Atoms do not have these little particles moving around them in well-defined, circular orbits. The “particles” we call electrons do not orbit in circles around nuclei, nor do they have any well-defined position around the nucleus, nor do they have any well-defined speed (momentum, technically). It’s easy to imagine atoms with a nucleus and electrons orbiting it not only because that’s what we’re taught in school, but also because it’s much easier than imagining a dot with a cloud around it. We’re used to thinking of everything being definite, however that’s not how reality works on the subatomic scale.
Electrons do not have orbits, but probability clouds. Electron orbitals, also called atomic orbitals, are not definite orbitals but are probability clouds. Probability clouds are sections around atoms in which an electron has a chance to be found. The picture of the helium atom shown earlier shows that the closer to the center (nucleus) one looks, the darker the cloud gets. Darker regions relate to higher probabilities of an electron being found, and lighter regions relate to lower probabilities.
There are four main types of orbitals: s, p, d, and f orbitals. These depend on how many electrons are in each element and are described by quantum numbers. The aim of this post is for conceptual understanding, so for those who wish to learn how to find electron configurations, continue reading here.
Why do these shapes occur?
The laws of nature favor efficiency. When given the opportunity, atoms, particles, etc., will pack themselves as close as possible. Atoms will do this in materials, creating what’s called close packed planes. Electrons do something similar with electron orbital shapes by making them as close to spheres as possible, since spheres are the closest packed shape. Upon looking at the periodic table of clouds above, it may seem ironic that some clouds appear to be quite open. Due to atomic forces, the shapes are not always close to spheres, but they are as close as physically possible.
How do we make these shapes? We use VSEPR theory (commonly pronounced “vesper”). It stands for Valence Shell Electron Pair Repulsion. The name is pretty self explanatory, but the method of forming the shapes is not. If you’d like to find out how to do it, check out this link to learn some VSEPR basics.\
To be technical, the shapes are results of solutions to the Schroedinger wave equation. Each orbital is actually a mode of the wave functions of electrons in an atom. Each wave function is described by a quantum state. Not every one is unique in energy, a phenomenon dubbed degeneracy.
Pi and sigma bonds
We learned about chemical bonds in a previous post, but I decided not to mention that chemical bonds influence orbital shapes. Typically, bonds produce ligands which are shaped similarly like p orbitals, but with only one lobe. The main bonds are ionic, metallic, covalent, van der Waals, and hydrogen. There are two special bonds, which will be covered in another post, called pi and sigma bonds. These bonds produce their own special orbitals.
Remember, there are four subshells: s, p, d, and f. The s and p subshells are able to combine, or hybridize into the sp orbitals. This occurs typically with group IV elements. An individual atom will not hybridize unless in the presence of other atoms, so as to reduce their electrons’ potential energy. There can be sp3 orbitals in three dimensions, or sp2 orbitals in two dimensions (as seen in graphene).