Download Covalent and Metallic Bonding

Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Covalent and Metallic
Bonding
Chemistry for Earth Scientists,
DM Sherman
University of Bristol
Failures of Ionic Model: Ionic radius of S-2
NaCl structure
CaS is highly ionic.
Cell constant 5.70 Å
Ca+2 radius = 1.14 Å*
S-2 radius = 1.71 Å
PbS (Galena) has
cell constant of 5.94 Å
Bond length =
½ x cell constant
Pb+2 radius = 1.33 Å*
S-2 radius = 1.64 Å
* from bond lengths in oxides (Shannon, 1976)
Page 1
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Failure of Ionic Model: Structure of CaF2
(Fluorite)
Ionic Radius
Ion
IV
Ca+2
F-
1.17
VI
VIII
XII
1.14
1.26
1.48
1.19
Using Pauling’s first rule:
RCa (VI)/RF(IV) = 0.97
RCa (VIII)/RF(IV) =1.07
Predict Ca in
12-fold
coordination
RCa (VIII)/RF(IV) =1.24
Ionic radius of Fderived from one
ionic compound
does not transfer to
another.
Failure of Ionic Model: Sulfide Structures
Triolite/Pyrrhotite
(FeS)
Molybdenite
(MoS2)
Cinnabar
(HgS)
Mackinawite
(FeS)
Page 2
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Chemical bonding: ionic vs. covalent
When electrons are completely transferred between
atoms to yield cations and anions, the atoms will be
held together by ionic bonds.
If atoms have similar
electronegativities, they
adopt closed-shell
configurations by sharing
electrons with each other;
the atoms are held together
by covalent bonds.
Covalent Bonds
• 
• 
• 
• 
Formed between atoms of similar electronegativity.
Atoms are held together by “sharing electrons”.
Sulfide minerals.
Most organic compounds.
In anhydrite (CaSO4), the S-O
bond in SO4-2 ions is very
covalent. The Ca-O bond is
ionic.
Page 3
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Metallic Bond
•  Extreme example of covalent bond: electrons are
delocalized throughout the crystal.
•  Formed between metal atoms of similar
electronegativity and with weakly held electrons.
•  Can form between metal atoms in sulfide minerals.
Mackinawite (FeS) has metallic
Fe-Fe bonds between shared FeS4
tetrahedra.
Chalcophiles, Lithophiles, Siderophiles.."
Page 4
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Chemical Bonding: Theoretical Pictures"
Ionic Approximation
Localized
electrons
(+ Crystal Field Theory)
MgO
FeO,
SiO2
Molecular Orbital Theory
(Covalent Bonds)
Delocalized
electrons
Band Theory
(Metallic Bonds)
FeS
Molecular Orbital Theory"
Linear Combination of Atomic Orbitals (LCAO)
The quantum states of a molecule are molecular orbitals (ψi). These
are constructed by taking linear combinations of atomic orbitals (φi)
to yield bonding molecular orbitals
ψ = c1φ1 + c2φ2
−
+
+
+
=
−
−
+
−
and antibonding molecular orbitals
€
ψ = c1φ1 − c2φ2
−
+
-
+
−
=
+ − + −
€
Page 5
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Molecular Orbital Theory: π vs σ bonds"
−
+ −
σ-antibonding
+
π-antibonding
+
−
−
+
−
+
+
−
−
+
+
+
−
−
−
+
py px
π-bonding
+
− −
+
σ-bonding
Molecular Orbital Theory:
Simple Diatomic Molecules"
Page 6
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Molecular Orbital Theory of Si-O bond"
Si Atomic
Levels
In quartz, the Si-O bond is
partially covalent: electrons
are shared by the O(2p) and
Si(3p) orbitals.
3p
O Atomic
Levels
2p
π
σ
Energy
The “core” atomic orbitals
(e.g., Si 1s, 2s, 2p and O 1s)
are highly localized and do
not participate in bonding;
they retain their atomic
character.
σ*
π*
σ*
3s
σ
2s
1s
2p
2s
1s
Molecular orbitals involving ligand p-orbitals and
metal d-orbitals"
−
+
σ-antibonding
(eg symmetry)
−
+
+ − +
− +
−
+
−
σ-bonding
(eg symmetry)
−
−
+ +
−
−
+
+
−
−
+
+
−
+
+
−
−
+ −
− +
−
+
+
π-antibonding
(t2g symmetry)
+
−
+ −
+
−
− +
−
π-bonding
(t2g symmetry)
−
+
+
Page 7
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Electronic Structures of Fe-Mn Oxides
The d-orbitals can be
viewed as antibonding
molecular orbitals. The
crystal-field splitting
results from σ- vs. πantibonding.
