Bond energies, as tabulated in Table 8.4 of your text (p 374) can be used much like heats of formation to calculate the heat (energy) involved in a reaction. Note that in the table all of the bond energies are positive values, so we have to think and assign the appropriate sign depending on what's occuring. Thus, it takes energy to break a bond (in a sense a bond is a situation where the energy is lower, or it wouldn't be a bond) - the tabulated bond energy is positive, but energy will be released when a bond is made - so in fact the bond energy is negative.

Let's try an example: How much energy is released in the complete combustion of methane?

Writing a balanced equation:

CH _{4}+ 2 O_{2}CO_{2}+ 2 H_{2}OFrom the table the bond energies are:

- C-H 413 kJ/mol
- O=O 495 kJ/mol
- C=O 799 kJ/mol
- O-H 467 kJ/mol
Combining the bond energies (reactants - products):

4 (413 kJ/mol) + 2 (495 kJ/mol) - 2 (799 kJ/mol) - 4 (467 kJ/mol) With the 2642 kJ/mol - 3466 kJ/mol =

-824 kJ/mol

A Quantum View of Bonding of classical bonding models in mind, let's explore how we might view covalent bonding from a more modern, quantum, point of view.successes and failuresTo do this we will need to look briefly again at atomic orbitals and ask what they can tell us about how atoms might share electrons.

But before we even do that, I want to look at some simple atoms and molecules calculated at the highest level of theory, and thus the best approximation we have of what real atoms and molecules look and behave like. In order to do these calculations, we are assuming our atoms or molecules are in a vacuum, and essentially alone in the Universe. First let's look at ionic bonding using the example of sodium chloride (one of the best "pure" ionic compounds). The images. animations etc. are available in the initial section on ionic bonds in the Bonding Supplement.

We have looked at a quantum model for ionic bond formation, now I want to continue our discussion with a model for covalent bond formation using two well studied diatomic molecules: Cl

_{2}and H_{2}. The animations and images are available in the Bonding Supplement.

In viewing these models we should keep in mind that:

- When atomic orbital sets are filled, or half-filled they become completely symmetrical.
- We should expect orbitals in molecules to be different than those in atoms since the electrons are shared by two nuclei rather than distributed around a single nucleus.
- Orbitals are orbitals
- Only two electrons can be accommodated in any orbital
- No two electrons can have the same "address" (the same set of quantum numbers).
- For a molecules the "address" becomes the molecule over which the electrons are shared rather than the atom.

- We have conservation of orbitals - a molecule will have the same number of orbitals as the atoms which make up the molecule.
- For our purposes we can also assume a conservation of orbital energy.

With these thoughts in mind, lets look further at bonding and bond formation.

For both Cl_{2} and H_{2} you will note that we have a cylindrical distribution of the electrons in the single bond around the axis between the nuclei. Obviously in both cases the shapes of the orbitals have changed.

In order to understand this change, let's go back and review the shapes and electron distribution of atomic orbitals. The animations and images from this discussion are available at the Atomic Orbital Supplement.

For our discussion of bonding we need to look at *s, p, *and *d* orbitals. Higher orbitals are not involved in any of the substances we are interested in in this course.

**Electronic Energy Levels Review:**

- We will designate the primary energy level, corresponding to the average radial distance of the electron from the nucleus as a
**shell**, and give it the symbol**n**. The lowest possible energy level is then the*ground state with n = 1*. - The value of n also gives the number of nodes in each of the orbitals in that shell, with each shell having one node at infinity, where:
- A node is a region of zero probability of finding an electron.
- Nodes can have two general geometries:
- radial (or spherical, since they describe a spherical shell at a specific radial distance from the nucleus), with each atom having at least one radial (spherical) node at infinity;
- angular (either planar, e.g. as in the planar p-node and diagonal d-nodes, or cone shaped, e.g. as in the cone-shaped nodes of the d
_{z2}orbitals which results in the donut shaped orbitals).

- Shells with n > 1 may have
*subshells*which are different geometrical patterns of electron distribution. Thus:- The lowest energy pattern is spherical and given the designation
*s.* - The next lowest energy distribution is bi-lobed with a planar symmetry. It is given the designation
*p.* - The third lowest energy distribution has diagonal planes of symmetry and is designated
*d.* - The fourth lowest energy distribution is designated
*f.*This is the highest subshell type occupied by ground state electrons in any atom, so we will not look any further (an infinite number of subshells exist in theory for excited states, but they are not important to our understanding).

