At almost exactly the same time that chemists were developing the valence bond model for coordination complexes, physicists such as Hans Bethe, John Van Vleck, and Leslie Orgel were developing an alternative known as crystal field theory. Valence bond theory was used to explain the chemical properties of coordination complexes, such as the fact that the Co3 ion forms a six-coordinate Co(NH3)63 complex. Crystal field theory was developed to explain some of the physical properties of the complexes, such as their color and their behavior in a magnetic field.
hg hg hg h h 3d
Ni(NH3)62 hg hg hg hg hg hg
sp3d2 Ni2 hg hg hg h h
3d 4s 4p
Fe(CN)64 hg hg hg hg hg hg hg hg hg
3d d2sp3
Fe2 hg hg hg
3d 4s 4p
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Crystal-field theory can be understood by thinking about the effect of the electrical field of neighboring ions on the energies of the valence orbitals of the transition-metal ions in manganese(II) oxide, MnO, and copper(I) chloride, CuCl.
MnO: Octahedral Crystal Fields
Each Mn2ion in manganese(II) oxide is surrounded by six O2ions arranged toward the corners of an octahedron, as shown in Figure TM.14. MnO is therefore a model for an oc-tahedral complex in which a transition metal ion is coordinated to six ligands.
O2–
O2–
O2–
O2–
O2–
O2–
Mn2+
FIGURE TM.14 The octahedral geometry of O2 ions that surround each Mn2
ion in MnO.
Repulsion between electrons on the O2 ions and electrons in the 3d orbitals on the metal ion in MnO increases the energy of these orbitals. But this repulsion doesn’t affect the five 3d orbitals the same way. Let’s assume that the six O2 ions that surround each Mn2ion define an xyz coordinate system. Two of the 3d orbitals (3dx2y2and 3dz2) on the Mn2ion point directly toward the six O2ions, as shown in Figure TM.15. The other three orbitals (3dxy, 3dxz, and 3dyz) lie between the O2 ions.
x z
3dx2 – y2
y y
x
3dz2
z
x z
3dxy
y y
x z
3dxz
y
x z
3dyz
FIGURE TM.15 The five orbitals in a d subshell.
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The energy of the five 3d orbitals increases when the six O2 ions are brought close to the Mn2ion because of repulsion between the electrons on the O2 ions and the electrons in the d orbitals on the Mn2 ion. The energy of two of these orbitals (3dx2y2and 3dz2), how-ever, increases much more than the energy of the other three (3dxy, 3dxz, and 3dyz), as shown in Figure TM.16. The crystal field of the six O2ions in MnO therefore splits the degeneracy of the five 3d orbitals. Three of the orbitals are now lower in energy than the other two.
Isolated atom or ion
dx2 – y2 dz2
dxy dxz dyz Octahedral
crystal field
∆o
E
eg
t2g
FIGURE TM.16 The two d orbitals that point toward the ligands in an octahedral complex are higher in en-ergy than the three d orbitals that lie between the ligands.
By convention, the dxy, dxz, and dyzorbitals in an octahedral complex are called the t2g
orbitals. The dx2y2and dz2orbitals, on the other hand, are called the egorbitals. The eas-iest way to remember this convention is to note that there are three orbitals in the t2g set.
t2g dxy, dxz, and dyz
eg dx2y2and dz2
The difference between the energies of the t2gand eg orbitals in an octahedral complex is represented by the symbol o. The splitting of the energy of the d orbitals is not trivial; o
for the Ti(H2O)63ion, for example, is 242 kJ/mol. Which is roughly the same as the en-ergy given off when one mole of water is produced by burning a mixture of H2 and O2. The magnitude of the splitting of the t2g and eg orbitals changes from one octahedral complex to another. It depends on the identity of the metal ion, the charge on that ion, and the nature of the ligands coordinated to the metal ion.
CuCl: Tetrahedral Crystal Fields
Each Cu ion in copper(I) chloride is surrounded by four Cl ions arranged toward the corners of a tetrahedron, as shown in Figure TM.17. CuCl is therefore a model for a tetra-hedral complex in which a transition metal ion is coordinated to four ligands.
Cu+
Cl– Cl– Cl–
Cl–
FIGURE TM.17 The tetrahedral geometry of Clions that surround each Cuion in CuCl.
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Once again, the negative ions in the crystal split the energy of the d atomic orbitals on the transition metal ion. The tetrahedral crystal field splits these orbitals into the same t2g
and egsets of orbitals as does the octahedral crystal field.
t2g dxy, dxz, and dyz
eg dx2y2 and dz2
But the two orbitals in the egset are now lower in energy than the three orbitals in the t2g
set, as shown in Figure TM.18.
Isolated atom or ion
dxy dxz
dx2 – y2 dz 2 Tetrahedral
crystal field
∆t ––4
= ∆9 o
E
dyz
eg t2g
FIGURE TM.18 In a tetrahedral complex, the egorbitals are lower in energy than the t2gorbitals. The differ-ence between the energies of the orbitals is smaller in tetrahedral complexes than in an equivalent octahe-dral complex.
To understand the splitting of d orbitals in a tetrahedral crystal field, imagine four li-gands lying at alternating corners of a cube to form a tetrahedral geometry, as shown in Figure TM.19. The dx2y2and dz2orbitals on the metal ion at the center of the cube lie be-tween the ligands, and the dxy, dxz, and dyz orbitals point toward the ligands. As a result, the splitting observed in a tetrahedral crystal field is the opposite of the splitting in an oc-tahedral complex.
x
y z
FIGURE TM.19 In a tetrahedral complex, dxy, dxz, and dyzorbitals point toward the ligands; the dx2y2and dz2orbitals point between the ligands.
Because a tetrahedral complex has fewer ligands, the magnitude of the splitting is smaller. The difference between the energies of the t2g and eg orbitals in a tetrahedral
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24 TRANSITION METAL
complex (t) is slightly less than half as large as the splitting in analogous octahedral com-plexes (o).
t4/9 o
Square-Planar Complexes
The crystal field theory can be extended to square-planar complexes, such as Pt(NH3)2Cl2. The splitting of the d orbitals in these compounds is shown in Figure TM.20.
Isolated atom or ion
dxy dz2
dx2 – y2
dyz dxz
Square-planar crystal field
∆O
––2
∼ ∆3 O
E
FIGURE TM.20 The splitting of the d orbitals in a square-planar complex.