photochemical processes often require an explicit treatment of doubly excited states
and these are beyond the scope of conventional LR-TD-DFT. There are several
ways to remedy this problem which have been discussed in a previous review
article [8]. In this chapter we concentrate on one way to explore and correct the
double excitation problem using a hybrid MBPT/LR-TD-DFT approach.
The rest of this chapter is organized as follows. The next section (Sect. 2)
provides a small review of the current state of DFT, TD-DFT, and LR-DFT.
Section 3 begins with an introduction to the key notions of MBPT needed to derive
corrections to approximate LR-TD-DFT and derives some basic equations. Section 4 shows that these corrections can be used in practical applications through an
exploration of dressed LR-TD-DFT. Ideally it would be nice to be able to use these
corrections to improve the xc functional of TD-DFT. However, this involves an
additional localization step which is examined in Sect. 5. Section 6 sums up with
some perspectives.
2 Brief Review
This section reviews a few concepts which in some sense are very old: DFT is about
50 years old, TD-DFT is about 30 years old, and LR-TD-DFT (in the form of the
Casida equations) is about 20 years old. Thus many of the basic concepts are now
well known. However, this section is necessary to define some notation and because
some aspects of these subjects have continued to evolve and so need to be updated.
Fig. 1 Typical curves for
the singlet photochemical
isomerization of ethylene
4
M.E. Casida and M. Huix-Rotllant
and these are beyond the scope of conventional LR-TD-DFT. There are several
ways to remedy this problem which have been discussed in a previous review
article [8]. In this chapter we concentrate on one way to explore and correct the
double excitation problem using a hybrid MBPT/LR-TD-DFT approach.
The rest of this chapter is organized as follows. The next section (Sect. 2)
provides a small review of the current state of DFT, TD-DFT, and LR-DFT.
Section 3 begins with an introduction to the key notions of MBPT needed to derive
corrections to approximate LR-TD-DFT and derives some basic equations. Section 4 shows that these corrections can be used in practical applications through an
exploration of dressed LR-TD-DFT. Ideally it would be nice to be able to use these
corrections to improve the xc functional of TD-DFT. However, this involves an
additional localization step which is examined in Sect. 5. Section 6 sums up with
some perspectives.
2 Brief Review
This section reviews a few concepts which in some sense are very old: DFT is about
50 years old, TD-DFT is about 30 years old, and LR-TD-DFT (in the form of the
Casida equations) is about 20 years old. Thus many of the basic concepts are now
well known. However, this section is necessary to define some notation and because
some aspects of these subjects have continued to evolve and so need to be updated.
Fig. 1 Typical curves for
the singlet photochemical
isomerization of ethylene
4
M.E. Casida and M. Huix-Rotllant