6 Comparison of TDDFT and the BSE
Exciton binding energies in TDDFT are determined via (40). The Hxc coupling
matrix is given by
K
Hxc
iak, jbk 0 ¼ K
H
iak, jbk 0 þ K
xc
iak, jbk 0 ;
ð68Þ
where the Hartree and xc matrices are defined in (41) and (42). It turns out that the
BSE leads to an equation for exciton binding energies which is formally identical to
(40), except that it features the coupling matrix
12
14
16
ω (eV)
ω (eV)
18
Im[ε
M ]
25
20
15
10
5
0
15
10
Abs(ω)
5
0
10
11
12
13
14
LRC fit
RPA
n=1
n=2
n’=1
n’=2
BSE
f xc
ex
ALDA
Experiment
Fig. 5 Absorption spectra of solid Ar obtained from (43) (top panel) and from (30) (bottom panel,
adapted from Sottile et al. [128]). Reproduced with permission from APS from Sottile
et al. [128]. ©2007
210
C.A. Ullrich and Z.-h. Yang
Exciton binding energies in TDDFT are determined via (40). The Hxc coupling
matrix is given by
K
Hxc
iak, jbk 0 ¼ K
H
iak, jbk 0 þ K
xc
iak, jbk 0 ;
ð68Þ
where the Hartree and xc matrices are defined in (41) and (42). It turns out that the
BSE leads to an equation for exciton binding energies which is formally identical to
(40), except that it features the coupling matrix
12
14
16
ω (eV)
ω (eV)
18
Im[ε
M ]
25
20
15
10
5
0
15
10
Abs(ω)
5
0
10
11
12
13
14
LRC fit
RPA
n=1
n=2
n’=1
n’=2
BSE
f xc
ex
ALDA
Experiment
Fig. 5 Absorption spectra of solid Ar obtained from (43) (top panel) and from (30) (bottom panel,
adapted from Sottile et al. [128]). Reproduced with permission from APS from Sottile
et al. [128]. ©2007
210
C.A. Ullrich and Z.-h. Yang