A molecular orbital is essentially the path which an electron takes around a molecule. This is very similar to an atomic orbital, except that a molecular orbital is a path which takes into account the field of more than one nucleus. There are two types of molecular orbital, a bonding one and an anti-bonding one. This is basically decided by whether the orbiting electrons move around the nuclei in-phase or out of phase. Molecular orbitals are basically overlapping atomic orbitals, and the degree by which they go together determines whether the atoms will bond or not.
Before being able to understand orbitals, it is important to know the structure of an atom. Protons and neutrons occupy the nucleus of the atom, which is a very condensed container which sits at the center of an atom. Electrons whiz around the outside of the nucleus, essentially in the same way planets orbit the sun. A simplistic description of how electrons orbit a nucleus splits the electrons into “shells,” which are basically large circles surrounding the nucleus which can contain a set amount of electrons. Just as with planetary orbits, electron orbitals do not take the shape of perfect circles.
Electrons don’t all make their way around an atom in set, orderly circles. Instead, they often have more unusual orbits, and the specific orbit which they have is described by the atomic orbital theory. The “s” orbital is the simplest one, and this is essentially a spherical orbital. There are also dumbbell shaped orbitals, called “p” orbitals, which come in three different alignments. The interaction between the two atomic orbitals determines the type of the molecular orbital.
When two atoms bond, the electrons are still trying to follow their set orbital pattern, and their positions determine the type of molecular orbital. The first type of molecular orbital comes when the electrons orbit both nuclei in-phase, and overlap at some point. This creates a “bonding” orbital, because the electrons’ overlapping intensifies the negative charge and lowers the molecule’s potential energy. It would therefore require energy to split them back off into their separate atoms, and the atoms stay together.
The other type of molecular orbital is when the electrons orbit out-of-phase. This decreases the negative charge that they create, which in turn increases the overall potential energy stored in the molecule. Electrons like a low potential energy, so they are more likely to separate than orbit out-of-phase. The low potential energy of an out-of-phase orbit, then, means that the atoms split up, and the bond is not formed.