Atomic and Molecular Orbitals Page
Several hydrogenic atomic orbitals, hybrid orbitals, and
molecular orbitals for some small molecules are listed below.
The data files for
the orbitals are given in "Protein DataBank" format and the data
files have a ".PDB" extension. You can view these molecules with a
program that reads files which are in .PDB format. If you do not have such a program
you can download one from the Internet. Instructions for downloading a
molecular viewing program named RasMol are given on the Molecular
Viewing Information page.
You can download the RasMol program and the .PDB files for the orbitals
you want to see, or you can download the RasMol program and set it up as
a "helper application" in your web browser. In the latter case,
when you select one of the orbitals below, your browser will automatically
launch RasMol and load the .PDB file for the orbital you selected.
(At present the general access computer labs on the UofA campus have not
as a helper application for Netscape - they may eventually do so. However,
they do have the program loaded on the servers in each of the labs.
You can download the .PDB files to a floppy disk and then run the program
from the server using your floppy as the data file source.)
The orbital data files are fairly large, most of them are over 300KB, so it may take several
seconds for RasMol to load them. Also, after the file loads there may be nothing
showing on your RasMol screen, or there may be a few "scratch marks" here and
there. To see the orbitals click on "Display" and select either "Ball & Stick"
or "Spacefill" mode.
Once you have the orbital showing on your screen you can rotate it by moving
the mouse with the left mouse button held down. (Or
you can use the slide bars at the right and bottom of your screen.) You can
make the orbital larger or smaller by moving the mouse with the left mouse
button and the shift key held down. You can move the
image around on the screen by moving the mouse with the right mouse button held
down. (You can get another rotation angle by moving the mouse with the
right button and the shift key held down.)
The orbitals are not all shown on the same scale (except for the 1s
2s orbitals, which are on the same scale). For example, when you load
the 2s orbital it will fill your screen the same as one of the 4f orbitals,
etc. In actual fact, the 2s orbital is much smaller than the 4f orbitals.
For people who might be interested in such things, we are plotting surfaces
of constant probability density. That is, we set the (absolute value of)
the square of the wave function equal to a constant and plot the values
of the coordinates which satisfy this equation.
Hydrogen Atomic Orbitals
The 1s orbital is not very interesting, comparatively.
It has spherical symmetry and has no nodes.
The 2s orbital is a little more interesting because
it has a spherical nodal surface. You can see evidence of this node although
you probably can't tell that it is a node. The 2s orbital graphic here
just looks like a ball within a ball.
The 2pz orbital has a nodal plane
(the x-y plane).
The orbital is plotted so that the z-axis is "up" on your screen, the
y-axis is to your right, and the x-axis is perpendicular to the screen
toward you. We only show one of the 2p orbitals. To see what the
others look like you need only rotate this one 90 degrees either to the
right or toward you. If you rotate the orbital toward you, you will see
that the orbital has cylindrical symmetry.
We show one other p orbital, the 3pz orbital
, so that
you can see how orbitals of a given type (the p orbital here) change as we
go to higher principal quantum numbers. In this orbital most of the
electron "density" is in the two outer lobes of the orbital, but there is
some electron density in the two small inner lobes. (Just for the record
we remind you that this is all one orbital, not several orbitals.) This
orbital has cylindrical symmetry, as do all p orbitals.
The "d" orbitals have more lobes. The orbitals are named in terms of the
cartesian coordinate directions in which the lobes point.
We show here one of each type of 3d
orbital. The 3dz2 orbital
(read "3 d z squared")
has cylindrical symmetry. The other 3d orbitals, such as the
3dzx orbital (read "3 d z x") and the
(read "3 d x squared minus y
squared") all have the same shape, but differ in the directions in which the lobes
point. You will have to rotate each of these last two orbitals to see that
they each have four lobes. (There are two more 3d orbitals which
are not shown here, but they have the same shapes as these last two. Their
names are 3dxy and 3dyz. See if you can rotate one of the above orbitals
to make it look like one of these.)
Most people, even chemists, have never seen the shapes of "f" orbitals.
