on the Path of Electron Movement are not involved in electron movements.

      • Do not draw an arrow from a bond to one of its atoms and another one that starts at the same atom, the two arrows should be replaced by one.

        

      • Do not draw arrows that start at atoms that do not have available lone pairs.  In particular, remember that hydrogen ions (H⁺) and tetravalent carbon atoms do not have lone pairs, and curved arrows should never start at them.  In the same way, do not draw two arrows starting from a single bond, there is only one shared pair in a single bond.

        A related case is that you should not draw two arrows starting from same neutral atom, even if it has two or more lone pairs.  Atoms never 'lose' more than one lone pair, to form a shared pair, because they become positively charged and the remaining lone pair(s) is(are) held very tightly.

        

      • Do not draw arrows that represent the formation of a bond between ions that do not become covalently bonded.