1. Metals form solid states where the atomic orbitals overlap to form continuous bands of energy levels that allow electrons to move freely. This gives metals their conductive properties. 2. Semiconductors have a small band gap between the valence and conduction bands. Adding small amounts of impurities can increase or decrease conductivity by introducing more charge carriers. 3. Metal oxides and metal-organic frameworks use different structures and bonding to exhibit properties like magnetism, photocatalysis and gas storage that depend on their electronic band structures.

1. Inorganic Materials
UP, Dr. Chris 2019

2. Subjects

3. SOLID STATE OF METALS

4. https://is.muni.cz/el/1431/podzim2017/C7780/um/L4_band_theory.pdf

7. Metals - Conductors
Example:
Combining the 2s
orbitals of several Li-
atoms
=> For each 2s AO we
get one MO
https://chem.libretexts.org/Textbook_Maps/General_Chemistry_Textbook_Maps/Map%3A
_Chem1_(Lower)/09._Chemical_Bonding_and_Molecular_Structure/9.10%3A_Bonding_in
_Metals

8. Finally we end up with
2 “bands”
Electrons can move
freely in the empty
orbitals
(anti-bonding MO’s)

9. In conductors, there is overlap between the filled and empty orbitals
=> Electrons from the valence band can easily move into the conduction band
Conduction
band
Valence
band

10. SOLID STATE: SEMICONDUCTORS

11. Semiconductors
http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/band.html#c1

12. Example: Silicon as “IV semiconductor”

13. Example: Si crystal
The closer the atoms come together, the higher the band gap will be !
LUMO
HOMO
https://www.youtube.com/watch?v=k_tFJin_YoQ

14. http://hyperphysics.phy-astr.gsu.edu/hbase/Solids/bandper.html#c1

15. Group 4 elements
covalent metallic

17. Questions
empty
electrons

18. https://chem.libretexts.org/LibreTexts/University_of_Missouri/MU%3A__1330H_(Keller)/
12%3A_Solids_and_Modern_Materials/12.1%3A_Classes_of_Materials

19. The probability to find an electron
in the conductor band can be
calculated as:
https://chem.libretexts.org/Core/Physical_and_Theoretical_Chemistry/Chemical_Bonding/F
undamentals_of_Chemical_Bonding/Band_Structure

20. Influence of Temperature

21. Fermi Level EF (metals)
EF = 50% probability level to find an electron
https://www.youtube.com/watch?v=zWOSAzbxTrE

22. For semiconductors, EF is in the middle of the band gap
The higher T, the more electrons
will come up to the conductive
band –
at 0 K, all electrons are in the
valence band
T up
Charge
carriers are
electrons
and holes

23. Example of practical applications
for TiO2
(J. of CO2 utilization 1 (2013),8-17)

24. Photocatalysis TiO2
Light energy promotes electrons in antibonding orbitals,
leaving a positive charged “hole” in the lower orbitals

25. Splitting of water by sunlight

26. Reactions with CO2

27. https://www.azonano.com/article.aspx?ArticleID=4226
Measure the band gap energy by UV/VIS

29. RELATION MO DIAGRAM - BANDS

30. Extend MO theory
Simple model: a string of 5 H-atoms
2 H-atoms can be
combined
to form 2 orbitals,
with no node and
with 1 node
For 5 H atoms we get 5 combinations
with 0, 1, 2, 3 and 4 nodes
Nodes:
0
1
2
3
4
Draw the missing 4 MO’s for H5
And find if they are :
bonding, non-bonding or
anti-bonding

33. Vector k
We can define a wavenumber for the
electrons that move in a crystal:
k = 2π/λ = 2πp/h
k is proportional to the number of the
nodes n in a molecular orbital
In a linear system with N unit cells
separated by distance a:
(MO with n nodes) λ = 2 Na/n
and k = π n / Na
At the bottom of a bond with λ = infinite: k = 0
and at the top of band with the MO having N nodes: k = π/a and λ = 2a
https://en.wikibooks.org/wiki/Introduction_to_Inorganic_Chemistry/Metals_and_Alloys:_
Structure,_Bonding,_Electronic_and_Magnetic_Properties

36. H2 in unit cell
Unit cell
with 2 el

37. • The valence band runs “uphill”
• The conduction band runs “downhill”
• The bands are narrower due to less overlap between the H2 molecules
compared to the H atoms
• The material now is not metallic anymore compared to H atom chain
• The minimum energy gap between bands occurs at k = /a
Valence band
(full of electrons)
Conduction band
(empty, anti-bonding)
https://cbc-wb01x.chemistry.ohio-state.edu/~woodward/ch754/bandstr.htm

38. DOS – Density 0f States
The density of states is defined as the number of orbitals per unit of energy
within a band.
Because of the parabolic relation between E and k, the density of states for
a 1D metallic crystal is highest near the bottom and top of the energy band
where the slope of the E vs. k curve is closest to zero.

