Density of States: The density of states (DOS) is ...
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The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy. Density of States:
Transcript of Density of States: The density of states (DOS) is ...
The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy.
Density of States:
φ2 φ1 ψ1 = αφ1+βφ2
ψ2 = βφ1-‐αφ2
φ2 φ1 ψ1 = αφ1+βφ2
ψ2 = βφ1-‐αφ2
DOS/energy
Ener
gy
0.5 1.0
φ2 φ1 ψ1 = αφ1+βφ2
ψ2 = βφ1-‐αφ2
DOS/energy
Ener
gy
0.5 1.0
E=-0.618
E=1.618
DOS/energy En
ergy
0.5 1.0
0
1
-0.6
1.6
The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy.
Density of States:
Projected/Partial Density of States:
The projected/partial density of states (PDOS) is the relative contribution of a particular atom/orbital to the total DOS
φ2 φ1
ψ1 = αφ1+βφ2
ψ2 = βφ1-‐αφ2
Contribution of φ1 in ψ1 = α2
Contribution of φ2 in ψ2 = β2 projected density of states
ψ1 =
α β
DOS/energy
Ener
gy
0.5 1.0
0
DOS/energy
Ener
gy
0.5 1.0
0
DOS/energy En
ergy
0.5 1.0
0
Total DOS PDOS PDOS
E=-1
E=1
-1
1 1 1
-1 -1
α2(E=0) = 0.5 β2(E=1)
= 0.5
β2(E=0) = 0.5 α2(E=1) = 0.5
Total DOS PDOS PDOS
DOS/energy
Ener
gy
0.5 1.0
0
1
-0.6
1.6
DOS/energy
Ener
gy
0.5 1.0
0
1
-0.6
1.6
DOS/energy En
ergy
0.5 1.0
0
1
-0.6
1.6
α2(E=0) = 0.723 β2(E=1)
= 0.276
β2(E=0) = 0.276 α2(E=1) = 0.723
E=-0.618
E=1.618
The density of states (DOS) is essentially the number of different states at a particular energy level that electrons are allowed to occupy, i.e. the number of electron states per unit volume per unit energy.
Density of States:
Projected/Partial Density of States:
The projected/partial density of states (PDOS) is the relative contribution of a particular atom/orbital to the total DOS
First moment:
The first moment is the center of gravity of PDOS. In other words, first moment is exactly the on-site energy.
DOS/energy
Ener
gy
0.5 1.0
0
DOS/energy
Ener
gy
0.5 1.0
0
DOS/energy En
ergy
0.5 1.0
0
Total DOS PDOS PDOS
E=-1
E=1
-1
1 1 1
-1 -1
α2(E=0) = 0.5 β2(E=1)
= 0.5
β2(E=0) = 0.5 α2(E=1) = 0.5
(-1*0.5) + (1*0.5) = 0 (-1*0.5) + (1*0.5) = 0
Total DOS PDOS PDOS
DOS/energy
Ener
gy
0.5 1.0
0
1
-0.6
1.6
DOS/energy
Ener
gy
0.5 1.0
0
1
-0.6
1.6
DOS/energy En
ergy
0.5 1.0
0
1
-0.6
1.6
α2(E=0) = 0.723 β2(E=1)
= 0.276
β2(E=0) = 0.276 α2(E=1) = 0.723
(-0.618*0.723) + (1.618*0.276) = 0
(-0.618*0.276) + (1.618*0.723) = 1
E=-0.618
E=1.618
KTi(SO4)2.H2O
E ε1 ε2 ε3 ε4 ε5 ε6 ε7
DO
S
E ε1 ε2 ε3 ε4 ε5 ε6 ε7
DO
S
E ε1 ε2 ε3 ε4 ε5 ε6 ε7
DO
S DOS =
€
1Ne−E −ε iΓ
%
& '
(
) * 2
