<P> The naïve application of the Aufbau principle leads to a well - known paradox (or apparent paradox) in the basic chemistry of the transition metals . Potassium and calcium appear in the periodic table before the transition metals, and have electron configurations (Ar) 4s and (Ar) 4s respectively, i.e. the 4s - orbital is filled before the 3d - orbital . This is in line with Madelung's rule, as the 4s - orbital has n+l = 4 (n = 4, l = 0) while the 3d - orbital has n+l = 5 (n = 3, l = 2). After calcium, most neutral atoms in the first series of transition metals (Sc - Zn) have configurations with two 4s electrons, but there are two exceptions . Chromium and copper have electron configurations (Ar) 3d 4s and (Ar) 3d 4s respectively, i.e. one electron has passed from the 4s - orbital to a 3d - orbital to generate a half - filled or filled subshell . In this case, the usual explanation is that "half - filled or completely filled subshells are particularly stable arrangements of electrons". </P> <P> The apparent paradox arises when electrons are removed from the transition metal atoms to form ions . The first electrons to be ionized come not from the 3d - orbital, as one would expect if it were "higher in energy", but from the 4s - orbital . This interchange of electrons between 4s and 3d is found for all atoms of the first series of transition metals . The configurations of the neutral atoms (K, Ca, Sc, Ti, V, Cr, ...) usually follow the order 1s, 2s, 2p, 3s, 3p, 4s, 3d, ...; however the successive stages of ionization of a given atom (such as Fe, Fe, Fe, Fe, Fe) usually follow the order 1s, 2s, 2p, 3s, 3p, 3d, 4s,...</P> <P> This phenomenon is only paradoxical if it is assumed that the energy order of atomic orbitals is fixed and unaffected by the nuclear charge or by the presence of electrons in other orbitals . If that were the case, the 3d - orbital would have the same energy as the 3p - orbital, as it does in hydrogen, yet it clearly doesn't . There is no special reason why the Fe ion should have the same electron configuration as the chromium atom, given that iron has two more protons in its nucleus than chromium, and that the chemistry of the two species is very different . Melrose and Eric Scerri have analyzed the changes of orbital energy with orbital occupations in terms of the two - electron repulsion integrals of the Hartree - Fock method of atomic structure calculation . More recently Scerri has argued that contrary to what is stated in the vast majority of sources including the title of his previous article on the subject, 3d orbitals rather than 4s are in fact preferentially occupied . </P> <P> Similar ion - like 3d 4s configurations occur in transition metal complexes as described by the simple crystal field theory, even if the metal has oxidation state 0 . For example, chromium hexacarbonyl can be described as a chromium atom (not ion) surrounded by six carbon monoxide ligands . The electron configuration of the central chromium atom is described as 3d with the six electrons filling the three lower - energy d orbitals between the ligands . The other two d orbitals are at higher energy due to the crystal field of the ligands . This picture is consistent with the experimental fact that the complex is diamagnetic, meaning that it has no unpaired electrons . However, in a more accurate description using molecular orbital theory, the d - like orbitals occupied by the six electrons are no longer identical with the d orbitals of the free atom . </P>

The scientist who first proposed the order of electron distribution within subshells was