D electron count
The d electron count or number of d electrons is a chemistry formalism used to describe the electron configuration of the valence electrons of a transition metal center in a coordination complex. The d electron count is an effective way to understand the geometry and reactivity of transition metal complexes. The formalism has been incorporated into the two major models used to describe coordination complexes; crystal field theory and ligand field theory, which is a more advanced version based on molecular orbital theory. However the d electron count of an atom in a complex is often different from the d electron count of a free atom or a free ion of the same element.
Electron configurations of transition metal atoms
For free atoms, electron configurations have been determined by atomic spectroscopy. Lists of atomic energy levels and their electron configurations have been published by the National Institute of Standards and Technology for both neutral and ionized atoms.For neutral atoms of all elements, the ground-state electron configurations are listed in general chemistry and inorganic chemistry textbooks. The ground-state configurations are often explained using two principles: the Aufbau principle that subshells are filled in order of increasing energy, and the Madelung rule that this order corresponds to the order of increasing values of where n is the principal quantum number and is the azimuthal quantum number. This rule predicts for example that the 4s orbital is filled before the 3d orbital, as in titanium with configuration 4s23d2.
There are a few exceptions with only one electron in the ns orbital in favor of completing a half or a whole d shell. The usual explanation in chemistry textbooks is that half-filled or completely filled subshells are particularly stable arrangements of electrons. An example is chromium whose electron configuration is 4s13d5 with a d electron count of 5 for a half-filled d subshell, although Madelung's rule predicts 4s23d4. Similarly copper is 4s13d10 with a full d subshell, and not 4s23d9. The configuration of palladium is 4d10 with zero 5s electrons. However this trend is not consistent: tungsten, a group VI element like Cr and Mo has a Madelung-following 6s24f145d4, and niobium has a 5s14d4 as opposed to the Madelung rule predicted 5s24d3 which creates two partially-filled subshells.
When a transition metal atom loses one or more electrons to form a positive ion, overall electron repulsion is reduced and the n d orbital energy is lowered more than the s orbital energy. The ion is formed by removal of the outer s electrons and tends to have a dn configuration, even though the s subshell is added to neutral atoms before the d subshell. For example, the Ti2+ ion has the ground-state configuration 3d2 with a d electron count of 2, even though the total number of electrons is the same as the neutral calcium atom which is 4s2.
In coordination complexes between an electropositive transition metal atom and an electronegative ligand, the transition metal is approximately in an ionic state as assumed in crystal field theory, so that the electron configuration and d electron count are those of the transition metal ion rather than the neutral atom.
Ligand field perspective
According to Ligand Field Theory, the ns orbital is involved in bonding to the ligands and forms a strongly bonding orbital which has predominantly ligand character and the correspondingly strong anti-bonding orbital which is unfilled and usually well above the lowest unoccupied molecular orbital. Since the orbitals resulting from the ns orbital are either buried in bonding or elevated well above the valence, the ns orbitals are not relevant to describing the valence. Depending on the geometry of the final complex, either all three of the np orbitals or portions of them are involved in bonding, similar to the ns orbitals. The np orbitals if any that remain non-bonding still exceed the valence of the complex. That leaves the d orbitals to be involved in some portion of the bonding and in the process also describes the metal complex's valence electrons. The final description of the valence is highly dependent on the complex's geometry, in turn highly dependent on the d electron count and character of the associated ligands.For example, in the MO diagram provided for the 3+ the ns orbital – which is placed above d in the representation of atomic orbitals – is used in a linear combination with the ligand orbitals, forming a very stable bonding orbital with significant ligand character as well as an unoccupied high energy antibonding orbital which is not shown. In this situation the complex geometry is octahedral, which means two of the d orbitals have the proper geometry to be involved in bonding. The other three d orbitals in the basic model do not have significant interactions with the ligands and remain as three degenerate non-bonding orbitals. The two orbitals that are involved in bonding form a linear combination with two ligand orbitals with the proper symmetry. This results in two filled bonding orbitals and two orbitals which are usually the lowest unoccupied molecular orbitals or the highest partially filled molecular orbitals – a variation on the highest occupied molecular orbitals.
Crystal field theory is an alternative description of electronic configurations that is simplified relative to LFT. It rationalizes a number of phenomena, but does not describe bonding nor offer an explanation for why ns electrons are ionized before d electrons.