What is the correct electron configuration of scandium?

There is some doubt about the correct electron configuration of transition metals. Is the 4s sub-level still lower than the 3d sub-level, as it definitely is for potassium, [Ar]4s¹ and calcium, [Ar]4s², or is the 3d sub-level lower than the 4s sub-level so that the electron configuration of scandium, for example, is [Ar]3d¹4s² rather than [Ar]4s²3d¹?

At first sight the experimental evidence for the configuration of scandium being [Ar]3d¹4s² is quite strong. There are basically two supporting arguments. One is that the atomic spectrum of Sc²⁺ gives  the ground state electron configuration as [Ar]3d¹ which shows that the 3d level fills before the 4s. The second argument is based on the fact that when elements ionize it is an outer electron that is lost. The atomic spectra of Sc⁺ shows it contains one 4s electron and one 3d electron. Since the ion contains one 4s electron less than the atom it is argued that the 4s level must be higher in energy than the 3d level in the neutral scandium atom. The problem with these arguments is that it is assumed that the relative positions of the 3d and 4s levels remain the same in all the positive ions as they are in the atom.

The atomic spectra for all elements and their ions are available in great detail from the National Institute of Standards and Technology (NIST). These are a compilation drawn from a variety of different experimental sources. Many of the energy levels for the spectral lines are given to nine or ten significant figures so are extremely accurate. Spectroscopists list energy levels in order of principal quantum numbers so although they give the ground state configuration of Sc⁺ as [Ar]3d¹4s¹ this does not confirm that the 3d level is lower than the 4s level in Sc⁺. What the spectra do provide is the precise energy levels of all the excited states. When these are considered there is good evidence that as the charge of the ion decreases the 3d level gains more in energy than the 4s level and at a certain point the order of the levels switches.

Sc³⁺ has eighteen electrons. Other species with 18 electrons are K⁺ and Ca²⁺. They are isoelectronic and have the same ground state electron configuration as argon, [Ne]3s²3p⁶. However the order of the energy levels is different in their excited states (Fig 1).

In argon the first excited state is [Ne]3s²3p⁵4s¹. This is still the case (but only just by 11 kJ mol^-1) for K⁺, whereas for Ca²⁺ and Sc³⁺ the first excited state is [Ne]3s²3p⁵3d¹. The number of electrons remains constant and so an assumption can be made that the way in which the electrons will interact with each other will remain reasonably constant. Although the number of electrons remains the same, the number of protons is increasing so the attraction of the nucleus to the electrons increases moving from Ar to Sc³⁺. This produces two effects. The actual energies of all the levels are lowered considerably each time a proton is added. The ionization energy to remove one electron from the 3p sub-level to infinity increases from 1521 kJ mol^-1 for Ar through to 7091 kJ mol^-1 for Sc³⁺.  This change in energy is related directly to the amount the ground state has been lowered.   The second effect shows that as the energy of the ground state decreases the ordering of the sub-levels also changes. In Ar and K⁺ the 3d sub-level is above the 4s sub-level whereas for Ca²⁺ and Sc³⁺ the 3d sub-level has moved below the 4s sub-level.

These experimental facts cast doubt on the argument that building up the scandium atom configuration from the Sc³⁺ ion is evidence that the 3d sub-level in a neutral scandium atom is lower than the 4s sub-level. It can now be seen that this is not necessarily a valid argument as it ignores the fact that each time the charge on the ion changes the energy of the ground state changes which also changes the energies of the 3d and 4s sub-levels relative to each other. If it were a valid argument then when an electron is added to Ca²⁺ it would be expected to occupy the lower 3d sub-level but the atomic spectrum of Ca⁺ confirms that the configuration is [Ar]4s¹. This is because the 3d-4s order has switched in going from Ca²⁺ to Ca⁺ so that the 3d sub-level is now above the 4s sub-level (Fig. 2).

When Sc³⁺ gains an electron the electron goes into the 3d sub-level because the 3d sub-level is still lower than the 4s sub-level in Sc²⁺. As more electrons are added the gap between 3d and 4s closes further. In Sc⁺ the two levels are obviously very close in energy as each contain one electron. The first excited state for Sc⁺ is [Ar]3d² which suggest that the 3d level is actually slightly higher than the 4s level. Looking at the excited state of Sc itself the 3d level would appear to be some 138 kJ mol^-1 higher than the 4s level with the first excited state being [Ar]4s¹3d² (Fig 3).

Further evidence that increasing the positive charge on an ion lowers the 3d level more than the 4s level can also be obtained by considering the isoelectronic species Sc, Ti⁺ and V²⁺. All have 21 electrons. As the charge increases the electron configuration changes from [Ar]4s²3d¹ for Sc to [Ar]4s¹3d² for Ti⁺ and [Ar]3d³ for V³⁺. If the 3d level was lower than the 4s in scandium then it is legitimate to ask why Sc does not have the same ground state configuration as V²⁺. The configuration [Ar]3d³ does exist for Sc in the excited state but it is over 400 kJ mol^-1 higher than the ground state which supports the fact that two electrons from the lower 4s sub-level can be excited to the higher 3d sub-level when this amount of energy is supplied.

What this analysis of the experimental evidence shows is that the generally held view that scandium loses a 4s electron when it ionizes would be much better stated as “when scandium ionizes the ion formed contains one less 4s electron than the neutral atom”. A detailed examination of the spectra shows that as in potassium and calcium, the 4s level in the neutral scandium atom is most probably below the 3d level and that when scandium loses the 3d electron during ionization the order of the levels rearranges as the ion is formed.

The IB is right to accept either configuration as correct as the situation is not straightforward. It is also worth remembering that the electron configurations of all elements refer to their gaseous atoms at low pressure, not necessarily to their normal elemental states. Carbon has the electron configuration 1s²2s²2p² but this refers to C(g).  In its natural allotropic forms of diamond, graphite, and C₆₀ the orbitals in the 2s and 2p sub-levels are hybridized. Similarly, scandium is a metal. Metallic bonding is usually loosely described as an array of cations in a sea of delocalized electrons so the outermost electrons are not associated with a particular orbital on a particular scandium atom. As Schwarz wrote in the abstract to his 2010 paper detailing a quantum mechanical theoretical approach to this problem “ There is a conceptual difference between spectroscopic ground states and chemically dominant ground configurations. The ground states of unbound atoms mentioned in most chemistry textbooks have little meaning in chemistry.”