Molecular Orbitals and Bonding

The rather patchwork nature of theories describing bonding in the valence bond package described on the other page led theorists in the early part of this century to develop more robust and exact theoretical treatments. [Note: this statement may not be Y2K compliant] When one asks the question, "But where are the electrons?" molecular orbital treatments attempt to answer the question exactly.

Orbitals are generally described as a region, or volume, inside which we are most likely to find a pair of electrons, if the orbital is filled. Atomic orbitals are such regions around single atoms. We are not likely to use many single atoms; organic chemists find them a bit drab. However, we will look at atomic orbitals as a starting point. Molecular orbitals are similar regions around and among the atoms that make up molecules. In each case, what holds the electrons in the neighborhood is the positive charge of the atomic nucleii.

In this course, we will use a very, very, very restricted set of ideas about molecular orbitals. This is not a course in quantum mechanics. We will look at atoms and atomic orbitals, and try to figure out how they change when they come into the company of other atoms. That's the bonding process.

We will look at pictures of orbitals produced by the calculations of very complex theory. Fortunately, since the pictures are generated using computer programs that others wrote, we will be taking advantage of the expertise of others, and not pretending to have it ourselves.

Hybridization

An isolated carbon atom has the electron configuration 1s2 2s2 2p2, for six electrons. Did you ever think about how the carbon feels about this? Carbon is a very gregarious element, and isolation is pure torture for any carbon atom. [Excuse me. Scientists are not supposed to anthropomorphize]

Hybridization analysis is an early attempt at figuring out the actual shapes of the bunches of electrons involved in bonds. This is an attempt to reconstitute the atomic orbitals (which were known from atomic spectroscopy) into orbitals which made sense according to some very "Lewis-like" rules: one molecular orbital would be constructed (by combining atomic orbitals constructively) to correspond with each Lewis bond. We will use this a lot, because it is easy to follow.

Step back and look at orbitals. A 2s is spherically symmetrical. A 2p orbital is dumbell shaped, as you know. But, when you add up all the 2p's, the net result is spherically symmetrical [this may be news to you]. So the electron density presented to substituents coming in is spherically symmetrical, and the substituents will likely arrange themselves so as to be farthest apart, as predicted by VSEPR, and measured in many molecules.

Four substituents around carbon

Let's imagine that we have four hydrogen atoms coming in to bond to carbon. Textbooks do this imaginary exercise all the time, ignoring the fact that molecules are almost never made by assembly from single atoms, and even if they were, they wouldn't all come in at the same time. However, let's press on, because it makes the description simpler.

If the four carbons come in at the same time, they will try to be as far apart as possible. This means that they will be on the corners of a tetrahedron, which is the only way you can symmetrically (all H-H distances the same) distribute four substituents around a center.

Result: bonds get electrons from one wedge of the pie, therefore more than one orbital. All four H's share the s orbital and the three p orbitals. Each resulting bond is formed from the 1s orbital of the hydrogen, and from 1/4 s and 3/4 p on the carbon. We call the carbon orbital a "hybrid orbital, and write it thus:

sp3

[one part s, three parts p]

Let's take another look at the electron distribution now. In a sense, these hybrid orbitals can be thought of as a mixture of s and p in the right proportions (1 to 3) to give 4 new hybrid orbitals:

These orbitals are, moreover, directed toward the H's at the corners of the tetrahedron. The electron distribution has not changed, but our way of thinking about it has, in an important way.

The bond formed by a direct overlap of two orbitals, as described above, is called a sigma bond. This is because sigma is the Greek letter most similar to s, the lowest atomic orbital in a shell. Honest.

Three substituents around the carbon

What about the case in which there are only 3 substituents? This can happen, and form a stable molecule only under special circumstances. This can also happen and make an unstable molecule under other circumstance.

Three substituents are most comfortably formed by placing them equally spaced around the equator. Hence, we would expect when the subst. come in, there would be three hybrid orbitals. Hybridize the orbitals to form three equal orbitals, and leave one p-orb. alone.

This makes sp2 orbitals, with greater s-character (1/3 instead of 1/4) and with different geometry (120° angles). What happens to the poor p-orbital? Here's the special circumstance. This only happens (in stable molecules) when there is another atom bonded to this one, which also has a half-filled p orbital. For example, let's do the mirror image routine again, and generate another sp2 hybridized carbon. Then, the overlap is strong between the two sp2 hybrid orbitals. There can also be some overlap between the two half-filled p-orb's, but note that they are not pointed at each other. Hence, the bond strength will be weaker (think of how hard it is for a gymnast to perform the Iron Cross on the rings, in which his arms are perfectly horizontal). This is a special bond called a pi-bond (from p --> pi, get it?).

The two kinds of bonding in this molecule are shown in red and blue in the diagram above. The double bond is comprised of a single sigma bond, made up of sp2 hybrid carbon orbitals shown in red, and a single pi bond, made up of unhybridized p orbitals, shown in blue. The blue dotted lines show the region of overlap in this diagram, which shrinks the p orbitals for clarity.

You should also remember that the centers of the three sp2 hybrid carbon orbitals are all in one plane, making it flatter than I have drawn here.

Important: The pi bond is not cylindrically symmetrical. There can be no rotation around this bond without drastically changing the nature of the bond (breaking it).

Qualitative Molecular Orbital Pictures

The picture above on the left is of the principle atomic orbitals which are used to construct the bonding in ethene (more commonly known as ethylene). There are two types of bonds in ethene: sigma bond and pi bonds. The directed sigma bond between the carbons is far stronger that the pi bond, due to greater overlap. Since the electrons in the sigma bond are much more tightly held, the pi electrons are much more available for bonding to electrophiles, or electron-seeking reactants.

When dealing with carbon, we will only need to use sigma bonds and pi bonds. There. Isn't that simple?


Exact Molecular Orbital Theory

Below, we see the highest occupied molecular orbital (HOMO) of ethene and the two HOMO's of ethyne. This highest energy obital dominates the chemistry of alkenes and alkynes. In each case, there are two pieces of each orbital, color-coded red and blue below, separated by a node (zero electron density). These pieces are not separate orbitals.

Ethyne (ethylene)

Ethyne (Acetylene)