Chemical bonding
Inorganic materials chemistry
and functional materials
Helmer Fjellvåg and Anja Olafsen Sjåstad
Lectures at CUTN spring 2016
Chemical bonding - electronegativity
OLD
Size of atoms
Nuclear charge (protons) Z
No. of electrons Z
Shielding
Attractive forces
nucleus – electrons
Repulsive forces
electron – electron
Effective nuclear charge ....
”how strongly does the nucleus attract electrons”
Depends on how well do inner electrons shield outer electrons
Na  Mg ----- Si -----Cl: increasing effective nuclear charge
 consequence: reduction in atomic size (atomic radius)
Chemical bonding - electronegativity
Zeff = Z – s
s = Slater shielding constant
Net attraction experienced – values of effective nuclear charge
OLD
Chemical bonding - electronegativity
OLD
Trends – ionization enthalpies; 1st, 2nd, 3rd,...
Cations are formed
In compounds; more oxidation states may be feasible
Increasing DHionization
Huge increase when
noble gas electron
configuration is broken
A2+(g) = A3+(g) + e- Cf. change in effective
nuclear charge
A+(g) = A2+(g) + eA(g) = A+(g) + e1 eV = 96 kJ/mol
Rule of thumb:
noble gas configuration
is never broken:
HENCE: Alkali(I)
Alkaline earths (II) etc.
Chemical bonding - electronegativity
Electronaffinity: Eea
OLD
A(g) + e- = A-(g)
Eea is defined as the negative enthalpy change for this reaction
EXAMPLE: F(g) + e- = F- (g) DH = -328 kJ/mol Eea = +328 kJ/mol
 A positive electron affinity implies an exothermic reaction
Why O lower value than S, Cl ? e – e repulsions...
DH values:
Chemical bonding – oxidation numbers
OLD
Simple rules, extremely useful in chemistry
The most electronegative elements; oxygen (-II), fluorine (-I)
exceptions compounds between oxygen and fluorine; like OF2....
Never break a closed noble gas electron shell;
hence alkali(+I), alkaline earth(+II),..
Group 13, 14, 15 possibility of [ns2] lone pair for the heavier group elements
Tl(III) [s0] and Tl(I) [s2];
Pb(IV) [s0] and Pb(II) [s2]; these lone pairs may have be stereoactive
Bi(V) [s0] and Bi(III) [s2]:
d-elements; many oxidation states; jumps of 1 in ox.state possible
QUESTIONS
What is the oxidation state for the cations in:
 BaO2
 CsO2
 Mn3O4
 Pb3O4
 TiS2
 FeS2
Several functional oxides
show mixed valence state
=> not integer ox.state numbers
Can be tuned by substitution/doping
YBa2Cu3O7
LaMnO3.15
(La,Sr)FeO3
Chemical bonding
Chemical bonding
Chemical bonding is in reality a mixture of two or three of the (extreme)
components ionic, covalent and metallic
OLD
Chemical bonding - trends
Chemical bonding - electronegativity
OLD
The difference in Pauling electronegativity between atoms A and B is defined
by:
where Ed is the dissociation energies of A–B, A–A and B–B bonds in eV.
Example:
Difference in Pauling
electronegativity between
H and Br is 0.76
Dissociation energies:
H–Br = 3.79 eV
H–H = 4.52 eV
Br–Br = 2.00 eV
Chemical bonding - electronegativity
Mulliken electronegativity
On an absolute scale (kJ or eV)
Arithmetic mean of first ionization enthalpy and electron affinity of involved
atoms
Pauling
Are given in relative units (as Pauling electronegativity) by (E in eV):
Mulliken
Chemical bonding - electronegativity
Sanderson electronegativity
method of calculation based on the reciprocal of the atomic volume.
Based on concept of electronegativity equalization = electrons
distribute themselves in such a way that Mulliken electronegativity
differences are minimized. This is analogous to equalization of
chemical potential in macroscopic thermodynamics.
S = Sanderson electronegatiivty
D = electron density or atomic volume of an atom
Da = density or volume based on interpolation
between noble gas elements
Pauling
Electronegativity is a measure of the attractive forces between the
effective nuclear charge and an outermost electron, hence, it also relates to the
compactness of the atom (i.e. its volume; electron density)
Sanderson
Chemical bonding - electronegativity
Sanderson electronegativity
Principle of electronegativity equalization:
When atoms combine in a chemical compound, they get adjusted to take
the intermediate electronegativity (of the compound)
This electronegativity is given as the geometric mean.
Example for NaF:
The values for SNa etc are tabulated
Two assumptions:
- NaF is 75% ioinc (quite reasonable; group 1 and 17)
- Electronegativity changes linearly with charge.
Then: the change in electronegativity DSc of at atom aquiring a unit positive or
Negative charge is given by
Partial charge, d, is defined then as
where
Chemical bonding - electronegativity
Chemical bonding – electronegativity - examples
Sanderson electronegativity; examples
BaI2: Tabulated values: SBa = 0.78, SI = 3.84, DSc(Ba) = 1.93; DSc(I) = 4.08
DSBa = 2.26 – 0.78 = 1.48
DSI = 2.26 – 3.84 = -1.58
 Calculated charges are then
dBa = 1.48/1.93 = 0.78 and dI = 1.58/4.08 = -0.39
which implies 39% ionic
The radius of the atoms (cations and anions) depends on their charge:
Uses rc = 1.98Å and B = 0.78 for Ba
And rc = 1.33Å and B = 1.384 for I
 Calculated size of the atoms/ions are: Barium: 1.71Å
