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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Ch i l B di TICUM Chemical Bonding UM HELVE type Energies Forces COLLEGIU ionic E ~ 1/r F ~ 1/r 2 ZÜRICH & covalent E ~ 1/r 3 F ~ 1/r 4 PER ETH van der Waals E ~ 1/r 5 F ~ 1/r 6 R. NES 20.10.2008 Nanochemistry UIO Chemical Bonding TICUM UM HELVE & COLLEGIU ZÜRICH & PER ETH R. NES 20.10.2008 Nanochemistry UIO

Transcript of Ch i l B di Chemical Bonding - Universitetet i oslo · Ch i l B di E TICUM Chemical Bonding U M...

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

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

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

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

Chemical BondingE

TIC

UM

UM

HE

LVE

Inmixing

& C

OLL

EG

IU Inmixing of sodium states

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

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

Collective CouplingsE

TIC

UM

p gU

M H

ELV

E

ferro

& C

OLL

EG

IU

antiferro

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

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

LCAO in P l

ET

ICU

M

PolymersU

M H

ELV

E&

CO

LLE

GIU

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

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

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

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

2D LCAO combinations

ET

ICU

M

combinationsU

M H

ELV

E&

CO

LLE

GIU

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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