4 Nanoscale First-Principles Electronic Structure Simulations of Materials. . .
103
-2.0
0.0
2.0
4.0
Y
HC
E
A
X
Z
(a)
(b)
H
H−1
H−2
H−3
L
L+1
M 1
Energy (eV)
Energy (eV)
H
H−1
H−2
H−3
L
L+1
Exp.
DOS (states·eV −1
)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0
DOS (arb. unit)
W H
W L
E g
Fig. 4.3 (a) The band structure of the anthracene crystal calculated within the G 0 W 0 approximation. The energy zero is set to the top of the highest occupied band. The atomic configurations and
the lattice constants are optimized with the rev-vdW-DF2 functional (Table 4.1). We transformed
the lattice parameters to adopt the symmetry points and lines in the Brillouin zone defined in Ref.
[97], to obtain a =5.948 Å, b =8.339 Å, c =9.242 Å, α =78.00 ◦ , and β = γ =90.0 ◦ . The
high-symmetry points in the BZ are: (0,0,0), Y(0,0, 0.5), H(0, 0.425, 0.598), C(0, 0.5, 0.5), E(0.5,
0.5, 0.5), M 1 (0.5, 0.575, 0.402), A(0.5, 0.5, 0), X(0, 0.5, 0), Z(0.5, 0, 0) in the unit of the basic
reciprocal lattice vectors. (b) The density of states (DOS) based on the G 0 W 0 band structure. The
experimental photoemission data (Ref. [81]) is displayed. The convention is the same as that in
Fig. 4.2. The band widths (W H and W L ) and band gap (E g ) are indicated by the double-headed
arrows for guides to the eyes. (Reprinted from [13], with the permission of AIP Publishing)
103
-2.0
0.0
2.0
4.0
Y
HC
E
A
X
Z
(a)
(b)
H
H−1
H−2
H−3
L
L+1
M 1
Energy (eV)
Energy (eV)
H
H−1
H−2
H−3
L
L+1
Exp.
DOS (states·eV −1
)
0.0
2.0
4.0
6.0
8.0
10.0
12.0
-6.0 -5.0 -4.0 -3.0 -2.0 -1.0 0.0 1.0 2.0
DOS (arb. unit)
W H
W L
E g
Fig. 4.3 (a) The band structure of the anthracene crystal calculated within the G 0 W 0 approximation. The energy zero is set to the top of the highest occupied band. The atomic configurations and
the lattice constants are optimized with the rev-vdW-DF2 functional (Table 4.1). We transformed
the lattice parameters to adopt the symmetry points and lines in the Brillouin zone defined in Ref.
[97], to obtain a =5.948 Å, b =8.339 Å, c =9.242 Å, α =78.00 ◦ , and β = γ =90.0 ◦ . The
high-symmetry points in the BZ are: (0,0,0), Y(0,0, 0.5), H(0, 0.425, 0.598), C(0, 0.5, 0.5), E(0.5,
0.5, 0.5), M 1 (0.5, 0.575, 0.402), A(0.5, 0.5, 0), X(0, 0.5, 0), Z(0.5, 0, 0) in the unit of the basic
reciprocal lattice vectors. (b) The density of states (DOS) based on the G 0 W 0 band structure. The
experimental photoemission data (Ref. [81]) is displayed. The convention is the same as that in
Fig. 4.2. The band widths (W H and W L ) and band gap (E g ) are indicated by the double-headed
arrows for guides to the eyes. (Reprinted from [13], with the permission of AIP Publishing)