- The lowest energy pattern is spherical and given the designation
- The average energies of the different subshells are the energy of the shell, thus when subshells are present the energy of the shell is
*split.*For example, in the n=2 shell the 2s orbital becomes lower in energy than the shell, while the 2p orbitals become higher in energy. - The regions of electron occupancy in subshells are called
*orbitals.*- For each shell there is one
*s*orbital. - For each shell with n = 2 or greater there are three
*p*orbitals: p_{x}, p_{y}, and p_{z}. - For each shell with n = 3 or greater there are five
*d*orbitals: d_{xz}, d_{yz}, d_{xy}, d_{x2- y2}, and d_{z2}

- For each shell there is one

Hybrid Atomic Orbitals We've reviewed atomic orbitals and classical bonding theory, now our question is how can we best understand bonding in molecules, including their shapes etc., in light of modern theory (quantum mechanics)?

We need to keep in mind that our modern picture of simple molecules

mustbe consistent with the classical picture, since it gave us good approximations to observation!However, when we look at the atomic orbitals for the valence electrons they are generally

notarranged in a way that would give the shapes predicted by VSEPR Theory. Thus, the four valence orbitals of atomic carbon are the spherical 2s orbital and the three mutually perpendicular 2p orbitals, while VSEPR predicts that carbon surrounded by four hydrogens will be tetrahedral in shape.[text Fig 9.1]So what do we do? Recall that the specific shapes of the orbitals result from the interactions of the electrons with a central positive charge (and each other), so we might expect they would change shape if exposed to an external charge (like a second atom).

One way to model this new situation then is to assume that all four of the atomic orbitals are perturbed into a new configuration. If we assume they all have the same energy (required if they are to form a symmetrical set around the carbon nucleus, for example), then we can assume they each have the average energy of the original four orbitals.

[text Fig 9.5]We can now come up with a new orbital set by adding the orbitals together, and keeping in mind that we must end up with the same number of orbitals as we started with. If we make this calculation we find there are now four equivalent orbitals arrayed in a tetrahedral geometry, just as we predicted with VSEPR Theory - ta da![text Fig 9.3, 9.4 (xs)]Remember, that with

Hybrid Orbital Theorywe are looking at individual atoms, not molecules. It is aall of our calculations and predictions are for theLocalized theory,atoms. We make molecules by overlapping the newhybrid orbitalswith other hybrid orbitals or with atomic orbitals of other atoms to make molecules.Let's look now at some examples and illustrations in your text , noting single and multiple bonds etc.

## Tetrahedral Electronic Geometry = sp

^{3}.

- Four orbitals (s + 3 p's) combined. (Note the sum of "exponents" = number of orbitals)
[text Fig 9.3]

- Note in the following example text figures the side Hs should be behind the hybrid orbitals.

- Methane (CH
_{4}) - tetrahedral molecule.[text Fig 9.6]- Ammonia (NH
_{3}) - trigonal bipyramidal molecule.[text Fig 9.7]## Trigonal Planar Electronic Geometry = sp

^{2}.

- Three orbitals (s + 2 p's) combined, one p orbital left as is.
[text Fig 9.8, 9.9]

- Ethylene (H
_{2}CCH_{2}) - each carbon has trigonal planar geometry.[text Fig 9.10, 9.12, 9.13]## Linear Electronic Geometry = sp

^{1}, or sp.

- Two orbitals (s + p) combined, two p orbitals left as is.
[text Fig 9.14, 9.15, 9.16]

- Carbon dioxide (CO
_{2})[text Fig 9.17, 9.18, 9.19]- Nitrogen (N
_{2})[text Fig 9.20]Note we get two basic bond types when we overlap orbitals:

- Sigma (
sigma) bonds: These are cylindrically symmetrical around the axis connecting the bonded atoms. Single bonds are always sigma bonds, and in a multiply bonded system the "first" or "central" bond is a sigma bond.[text Fig 9.20b]- Pi (
pi) bonds: these are made up of two lobes with planar symmetry round a plane though the nuclei of the two bonded atoms. The "second" and "third" bond of multiply bonded atoms are pi bonds. For systems with two pi bonds the bond panes are perpendicular to each other.[text Fig 9.20c].

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*© R A Paselk*

*Last modified 13 April 2015*