ch i l b di chemical bonding - universitetet i oslo · ch i l b di e ticum chemical bonding u m...
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![Page 1: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/1.jpg)
Ch i l B diE
TIC
UM
Chemical BondingU
M H
ELV
E
type Energies Forces
& C
OLL
EG
IU
ionic E ~ 1/r F ~ 1/r2
ZÜ
RIC
H &
covalent E ~ 1/r3 F ~ 1/r4
SP
ER
E
TH
van der Waals E ~ 1/r5 F ~ 1/r6
R. N
ES
20.10.2008 Nanochemistry UIO
Chemical Bonding
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 2: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/2.jpg)
Chemical BondingE
TIC
UM
UM
HE
LVE
Inmixing
& C
OLL
EG
IU Inmixing of sodium states
ZÜ
RIC
H & states
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
Antiparallel Couplings
ET
ICU
M
Antiparallel Couplings
UM
HE
LVE
Chemical bond
& C
OLL
EG
IU Chemical bond
ZÜ
RIC
H &
Cooper pair (superconductivity)~~
SP
ER
E
TH
Antiferromagnetic coupling
R. N
ES Antiferromagnetic coupling
20.10.2008 Nanochemistry UIO
![Page 3: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/3.jpg)
Collective CouplingsE
TIC
UM
p gU
M H
ELV
E
ferro
& C
OLL
EG
IU
antiferro
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
ferri
20.10.2008 Nanochemistry UIO
Molecules and Solids
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 4: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/4.jpg)
LCAO in P l
ET
ICU
M
PolymersU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
What is k ?
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
π/a
20.10.2008 Nanochemistry UIO
π/a
![Page 5: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/5.jpg)
What is k ?E
TIC
UM
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
k-Vektors and Brillouin Zones
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
The Brillouin zone contains all the reciprocal vectorshalf way inbetween the first Bragg reflections
20.10.2008 Nanochemistry UIO
![Page 6: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/6.jpg)
2D LCAO combinations
ET
ICU
M
combinationsU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
2D LCAO combinations
ET
ICU
M
combinations
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
![Page 7: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/7.jpg)
Bandstructure of Silicion XE
TIC
UM
UM
HE
LVE
L
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Strength of Interaction and Band Width
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 8: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/8.jpg)
Strength of Interaction and Band Width
ET
ICU
MBand Width
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Solids
ET
ICU
M
Solids
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
![Page 9: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/9.jpg)
SolidsE
TIC
UM
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Degeneracy and Distortions
ET
ICU
M
Distortions
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
![Page 10: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/10.jpg)
Degeneracy and DistortionsE
TIC
UM
Peierls distortion in
UM
HE
LVE Peierls distortion in
1D systems
Cf Jahn Teller
& C
OLL
EG
IU Cf. Jahn-Teller distortions
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
Graphite
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 11: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/11.jpg)
Bornitride - BNE
TIC
UM
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Bornitride - BN
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 12: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/12.jpg)
Density of States (DOS)E
TIC
UM
UM
HE
LVE
(DOS)band
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
DOS –PtH4
Polymer
ET
ICU
M
-Polymer
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
![Page 13: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/13.jpg)
DOS of PtH4 Chain
ET
ICU
MPtH4 Chain
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Band structure of ??
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 14: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/14.jpg)
Where are the electrons of …?
ET
ICU
Melectrons of …?
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Structure and DOS
ET
ICU
MU
M H
ELV
E&
CO
LLE
GIU
ZÜ
RIC
H &
SP
ER
E
TH
R
. NE
S
20.10.2008 Nanochemistry UIO
![Page 15: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/15.jpg)
Structure and DOSE
TIC
UM
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO
Where are the Bonds?
ET
ICU
M
the Bonds?
UM
HE
LVE
& C
OLL
EG
IUZ
ÜR
ICH
&
Choose a bond or a set of bonds and calculate overlap weighted DOS
SP
ER
E
TH
overlap weighted DOS
cicj Sij
S 0 tib di
R. N
ES Sij < 0 antibonding
Sij > 0 bonding
20.10.2008 Nanochemistry UIO
![Page 16: Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M HELV type Energies Forces COLLEGI ionic E ~ 1/r F ~ 1/r2 ZÜRICH covalent E ~ 1/r3](https://reader034.vdocuments.us/reader034/viewer/2022051922/600fb558e96e666fc519a737/html5/thumbnails/16.jpg)
From DOS to BondsE
TIC
UM
DOS COOP
UM
HE
LVE DOS COOP
& C
OLL
EG
IUZ
ÜR
ICH
&S
PE
R
ET
H
R. N
ES
20.10.2008 Nanochemistry UIO