Iodine: 1.87Å
 Sum 1.71Å + 1.87Å = 3.58Å corresponds
well to the experimental value of 3.59Å
Chemical bonding – electronegativity - Sanderson
The numbers should not be considered as accurate, however, they
show the main trends!  Size of anion depends on chemical environment
The charge on chlorine is never as negative as -1 !
Chemical bonding – electronegativity - Sanderson
OXIDES: the charge on oxygen is far less negative than -2 !
Chemical bonding - electronegativity
Electronegativity – remarks on oxidation states
Many atoms in inorganic chemistry may take more than one oxidation state;
e.g. group 13, 14, 15, 16, 17 and the d-elements.
The simple concept with a single value for the electronegativity is “valid” for
"normal" situations, but not when more oxidation states are feasible
Electronegativity is not an invariable atomic property
Detailed data exist for a few elements where analysis been possible. For delements, tabulated electronegativities are averages for more oxidation states.
In general: electronegativity increases with oxidation number.
The chemical implication is seen in the crystal structures; in the acidity of
oxides and acid strength of oxoacids (dissociation constants)
CrO3 acidic and low melting point; Cr2O3 amphoteric and high melting point;
HnClOm oxoacids pKa = 8 – 5p (p = nb. non-protonated O-atoms)
Acid strength of cations in water
 Chemical consequences
Chemical bonding – reactivity – example acid/basic oxides
H3
O+
+
OLD
Acidic versus basic (hydr)oxides
MOnx-
Acidic oxide
Very electronegative cation
H
e
e
+d
H2O
:
H
O
M
on SURFACE
BULK
H
Electropositive cation
Mn+ + OH-
Basic oxide
19
Rule of thumb: DC (el.neg) > 1.4 between M and O  basic
Chemical bonding – reactivity – example acid/basic oxides
Basic
Amphoteric
Acidic
OLD
20
Chemical bonding – polarization – example acidity of cations
OLD
B3+(aq) ???
Does NOT exist as such
But as  B(OH)3
Al3+(aq)
?
Z2/r
Forms at pH7
Example
0-0.04
hydrated
cation
NaI (H2O)6+
0.04-0.22
hydroxide,
oxide,
or oxidehydroxide
AlIII
(H2O)3(OH)3
oxidehydroxide or
hydroxo anion
SeVI O3(OH)-
oxoanion
BrVII
[Al(H2O)6]3+
Cationic acid
Protolysis:
[Al(H2O)6]3+
0.22-0.8
2+
+
 [Al(H2O)5(OH)] + H
> 0.8
O4
-
21
Chemical bonding – polarization – example oxoacids
1) Oxoacids: The acid strength increases with the number of nonprotonated O-atoms bonded to the central cation
H–O–N=O
m=1
m=2
H–O–N
generalize the formula to: (HO)nXOm
RULE:
or RULE:
m = 0; pKa = 8
m = 2; pKa = 1
m = 1; pKa = 2
m = 3; pKa = 8
Alternative evaluation of pKa value:
pKa = 8 - 5p
2) Electronegativity and size of central atom for the oxoanion also affects
the acidity
22
Chemical bonding - electronegativity
Van Vechten electronegativity scale
Restricted to ANB8-N compounds
Following the 8-N rule
Dielectrically defined
Quantum mechanical foundation
Additional ionic component to the band gap
Heteropolar energy; homopolar energy
and «ionic energy»
Tetrahedral structures
Elements, AB compounds...
Chemical bonding - electronegativity
Van Vechten electronegativity scale
Dielectricaly defined sp3 electronegativities
Chemical bonding - electronegativity
Van Vechten electronegativity scale
Correlation with
Pauling electronegativity
Chemical bonding - electronegativity
Van Vechten electronegativity scale
Critical ionicity
CN = 6
CN = 4
Scale for ionicity
Chemical bonding – examples compounds; radius ratio rules
Radius – ratio rules
Sphere packings
rK/rA
Geometry
CN
cube
(8)
Octaedral
(6)
Tetrahedral
(4)
1.000
0.732
0.414
0.225
Trigonal planar (3)
0.155
Linear
(2)
Chemical bonding – size of ions/atoms - trends
Size, charge, spin states - trends
Isolectronic series:
Na(I), Mg(II), Al(III), Si(IV)
Effect of oxidation nb:
V(II)
V(IIII)
Effect of spin state:
Fe(III)HS Fe(III)LS
V(IV)
V(V)
Octahedral site: eg orbitals
28
Chemical bonding – examples compounds; cation constant
AlF3
AlF3 is most ionic of
these three examples;
3D strutcure; corner
shared octahedra
AlCl3
AlCl3 is more covalentCN(Al) still 6. Now a 2D
structure. Lower Tm than
the fluoride.
AlBr3
Is molecular; consists of
dimers; Al2Br6
with edge shared tetrahedra.
CN=4 (cf. radius ratio rule)
Low melting point.
OLD
Chemical bonding – examples compounds; anion oxygen
H
Li
Electrondensity
3
11
Na
K
19
37
Rb
55
Cs
Na2O
Fr
MgO
87
Be
4
12
Mg
20
Ca
Sr
38
56
Ba
5
B
Al
13
31
Ga
49
In
Tl
81
1
He
6
C
Si
14
Ge
32
50
Sn
82
Pb
7
N
P
15
33
As
51
Sb
Bi
83
8
O
S
16
Se
34
Te
52
9
F
Cl
17
Br
35
53
I
Ne
Ar
Kr
2
10
18
36
Xe
54
Na(I), Mg(II), Al(III), Si(IV)
86
84
85
isoelectronic
[Ne]
Rn
Poare At
Increasing Z2/r
Al2O3
 more polar covalent
Normale oksider O oksidasjonstall
(cf. Fajan-2
rules)
We observed more electron
Oksidasjonstall –1 i peroksider
density inbetween
cation and anion.
30
SiO2
88
Ra
Chemical bonding – examples compounds; anion oxygen
H
Li
3
11
Na
K
19
37
Rb
55
Cs
Na2O
Fr
87
Be
4
12
Mg
20
Ca
Sr
38
56
Ba
5
B
Al
13
31
Ga
49
In
Tl
81
1
He
6
C
Si
14
Ge
32
50
Sn
82
Pb
7
N
P
15
33
As
51
Sb
Bi
83
8
O
S
16
Se
34
Te
52
84
Po
9
F
Cl
17
Br
35
Ne
Ar
Kr
53
I
At
85
2
Decreasing
radius ratio

