CHEM 1103 Lecture Notes - Lecture 1: Creative Commons License, Molecular Orbital Theory, Openstax
19 Dec 2016
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OpenStax-CNX module: m51059 1
Molecular Orbital Theory∗
OpenStax College
This work is produced by OpenStax-CNX and licensed under the
Creative Commons Attribution License 4.0†
Abstract
By the end of this section, you will be able to:
•Outline the basic quantum-mechanical approach to deriving molecular orbitals from atomic orbitals
•Describe traits of bonding and antibonding molecular orbitals
•Calculate bond orders based on molecular electron congurations
•Write molecular electron congurations for rst- and second-row diatomic molecules
•Relate these electron congurations to the molecules' stabilities and magnetic properties
For almost every covalent molecule that exists, we can now draw the Lewis structure, predict the electron-
pair geometry, predict the molecular geometry, and come close to predicting bond angles. However, one of
the most important molecules we know, the oxygen molecule O2, presents a problem with respect to its
Lewis structure. We would write the following Lewis structure for O2:
This electronic structure adheres to
all the rules governing Lewis theory. There is an O=O double bond, and each oxygen atom has eight electrons
around it. However, this picture is at odds with the magnetic behavior of oxygen. By itself, O2is not
magnetic, but it is attracted to magnetic elds. Thus, when we pour liquid oxygen past a strong magnet,
it collects between the poles of the magnet and dees gravity, as in here1. Such attraction to a magnetic
eld is called paramagnetism, and it arises in molecules that have unpaired electrons. And yet, the Lewis
structure of O2indicates that all electrons are paired. How do we account for this discrepancy?
Magnetic susceptibility measures the force experienced by a substance in a magnetic eld. When we
compare the weight of a sample to the weight measured in a magnetic eld (Figure 1), paramagnetic samples
that are attracted to the magnet will appear heavier because of the force exerted by the magnetic eld. We
can calculate the number of unpaired electrons based on the increase in weight.
∗Version 1.5: May 19, 2015 12:34 pm +0000
†http://creativecommons.org/licenses/by/4.0/
1"Introduction", Figure 1 <http://cnx.org/content/m51054/latest/#CNX_Chem_08_00_LiqO2>
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OpenStax-CNX module: m51059 2
Figure 1: AGouy balance compares the mass of a sample in the presence of a magnetic eld with the
mass with the electromagnet turned o to determine the number of unpaired electrons in a sample.
Experiments show that each O2molecule has two unpaired electrons. The Lewis-structure model does not
predict the presence of these two unpaired electrons. Unlike oxygen, the apparent weight of most molecules
decreases slightly in the presence of an inhomogeneous magnetic eld. Materials in which all of the electrons
are paired are diamagnetic and weakly repel a magnetic eld. Paramagnetic and diamagnetic materials
do not act as permanent magnets. Only in the presence of an applied magnetic eld do they demonstrate
attraction or repulsion.
note: Water, like most molecules, contains
all paired electrons. Living things contain a large percentage of water, so they demonstrate dia-
magnetic behavior. If you place a frog near a suciently large magnet, it will levitate. You can see
videos2of diamagnetic oating frogs, strawberries, and more.
2http://openstaxcollege.org/l/16diamagnetic
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OpenStax-CNX module: m51059 3
Molecular orbital theory (MO theory) provides an explanation of chemical bonding that accounts for the
paramagnetism of the oxygen molecule. It also explains the bonding in a number of other molecules, such
as violations of the octet rule and more molecules with more complicated bonding (beyond the scope of this
text) that are dicult to describe with Lewis structures. Additionally, it provides a model for describing
the energies of electrons in a molecule and the probable location of these electrons. Unlike valence bond
theory, which uses hybrid orbitals that are assigned to one specic atom, MO theory uses the combination
of atomic orbitals to yield molecular orbitals that are delocalized over the entire molecule rather than being
localized on its constituent atoms. MO theory also helps us understand why some substances are electrical
conductors, others are semiconductors, and still others are insulators. Table 1 summarizes the main points of
the two complementary bonding theories. Both theories provide dierent, useful ways of describing molecular
structure.
Comparison of Bonding Theories
Valence Bond Theory Molecular Orbital Theory
considers bonds as localized between one pair of
atoms
considers electrons delocalized throughout the en-
tire molecule
creates bonds from overlap of atomic orbitals (s, p,
d. . .) and hybrid orbitals (sp, sp2,sp3. . .)
combines atomic orbitals to form molecular orbitals
(σ,σ*, π,π*)
forms σor πbonds creates bonding and antibonding interactions based
on which orbitals are lled
predicts molecular shape based on the number of
regions of electron density
predicts the arrangement of electrons in molecules
needs multiple structures to describe resonance
Table 1
Molecular orbital theory describes the distribution of electrons in molecules in much the same way
that the distribution of electrons in atoms is described using atomic orbitals. Using quantum mechanics, the
behavior of an electron in a molecule is still described by a wave function, Ψ, analogous to the behavior in an
atom. Just like electrons around isolated atoms, electrons around atoms in molecules are limited to discrete
(quantized) energies. The region of space in which a valence electron in a molecule is likely to be found is
called a molecular orbital (Ψ2). Like an atomic orbital, a molecular orbital is full when it contains two
electrons with opposite spin.
We will consider the molecular orbitals in molecules composed of two identical atoms (H2or Cl2, for
example). Such molecules are called homonuclear diatomic molecules. In these diatomic molecules,
several types of molecular orbitals occur.
The mathematical process of combining atomic orbitals to generate molecular orbitals is called the linear
combination of atomic orbitals (LCAO). The wave function describes the wavelike properties of an
electron. Molecular orbitals are combinations of atomic orbital wave functions. Combining waves can lead
to constructive interference, in which peaks line up with peaks, or destructive interference, in which peaks line
up with troughs (Figure 2). In orbitals, the waves are three dimensional, and they combine with in-phase
waves producing regions with a higher probability of electron density and out-of-phase waves producing
nodes, or regions of no electron density.
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