Ask A Scientist Chemistry Archive

Question:
Can anyone answer this question?  The question is on
F Orbitals.  Please tell me how this looks like.
I've gone to many libraries but I cound't find anything.
 peter tran

Answer:
You have asked a very difficult question.  First, because it requires
a verbal written response rather than a face-to-face interaction with
a blackboard that we can draw on, and secondly because most of us have
probably never seen drawings of f-orbitals.  After all, drawings are only
two dimensional and the orbitals are 3-d, well 4-d since there are three
coordinates (x,y,z) and the magnitude of the orbital.  It is very
difficult to draw 4-dimensional objects on a 2-d paper.  To make it
easier, one convention is to try to represent the orbital as a funny
shaped balloon that would "contain" a certain amount (say 95%) of the
electron density of the selected orbital.  Using this convention an
s-orbital looks like a perfectly round ball.  Any of the p-orbitals (there
are 3 of them) look like two  sno-cones arranged so the cups point
directly at each other.  The d-orbitals (except for d(z^2) are
_represented_ as four sno-cones, all in the same plane and with their
cups pointing at the center (like the blade of a fan).  Notice that
there is a progression here, as we go from s to p to d-orbitals we go from
0 to 1 to 2 nodal planes (a nodal plane is a plane that can be placed
between two -or more - of the balloons without touching any of them).
The next step, f-orbitals, will have 3 nodal planes.  I will attempt to
describe what ONE of them might look like -- there are a total of 7
and will not all look alike (notice the d-orbitals don't all look alike!)

Now to describe what ONE of the f-orbitals might look like.  Remember,
it has to have 3 nodal planes.  Let's just use the x-y, x-z, and y-z
planes of cartesian coordinate systems.  If each plane were a sheet
of plastic it would divide space up into 8 octants (ask a geometry
teacher if you cannot "see" this).  Now, place a sno-cone in each
octant with the point toward the origin.  Use 4 red sno-cones and
4 blue-sno-cones and make sure that you alternate red and blue when
going from one octant to its neighboring octant (i.e., when crossing
a single sheet of plastic).  The colors of the sno-cones represent
the sign of the wavefunction in that region of space, either positive
or negative (which you want to call positive and where you put the
first one is completely arbitrary).  Remeber, the signs do NOT represent
an electrostatic charge -- electrons are always negatively charged!
The sign is ONLY the sign of the function used to mathematically
represent the magnitude of the electron's wave function in that region
of space.  Also, you should be aware that one reason more
people aren't concerned about the f-orbitals is that they aren't important
in most chemical bonds.
Hope this helps!
Greg

Good news!  I just found pictures for f-orbitals in "Quanta:  A Handbook
of Concepts, 2nd Ed.", pg 119.  The orbital I described is the f(xyz)
orbital.