Change in
coordination
10
18
36
Xe
54
86
Rn
88
RaAl O
2 3
ClO2
P4O10
Normale oksider O oksidasjonstall -2
«ionic»
CN = 4
Polar
covalent
Oksidasjonstall –1 i peroksider
MgO
SiO2
S3O9
31
Chemical bonding – examples compounds; anion fluorine
Increasing covalent character
11
12
Na
Mg
NaF
MgF2
Al
13
Si
14
P
15
PF3
AlF3
SiF4
PF5
S
16
SF4
Cl
17
ClF5
SF6
molecular
32
Chemical bonding – examples structure – thermal stability
Relative melting(boling point
Termal stability versus oxidation state & structure
Ionic
Layered or
Structure 3D network
Chain Molecule
Polymer Dimer,..
Oxidation number (for central cation)
(Here: maximum expected for en given group)
The drop in stability
reflects differences
In the long range
crystal structure
Again a result of
size of cations
and bonding
33
Chemical bonding – examples
Cations with stereoactive lone pairs (i.e. hybridized; not pure s-character...)
 may stabilize non-centrosymmetric structures; e.g. PZT Pb(Zr,Ti)O3
PbO2
Ox.state +IV
Ox. state +II
Pb3O4
PbO2.2PbO
PbO
yellow
orthorhombic
491 oC
brown
PbO
red
tetragonal
34
Chemical bonding – examples and questions
How will you compare/describe the chemical bonding in:
-
MgO, BaO, NiO, ZnO?
NaH, MgH2, SiH4, HCl?
Na4C, SiC, CO2?
Mg2Si, Si, GaAs?
LaAlO3, LaFeO3, LaNiO3?
NaAlH4, Li3AlH6, LiBH4?
Na4SiO4, FePO4, Na2SO4, LiClO4?
QUESTIONS:
 Consider AgO. It is diamagnetic. How will you explain that based on
likely oxidation states and local geometry for the Ag-cations?
 Consider Cr8O21. This compound conistst of Cr(III) and Cr(VI) as cations.
Provide a formula highlighting the oxidation states. What geormetry do you
expect for the Cr(III) and Cr(VI) coordination polyhedra with oxygen?
Chemical bonding – charge neutrality
Pauling's rules are five rules published in 1929 for predicting and rationalizing
structures of ionic compounds
1. Minimum size to fit into a void/hole;
rattling is not a stable situation
Rcation/Ranion
2. For a given cation, the electrostatic bond strength to each coordinated anion is
s = z/n , with z = cation charge and n = cation coordination number. The atomic
arrangement of a stable ionic structure preserves local electroneutrality.
Hence, the sum of the electrostatic bonds strengths to an anion equals the anion
charge.
In Li2O, Li has four oxygen atoms in tetrahedral surroundings; s = ¼
The O-atom has eight neighbouring Li-cations; hence x = 8 x ¼ = 2 equal to O-charge
3. The sharing of edges and faces by anion polyhedra decreases the stability
Corner sharing more stable > edge sharing > face sharing
4. When different cations, those of high valence and low
coordination number tend not to share polyhedra
Chemical bonding – examples
Other routes to non-centrosymmetry; piezo/pyro/ferroelectrics
By hybridization (d0 cations); by rattling (size; see e.g. t-factor)
Perovskite type BaTiO3
183 K < T
Paraelectric to ferroelectric (T < 393 K)
Chemical bonding – charge neutrality - examples
AaBb compounds of regular type (ionic/covalent – insulator/semiconductor)
a . CN(A) = b . CN(B)
TiO2: Ti in octahedral holes; CN(Ti) = 6;  CN(O) = 3
SiO44- tetrahedra are building bricks in silicates.
Highly charge Si(IV); only corner sharing acceptable
How many SiO4-tetrahedra may share the same O-atom/corner?
Electrostatic bond strength (ebs) s = 4/4 = 1
Charge of O-atom is -2; hence maximum 2 surrounding Si-cations
Maximum 2 SiO4-tetrahedra can share the same O-atom/corner
Wüstite Fe1-xO; stoichiometric FeO is metastable; instead some Fe(II) oxidizes
to Fe(III) and the non-stoichiometric wüstite forms.
The Fe(III) atoms are smaller in size and has higher charge
Will take tetrahedral interstices in the ccp of O-anions
Such interstital Fe(III) will repel the Fe(II) at regular octahedral sites.
 Defect clusters (complexes) are formed; Fe-vacancies cluster around
the Fe(III) interstitials
Chemical bonding – charge neutrality - solid solutions
Aliovalent (heterovalent) substitution – in ionic compounds AOx
Defect formation; charge compensation
Too much positive charge
Substitution by higher valence cations (B) into AOx
Cation vacancies
Interstitial anions
Too much negative charge
