1. Bonding

2. 10+ Bohr's atom model Bohr’s atom model The neon atom (Ne) electron(s)
nucleus
(10 protons,
10 neutrons)
K-shell: max. 2 electrons
L-shell: max. 8 electrons
M-shell: max. 18 electrons
N-shell: max. 32 electrons
K-shell
L-shell

3. Schrödinger’s atom model
Probability
P to find an
electron for
a s-orbital
(K-shell)
distance from the nucleus
in all directions
Radial probability to find an electron z x y r
r = Bohr radius
proportional
to total probability
to find an electron
ptot
s-orbital z y x pz P
(L-shell)
distance from
the nucleus y z x py px
p-orbitals

4. 1s,2s and 3s orbitals in hydrogen atoms
Diagram showing the position of an electron over time t (15'000 points) in the hydrogen (from right to left) 1s, 2s and 3s orbital. In the ground state the electron will remain in the 1s orbital.
Idem for one of the 2p and 3p orbitals.

5. Boron atom
The boron atom: 5 electrons distributed among K- and L-shell z x y
distance from the nucleus
Probability
P to find an
electron
in z direction
Radial distribution along the z-axis of
K-shell 2 s-orbital electrons
L-shell 2 s-orbital electrons
L-shell 1 P-orbital electron

6. Filling of orbitals
„Relationship“ between Bohr shells and Schrödinger orbitals: Each shell is decomposed into orbitals
K-shell: s-orbital
L-shell: s-orbital, 3 p-orbitals
M-shell: s-orbital, 3 p-orbitals, 5 d-orbitals etc.
Shell designations by quantum numbers
Filling of shell’s
General rules:
Electrons are filled into orbitals in
increasing order of their energy levels
An orbital can have maximum two
electrons with opposite spin.
Every orbital of a subshell has to
be filled at least with one electron
before they can be occupied by
pairs (Hund’s rule). f
Energy f d s p d s p d s p s p s
Many exceptions to the rules!
K-shell
L-shell
M-shell
N-shell
O-shell

7. Silicon atom
Notation for orbital occupation: Prinicipal quantum number - letter for orbital type - number of electrons Electron distribution in silicon: 1s2 2s2 2p6 3s2 3p2 z y x
Filling scheme:
total of 14 electrons
2 electrons into s orbital of K-shell
2 electrons into s orbital of L-shell
2 electrons into px orbital of L-shell
2 electrons into py orbital of L-shell
2 electrons into pz orbital of L-shell
2 electrons into s orbital of M-shell
1 electron into px ,py or pz orbital of L-shell
1 electron one of the two other p orbitals of L-shell

8. Electronegativity
Electronegativity is a measure of the ability of an atom or molecule to attract respectively to give off an electron. Pauling's electronegativity scale is given in dimensionless units and ranges from 0 to 4:
EN < 1.9: element gives up electrons, metallic character (except noble metals)
EN > 2.1: element acquires electrons, non-metallic character
1.9 > EN > 2.1: amphoteric character

9. Covalent bonds I
Covalent bonds: sharing of electrons between atoms = overlap of orbitals.
Only between atoms with smallE (Electronegativity difference), perfect covalent bond only when E = 0 => between like atoms
Example: Fluorine electron configuration: 1s22s2 p5
2 p - orbitals of fluorine
red: occupied by two electrons
blue: occupied by one electron
Overlap of the two single
occupied 2p-orbitals (= sharing
of the single electrons)
Overlapping orbitals: molecular orbitals
Hybrid orbitals with axial symmetry: - bonds
Directionality is the major difference of covalent bonds compared to ionic bonds.
Most bonds are mixed in character. The covalent contribution is given by:
CC(%)= (16E E2)

10. Covalent bonds II
Hybridization (recombination) of orbitals of different types to form orbitals with new shape and orientation.
Example hybridization of s- and p- orbitals in diamond
Electronconfiguration of carbon: 2s2p2
Overlap of 2sp3 orbitals results in the
crystal structure of diamond:
Hybrid 2sp3 - orbitals
Hybridization
1s2
2s2
2px1
2py1
2pz0
1s2
2sp1
2sp1
2sp1
2sp1
2px1py1pz0
empty
2sp3
2s2 + =
Bonding between two
carbon atoms through
the overlap of two 2sp3
hybridized orbitals

11. Covalent bonds III + = -bond
Example hybridization of s- and p- orbitals in graphite
Electronconfiguration of carbon: 2s2p2
1s2
2s2
2px1
2py1
2pz0
Van der Waals bonds
1s2
2sp1
2pz1
2sp2
2pz1
2px1py1pz0
2s2 + =
Overlap of 2sp2 orbitals lead to hexagonal
carbon sheets. The lonely 2pz1 electrons
overlap sideways and form  - bonds. The
hexagonal sheets are only hold together by
very weak bonds.