Energy Bands in Solids
Page 8
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Insulators, Metals and Semiconductors
Semiconduction in Sulfides
Sulfide minerals tend to be opaque because of the small bandgap
Pyrite (FeS2)
Galena (PbS)
Sphalerite (ZnS)
Chalcopyrite (CuFeS2)
Triolite (FeS)
Molybdenite (MoS2)
Page 9
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Semiconduction in Sulfides
The semiconducting properties of sulfides can be exploited using
geophysical measurements of outcrop electrical resistivity (conductivity).
Mineral
Formula
Conductivity (S/m)
Pyrite
FeS2
20 to 2 x 104
Chalcopyrite
CuFeS2
1 x 104
Pyrrhotite
Fe1-xS
1 x 105
Arsenopyrite
FeAsS
3 x 103
Galena
PbS
3 x 104
Copper Wire:
Cu
5.9 x 107
The “Octet Rule” and Valence Shell
Electron Pair Repulsion Theory
This is a useful model for predicting the structures of
covalent molecules. It is especially useful for
molecules constructed of first-row atoms (e.g., N, C,
O and F).
•  In a molecule, each atom contributes the electrons
in its outer shell (n-quantum number) as “valence
electrons.
•  The total valence electrons are then grouped into
electron pairs.
•  The electron pairs are distributed in the molecule
so that each atom is surrounded by 8 valence
electrons (except for H, which only wants 2).
Page 10
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
The “Octet Rule” and Valence Shell
Electron Pair Repulsion Theory
Example: the water molecule (H2O)
Each H (1s1) contributes 1 valence electron.
The O atom (1s22s22p4) contributes 6 valence
electrons.
The only way to distribute the valence electrons in
the molecule is as follows:
Note: each line represents a pair of
electrons. Repulsion between electron pairs
causes the bent geometry..
Summary
• Covalent bonds form when ions of high charge
(e.g., Si+4, S+6) bond with anions (O-2).
• Bonds with S-2 tend to be covalent.
• Metallic bonds may form when transition metal
cations are in close proximity.
• Molecular Orbital Theory is the complete picture of
bonding that embraces ionic, covalent and metallic
bonds.
• VSEPR can be used to predict the structures of
covalent molecules.
Page 11
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Crystal Field Theory
The d-orbitals:
Recall the shapes of the atomic
orbitals. The d-orbitals are unique:
the xy,yz and xz orbitals do not
have electron density along the x, y
and z-axes. The z2 and x2-y2
orbitals, however, point along the x
y and z-axes..
Crystal Field Theory
Splitting of the d-orbital energies when
surrounded by ligands:
Δtet = 4/9Δoct
Energy
xy
(2/5)Δtet
xz
(3/5)Δoct
yz
xy
(3/5)Δtet
x2-y2
z2
x2-y2
z2
xz
yz
x2-y2 z2
(2/5)Δoct
xy
xz
yz
Page 12
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Crystal Field Stabilization Energy (CFSE)
d3 configuration: (Mn+4 or Cr+3)
z2
Energy
x2-y2
xy
xz
yz
xy
xz
yz
x2-y2 z2
z2
x2-y2
xy
CFSE =(2/5)Δtet
xz
yz
CFSE = (6/5)Δoct
Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 1.02Δoct
Δoct = 200-300 kJ/mole
Crystal Field Stabilization Energy (CFSE)
d5 configuration: (Mn+2 or Fe+3)
z2
Energy
x2-y2
xy
xz
yz
xy
x2-y2
CFSE = 0
z2
xz
yz
x2-y2 z2
xy
xz
yz
CFSE = 0
Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 0Δoct
Page 13
Chemistry for Earth Scientists
DM Sherman, University of Bristol
2011/2012
Crystal Field Stabilization Energy (CFSE)
d8 configuration: (Ni+2)
z2
Energy
x2-y2
xy
xz
yz
xy
x2-y2
z2
CFSE =(2/5)Δtet
xz
yz
x2-y2 z2
xy
xz
yz
CFSE = (6/5)Δoct
Octahedral site preference energy = (6/5-4/9*2/5)Δoct = 1.02Δoct
Δoct = 200-300 kJ/mole
Page 14