Substitution by lower valence cations (C)
Anion vacancies
Interstitial cations
Side note: Similar patterns can be made for anion substitution; but are not included
here as aliovalent anion substitution occurs to lesser extent in solid solutions
Chemical bonding – charge neutrality - solid solutions - diffusion
Interstitial anions – ionic conductitivity
Possible
interstitial site
AB2
with A6B8 neighbors
octahedral site
(in ccp of A atoms)
The interstitial site can typically be filled with anions;
AB2+d
= dominating defect for CaF2-type phases
Possible route for anion transport
PbF2+d
(Y, Zr)O2-d
Chemical bonding – charge neutrality - solid solutions - diffusion
Interstitial anions – ionic conductitivity
(Y, Zr)O2-d
YSZ: yttria stabilized zirconia
Solid solution; Y(III) on Zr(IV) site  O-vacancies
Technologcal issue: phase compatibility
Interface reactions - interdiffusion
The interstitial site can typically be filled with anions;
AB2+d
= dominating defect for CaF2-type phases
Possible route for anion transport
PbF2+d
Chemical bonding – defects - diffusion
Mint
Voct
Moct
Mint
Activation energies for
creation of Frenkel defects
for movement of cations
 What will be the transport mechanism
of diffusing cations; in NaBr and in AgBr (consider ionicity)?
Chemical bonding – bond valence
Calculation of bond valence is a useful method for evaluating oxidation
states and certain structural aspects of compounds.
The valence V of an atom = sum of individual bond valences vi surrounding the atom:
The individual vi bond valences are calculated from observed bond lengths, Ri.
Ri is observed bond length
R0 tabulated parameter for (ideal) bond length when
element i has valence 1,
and b is an empirical constant, typically 0.37Å
The bond valence model is an extension of the electron counting rules; its strength
lies in simplicity and robustness. It does not require a prior knowledge of the atomic
positions and so can be used to construct chemically plausible structures given only
the composition. However, the bond valence model has limitations. It is restricted to
compounds with localized bonds; it does not apply to metals or aromatic compounds
where the electrons are delocalized.
Chemical bonding - examples
Software for bond valence calculations:
http://www.ccp14.ac.uk/solution/bond_valence/
More details on bond strength and bond valence: see slides
http://www.mrl.ucsb.edu/~seshadri/2011_218/2011_218_BondValenceSums.pdf
Chemical bonding - examples
http://www.mrl.ucsb.edu/~seshadri/2011_218/2011_218_BondValenceSums.pdf
Chemical bonding - examples
High-Tc superconductors - cuprates
Planes; square pyramidal units
YBCO = YBa2Cu3O7
TC = 92 K
Chains; square planar units
Chemical bonding - examples
Evident from the formula (Y0.33Ba0.67)CuO3−0.67 there are oxygen vacancies in the
O-substructure. In YBCO these vacancies are ordered. The YBCO structure does
never have any O-atoms in the positions described as vacancies
Where are the new vacancies located; how does the Cu-coordination polyhedra
change; and what happens with the electronic properties (superconductivity)?
In YBa2Cu3O6 the average Cu-oxidation state is 1.67. This stoichiometry is
consistent with the formal description YBa2Cu(I)Cu(II)2O6.
 Look up crystal structure and bond valence data: Calculate B.V. For the Cu-atoms.
Chemical bonding – elements - structure
(8-N) rule
Carbon group: N = 4  4 bonds
Nitrogen group: N = 5  3 bonds
How to obtain a filled octet....
Can be achieved in different ways  allotropic forms of the elements
Diamond sp3
N
N
Graphite: sp2 + pz
Nitrogen: triple bond
White phosphorus
Molecular P4
Three single
bonds
Layered red and black
48
phosphorus
Chemical bonding - compounds
Compounds with «unusual» compositions; how to explain them?
Zintl phases; group 1 and 2 + an element from group 13, 14, 15 or 16
 Typically diamagnetic
 Typically semiconductors or poor conductors
Example: NaSi
Na must have oxidation state +I. On average silicon is then –I. How possible?
Silicon forms a tetrahedron; Si44Charge compensated by 4 Na+
Na4Si4
NOTE: Si44- is isoelectronic to P4
NaSi is a polyanion compound
