July 08, 2006

The Chemical Bond

Linus Pauling, The Shared-Electron Chemical Bond, 1928

Molecules are created by two basic kinds of bonds between atoms. In polar bonds, atoms with net positive charges attract atoms with net negative charges. This often occurs when a neutral atom loses an electron to another neutral atom. Although easily understood by early chemists (who already knew about electrical attraction and repulsion), polar bonds are weaker and have fewer interesting properties than non-polar bonds.

The discovery of the electron and Rutherford's discovery of the nucleus helped clarify what was going on in non-polar bonds: two atoms actually approach closely enough for electrons between the atoms to attract both nuclei. The electrons are effectively shared by both atoms. (Polar and non-polar bonds are actually the end-points of a scale. Real bonds are usually some mixture of sharing electrons and atom/atom attraction, as with H2O, where the Oxygen atom has a stronger grip on the shared electrons than the Hydrogen atoms, meaning that the O end has a slight negative charge and the H ends have a slight positive charge.)

Between 1913 and 1928, Bohr's quantum model of the atom aquired a lot more detail and complexity. In particular, it was discovered that only certain numbers of electrons can co-exist at each energy level: 2 at the lowest energy level, 8 on the 2nd and 3rd lowest energy levels, and 18 in the next few levels. This is, in fact, the reason that the periodic table's first five rows contain 2, 8, 8, 18, and 18 elements, respectively.

At each energy level, or shell, there are only a few stable orbits an electron can take. The quantum model of the atom describes these as wave functions (another example of jargon with distracting and incorrect connotations), which give the probability that an electron will be at a particular place at a particular time. These wave functions take many interesting shapes, ranging from spheres and dumbbells through cloverleaves and beyond. However, strictly speaking, the model only describe the orbits of single electrons around a single nucleus. As soon as additional electrons (which repel each other) are added to an atom, or worse, another atom comes close enough to form a non-polar bond, all the wave functions become approximations at best, and complete fictions at worst.

Linus Pauling, arguably the greatest chemist of all time, published a series of papers beginning in 1928 that detailed how to calculate the wave functions of electrons participating in a non-polar bond. Pauling knew that hybridizations of wave functions were possible, that is, that the actual wave function of an electron could take some of its properties from two or more of the basic wave functions. He realized that the most likely wave functions for electrons being shared between atoms would be those that were as asymetric as possible, so that the electron would spend most of its time between the atoms participating in the bond, as opposed to spending half its time between the atoms and half on the far side of one. Pauling figured out how to identify the most asymetrical hybridization possible.

One of the first practical results of this theory explained the structure of methane, CH4. Without hybridization, CH4 is predicted to have 3 bonds on the same plane, and a fourth in an arbitrary direction. With hybridization, CH4 is predicted to have 4 bonds pointing to the corners of a tetrahedron, which matches real observations of the molecule.

My own thoughts on this:

Hybrid orbitals are effectively a hack. A useful hack, since they work well in predicting the structure of molecules composed of relatively light atoms like carbon, nitrogen, and oxygen, but still approximations of the real situation. In particular, hybrid orbitals don't work well to explain bonds involving transition metals or other heavy atoms. Hybridization theory is, in fact, part of a whole series of increasingly sophisticated hacks that describe approximately how electrons behave in molecules. This is not meant to trivialize Pauling's work: hybridization theory is an effective way to predict the structure of organic molecules.

Figuring out how the electrons and nuclei in a molecule behave seems a lot like trying to solve the n-body problem. It looks to me like the whole thing is leading towards simply simulating all the attractive and repulsive forces between the electrons and nuclei involved in a molecule, much like a gravity simulation involving dozens of particles. If you were to do that, you could run the simulation for a while, and come up with some very accurate wave functions for the electrons. (Or rather, probability maps, since at this point they are neither waves nor functions.)


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