12. Ionization I
Most stable electron configuration: s2p6 in the outermost shell = Noble gas configuration
Atoms can get this configuration by loosing or acquiring electrons, becoming charged ions by this process
positive ions:
cations
negative ions:
anions
fluor atom
negative fluor anion
sodium atom
positive sodium cation

13. Ionization II
Tendency for ionization ionization potential electron configuration
s2p6: most stable configuration, “noble gas” configuration => high ionization potential
Tendency to give off an electron increases when:
- no other electron was added or subtracted before
- the valence shell of the ion gets closer to a s2p6 configuration
- the electron is in a low energy orbital, far from the nucleus
Examples:
Element electron configuration 1st ionization potential
Lithium 1s22s eV
Caesium 1s22s2 p63s2p6 d104s2 p6d10 5s2p66s eV
Neon 1s22s2p eV
Krypton 1s22s2p63s2p6 d104s2 p eV
Ability to acquire a valence electron: Electron affinity. Positive affinities =
release of energy
Example Electron affinity
Chlorine 1s22s2 p63s2p eV

14. Ionic bonding I
- Large electronegativity difference E between two atoms => complete transfer of electrons from one atom to the other.
- Opposite charge of the atoms => Coulomb attraction = ionic bond with gain of cohesive energy.
Energetics of sodium chloride formation from the gaseous elements
Energy budget Na
Gas
Gas
Na +
Na+
+ e - eV eV
Ionization energy
Cl -
Gas Cl
Gas
e - + eV eV
Electron affinity
Gas
Cl -
Na +
Cl -
Crystal
Na +
Gas +
+ 7.9 eV
Cohesive energy
+7.90 eV
Total: eV

15. Ionic bonding II
Attractive and repulsive forces between a fixed cation located at the origin and an anion approaching from the right:
The configuration for which attractive
and repulsive forces between atoms
cancel each other is the minimum
energy configuration. The distance
between the center of one atom to the
center of the other is called bond length.
Force
Distance R between
cation and anion (Å)
(arb. units)
Coulomb forceq2R
Total force
REq
Repulsive forceA exp(-R/B)
 C/Rn
Born potential
Ftot = q2R + C/Rn
Equilibrium distance REq: F = 0 => bond length

16. Ionic bonding III
Direction in which the force is acting
When two or more anions are in the surrounding of a cation, the forces at the cation position will cancel each other. In most cases this will occur only at one single position, but it is also possible (b) that the forces cancel each other at more than one location. There is a equal likelyhood to find the cation in positions B or D.

17. + = Atomic and ionic radii I
Electron distribution around atoms and ions are not perfectly spherical, but are assumed so in the ionic model.
Assumption:
bond length = sum of radii of spherical atoms or ions + =
anion radius RA
cation radius Rc
ionic bond length L RA RC
L= RA +RC

18. O Mg O Ca Atomic and ionic radii II RO RO Determination of ion radii:
- Fixing the radius of one ion e.g. oxygen anion RO e.g. O-2
- Measuring cation - oxygen bond length L in different
oxides with similar structure, e.g. RO O Mg
RMg
Mg-O bond length in MgO
LMgO= RO +RMg
=> ionic radius of Mg = LMgO - RO RO O Ca
RCa
Ca-O bond length in CaO
LMgO= RO +RMg
=> ionic radius of Ca = LCaO - RO
A set of radii is only valid for the same coordination number. Standard ionic
radii:Shannon and Prewitt (1969, revised by Shannon 1976) based onthe radius of VIO2- taken as 1.4Å.

19. rCl rNa Electron density I bondlength
What is the absolute (numerical) value of a specific ionic radius?
Section of the electron density contours in NaCl, determined by x-ray diffraction. The contour indicate a certain electron "concentration". The contours close to the nuclei are not shown, they would be too close together. Ionic radii correspond to distance between electron density maxima (= center of atoms) and minima on a line connecting neighboring ions.

20. Electron density II F Li Electron density contours in x
LiF, determined by x-ray diffraction.
Ionic radii in tables deviate slightly
from the actual values, because the
anion radius is taken as a fixed value. x
Interatomic distance
electron
density
F- (Shannon & Prewitt)
Li+ (Shannon & Prewitt) F Li
Minimum density x

21. + + + + + + + + + + + + + + + Metallic bonds
Metallic bonding is characteristic among elements in ± the left part of the periodic table.
Each atom gives off its valence electrons. The valence electronscan move freely, forming an „
electron gas“ between the positively charged nuclei.
Schematic example of metallic sodium:
free electrons + + + + + + + + + + + + + + +

22. - + - + - - + + Van der Waals bonds
Non-metallic elements like nitrogen, oxygen and fluorine form molecules with no extra electrons remaining in the valence shell for further bonding. In the fluorine molecule, the two atoms of the molecule share the their single valence electrons, which are located in the single occupied valence orbitals. Fluorine is a gas at high temperature. At low temperature, the electrons of neighboring molecules influence each other. Negative and positive charges are not longer homogeneously distributed. The molecules are polarized. Positive and negative ends of neighboring molecule attract each other and form bonds (named after the physicist Van der Waals)
Orbital model of the fluorine atom - + - +
Polarization of the fluorine
molecules and formation
of Van der Waals bonds
at low temperature + - + -

23. Hydrogen bonds
The polarization of the charge distribution in molecules such as O2 , N2 or F2 is not permanent and is only strong enough at low temperature to create bonds between the molecules. Bonds between hydrogen and atoms like oxygen or nitrogen lead to a permanent polarization of the resulting molecule. The hydrogen atom will be attracted by other positively charged ions and form a hydrogen bond. H H O O H H H H O
Hydrogen bonds between
water molecules
Structure of ice II (box: unit cell)
Some of the hydrogen bonds are shown
as stippled lines