Chemical bonding - examples
The (8-N)-rule provides the number of bonds in a compound (N = number
of valence electrons of the element which builds the compound)
Example: Phosphorus (P): N = 5; (8 - N) = 8 - 5 = 3. Hence, phosphorus
has 3 bonds, i.e. white phosphorus exists as a P4-tetrahedron
Polyanion compounds (and polycation):
The (8 - N)-rule is then expanded
(8 - VEC) = number of bonds
VEC = valence electron concentration = [m × e(M) + x × e(X)]/x for a
compound MmXx where e(M) and e(X) equals the number of valence
electrons of the elements M and X, respectively
Example NaSi:
VEC = [4 × 1 + 4 × 4]/4 = (4 + 16)/4 = 5
Si44- behaves like an element of the 5th main group (group 15)
The crystal structure correspond to that of white phosphorus
Bonds: (8 - VEC) = 3; for each silicon atom 3 bonds exists
Chemical bonding - examples
Example NaTl
VEC = [1 × 1 + 1 × 3]/1 = 4
The electronegative part of the structure (the polyanion) behaves
like an element of the 4th main group (group 14).
The crystal structure of the polyanion (Tl-) is of diamond type
(8 - VEC) = (8 - 4) = 4
For each Tl-atom 4 bonds exists
The Tl- polyanion has a 3D-structure
based on 2e-bonds between each Tl-atom
Chemical bonding - examples
Checking out on MgB2
VEC = [1 × 2 + 2 × 3]/2 = 4
The electronegative part of the structure (polyanion) behaves like
an element of the 4th main group (group 14).
If behaving like a Zintl phase; then
The crystal structure of the polyanion (B22-) is of diamond type
(8 - VEC) = (8 - 4) = 4
This is not the case:
For each B-atom 3 bonds exists + one electron
This is, however, corresponding to graphene
The band near the Fermi level is mainly derived
from boron orbitals: sp 2 (σ) states and pz(π)
states. The σ bands are 2D in character and form
cylindrical Fermi surfaces, whereas the π bands
have more of a 3D character.
Chemical bonding - examples
Note; this also covers small polyanions
BaO2 with peroxide anion O22VEC = [1 × 2 + 2 × 6]/2 = 7
The electronegative part of the structure (polyanion) behaves like
an element of the 7th main group (group 17); the halogenes (like F2)
HgCl
Is a polycation compound with Hg-Hg bonding; forming a dimer
Hence; Hg2Cl2 is a better chemical formulation
QUESTION:
Do you expect different crystal structure for TiS2 and FeS2?
Consider oxidation states:
Ti(IV)
Fe(IV) or not??
S(-II)
 answer: layered structure for TiS2 with Ti(IV) and S(-II)
 Polyanion for FeS2 with Fe(II) and S22 Why so? Fe(IV) too strong oxidizing agent to coexist with reduced S(-II)
Chemical bonding - examples
Oxygen species...
O22- peroxide
O24Li(s) + O2(g)
(4Na + O2
O2- superoxide
(hyperoxide)
2Li2O(s)
2Na2O)
2Na + O2
Na2O2
( 2K + O2
K2O2 )
K + O2
KO2
Rb + O2  RbO2
Cs + O2  CsO2
Chemical bonding - examples
½+½
S = Sms = 1
Ground stated
2S+1=3; triplet
Paramagnetic
Oxygen O2
MO-diagram
½-½
S = Sms = 0
Exited state
2S+1=0; singlet
Diamagnetic
O2
O2-
O22-
O2 oxygen
O2- superoxide
O22- peroxide
Bond order:
2
1.5
1
Has
longer
O-O bonds
Chemical bonding – intermolecular forces
Intermolecular forces
Consider here molecules and forces acting between them.
Also relevant for 1D-chain structures and 2D-layered structures
Some such forces relevant for certain 3D regular structures
Induced dipole forces [dispersion forces]
Dipole – dipole interactions
Ion – dipole interactions
Hydrogen bonding as a special case
Chemical bonding – intermolecular forces – 1D chain structure - example
CrO3
1D-Ca3Co2O6
2D-LiCoO2
Quasi 2DLa2CoO4
3D-LaCoO3
Chemical bonding – intermolecular forces – 2D layer structure - example
Layered double hydroxides
Graphite (and h-BN)
MoS2
Layered silicates
Oxyhalides – FeOCl
Layered Materials
Perovskite related materials
Metal halides
MoCl2 – CrCl3
III-VI layered
Semiconductors – GaSe
Chemical bonding – intermolecular forces
Dispersion forces
Average electron
density
Instantaneous electron
density giving a
temporary dipole
Continuous generation of instantaneous dipoles
Approximation:
Forces are proportional to number of electrons of atom
Instantaneous attraction between
two molecules
And reversal of polarity in the
next instant
Physical consequence:
Increasing mellting and