39. Compare Graphite - Diamond

40. Graphite similar to benzene

41. Combination of many benzene MO’s
https://www.seas.upenn.edu/~chem101/sschem/conduction.html

42. Diamond structure
only  bonds
https://www.seas.upenn.edu/~chem101/sschem/conduction.html

43. TiO2 structure
Ti(4+) MOs
(crystal field)
Electrons in the Ti-O bonds
(coming all from O2-)

44. Photocatalysis TiO2
Light energy promotes electrons in antibonding orbitals,
leaving a positive charged “hole” in the lower orbitals

45. TM OXIDES

46. (1) Rocksalt Structure
Metal monoxides MO

50. Super-exchange leads to
anti-ferromagnetism
http://web.mit.edu/3.23/www/Lecture%2015.pdf

51. (2) Perovskite Structure ABO3

52. https://cbc-wb01x.chemistry.ohio-
state.edu/~woodward/ch754/lect2003/perovskites_lect24.pdf

53. Preparation of metal oxides
Molecular Synthesis Solid state synthesis
• In a solvent
• Low reaction T
(-80 to 250 C)
• Kinetic control
eg. oxidation of alcohol:
CH3CH2-OH  CH3COOH
(thermodynamic:
oxidation leads to CO2 + H2O)
• Normally solvent-free
• High reaction T
( > 300 C)
• Thermodynamic control
Solid state reaction are slow and require high temperatures because ions
have to diffuse from one crystal structure to another

55. Liquid to solid preparation – hydrothermal methods
Similar to reaction – crystallization methods in molecular reactions:
The zeolites framework is made up of SiO2 tetrahedra with the occasional
substitution of Al for Si. To compensate the charge difference (Si(+4), Al(+3))
sodium cations are accommodated on the inner surface of the framework.

56. METAL ORGANIC FRAMEWORKS
(MOF)

58. Solvo/hydro thermal preparation

59. Zeolite-like MOFs = ZIF
http://www.chemtube3d.com/solidstate/MOF-ZIF8.htm

60. Simplified representation
The building units of Zn4O(BDC)3
(a) A central OZn4 unit filled circles are Zn) linked to six CO2
units of BDC groups (shaded circles are C).
https://docs.google.com/viewer?a=v&pid=sites&srcid=ZGVmYXVsdGRvbWFpbnxwZXJp
b2RpY3N0cnVjdHVyZXxneDo3YTY0YmQxYTU0ZGE4NDM4

61. Secondary building units of metal ions:
http://cloud.crm2.univ-lorraine.fr/pdf/Manila/Okeeffe_1.pdf
HKUST-1
MOF-5

62. Acc.Chem.Res.2005,38,176-182

63. Secondary building units SBU
https://phys.org/news/2018-10-secondary-
sbusthe-metal-organic-frameworks-mofs.html

64. Example MOF 5
http://science.sciencemag.org/content/309/5739/
1350/F2

65. MOF-5
Science 341, (2013);
Hiroyasu Furukawa et al.
The Chemistry and Applications of Metal-
Organic Frameworks

66. MOF-5 (Zn4O(1,4-benzenedicarboxylate)3, 0.13-0.20 g/cm3)
consists of tetrahedral [Zn4O]6+ units that are linked together
with 1,4-benzene-dicarboxylate units. The opening in the
structure is 9.3-13.8 Å depending on the orientation of the
ring.
MOF-5 can store a significant amount of hydrogen at low
temperature (77 K: 7.1 wt % (40 bar), 10 wt % (100 bar)).
While the hydrogen storage capacity in decent at 77 K (66
g/L), its ability to store hydrogen at room temperature is
significantly lower (9.1 g/L), which limits its use as
hydrogen storage medium

67. Variation of linkers
https://www.researchgate.net/publication/264497783_Hydrogen_adsorption_in_metal
-organic_frameworks_The_role_of_nuclear_quantum_effects

68. Preparation

70. Preparation examples
https://hydra.hull.ac.uk/assets/hull:14433a/content

73. Zeolite-like MOF’s with Zn(2+) and Imidazole

74. Common MOF’s for gas storage

75. Search from Sigma Aldrich
https://www.sigmaaldrich.com/materials-science/learning-
center/mof-constructor.html

76. MOF Maker
http://mausdin.github.io/MOFsite/maker.html

77. Post-synthetic modifications
Z.Q.WangandS.M.Cohen,Chem.Soc.Rev.,
2009,38,1315-1329

78. CrystEngComm, 2016,18, 3524-3550

79. APPENDICES

80. The melting points ( ~ the strength which
that atoms are held together) first
raise from 1st row onwards, since more
and more electrons are in valence bands.
But there is a maximum in the middle of
the Periodic Table:
with increasing nuclear charge, the
harder it is to remove electrons into the
conduction band.
https://chem.libretexts.org/Textbook_Maps/Ge
neral_Chemistry_Textbook_Maps/Map%3A_Ch
emPRIME_(Moore_et_al.)/22Metals/22.01%3A
_Metallic_Bonding
Melting points of metals

82. Acc. Chem. Res.2005,38,176-182
At level 1, a four-
coordinated atom linked
by ditopic linkers will
almost invariantly form a
structure based on
diamond net.
Level 2 gives examples
of structures by design.
Joining copper acetate
paddlewheels by
ditopic carboxylate
linkers of the
geometries shown
schematically (the
orange ball could stand
for a phenyl group, for
example) have the
default structures
shown (paddlewheels
now shown as squares)