Ionic Bonding Electrostatic Interactions
and Polarization
Chemistry 754
Solid State Chemistry
Dr. Patrick Woodward
Lecture #13
Electron Transfer & Ionic Compounds
•
Which of the following processes is exothermic?
1. Li(g) + F(g) → Li+(g) + F-(g)
2. Na(g) + Cl(g)
Cl(g) → Na+(g) + Cl-(g)
3. Cs(g) + Cl(g)
Cl(g) → Cs+(g) + Cl-(g)
4. Mg(g) + O(g) → Mg2+(g) + O2-(g)
5. 2K(g) + O(g) → 2K+(g) + O2-(g)
1
Electron Transfer & Ionic Compounds
1. Li(g) + F(g) → Li+(g) + F-(g)
ΔH = +1.94 eV
2. Na(g) + Cl(g)
Cl(g) → Na+(g) + Cl-(g)
ΔH = +1.43 eV
3. Cs(g) + Cl(g)
Cl(g) → Cs+(g) + Cl-(g)
ΔH = +0.18 eV
4. Mg(g) + O(g) →
Mg2+(g)
+
O2-(g)
5. 2K(g) + O(g) → 2K+(g) + O2-(g)
Ionization Energies (eV
/atom)
(eV/atom)
Li
+5.39
Na +5.14
K
Be
+27.53
Mg +22.68
ΔH = +28.7 eV
ΔH = +14.7 eV
Electron Affinities (eV
/atom)
(eV/atom)
F
-3.45
O
-1.46
Cl -3.71
S
-2.15
+4.34
Ca
+17.98
Br -3.49
Se -2.20
Rb +4.18
Sr
+16.72
I
Te
Cs +3.89
Ba
+15.22
-3.19
-2.30
O-
+7.46
S-
+4.34
Se-
+5.07
Te- +4.21
Born-Haber Cycle for NaCl
It is energetically unfavorable
for Na metal and Cl gas to react
to form Na+(g) + Cl-(g).
This highly exothermic reaction
occurs because of the large lattice
energy, that comes largely from
ionic bonding.
The Born-Haber cycle is used as a
tool for determining lattice energy
given standard thermodynamic data
How can we calculate lattice energy without experimental data?
2
Electrostatic Interactions
The potential energy of two interacting charges is given by
the following equation:
E = Q1Q2/(4πε0r)
E = e2 Z1Z2 /(4πε0r)
Q1,Q2 = The absolute charges on the two particles
Z1,Z2 = The integral charges on the two particles (Q = Ze)
Ze)
e = The charge of an electron = 1.602 × 10-19 C
ε0 = The permitivity of free space = 8.85 × 10-12 C/(mC/(m-J)
r = The distance between particles (meters)
Madelung Energy
We can calculate the total potential energy holding an ionic crystal
crystal
together (the total ionic bonding if you will) by summing up all of the
electrostatic interactions, both attractive (cation(cation-anion) and repulsive
(anion(anion-anion, cationcation-cation). To do so we need to know the charges on
the ions and the geometry of the crystal. This is done below for
for NaCl,
NaCl,
where r is the NaNa-Cl distance.
A = Madelung Constant
E = [e2Z+Z-/(4πε
√3)/(4πε0)] {(6/r){(6/r)-(12/r√
(12/r√2)+(8/r
2)+(8/r√
3)-(6/r
(6/r√4)+…
4)+…}
Nearest
Neighbor
(Na(Na-Cl)
Cl)
Next
Nearest
Neighbor
(Na(Na-Na)
Next, Next
Nearest
Neighbor
(Na(Na-Cl)
Cl)
E = [e2Z+Z-/(4πε0r)] ANA
•A = Madelung Constant (depends on structure type)
•NA = Avogadro’s Number
•r = CationCation-Anion distance
3
Lattice Energy
MX
Lattice Energy
LiF
NaF
KF
RbF
10.73 eV
9.56 eV
8.51 eV
8.13 eV
NaF
NaCl
NaBr
NaI
9.56 eV
8.14 eV
7.74 eV
7.30 eV
d0 (A)
2.01
2.32
2.67
2.83
2.32
2.82
2.99
3.33
MX
Lattice Energy
MgO
CaO
SrO
BaO
d0 (eV)
39.33 eV
35.38 eV
33.34 eV
31.13 eV
2.11
2.41
2.58
2.77
These are experimental values,
determined from a BornBorn-Haber cycle.
The lattice energy increases as
1. The ionic charges increase (primary importance)
2. The distance between ions decreases (secondary importance)
Electrostatic Considerations
Factors that maximize the electrostatic interactions
(ionic bonding) holding a crystal together optimize the
cationcation-anion distance (dictated largely by ionic radii) and
maximize the cationcation-cation and anionanion-anion distances.
The latter condition is optimal for:
•High Symmetry
•Regular Coordination Environments
•High Coordination Number
Structure
CsCl
NaCl
Wurtzite
Sphalerite
CN
8,8
6,6
4,4
4,4
A
1.763
1.748
1.641
1.638
Structure
Fluorite
Rutile
CN
8,4
6,3
A
5.038
4.816
4
Limitations of Madelung Energy Calc’s
1.
