Excited States from Time-Dependent Density Functional Theory - Reviews in Computational Chemistry - page 139

(infinitesimal) perturbations around the ground state, without relaxation.
Thus, linear response is a poor method to use for problems involving charge
transfer and many researchers are attempting to find practical solutions
around it. 88,302-305

OTHER TOPICS

We now discuss several topics of specialized interest where TDDFT is
being applied and where development has been beyond simple extraction of
excitations from linear response theory. First we will show how TDDFT can
be used to construct entirely new approximations to the ground-state XC
energy, which is particularly useful for capturing the long-range fluctuations
that produce dispersion forces between molecules that are notoriously absent
from most ground-state approximations. We will then survey strong field
applications in which TDDFT is being used to model atoms and molecules
in strong laser fields. Finally, we discuss the more recent and hot area of mole-
cular electronics. Here, many workers are using ground-state DFT to calculate
transport characteristics, but a more careful formulation can be done only
within (and beyond) TDDFT.

Ground-State XC Energy
A more sophisticated ground-state approximate energy functional can be
constructed 306-310 using the frequency-dependent response function of linear
response TDDFT. We now introduce the basic formula and then discuss
some of the systems this method is being used to study.
To construct the ground-state energy functional we use the long known
adiabatic connection fluctuation-dissipation (ACFD) formula:

ð 1 ð d 3 r ð d 3 r 0

P l ð r 0 Þ

j r r 0 j

1
2

r ;

½ ¼ l ½ 63

E XC n 0 d

0

where the pair density is

!

ð 1

X

d o

p w ss 0 ½

n 0 ð r Þ d ð3Þ ð r r 0 Þ

P l ð r 0 Þ¼ n 0 ð rr 0 ;

r ; i o Þ ½ 64

0

ss 0

and the coupling constant is defined so as to multiply the electron-electron

repulsion in the Hamiltonian but where the external potential is adjusted to
keep the density fixed. 311,312 The quantity

l

w ss 0 is given by Eq. [42] with the
XC kernel f XC ss 0 . Any approximation to the XC kernel yields a sophisticated
XC energy E XC ½ n .