Bonding and Bond Formation
a Quantum Picture*
Richard A. Paselk
Note to the User: all of the animations are set to go through one cycle of rotation or bond formation. After an initial viewing you may want to click on the scrollbar and arrow-keys to its right to "step-through" the animations.
Review terms: valence shell, electropositive and electronegative,
ionic and covalent bonds, molecule, Lewis structure, non-bonding & lone-pair electrons.
Ionic bonds are formed when one
or more electrons are transferred from one atom to another, with
the resulting ions held together by electrostatic forces. Note
that these are strong, but they are non-specific and can easily
"transfer" from one ion to another, so they tend to
be unstable. Sodium chloride is an excellent and clear-cut example
of ionic bonding . To help understand this system images and movies
are provided for sodium and chlorine atoms and an ion pair. Note
that the inner, "core" electrons for both atoms are
shown as yellow dots, while the valence electrons for both atoms
are shown as green.
- Notice how spread-out the outer electron (green dot-cloud)
of sodium is - it is not very tightly held to the atom.
- On the other hand the outer (green dot-cloud) seven electrons
are much more tightly held to the atom - much of the electron
density overlaps with the core electrons.
- Note that both atoms show completely spherical distributions
of electrons in the cores (as expected since all orbital sets
- Both atoms also show spherical distributions of electrons
in the valence shells.
- This is expected for sodium since the single valence electron
is in a spherical s shell.
- More subtly, the valence p shell electrons should
also be spherically distributed because we cannot distinguish
the three orbitals under normal circumstances (we only "see"
them spectroscopically when an atom is in an external magnetic
- Finally, in the ionicly bonded Na-Cl ion pair note how the
outer electron has been stripped from sodium, and the valance
shell of chlorine has expanded to accommodate the completed shell with its negative charge.
- The movie accessed through the Na + Cl figure below shows the formation
of a NaCl ion pair in vacuo.
- Notice how the outer electron of the sodium atom "jumps"
to the chlorine atom when the atoms are still well separated.
- The resulting ions are then attracted to each other until
the electron clouds "touch" - interpenetrating slightly
- The energy released in this process will show up as vibration and/or rotation. On the macroscopic scale when sodium metal and chlorine gas are combined we see this energy as heat and light.
Covalent bonds are formed when
we have a sharing of electrons.
- You will note in the Cl(2) figure showing the inner, core,
electrons of a chlorine molecule (Cl2) show no
overlap. Thus they are not involved in bonding at all, just as
you might expect from the Lewis model and Lewis structures.
- The two Cl(2) molecule figure and movies show the overlap
of the outer electrons - covalent bonding is a phenomena of the
outer, valence electrons.
- In the middle figure the upper diagram is a plot of the electron
density in the x-y plane. There doesn't appear to be much overlap
at all of the outer electrons. but keep in mind that only 2 of
the 14 outer electrons of the Cl2 molecule are involved
in the bond (and that all of the sp3 electrons
are equal and indistinguishable in the filled orbital sets).
- The lower diagram in this figure shows the corresponding
dot-image, while the figure at the right shows the dot-image
again in larger size with higher resolution.
- Covalent bond formation
- As we saw in the QuickTime movies above, covalent bonds are
formed when two atoms share one or more electron pairs - there
is an overlap of the orbitals of the two atoms. In the simplest
case, that of hydrogen, the resulting bond and molecule are cylindrically
symmetrical, as seen in the figure and QuickTime movie of hydrogen.
You might also note that hydrogen is nearly spherical as a molecule
because the nuclei can approach each other so closely since there
is no inner electron shell. Cylindrically symmetrical bonds like
hydrogen's are known as sigma bonds. They may be formed
by overlap of two s orbitals as in hydrogen, an s orbital
and a p orbital lobe, two p orbital lobes (as seen
in Cl2 above) etc.
- Another view of the bonding process is shown in the false
colors below, where the electron density is indicated by a rainbow
pallet with red symbolizing the highest density and violet the
- Notice the changing electron density during the bonding process. The formation of the bond results in an increase in electron density between the two nuclei and a significant increase in the density around the nuclei, as symbolized by the red color. Bringing the negative charge density of the electron distribution in closer to the positive nuclei decreases the energy of the system, and therefore contributes to the bond.
- As seen in the Morse curve below the two hydrogen atoms come
together until the energy is minimized. The H2 bonding QuickTime
movie visualizes this process, the movement of the atoms corresponding
to the colored region of the Morse curve.
- The animations do not show the dissipation of the bonding energy, which appears in the resultant molecule as vibration and/or rotation around the molecular center of mass.
Finally, the bonding movie for chlorine is shown below along
with its Morse curve. The green region of the curve corresponds
to the movie. If you are off campus note the large download
size of the movie!
As noted above for the formation of hydrogen molecules, the energy of bond formation appears as vibration and/or rotation of the new molecule around its center of mass.
- Notice the gradual overlap which occurs as the atoms approach.
- As noted above, the limited overlap occurs because only 2 of the 14 outer electrons of the Cl2 molecule are involved in the bond.
- The Morse curve plots the energy of the system vs. the separation of the nuclei.
- The stable bond occurs at the low point of the curve, corresponding to the maximum overlap in the bond formation movie.
- The black portion of the curve shows the very rapidly increasing repulsion as the non-bonding electron clouds begin to overlap.
*The animations and visualizations on these pages are copyrighted.
They were created by Mervin P. Hanson, Richard L. Harper, Richard
A. Paselk and John B. Russell from calculations performed by Mervin
P. Hanson. This work was supported by the National Science Foundation,
Apple Computer, and Humboldt State University.
© R A Paselk
Last modified 1 May 2007