Boiling point for molecules
(in a given series)
 More complicated in reality
Geometry is also parameter
SF6 versus dekan C10H22
Tm: -51 oC versus -30 oC
Chemical bonding – intermolecular forces - example
Melting point – structure covalent molecules
At room temperature:
9
Colorless gas
-219°C
17
Yellow gas
-101°C
35
Brown liquid
F
Cl
Br
I
Tm
53
At
85
Structure
-7°C
Lustreous solid
*sublimes
Metalic
+114°C*
+302oC
Increasing strength
of induced dipoles
F2(s)
Cl2(s)
Br2(s)
I2(s)
Molecular; X2 two atomic molecules
Only weak dispersion forces
61
Chemical bonding – intermolecular forces
Dipole – dipole forces
Molecules may have a permanent dipole moment
Origin in electronegativity differences
Will have shift in electron density; with positive and negative partial charges
EXAMPLE:
CO versus N2 The are isoelectronic molecules (14 electrons);
But 5 K difference in both Tm and Tb
Must consider dipole – dipole
PLUS dispersion forces
EXAMPLE:
Tb for HBr is 206 K 36 electrons
Tb for HCl is 188 K 18 electrons
Stronger dispersion forces in HBr
Permanent No permanent dipole
dipole
Canellation owing to symmetry Dominates over stronger
Dipole – dipole forces in HCl.
Chemical bonding – intermolecular forces - Hydrogen bonding
H2O – water/ice
97 % of all water on earth is salt water.
2% is ice, mainly in Antarktica
100
Importance of hydrogen
bonding for melting and
boling point
60
40
o
Temperatur ( )
Hydrogen bonding
Mainly electrostatic
component
-O-H OLow el.density shared
ONLY for hydrogen in
combination with the
most electronegative
elements; F, O, (N),..
ANOMALY
for H2O
80
20
0
Trend:
Dispersion forcesr
dominant
-20
-40
-60
-80
-100
0
6
H2O2 H2S4 H2Se
H82Te 10
X Axis Title
63
Chemical bonding – intermolecular forces - Hydrogen bonding
H2O – dihydrogenoxide…
In solid state: The O-atom of H2O has
tetrahedral surroundings of H-atoms
(corresponding to O-lone pairs)
In liquid state: short range correlations
 Hydrogen bonds
64
Chemical bonding – intermolecular forces
QUESTIONS
Consider the variation in boling point of H2X (X = O, S, Se, Te)
How do you expect that this compares with
(a) The series HX; X = F, Cl, Br, I
(b) The series XH4; X = C, Si, Ge, Sn, P
Make skematic drawings
Chemical bonding – ionic bonding
NOT
USED
Ionic radius
The ionic radius is not a fixed property of a given ion, but varies with:
- coordination number (increases with increasing CN)
- spin state (HS ion larger than LS ion)
Ionic radii are sufficiently transferable to allow periodic trends to be recognized:
s- and p-block:
radius increases with Z for any vertical group
s
d
Poorer shielding
p
Isoelectronic series of cations, radius decreases with
increasing charge: Na+, Mg2+, Al3+ and Si4+
Cation radius decreases with increasing oxidation
state: V2+, V3+, V4+, V5+
Lanthanide contraction and d-element contraction
due to poorer shielding (comparing ions with same
charge) of d- and f-electrons
Chemical bonding – ionic bonding – ionic radii
NOT
USED
A major review of high quality crystallographic data, led to the publication of a revised
set of ionic radii in 19761. These values are today the preferred once.
Li+
F-
F-
Li+
Electron density contour map of LiF
Variation in electron density along the
connecting line between Li and F nuclei
in LiF.
P = Pauling radius of Li+; G = Goldschmidt
radius; M = minimum in electron density;
Pauling's reference of rion(O2−) = 140 pm still in use (in Shannon referred to as
crystal radius “CR”)
Shannon: value as reference of oxide anion is rion(O2−) = 126 pm (“IR”)
1: Shannon R.D. Acta Cryst. A32 751-767 (1976) – reference is avaiable on Fronter.
NOT
USED
Chemical bonding – ionic bonding
Characteristics of ionic bonding:
 - Non-directional
 Ions have as high coordination number as possible
 ideally: charged, non-compressible,
non-polarizable spheres
Lattice energy for NaCl: Energy needed to break NaCl(s)  Na+(g) + Cl(g)
1) Long range electrostatic
attractive and repulsive forces:
Cl
Na
Na
2) Short range repulsive forces due to overlap of electron clouds
1) long range electrostatic forces:
Electrostatic energy of a pair of monovalent
Ions such as Na+ and Cl:
Ee

