Most compounds of second- and third-row nonmetals involve tetrahedral
or near- tetrahedral geometry around a central atom. We already
have discussed methane, CH,
which has ideal tetrahedral H-C-H angles of 109.5,
ammonia, NH,
with H-N-H angles of 107;
and water with an H-O-H angle of 105.
Tetrahedral bonding geometry can be obtained by combining an s and
three p atomic orbitals of the central atom before bringing in other
atoms, to produce a set of four new orbitals called hybrid atomic
orbitals, as at the right. These hybrid orbitals can be represented
by t, t,
t, and t,
and can be written formally as

t = s + p
+ p
+ p
t = s + p
-p
-p
t = s -p
+ p
-p
t = s -p
-p
+ p

All four hybrid orbitals have an equal contribution from the spherical
s orbital, but they point in different directions because they have
different contributions from p
p
and p
The four hybrid orbitals extend out in the four directions of the
vertices of a tetrahedron, or to four nonneighboring comers of a
cube. The signs of the p terms in the set of four equations above
are, in effect, the coordinates of each orbital The t
orbital, for example, has its maximum electron probability in the
-x, +y, -z direction, as can be seen to the right.