The properties of elements - Geochemistry: An Introduction - page 8

a 1s electron. The resulting electron configuration is more advantageous than that of iso-
lated hydrogen atoms and thus chemical bonding is favored. This is the essence of Pauling's
valence bond theory, which, however, fell into disfavor for its inability to explain the spec-
troscopic properties of substances. In contrast, the crystal field theory sees fully ionized
cations, such as Na + or Ca 2 + being hosted in sites defined by negatively charged “lig-
ands” such as the silicate network: the bond is assumed to be fully electrostatic. Although
the valence theory accounts for many properties of the transition elements, it is now also
considered as largely obsolete.
The dual character of most chemical bonds is accounted for by the concept of molecular
orbitals: when atoms and ions come close to each other, their individual electronic orbitals
merge into collective orbitals, which, however, in general remain difficult to calculate. The
type of chemical bonding is determined by the probability of the presence of the electron
next to one of the bound nuclei, which is exactly what the molecular orbitals are meant to
describe. If the electron is transferred permanently, ionic bonding has occurred: a sodium
atom in the presence of a chlorine atom will give up its isolated 3s electron because their
outer shells will then be completely occupied, with sodium configured like neon and chlo-
rine like argon. The ions formed in this way, noted as Na + and Cl − , are particularly stable;
their outer electron shell is largely spherical and these ions act like electrically charged
spheres mutually attracted by their electrostatic fields to form ionic compounds such as
table salt, NaCl. Conversely, when the number of electrons that can be exchanged fails to
fill the outer shells of the two partners, a covalent bond is formed. Two hydrogen atoms
lend one another their missing electron but must share the two 1s electrons over time by
forming hybrid orbitals of complex geometry thereby allowing them to fill the outer shell
of both atoms.
The transition elements (V, Fe, Cu, Zn, etc.) are particularly sensitive to their crystalline
environment. They differ from each other by a different filling of their d orbital ( Fig. 1.3 ) .
Two of these orbitals, called e g , have their lobes lying along the axes of rectangular coor-
dinates, while three orbitals, called t 2 g , lie in each plane defined by two axes but with their
lobes sticking out in between the axes. In the most common octahedral sites occupied by
transition elements in silicates, with an oxygen atom at each apex along the axes, an elec-
tron occupying a t 2 g orbital feels the repulsion by the electrons from the oxygen ions, the
so-called crystal field, much less than an electron occupying an e g orbital ( Fig. 1.7 ). Call-
ing the crystal field stabilization energy (CSFE), i.e. the difference in bonding energy

between t 2 g and e g , the energy shift of the three t 2 g orbitals is

− 2 / 5, while the shift for

the two e g orbitals is 5, thereby ensuring that the mean energy shift with respect to

a spherical environment is zero ( Fig. 1.8 ) .
Let us now give examples of how these concepts are relevant to the energetics of element
partitioning in crystallographic sites:

+ 3 /

1. Trivalent chromium ion Cr 3 + has electronic formula [Ar]3d 3 4s 0 ([Ar] stands for the
orbital filling of argon) in an octahedral site. One electron on each t 2 g orbital gives this
ion a bonding energy of 3 5. In spite of a charge at odds with the

major cations, such a large value makes Cr 3 + an element abundant in some Fe-Mg
minerals, most conspicuously pyroxene.

× ( − 2 / 5 ) =− 6 /