21.3 The CH 4 ,NH 3 , and H 2 O Molecules and thesp^3 Hybrid Orbitals 877
occupied by lone pairs of electrons. The electron configuration of the ground-state is
(1sO)^2 (2sp^3 (1))^2 (2sp^3 (4))^2 (σA)^2 (σB)^2. The electron configuration is also denoted in
Figure 21.7 by arrows pointing up and down to represent electrons occupying a space
orbital with spin up and spin down.
Our simple descriptions of the NH 3 and H 2 O molecules do not exactly correspond
to the experimental bond angles. Better descriptions can be constructed by carrying out
calculations using LCAOMOs that are linear combinations of all atomic orbitals in the
basis set. Hybrid orbitals are then not needed and the canonical molecular orbitals can
extend over the entire molecule prior to energy localization.^2 Improvements can also
be obtained by using a larger basis set.
We can now understand theoctet ruleof G. N. Lewis. According to this elementary
rule, atoms in molecules tend to have eight electrons in their valence shells, counting
both bonding and nonbonding electrons. This rule was proposed by Lewis prior to the
discovery of quantum mechanical shells and subshells and is remarkably effective in
predicting the electronic structure of many molecules. For the water molecule and other
molecules made from elements of the second row of the periodic table (Li through
Ne) the valence shell is the second shell, in which eight spin orbitals (four space
orbitals) occur. From an atomic orbital, one bonding LCAOMO and one antibonding
LCAOMO can be made with an atomic orbital on another atom. If the antibonding
orbitals remain vacant and nonbonding and bonding orbitals are occupied the total
number of occupied spin orbitals around a given nucleus of a second-row element
equals eight, corresponding to the octet rule.
There are exceptions to the octet rule. Some stable molecules, such as BeH 2 and
BH 3 , do not have enough valence electrons to form an octet. Other molecules con-
taining elements beyond the second row of the periodic table involvedorbitals in the
bonding and can have “expanded octets” with more than eight electrons in bonding
and nonbonding orbitals around a given atom.Gilbert NewtonLewis,1875–1946,was
along-time professor at the University
of California at Berkeley. He made
contributions both to chemical
thermodynamics andto chemical
bonding,andwas among the first to
propose that a covalentbondinvolved
the sharingofanelectronpair.
Thevalence-shell electron pair repulsion(VSEPR) theory is an elementary theory
that is surprisingly effective in predicting the equilibrium nuclear conformation of cova-
lently bonded molecules. The basic idea is that electron pairs (or sets of pairs in a double
or triple bond), either in nonbonding or bonding orbitals, repel each other and are located
as far away from each other as possible. Four pairs of electrons maximize their distances
when located on alternate corners of a cube, which is called the tetrahedralelectron
geometry. The theory thus predicts that CH 4 has a tetrahedral electron geometry. The
H 2 O and NH 3 molecules also have a tetrahedral electron geometry. The molecular shape
involving only bonds and not lone pairs is called themoleculargeometry. We say that the
H 2 O molecule has angular molecular geometry and that the NH 3 molecule has trigonal
pyramidal molecular geometry. The VSEPR theory is usually elaborated by assuming
that lone pairs occupy a slightly larger volume than bonded pairs, since they have no
nucleus to attract them. For example, assigning a larger volume to the lone pairs in the
H 2 O molecule requires that the bond angle is slightly smaller than the tetrahedral angle
of 109.5◦, giving an explanation for the fact that the experimental angle is 104.5◦. The
VSEPR theory also includes conformations for expanded octets with five electron pairs
(trigonal bipyramidal electron geometry) and six electron pairs (octahedral electron
geometry).(^2) I. N. Levine,Quantum Chemistry, 5th ed., Prentice-Hall, Englewood Cliffs, NJ, 2000, p. 498ff.