Geos 306, Lecture 3
The Electronic Origins of Bonding
When atoms were formed, whether just after the big bang event, or during star evolution, or supernova, it was too hot for the electrons to be localized
around a nucleus. Only when the surrounding temperature cooled down enough,
could the electrons remain around a nucleus.
This tells us that the energy needed to keep electrons around a nucleus
is much lower than the energies associated with the nucleus or the formation
of electrons to begin with.
It is this low energy environment, where electrons are bound to a nucleus,
that define the conditions in which humans may exist, because groups of
atoms stay together as molecules or solids only by the bonding of their
electrons. Electrons are the glue that holds groups of atoms together.
Our mineralogy class is going to spend effort thinking about the valence states of the atoms in minerals.
You must understand valence states in order to understand and appreciate the complexities of mineralogy.
In fact, understanding the nature of valence states is also at the heart of biology.
"Life is based on energy gained by electron-transfer processes; these processes rely on oxidoreductase enzymes, which often
contain transition metals in their structures."
Moore et al (2017).
Let's review the nature of the atom from the point of view of the electrons.
The atom is mainly low-density space with a very dense, small nucleus that
defines its center.
Electrons are located in space around the nucleus, and the effective size of the atom is very dependent upon these electrons.
The distributions of electrons define the size of each atom.
These electrons can be classified in terms of shells that correspond to
the rows in the periodic table. Each shell can fit a certain number of
electrons, depending upon how far away from the nucleus it is. A shell
that is close to the nucleus can only contain a small number of electrons,
otherwise the electrons are too close together, and electrostatic repulsive
forces push them apart.
Shells of electrons are most stable when they contain the maximum number
of electrons that they can hold. On the one hand, if there are too few
electrons, then the electrons are constantly whizzing about, trying to
fill all of the available space. Therefore, they have high kinetic energy.
On the other hand, if there are too many electrons then electrostatic repulsion
takes over and pushes them apart.
Define the electrons in an unfilled outer shell as valence electrons.
Since these are the outermost electrons, these are the ones that are perturbed
by bringing another atom close by. These are the ones that are involved
Define: A chemical bond is the result of a redistribution
of electrons that leads to a more stable configuration between two or more
In a given column of the
atoms from lower rows (i.e. greater
principal quantum numbers, e.g. K) are larger than atoms from the higher rows (e.g. Li).
The reason is that atoms in lower rows have more electrons, these electrons
repel each other and so are spread out around the nucleus. The volume of
space occupied by electrons increases and so the size of the atom increases.
In a given row, the atoms are larger on the sides, but are smaller towards
the middle (e.g Na and Cl are comparatively large while Al and Si are smaller). The reason is that as you go from left to right across a given
row, the charge of the nucleus increases. Starting at the left side of a row, an increase in the charge of the nucleus pulls the electrons
in tighter but without much of an increase in electron-electron repulsion because there are so few electrons in the outermost shell.
Towards the middle of a row, there is a critical number of electrons that are spread out with a balance of attraction
to the nucleus and mutual repulsions with each other. At the far right of a row, the number of electrons is large enough that
their repulsion is significant and they push each other away, creating a larger atom.
Since the bond is formed by some sort of distribution of + and - charges,
then there is a force (called the bonding force) that can be ascribed
to the bond. The + charges repel each other, keeping the nuclei from getting too
close to each other, while the nuclei and electrons attract. A proton
generally does not leave the nucleus, so we consider it to be a point charge.
The electrons move about to try and stabilize the group. The more electrons
between a pair of atoms then the less the nuclei can repel each other.
We say that the electrons screen the nuclei.
But there is a limit to the number of electrons that can be put between
the nuclei because the electrons repel each other too. You can imagine
that with all the many types of atoms there are many types of bonds, all
of different strengths and properties. Each pair of unique elements has
its own unique bond.
Recent work has shown that a pair of atoms is bonded if and only if there
is a critical point in the electron density between the pair. Here is an
example of a Na atom moving closer to an O atom in a O-Si-O-Si-O linkage.
An O atom is stationary in the center of the image.
Notice the bond forming between Na (coming in from the top) and O.
Notice also the way that the electrons redistribute themselves, especially with regard to the central O and its associated Si-O bonds.
As the Na atom forms a bond to the central O atom, the electron density along the O-Si bonds decreases and electrons move into
the region between Na and O. The Si-O distance increases as Na-O gets shorter because the Si-O bond is losing electrons.
