Thed electron count or number of d electrons is achemistry formalism used to describe theelectron configuration of thevalence electrons of atransition metal center in acoordination complex.[1][2] 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 andligand field theory, which is a more advanced version based onmolecular orbital theory.[3] 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.
For free atoms, electron configurations have been determined byatomic spectroscopy. Lists of atomic energy levels and their electron configurations have been published by theNational Institute of Standards and Technology (NIST) for both neutral and ionized atoms.[4]
For neutral atoms of all elements, theground-state electron configurations are listed in general chemistry[5] and inorganic chemistry[3]: 38 textbooks. The ground-state configurations are often explained using two principles: theAufbau principle that subshells are filled in order of increasing energy, and theMadelung rule that this order corresponds to the order of increasing values of (n +l) wheren is theprincipal quantum number andl is theazimuthal quantum number. This rule predicts for example that the 4s orbital (n = 4,l = 0,n +l = 4) is filled before the 3d orbital (n = 3,l = 2,n +l = 5), as in titanium with configuration [Ar]4s23d2.
There are a few exceptions with only one electron (or zero forpalladium) in thens 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.[6] An example ischromium whose electron configuration is [Ar]4s13d5 with a d electron count of 5 for a half-filled d subshell, although Madelung's rule predicts [Ar]4s23d4. Similarly copper is [Ar]4s13d10 with a full d subshell, and not [Ar]4s23d9. The configuration of palladium is [Kr]4d10 with zero 5s electrons.[3]: 38 However this trend is not consistent:tungsten, a group VI element like Cr and Mo has a Madelung-following [Xe]6s24f145d4, andniobium has a [Kr]5s14d4 as opposed to the Madelung rule predicted [Kr]5s24d3 which creates two partially-filled subshells.[7]
When a transition metal atom loses one or more electrons to form a positive ion, overall electron repulsion is reduced and then d orbital energy is lowered more than the (n+1) s orbital energy. The ion is formed by removal of the outer s electrons and tends to have a dn configuration,[3]: 40 even though the s subshell is added to neutral atoms before the d subshell. For example, the Ti2+ ion has the ground-state configuration [Ar]3d2[8] with a d electron count of 2, even though the total number of electrons is the same as the neutral calcium atom which is [Ar]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.
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According to Ligand Field Theory, thens 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 (LUMO). Since the orbitals resulting from thens orbital are either buried in bonding or elevated well above the valence, thens orbitals are not relevant to describing the valence. Depending on the geometry of the final complex, either all three of thenp orbitals or portions of them are involved in bonding, similar to thens orbitals. Thenp orbitals if any that remain non-bonding still exceed the valence of the complex. That leaves the (n − 1)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 [Ti(H2O)6]3+ thens orbital – which is placed above (n − 1)d in the representation of atomic orbitals (AOs) – 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 isoctahedral, 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 (LUMO) or the highest partially filled molecular orbitals – a variation on the highest occupied molecular orbitals (HOMO).
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 whyns electrons are ionized before (n − 1)d electrons.
Each of the ten possible d electron counts has an associatedTanabe–Sugano diagram describing gradations of possible ligand field environments a metal center could experience in anoctahedral geometry. The Tanabe–Sugano diagram with a small amount of information accurately predicts absorptions in the UV and visibleelectromagnetic spectrum resulting from d to d orbital electron transitions. It is these d–d transitions, ligand to metal charge transfers (LMCT), or metal to ligand charge transfers (MLCT) that generally give metals complexes their vibrant colors.
Counting d electrons is a formalism. Often it is difficult or impossible to assign electrons and charge to the metal center or a ligand. For a high-oxidation-state metal center with a +4 charge or greater it is understood that the true charge separation is much smaller. But referring to the formal oxidation state and d electron count can still be useful when trying to understand the chemistry.
There are many examples of every possible d electron configuration. What follows is a short description of common geometries and characteristics of each possible d electron count and representative examples.
Electron Configurations of the Atoms of the Elements
In this table Ti I = neutral Ti atom and Ti III = Ti2+