 e e


40 r
 e2
40 r
NOT
USED
Chemical bonding – ionic bonding
Lattic energy - Ionic structures
Ee

 e e


40 r
 e2
40 r
r
 Opposite charges attract each other, same charges repell each other
 Electrostatic energy of a 3D lattice of cations and anions depends on atomic
arrangement = the geometry (expressed via the Madelung constant, )
  e2 
2

 2

e
  Geometry  ionic charge   N 
Ee  
Z
A
4

r
0 

 4 0 r 
 Madelung constant is used to calculate the effective electrostatic
potential energy with basis in a particular crystal structure. The ions are
treated as point charges.
NOT
USED
Chemical bonding – ionic bonding
NaCl
3D-periodic atom arrangement
1., 2., 3., …n.,… coordination sphere
1) Na+ is surrounded by 6 Cl
2
6
(
Z
)(
Z
)
e
 1 



E  
r
 4 0 
 1
+
+
2) Na surrounded by 12 next neighbour Na at √2r: E  
 4 0
3)
Na+
surrounded again by 8
 ( Z  )(Z  )e 2
E  
 4 0 r
Cl at
√3r:


12
8
6
 6 


 .... 
2
3
4


 1
E  
 4 0
 12( Z  )(Z  )e 2

2r

 8( Z  )( Z  )e 2

3r

A slowly converging series

Madelung constant = 
NOT
USED
Chemical bonding – ionic bonding
Reduced Madelung constant
MmXn
 N A * Z 2 e 2
Ee  
 4 0 r



