The five orbitals for I = 2, or d orbitals,
are more complicated. If we define a set of perpendicular x,
y, and z coordinates, then the ,
,
and
orbitals, have cloverleaf electron probability distributions in
the xy, yz, and xz planes respectively, as
shown opposite.
The
orbital has highest probability along the x and y
axes, and the
has maximum electron probability along the z axis. The f
and higher orbitals are even more complicated, but never need to
be visualized in any practical chemical situation. The s,
p, and d orbital shapes are sufficient for our purposes,
and you should know these well.

The illustrations shown on this page represent electron probabilities,
or values of the square of the wave function, .
These values always are positive, whereas the original wave function,
,
can be positive or negative. The signs of
in various lobes of the probability functions are indicated by +
and - signs. Whether the sign is positive or negative is not significant,
but the change in sign from one lobe of probability to the
next is. The signs of the wave functions become necessary as soon
as we begin to combine atoms to form molecules, as in the next chapter.