The Periodic Table and the Aufbau
One of the biggest topics in the teaching and learning of chemistry is the use of the aufbau principle to predict the electronic configurations of atoms and to explain the periodic table of the elements. This method has been taught to many generations of students and is a favorite among instructors and textbooks when it comes to setting questions. In this blog I am going to attempt to blow the lid off the aufbau because it is deeply flawed, or at least the sloppy version of the aufbau. The flaw is rather subtle and seems to have escaped the attention of nearly all chemistry and physics textbooks and the vast majority of chemistry professors that I have consulted on the subject.

The error comes from what may be an innocent attempt to simplify matters or maybe just an understandable slip as I will try to explain. Whatever the cause there is no excuse for perpetuating this educational myth.

So what’s the problem?
The aufbau method was originally proposed by the great Danish physicist Niels Bohr who was the first to bring quantum mechanics to the study of atomic structure and one of the first to give a fundamental explanation of the periodic table in terms of arrangements of electrons (electronic configurations). Bohr proposed that we can think of the atoms of the periodic table as being progressively built up starting from the simplest atom of all, that of hydrogen which contains just one proton and one electron. The other atoms differ from hydrogen by the addition of one proton and one electron. Helium has two protons and two electrons, lithium has three of each, beryllium has four of each, all the way to uranium which at that time, (1913), was the heaviest known atom, weighing in at 92 protons and 92 electrons. Neutron numbers vary and are quite irrelevant to this story incidentally.

The next ingredient is a knowledge of the atomic orbitals into which the electrons are progressively placed in an attempt to reproduce the natural sequence of electrons in atoms that occur in the real world. Oddly enough these orbitals, at least in their simplest form, nowadays come from solving the Schrödinger equation for the hydrogen atom but let’s not get too sidetracked for the moment.

The orbitals
The different atomic orbitals come in various kinds that are distinguished by labels such as s, p, d and f. Each shell of electrons can be broken down into various orbitals and as we move away from the nucleus each shell contains a progressively larger number of kinds of orbitals. Here is the well-known scheme,

First shell contains 1s orbital only
Second shell contains 2s and 2p orbitals
Third shell contains 3s, 3p and 3d orbitals
Fourth shell contains 4s, 4p, 4d and 4f orbitals and so on.

The next part is that one needs to know how many of these orbitals occur in each shell. The answer is provided by the simple formula 2+ 1 where  takes different values depending on whether we are speaking of s, p, d or f orbitals.

For s orbitals  = 0, for p orbitals  = 1, for d orbitals  = 2 and so on.

As a result there are potentially one s orbital, three p orbitals, five d orbitals, seven f orbitals and so on for each shell.

So far so good. Now comes the magic ingredient which claims to predict the order of filling of these orbitals and here is where the fallacy lurks. Rather than filling the shells around the nucleus in a simple sequential sequence, where each shell must fill completely before moving onto the next shell, we are told that the correct procedure is more complicated. But we are also reassured that there is a nice simple pattern that governs the order of shell and consequently of orbitals filling.

And this is finally the point at which the aufbau diagram, which I am going to claim lies at the heart of the trouble, is trotted out.

The order of filling of