96
S. Yanagisawa and I. Hamada
Table 4.1
Optimized lattice parameters (a, b, c, α, β,
and γ
), equilibrium volume (V
0 ), and lattice energies per molecule (E
b ) of the naphthalene and
anthracene crystals in the P
2
1 /a
symmetry, tetracene in the P
1 symmetry, and pentacene single crystal in the P ¯
1 symmetry obtained with rev-vdW-DF2,
along with experimental values. The Niggli cell parameters are used for tetracene. (Reprinted from [13], with the permission of AIP Publishing)
Naphthalene
a
b
c
α
β
γ
V
0
E
b
(Å)
(Å)
(Å)
(deg)
(deg)
(deg)
(Å 3
)
(eV)
rev-vdW-DF2 1
8.012
5.898
8.609
90.00
124.12
90.00
336.8
−0.803
rev-vdW-DF2 (ZPE) 2
—
—
—
—
—
—
347.2
—
PBE+TS-vdW 3
8.109
5.884
8.660
90.00
124.05
90.00
342.32
−1.035
PBE+MBD 3
7.970
5.868
8.570
90.00
123.11
90.00
335.70
−0.905
PBE0+MBD 3
—
—
—
—
—
—
—
−0.885
B86b-XDM 4
8.134
5.938
8.699
90.00
124.35
90.00
346.89
−0.784
B86b-XDM 5
—
—
—
—
—
—
335.8
−0.790
vdW-DF-cx 6
8.06
5.91
8.75
90.00
124.4
90.00
344.4
−0.92
Expt.
8.080 7
5.933 7
8.632 7
90.00
124.65 7
90.00
340.4 7
−0.847 8
Anthracene
a
b
c
α
β
γ
V
0
E
b
(Å)
(Å)
(Å)
(deg)
(deg)
(deg)
(Å 3
)
(eV)
rev-vdW-DF2 1
8.339
5.948
11.087
90.00
125.37
90.00
448.40
−1.081
rev-vdW-DF2 (ZPE) 2
—
—
—
—
—
—
460.8
—
PBE+TS-vdW 3
8.399
5.943
11.120
90.00
125.21
90.00
453.5
−1.392
PBE+MBD 3
—
—
—
—
—
—
—
−1.262
PBE0+MBD 3
—
—
—
—
—
—
—
−1.234
B86b-XDM 4
8.452
5.985
11.168
90.00
125.43
90.00
460.32
−1.049
B86b-XDM 5
—
—
—
—
—
—
448.4
−1.054
vdW-DF-cx 6
8.38
5.96
11.23
90.00
125.6
90.00
456.5
−1.23
Expt.
8.37 9
6.00 9
11.12 9
90.00
125.4 9
90.00
455.205 9
−1.168 8