It addition, the Si-O-Si angle decreases as the Na atoms gets closer and strengthens its Na-O bond.
The greater the electron density at the critical point then the stronger the bond
and the shorter the bond. Short bonds are strong, long bonds are weak.
The electron density of the free atom in space is spherical. Only in the
presence of an electric field do the electrons configure themselves into
orbitals of other shapes. We model the shapes after H, the only atom for
which we can do exact computations. The model is called the Linear Combinations
of Atomic Orbitals (LCAO), where the electrons for a given atom are
considered to be the combination of the many orbitals that were computed
for H. This seems to work well in practise.
When two or more atoms get close enough together the electrons may reorganize
themselves to achieve a different energy configuration. The resulting
shapes may be different than the s, p, d, or f
shaped orbitals. It is a shape that is determined by e--e-
and p+-p+ repulsion and e--p+
If the energy is lower when the electrons have reorganized
themselves, then the atoms will stay together and we say that a bond
has been formed.
Some electrons can no longer be associated only with one of the atoms,
but instead are associated with both atoms in a bond. In general, these electrons come from the set of
electrons. The others are called core electrons. Core electrons generally
have a closed shell configuration.
Types of bonds
Experience has shown us that we can classify bonds into 7 different
types, the first 3 of which are of major importance.
van der Waals
Definition of an ion: an atom in which the number of electrons does not equal the number of
There are several ways to turn an atom into an ion.
Light, e.g. photoelectric effect: where the energy of the incident photon kicks the electron out of its orbit
Heat, e.g. sun: where the kinetic energy of atom and electron vibrations is so large that the electron vibrates away from the atom and does not return.
Through the exchange of electrons with another atom, via the ionic bond.
Ionic bonding occurs between a pair of atoms when one of the atoms gives
up its valence electrons to the other. The result is that both atoms have
filled shells. Both atoms also end up with a charge, one negative, and
the other positive. We call the positive charged atom a cation,
and the negatively charged one, an anion.
A classic example of ionic bonding is between Na and Cl. Na is a silvery
metal. It has 1 valence electron. Cl is a yellow-green gas, and it needs
1 electron to fill its valence shell. If you put the gas and the metal
together, then they will burn as electrons are exchanged. The metal dissolves
and the gas disappears. The ions now have opposite charges and are attracted
to each other by electrostatic forces. They form a crystal with the rock
salt structure, as shown below.
Ionic bonds commonly form between atoms of the 1st column and the 7th,
and between the 2nd column and the 6th. E.g. NaCl, MgO
We assume that ions have a closed shell and so their shape can be assumed
to be spherical.
The elements that become cations generally have diffuse electron densities while the electron density in atoms that become anions tend to
drop off sharply. In the figure below we see that significant electron density from Na and Si, two cations,
continues out to almost 3 angstroms away from the nucleus.
In contrast, the electron densities of O and F, both anions, approach zero around 2 angstroms from the nucleus.
An interesting question to ask yourself is, at about 1 angstrom from the nuclues, why do Na and F appear to be the smaller atoms in this figure while O and Si appear to be the larger ones.
We earlier stated that outermost atoms are larger than innermost atoms.
Properties: Materials composed of ionic bonds have distinctive properties
that depend upon bond length, R. This is because the forces are coulombic (i.e. the force falls off as 1/r2).
Eg. Melting temperature versus R.
Ionic solids are strong when pushed together, but weak if cleaved or sheared.Once
the bond breaks it is not easy to put back together. For instance, suppose
you cleaved NaCl. Then, along the cleaved surface, Na1+ is short 1 electron and Cl1- has one extra.
They have no need to come close enough together to exchange electrons.
Ionic crystals tend to dissolve easily in water and have high melting temperatures.
So if you break a crystal apart, you can put it back together by dissolving
it and then reprecipitating it, or by heating it enough to excite the valence electrons off of the
Ionic bonding is most often understood as being between pairs of atoms. However, it can also occur within larger groups of atoms.
E.g. the three atom group CaCl2.
Problem: Determine the spin diagrams for O2-, Si4+, Mg2+, Fe2+, Fe3+
Problem: Rank the sizes of Li, C, F, Na, Mg, S6+, S2-, Ti, Fe2+, Fe3+, Pb
Problem: What are the charges of the anionic groups: SiO4, AlO4, AlO6, SO4, PO4, MgO6,
Suggested Reading: Wenk and Bulakh, 12-22; Klein, 53-57; Nesse, 46-56