D Electron Count - Standard Electron Configuration Perspective

Standard Electron Configuration Perspective

The electron configuration for transition metals predicted by the simple Aufbau principle and Madelung's rule has serious conflicts with experimental observations for transition metal centers under most ambient conditions. Under most conditions all of the valence electrons of a transition metal center are located in d orbitals while the standard model of electron configuration would predict some of them to be in the pertinent s orbital.

The valence of a transition metal center can be described by standard quantum numbers. The Aufbau principle and Madelung's rule would predict for period n that the ns orbitals fill prior to the (n-1)d orbitals. For example the 4s fills before the 3d in period 4. In general chemistry textbooks, a few exceptions are acknowledged with only one electron in the ns orbital in favor of completing a half or whole d shell. The usual explanation is that "half-filled or completely filled subshells are particularly stable arrangements of electrons". An example is chromium whose electron configuration is 4s1 3d5 with a half-filled d subshell, although Madelung's rule would predict 4s2 3d4. Similarly copper is 4s1 3d10 with a full d subshell, and not 4s2 3d9.

Matters are further complicated when metal centers are oxidized. Since the (n-1)d shell is predicted to have higher energy than the ns shell, it might be expected that electrons would be removed from the (n-1)d shell first. Experimentally it has been observed that not only are the ns electrons removed first, even for unionized complexes all of the valence electrons are located in the (n-1)d orbitals.

There are various hand waving arguments for this phenomenon including that "the ns electrons are farther away from the nuclei and thus ionized first" while ignoring results based on neutral complexes. This poor explanation avoids the basic problems with the standard electron configuration model. The standard electron configuration model assumes a hydrogen-like atom removed from all other atoms. This assumption is only truly relevant for esoteric situations. It is far more common for metal centers to have bonds to other atoms through metallic bonds or covalent bonds. These bonds drastically change the energies of the orbitals for which electron configurations are predicted. Thus for coordination complexes the standard electron configuration formalism is meaningless and the d electron count formalism is a suitable substitute.