Chemistry Reference
In-Depth Information
Louville equation in quantum mechanics, and, for a quantum mechanical den-
sity coupled to a heat bath (or reservoir), it is written as
d
dt
r
ð
;
r
ð
Þ þ
C
½
r
ð
t
Þ¼{½
H
t
t
Þ
½
66
where
C
is a superoperator acting on the density whose elements are calculated
using Fermi's golden rule with
V
el
-
ph
in a certain approximation (weak cou-
pling and instantaneous processes). A KS master equation
364
can be derived,
modifying C for single-particle reduced-density matrices, so that it gives the
correct steady state. The TDKS equations are then used to propagate forward
in time until the correct steady-state density is found, and the current is then
extracted from this. Recent calculations have shown that this master equation
approach can give correct behavior, such as hysteresis in I-V curves.
363;372
SUMMARY
We have conveyed some of the spirit and excitement of development and
uses of TDDFT in this review. We explained what TDDFT is and where it
comes from. While it often works well for many molecular excitations, its use-
fulness lies neither in high accuracy nor reliability but instead in its qualitative
ability to yield roughly correct absorption spectra for molecules of perhaps
several hundred atoms. We emphasize that there are usually many excitations
of the same symmetry, all coupled together, and that under these circum-
stances the theory will be of greatest use. TDDFT is now a routine tool that
produces accurate results with reasonable confidence for many molecular
systems.
That said, we have discussed some of the areas where TDDFT (in its
current incarnation) is not working, such as double excitations, charge trans-
fer, and extended systems. But there has been significant progress in all of
these, both in understanding the origin of the problem and finding alternative
approaches using orbital-dependent expressions that may ultimately yield a
practical solution. We also examined how well TDDFT works for a few cases
where the exact ground-state solution is known, describing the accuracy of
different functionals, and we surveyed some applications beyond simple linear
response for optical absorption, such as ground-state functionals from the
adiabatic connection, strong fields, and electron transport. In each of these
areas, more development is needed before TDDFT calculations can become
a routine tool with the accuracy needed by scientists and engineers.
Many wonder how long DFT's preeminence in electronic structure
theory can last. For sure, Kohn-Sham DFT is a poor player that struts and frets
its hour upon the stage of electronic structure and then is heard no more.
373
After all, its predecessor, Thomas-Fermi theory,
374,375
is now obsolete, being
