A few weeks ago, I was given this question to complete:

The ground state electronic configurations of Ti is $\ce{[Ar] 4s^2 3d^2}$
State whether it follows the Aufbau principle or not. If not, explain why and state what the configuration would be if the principle was followed.

Now, I know the Aufbau principle tells us that when filling orbitals with electrons, the lowest energy orbital is filled first.

Looking at this diagram and the periodic table, I thought the filling was right - $\ce{4s}$ is before $\ce{3d}$ so I thought it was reasonable.

enter image description here

However, according to the Lecturer this is apparently wrong.

He says:

The $\ce{3d}$ level is at a lower energy than the $\ce{4s}$ and should be filled first according to the principle. It takes the above configuration to minimise the d-d interelectronic repulsion energies. The alternative configuration of [Ar]3d4 would have a higher energy.

I'm slightly confused here.

How am I wrong?

  • $\begingroup$ The 3d/4s thing is much more complicated than textbooks would have you and I believe. The total energy of the system is not simply a sum of individual orbital energies (orbitals are quantum mechanical objects, and the maths doesn't work out that way). So, the fact that the aufbau principle works is a bit of a coincidence (and the "breakdown" of aufbau in some contexts should not come as a surprise). See e.g. chemistry.stackexchange.com/a/8426/16683 $\endgroup$ Commented Jan 6, 2019 at 17:01
  • $\begingroup$ But, afaik, your lecturer's interpretation is correct. There are some references in the disclaimer here: chemistry.stackexchange.com/a/33310/16683 (I suggest not bothering with the rest of the answer.) $\endgroup$ Commented Jan 6, 2019 at 17:02

1 Answer 1


The energy level diagram which you give and is to be seen in the standard textbooks is assumed to apply to all elements. This is not the case, nor would we expect it to be so. After calcium the 3d drops below the 4s so fills first. Coulombic repulsions tend to push electrons up into the larger 4s orbital where repulsion is less. This means the 4s electrons are the outer electrons which are lost first in chemical reactions and define the atomic radius of the atom.


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