Repulsive interactions arising from electronelectron-electron repulsion are
neglected. These decrease the lattice energy by 1010-15%.
2. van der Waals interactions and zero point energy are also
neglected. The former can be important, particularly when dealing
dealing
with polarizable anions.
3. The oxidation states are not the true charges.
–
–
–
The deviation between oxidation states and true charges increases
increases as
the oxidation states increase and/or as the electronegativity
difference decreases. Some estimates for true charges are
SiO2 → Si2+, O11.6CuO → Cu1.6+, O1.6-
4. Covalent contributions are not accounted for, yet they are always
always
present. Thus simple calculations tend not to be very accurate
when
–
–
The oxidation state of the cation and/or anion is high
The cation and/or anion is not a closed shell ion
Comprehensive Lattice Energy
A more complete equation for lattice energy is taken from West1 and
Greenwood2
r/ρ - CN r-6 + 2.25Nhν
U = [ANAe2Z+Z-/(4πε
/(4πε0r)] + Bne-r/ρ
2.25Nhνmax
A
[C] van der
Waals forces
[A] Coulomb energy of
point charges (assuming
full ionic charge)
[D] Zero point
vibrational
energy
[B] Repulsive energy
arising from overlap of
electronic charge clouds
Substance
NaCl (U=-766)
MgO (U=-3921)
[A] kJ
-859
-4631
[B] kJ
[C] kJ
[D] kJ
99
698
-12
-6
7
18
5
Polarization
If an ion is placed in an asymmetric environment its electron cloud
cloud can
be deformed or “polarized” by the potential field created by the
surrounding ions.
Anion core
Asymmetric environment →
anion polarized toward cations
← Symmetric environment
Anion valence
electron cloud
no dipolar polarization
The most important type of polarization is generally thought to
polarization of the anion electron cloud by smaller, more highly
charged cations. Polarization effects increase as the:
• Cations get smaller and their oxidation state increases (harder)
• Anions get larger and their oxidation state increases (softer)
• The asymmetry of the anion environment increases
Polarization is one way of introducing covalency into an ionic model.
Keep in mind though that covalency is a more general phenomenon.
Structures of MX2 Metal Halides
as predicted by lattice energy calculations
F (1.15 Å)
Cl (1.60 Å)
Br (1.74 Å)
I (1.95 Å)
Mg (0.86 Å)
Rutile
Cristobalite
Cristobalite
Cristobalite
Zn (0.95 Å)
Rutile
Cristobalite
Cristobalite
Cristobalite
Mn (1.01 Å)
Rutile
Rutile
Cristobalite
Cristobalite
Ca (1.20 Å)
Fluorite
Rutile
Rutile
Cristobalite
Sr (1.34 Å)
Fluorite
Fluorite
Rutile
Rutile
Ba (1.56 Å)
Fluorite
Fluorite
Rutile
Rutile
Fluorite
Rutile
Cristobalite
CdI2
6
Structures of MX2 Metal Halides
observed
F (1.15 Å)
Cl (1.60 Å)
Br (1.74 Å)
I (1.95 Å)
Mg (0.86 Å)
Rutile
CdI2/CdCl2
CdI2/CdCl2
CdI2/CdCl2
Zn (0.95 Å)
Rutile
CdI2/CdCl2
CdI2/CdCl2
CdI2/CdCl2
Mn (1.01 Å)
Rutile
CdI2/CdCl2
CdI2/CdCl2
CdI2/CdCl2
Ca (1.20 Å)
Fluorite
Rutile
Rutile
CdI2/CdCl2
Sr (1.34 Å)
Fluorite
Fluorite
PbCl2
SrI2
Ba (1.56 Å)
Fluorite
Fluorite
PbCl2
PbCl2
Fluorite
Rutile
Cristobalite
CdI2
Polarization and Layered Structures
•
•
In fluorite, rutile and sphalerite the anion environment is symmetrical and
polarization effects are minimal.
In the layered CdI2 and CdCl2 structures the anion environment is
pyramidal and polarization effects shift anion charge cloud toward
toward the
cations, thereby minimizing repulsions between halide layers and cationcationcation repulsions.
Calculated energies for MCl2 crystals as a
function of cation size, (a) fluorite, (b) rutile,
rutile,
(c) layered with polarization, (d) layered w/out
polarization. The energies of fluorite and
rutile are nearly identical with or without
polarization. [Taken from P.A. Madden & M.
Wilson, Chem. Soc. Reviews 25(5),
25(5), 339 (2000).
“Polarization favors pushing
highly polarizable anions into
unsymmetrical sites”
7
Polarization in SiO2 Cristobalite
Idealized β-Cristobalite (SiO2)
Space Group = Fd3m (Cubic)
SiSi-O-Si ∠ = 180°
180°
No polarization, sp bonding at O2Si O
Si
Optimized for electrostatic
interactions
Actual β-Cristobalite (SiO2)
Space Group = II-42d (Tetragonal)
SiSi-O-Si ∠ = 147°
147°
2
Some polarization, sp bonding at O2Si
Stabilized by
polarization/covalency
O
Si
8