The Foundations of Chemistry

The dx (^2) – y 2 , and dz 2 orbitals are directed along a set of mutually perpendicular x, y,and
zaxes (p. 212). As a group, these orbitals are called egorbitals.The dxy, dyz, and dxz
orbitals, collectively called t 2 gorbitals,lie between the axes. The ligand donor atoms
approach the metal ion along the axes to form octahedral complexes. Crystal field theory
proposes that the approach of the six donor atoms (point charges) along the axes sets up
an electric field (the crystal field). Electrons on the ligands repel electrons in egorbitals
on the metal ion more strongly than they repel those in t 2 gorbitals (Figure 25-6). This
removes the degeneracy of the set of dorbitals and splits them into two sets, the egset at
higher energy and the t 2 gset at lower energy.
The energy separation between the two sets is called the crystal field splitting energy,
(^) octahedral, or (^) oct. It is proportional to the crystal field strengthof the ligands—that is, how
strongly the ligand electrons repel the electrons on the metal ion.
The delectrons on a metal ion occupy the t 2 gset in preference to the higher energy
egset. Electrons that occupy the egorbitals are strongly repelled by the relatively close
approach of ligands. The occupancy of these orbitals tends to destabilize octahedral
complexes.
As always, electrons occupy the orbitals in the arrangement that results in the lowest
energy. The electron pairing energy,P,is the expenditure of energy that is necessary to
pair electrons by bringing two negatively charged particles into the same region of space.
We must compare this with the crystal field splitting energy, (^) oct, the difference in energy
between t 2 gand eg. Weak field ligands such as Fcause only small splitting energies,
whereas strong field ligands such as CNgive large values of (^) oct.
If the splitting energy, (^) oct, is smaller than the pairing energy, P,the electrons occupy
all five nondegenerate orbitals singly before pairing. After all dorbitals are half-filled,
dxy dxz dyz dx (^2) –y 2 dz 2
free metal ion
(no crystal field)
metal ion in
spherical
crystal field
dx (^2) –y 2 dz 2 }eg
dxy dxz dyz
metal ion in
octahedral
crystal field
}t 2 g
(^) oct (not to scale)
Recall that degenerate orbitals are
orbitals of equal energy.
992 CHAPTER 25: Coordination Compounds
Figure 25-6 Effects of the
approach of ligands on the energies
of dorbitals on the metal ion. In an
octahedral complex, the ligands (L)
approach the metal ion (M) along
the x, y,and zaxes, as indicated by
the blue arrows. (a) The orbitals of
the egtype—dx^2 – y^2 (shown here)
and dz^2 —point directly toward the
incoming ligands, so electrons in
these orbitals are strongly repelled.
(b) The orbitals of the t 2 gtype—dxy
(shown here), dxzand dyz—do not
point toward the incoming ligands,
so electrons in these orbitals are less
strongly repelled.
M
L
L
L
L
L
L
(b) t 2 g type orbitals (dxy shown here)
L
L
L
L
L
L
M
(a) eg type orbitals (dx (^2) – y 2 shown here)
Typical values of (^) octare between 100
and 400 kJ/mol.