Standard color scale
When we use the default color scale, we know that
the red and dark blue regions correspond to the extreme values
of the electrostatic potential, but how can we know what these extreme
potentials are? Different maps have different extremes. As a result,
if we don’t know the numerical value of the extreme potentials,
we might be fooled into thinking that we are looking at large extremes
(and large differences between extremes) when we are not.
Consider the potential map of propane, CH3CH2CH3,
shown below. This map is colored according to the default scale.
It turns blue near every hydrogen, and yellow-orange around every
carbon (the “cavity” at the top of the map is bordered
by all three carbons and is red). These colors seem to suggest that
the potential swings wildly between hydrogen (medium-dark blue)
and carbon (yellow-red).
Potential map of propane,
(default color scale)
Now examine the potential map of 1-propanol, CH3CH2CH2OH,
shown below. This map is also colored according to its default color
scale. Extreme potentials are located near the OH group. The CH3CH2CH2
group is almost uniformly green. This suggests that the potential
does not change much between hydrogen and carbon in this molecule.
map of 1-propanol, CH3CH2CH2OH
(default color scale)
There does not appear to be any consistency in these
maps. The CH3CH2CH2 group appears
to generate extreme potentials in propane, but a nearly constant
potential in 1-propanol. If we carry this idea to its logical conclusion,
we would say that the CH3CH2CH2
groups are radically different in these molecules. Unfortunately,
this conclusion is contradicted by several other types of data (bond
distances, isodensity surfaces, electronegativity data, and so on),
so we must seek another explanation.
The answer lies in the numerical value of the extreme
potentials. The potentials on the propane map swing from –22
to +4 kcal/mol, while the potentials on the 1-propanol map cover
a much wider range, -48 to +44 kcal/mol. Since both maps use the
same number of colors, each color on 1-propanol’s map covers
a wider range of potentials. This is why the entire CH3CH2CH2
group has roughly the same color on the 1-propanol map.
We can avoid these problems by giving the values of
the extreme potentials for every map. When the extreme potentials
are known, the meaning of other colors can be inferred as follows:
Green always corresponds to a potential halfway between
the two extremes (red/dark blue). Yellow and light blue split the
difference between the mean (green) and the extremes (red/dark blue).
Applying this to the 1-propanol map (red = –48 and blue =
+44 kcal/mol) gives green = –2, yellow = –25, and light
blue = +21 kcal/mol. Notice that the entire potential range of propane’s
map, –22 to +4 kcal/mol, would be assigned two colors, green
and yellow, on 1-propanol’s map.
Another solution that we can also use is to color
the maps of neutral molecules using a standard color scale.
My definition of this scale places the extremes at -40 (red) and
+40 kcal/mol (dark blue). This means that intermediate colors correspond
to modest potentials of –20 (yellow), 0 (green), and +20 (light
The following figure shows the potential maps of propane
and 1-propanol colored according to my standard color scale (remember
that we have not changed the potentials, just the colors assigned
to each potential). Now the CH3CH2CH2
group looks roughly the same in both molecules.
maps of propane, CH3CH2CH3,
CH3CH2CH2OH (standard color
The standard color scale is useful, but it is not
entirely free of problems. Suppose the potentials on a given map
lie outside the standard extremes, that is, suppose some
potentials are less than –40 or greater than +40 kcal/mol.
What colors does the standard color scale use for these potentials?
The answer is simple: red and dark blue. This means that the extreme
colors are not always trustworthy. They might identify potentials
of ±40 kcal/mol, or they might correspond to potentials outside
At this point, we have learned about several tools
for analyzing electron density clouds: contour graphs, isodensity
surfaces, and potential maps. The potential map is generally more
useful than the other tools, however, because it shows the interplay
between nuclear charge and electron density. The following sections
show some of the ways chemists use potential maps. As you read these
sections, pay equal attention to the ways in which potential maps
are used, and the chemical lessons that the maps teach. Both
topics are important.
Also, keep in mind the following points:
The potential at any location is a molecular
property. It is affected by all of the nuclei and the entire
electron density cloud. The “local” atom usually
make the largest contribution to the potential, but this is
not always the case.
When the potential is dominated by a “local”
atom, the sign and magnitude of the potential reflect the sign
and magnitude of the “local” atom’s charge.
Potential maps of different molecules can be compared,
but only if quantitative information about map potentials
is available. This information can be expressed by 1) giving
the potential range for each map, or 2) by coloring each map
with the same color scale (if the molecules are neutral, then
the standard color scale is a good choice).