Chem 328 

Summer 2004 
Lecture Notes: 2 June 


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Another great limitation of Lewis structures is that they tell us nothing about molecular shape. So to determine shape we added another tool, VSEPR Theory, to our chemical toolbox.
VSEPR (Valence Shell Electron Pair Repulsion) Theory is based on three assumptions:
VSEPR predicts geometry based on these assumptions in a few simple, sequential, steps:
Examples of the various molecular geometries discussed below may be found in the Molecular Geometry Supplement.
For central atoms with eight outer electrons (octets) there are three possible electron pair geometries:
 Linear with angles of 180° ( a single pair and a triple bond, or two double bonds).
 Trigonal planar with angles of 120° (one double bond and two single pairs).
 Tetrahedral with angles of 109.5° (four single pairs). [model]
These three electron pair geometries can lead to five molecular geometries:
 Linear (e.g. carbon monoxide)
 CO_{2}
 valence electrons = 4 + 2x6 = 16
 6y + 2 = 20, thus 4 fewer electrons than required for all single bonds, 4/2 = 2 multibonds (2 double or 1 triple)
 LS: from symmetry C will be central atom, therefore= :O::C::O:
 Considering C as the central atom, have 2 bonded atoms and no lonepairs, therefore
 steric number = 2, so linear electronic geometry, and
 linear molecular geometry
 Trigonal planar (e.g. formaldehyde, CH_{2}O)
 formaldehyde, CH_{2}O
 valence electrons = 4 + 2x1 + 6 = 12
 6y + 2 = 6 x 2 + 2 = 14; so molecule has 2 fewer electrons than required for all single bonds, 1 double bond
 LS: from symmetry C will be central atom, therefore=
 Considering C as the central atom, have 3 bonded atoms and no lonepairs, therefore
 steric number = 3, so trigonal planar electronic geometry, and 3 atoms so
 trigonal planar molecular geometry
 Tetrahedral (e.g. methane, CH_{4})
 valence electrons = 4 + 4x1= 8
 four bonds possible, since only 4 pairs, single bonds because only have H's bound to C.
 LS: from symmetry C will be central atom, therefore=
 Considering C as the central atom, have 4 bonded atoms and no lonepairs, therefore
 steric number = 4, so tetrahedral electronic geometry, and 4 atoms so
 tetrahedral molecular geometry
 Trigonal pyramidal (e.g. ammonia, NH_{3})
 valence electrons = 5 + 3x1= 8
 only 4 pairs, single bonds because only have H's bound to N, 3 bonds, since only 3 H's
 LS: from symmetry N will be central atom, therefore=
 Considering N as the central atom, have 3 bonded atoms and one lonepair, therefore
 steric number = 4, so tetrahedral electronic geometry, but only 3 atoms so
 trigonal pyramidal molecular geometry
 Bent (e.g. water, H_{2}O)
 valence electrons = 6 + 2x1= 8
 only 4 pairs, single bonds because only have H's bound to O, 2 bonds, since only 2 H's
 LS: from symmetry O will be central atom, therefore=
 Considering O as the central atom, have 2 bonded atoms and 2 lonepairs, therefore
 steric number = 4, so tetrahedral electronic geometry, but only 2 atoms so
 bent molecular geometry
Electronegativity. Electronegativity is a periodic measure of how electrons are shared by atoms. It enables us to guess the degree of polarity of a bond between two atoms (i.e. how the bonding electrons are shared), from nonpolar covalent (equal sharing) to fully ionic bonds (no sharing). Recall that F has the highest electronegativity value for and Cs has the lowest. We have used two common ways of determining EN's:
Polarity: How can we predict electron density and thus charge distribution in a molecule? Need two bits of information:
Examples:

Formal charge is a simple model for determining how charges are distributed on atoms in a molecule or molecular ion. It is not always terribly acurate, but is very useful for approximating how molecules will behave in some situations. It is particularly useful in choosing among resonance structures in organic chemistry to determine which are likely to make the greatest contribution to the "real" (composite) structure.
Formal Charge (FC) = the charge an atom would have if all bonding pairs were shared equally (polar bonds don't exist in this model).
To assign Formal Charges:
 Draw a correct Lewis Structure.
 Assign both electrons of a lone pair to its associated atom.
 Divide all bonding pairs, giving one electron of each pair to each atom in the bond.
 Calculate FC = # electrons on the unbonded (elemental) atom  # electrons assigned to the bonded atom.
Examples:
 Phosphoric acid (H_{3}PO_{4})
 LS:
 FC_{P}: 5  4 = +1
 FC_{H}: 1  1 = 0
 FC_{O}: 6  7 = 1
 FC_{3 O's}: 6  6 = 0
 S FC = 1 + 3 (0) + (1) = 0. Notice that the Formal charges add up to give zero, the charge on the molecule.
 Perchlorate ion (ClO_{4}^{})
 LS:
 FC_{Cl}: 7  4 = +3
 FC_{O}: 6  7 = 1
 S FC = +3 + 4 (1) = 1. Notice that the Formal charges add up to give 1, the charge on the molecular ion.
I want to begin 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 at the Bonding Supplement.
In viewing these models we should keep in mind that:
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. Animations and images of orbitals are available at the Atomic Orbital Supplement.
For our discussion of bonding we need to look only at sand p orbitals. Higher orbitals are not involved in the substances we are interested in in this course.
Electronic Energy Levels Review. As we discussed last time:
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 must be 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 not arranged 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. [overhead]
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. 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! [overhead]
Notice, that with this Hybrid Orbital Theory we are looking at individual atoms, not molecules. All of our calculations and predictions are for the atoms. We now make molecules by overlapping the new hybrid orbitals with other hybrid orbitals or with atomic orbitals of other atoms to make a molecule.
Let's look now at some examples, noting single and multiple bonds etc.
Note we get two basic bond types when we overlap orbitals:
The hybrid atomic orbital model is a localized electron model  the quantum calculations are looking at the atoms individually. The hybrid orbital model is particularly useful to us at this time because it gives nice pictures of two aspects of bonding:
In the hybrid orbital model described we look at the atoms individually in creating the orbitals, then we allow them to overlap to give bonds. Of course in a real molecule nature does not distinguish between atoms and orbitals in this way, in fact when atoms form a bond new orbitals are formed based on the entire molecule.
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Last modified 2 June 2004