Rules for filling electrons in orbitals

The Aufbau principle was first proposed in 1927 by Walter Heitler and Fritz London to explain the ordering of electrons in atoms. The earliest theories of the atomic structure had been proposed by John Dalton in 1803 and by J. J. Thomson in 1904. Both theories were based on the idea that electrons orbited the nucleus of an atom, like planets orbiting a sun. However, it became clear that the planetary model failed to account for certain observed properties of atoms, such as their spectral lines.

There are some rules for filling electrons in the orbitals or the electron filling rules. The orbitals are filled with electrons in order of increasing energy levels. The highest occupied orbital is called the ‘highest occupied molecular orbital’ or HOMO. The lowest unoccupied orbital is called the ‘lowest unoccupied molecular orbital’ or LUMO. The Aufbau principle states that a series of electrons are placed into orbitals in order from low to high energy levels, filling one orbital before moving onto the next higher one.

The Aufbau principle is based on Hund’s rule, which dictates that electrons are first placed in the orbitals with the lowest value of the principal quantum number before they are placed in those with higher values. In other words, the orbitals have to be filled up one at a time, starting from the lowest energy level and proceeding until all orbitals are filled.

The name Aufbau principle comes from the German word ‘aufbauen’, which means construct or build up. Aleksandr Mikhailovich Burago introduced the term in 1947. The Aufbau principle is also known as the stepwise build-up principle or sequential build-up principle.

Important things about the Aufbau principle

The Aufbau principle is based on the assumption that orbitals with higher energies have a lower effective nuclear charge. The electrons in an orbit behave like a cloud of negative charge. The more electrons, the more negative the cloud is. So as an electron drops into a lower-energy orbital, it reduces the effective nuclear charge and attracts other electrons to the remaining orbitals. Aufbau has given many important things about the rules for filling electrons in orbitals. 

Taken together, these two principles imply that any given atom will never have more than one electron in any given orbital. This explains Bohr’s postulate: electrons fill up the orbitals in order of increasing energy, one electron per orbital, with no exceptions.

The (n+l) rule, also known as the Aufbau principle or Aufbau sequence, determines the energy of all atomic orbitals. The rule says that the orbital having a lower value of (n+l) is filled first. If two orbitals have the same n+l, the one with lower n is filled first.

The first orbital we fill in is the 1s orbital. This fills up with two electrons. The next orbital to fill in the 2s orbital. It fills with another two electrons. The third orbital to fill is the 2p orbital, which fills with six more electrons. The next orbitals to fill will be the 3s and 3p orbitals, each filled with eight more electrons.

The next highest energy level has four orbitals. We fill them as follows: 4s fills with two electrons; 4p fills with six; and then comes 4d, which fills with 10 electrons. Following that is the 5s filling with eight electrons; then comes 5d, which fills with 14 more; and finally comes the 5p filling, which completes our list of filled groups of orbitals by filling up with 18 more electrons.

Thus the following diagram can be used to visualise the filling of orbitals better.

We move from the tail of the arrow to the head and then move onto the tail of the arrow below.

Writing them down in this order gives us the increasing order of orbital energy as well as the order in which electrons should be filled in the atom.

Exceptions

Chromium is the element found in the paint used on automobiles. Its atomic number is 24, meaning that it has 24 protons in its nucleus and, as a result, has an atomic mass of about 51.99. It is a transition metal with an electron configuration of [Ar]3d54s1.

The electron configuration of chromium has been confirmed by X-ray absorption spectroscopy and photoelectron spectroscopy, which can be used to determine the ground-state electron configuration in atoms and molecules. The first experimental confirmation for the ground state was carried out by M. Jortner and W. Denk using X-ray absorption spectroscopy. The experiment confirmed that [Ar]3d54s1 was the ground-state electron configuration of chromium.

The ground-state electron configuration of chromium is [Ar]3d54s1 and not [Ar]3d44s2, as suggested by the Aufbau principle. Many factors contribute to this exception—the increased stability provided by half-filled subshells and the relatively low energy gap between the 3d and the 4s subshells.

This is also observed in Cu where the configuration is [Ar]3d104s1 and not [Ar]3d94s2 as full filled and half filled have greater stability than one full filled orbital.

Conclusion

In this article, we discussed the rules for filling electrons in orbitals: the Aufbau principle in detail. Afbau principle gives us an idea on how the electrons are filled in the orbitals of an atom by nature’s laws of approaching greater stability. It provides us with the n+l rule which is correct in most cases except a few exceptions.