We show here one of each type of "f" orbital. The f orbital analogous to
the dz2 orbital is the
orbital. There is one
other orbital with the same shape of the
4fz2x orbital. The
orbital also has a mate, and so does the
We have "prettier" versions of the 2pz and
"Mixtures" of atomic orbitals, called "hybrid orbitals" are sometimes useful
in discussiing molecular shapes and bonding. The three most common types
of hybrid orbitals are called the "sp hybrids," the "sp2 hybrids," and the
"sp3 hybrids." There are two sp hybrid orbitals and
we show one of them. There are three sp2 hybrid
orbitals of which a typical one is shown. There are four
sp3 hybrid orbitals of which one is shown. In all
cases the other orbitals of each set have the same shape but "point" in
different directions in space.
The two sp hybrids are arranged on a straight line with their major "lobes"
pointing 180 degrees away from each other. You can see this by viewing them
all at the same time.
The three sp2 hybrid orbitals are arranged in a plane pointing 120 degrees
apart. You can see this by viewing them all at
the same time.
Likewise the four sp3 hybrid orbitals are arranged in a tetrahedral
manner. You can see this by viewing them all
at the same time.
Simple Molecular Orbitals
Molecular orbitals, as the name implies, are orbitals representing the
motion of electrons in molecules. A molecular orbital encompasses
more than one nucleus. We give examples here of a few of the simplest
molecular orbitals. First we list some molecular orbitals for the
N2 molecule, and then the six simplest pi molecular orbitals
for benzene. (Benzene is C6H6. If you have forgotten
the structure of benzene you can check it out on the
Molecules and Crystal structures page.)
In these graphics the nuclei are represented by small - very small -
orange dots. (In actual fact, the nuclei are so small that you should not
even be able to see them on the scale of these pictures. However, the nuclei
are easier to see in Space Fill mode than in Ball & Stick mode.)
Molecular Orbitals for the N2 Molecule
The 2s-sigma orbital as a bonding orbital.
Note that there is a build-up of electron density between the nuclei. This
orbital is "occupied" by two electrons in the N2 molecule. The
2s-sigma star orbital is an "antibonding"
orbital. This orbital is not occupied in the ground-state N2
For this orbital, not only is there no build-up of electron density between
the nuclei, there is a node between them.
The 2p-sigma orbital is a bonding orbital which
approximated by two 2p orbitals with their electron density lobes pointing
other. This orbital is occupied by two electrons in the ground-state N
The 2p-sigma star orbital is an antibonding
orbital. This orbital is not occupied in the ground-state N2 molecule.
Note that there is a node between the nuclei.
The 2p-pi orbital is a bonding orbital. It is
two 2p orbitals aligned side-by-side. It has a nodal plane just like p
atomic orbitals do. There is another 2p-pi orbital that has the same
shape as this one. You can see what it looks like by rotating this one
by 90 degrees toward you. Both of these orbitals are occupied in the ground-state
N2 molecule. The
2p-pi star orbital is an antibonding orbital. It
has a node between the nuclei and a nodal plane containing the nuclei.
There is another 2p-pi star orbital with the same shape as this one in the
N2 molecule. You can see what it looks like by rotating this one by 90
degrees toward you. Neither of these orbitals is occupied in the ground-
state N2 molecule.
Pi Molecular Orbitals for Benzene
The six lowest energy pi molecular orbitals for benzene are relatively easy
to construct and show. Since there are only six pi electrons in the benzene
molecule only the lowest three pi orbitals will be occupied. We will label the
orbitals by their symmetry designation (for people who care about the symmetry
The lowest pi orbital of benzene is called the
A2u orbital. This orbital
is occupied by two electrons in the lowest energy state of benzene. Notice
that this orbital has a nodal plane in the plane containing the nuclei and
no other nodes. (You can tell the relative energies of a set of molecular
orbitals - or atomic orbitals, for that matter - by counting nodal surfaces.
The more nodes an orbital has the higher energy it has. If you like, you
can test this statement on the pi molecular orbitals of benzene.)
The second lowest energy pi orbitals of benzene are designated E1g
so we will call them
E1g-2. They are degenerate
(i.e., they have the same energy) so that all the remaining four pi electrons
occupy these orbitals.
Next up (in energy) is another set of two degenerate orbitals, the
E2u-2. These orbitals are
unoccupied in the ground electronic state of benzene.
The highest (in energy) of these six benzene pi orbitals is the
B2g orbital. This orbital is
unoccupied in the ground state of benzene.
Last updated 30 May 97
W. R. Salzman
Department of Chemistry
University of Arizona