 N A e 2 
mn


Z M Z X 
Ee  

2
 4 0 r 
Madelung constants
Structure type
Rock salt, NaCl
CsCl
Wurtzite, ZnS
Sphalerite, ZnS
Fluorite, CaF2
Rutile, TiO2
Maintains charge neutrality
mZM = nZX
*
1.748
1.763
1.641
1.638
2.520
2.408
Reduced Madelung constants, 
Structure type
Rock salt
CsCl
Wurtzite
Sphalerite
Fluorite
Rutile
M+XM+XM2+X2M2+X2M2+X2M4+X22-

1.748
1.763
1.641
1.638
1.68
1.60
Chemical bonding – ionic bonding
NOT
USED
2) short range repulsive forces due to overlap of electron clouds
Short range repulsive potential energy, Er = B/rn where B and n are constants
n is extracted from compressibility measurements
NOT
USED
Chemical bonding – ionic bonding
 NA * Z 2 e 2
UL  Ee  Er  
 4 0 r
 NAB
  n
 r
Long range electrostatic forces
Born repulsive term
Lattice energy at equilibrium
separation between ions, r0
 N A * e 2 Z 2
UL  
2
4

r
0 0

 1 
1  
 n 

Chemical bonding – ionic bonding - example
NOT
USED
Melting point
( Z  )( Z  )e 2
A
Lattice energy is proportional toV 
r
A = Madelung constant [depends on the 3D geometric
distribution of anions and cations]
r = M-X bond distance
Consider KF, KCl, KBr and KI. How do expect Tm to vary?
M-X distance depends on size of X anion
 Lattice energt will reduce from KF to KI (1/r dependency)
KF: Tm = 857oC; while for KI Tm = 685oC
Chemical bonding – ionic bonding
Ionic versus covalent
No clear border…..
NOT
USED
Chemical bonding – energies – bonding type
Comparison of typical bond energies for different types of bonds
NOTE: differences between compounds may be quite significant
Type
kJ/Mole
Species involved
Covalent
200-350
Atoms with shared electrons
Ionic
250
Ions
Metallic
200
Metal atoms
Ion-dipole
15
Ions and polar molecules
Dipole-dipole
2
Stationary polar molecules
Dipole-dipole
0.3
Rotating polar molecules
Dispersion
2
All atoms and molecules
Hydrogen bond
20
N,O,F in combiantion with H
Chemical bonding – binding energies – some comparisons
Binding energy kJ/mole
C-C
346 Si - Si
C-O
358 Si - O
222
452
Consequences:
Carbon forms easily C-C chains  organic chemistry and chemistry of life!
Silicon forms oxides; silicates; the main constituent of the earth crust
N
N
941 kJ/mol
P
P
481 kJ/mol
N
N
163 kJ/mol
P
P
200 kJ/mol
N
O
201 kJ/mol
P
O
335 kJ/mol
Concequences:
N2 extremely stable (trippel bond; cf. Its MO-scheme)
Formation of nitrogen oxides is endothermic
Several chemical reactions with nitrogen becomes «unusual»
Phosphates (P-O based compounds) are stable
No multiple bonds for phosphorus
Chemical bonding – stability of binary oxides
Enthalpies of formation - oxides
CO
CO2
N2O
NO
NO2
SO2
SO3
DHof = -110.5 kJ/mole
DHof = -393.5 kJ/mole
DHof = 82.1 kJ/mole
DHof = 90.3 kJ/mole
DHof = 33.2 kJ/mole
DHof = -296.8 kJ/mole
DHof = -395.7 kJ/mole
78
Chemical bonding – stability of binary oxides
Differences in electronegativity gives different
reaction pathways
NCl3(l) + 3H2O(l)  NH3(g) + 3HClO(aq)
PCl3(l) + 3H2O(l)  H3PO3(aq) + 3HCl(aq)
Differences in stability of binary oxides gives
different behavior on heating in air/oxygen
N2H4(g) + O2(g)  N2(g) + 2H2O(g)
C2H4(g) + 3O2(g)  2CO2(g) + 2H2O(g)
79
Chemical bonding – reactivity
3.04
3.44
3.16
2.20
NCl3(l) + 3H2O(l)  NH3(g) + 3HClO(aq)
NCl3
PCl3
PCl3(l) + 3H2O(l)  H3PO3(aq) + 3HCl(aq)
2.19
3.44
2.20
3.16
80