where ab initio quantum chemical methods can traditionally be applied. The
reluctance to use DFT for describing excited states has even given way as linear
response (LR-) time-dependent (TD-) DFT has become an established way to
calculate excited-state properties of medium size and large molecules. One of the
strengths of TD-DFT is that it is formally an exact theory. However, as in traditional
DFT, problems arise in practice because of the need to make approximations.
Of course, from the point of view of a developer of new methods, when people
are given a little then they immediately want more. As soon as LR-TD-DFT was
shown to give reasonably promising results in one context, many people in the
modeling community immediately wanted to apply LR-TD-DFT in a whole range
of more challenging contexts. It then became urgent to explore the limits of
applicability of approximate TD-DFT and to improve approximations in order to
extend these limits. Much work has been done on this problem and there are many
success stories to tell about LR-TD-DFT. Indeed, many of the chapters in this book
describe some of these challenging contexts where conventional LR-TD-DFT
approximations do work. In this chapter, however, we want to focus on the cutting
edge where LR-TD-DFT finds itself seriously challenged and yet progress is being
made. In particular, what we have in mind are photochemical applications where
interacting excited states of fundamentally different character need to be described
with similar accuracy and where bonds may be in the process of breaking or
forming. The approach we take is to introduce a hybrid method where manybody perturbation theory (MBPT) corrections are added on top of LR-TD-DFT.
We also use the tools we have developed to gain some insight into what needs to be
included in the TD-DFT exchange-correlation (xc) functional in order for it to
describe photochemical problems better.
Applications of LR-TD-DFT to photochemistry are no longer rare. Perhaps the
earliest attempt to apply LR-TD-DFT to photochemistry was the demonstration that
avoided crossings between formaldehyde excited-state curves could indeed be
described with this method [2]. Further hope for photochemistry from LR-TDDFT was raised again only a few years later [3, 4], with an example application to
the photochemistry of oxirane appearing after another 5 years [5, 6]. Casida
et al. [7] provides a recent review of the present state of LR-TD-DFT applied to
photochemistry and where some of the difficulties lie.
Let us try to focus on some key problems. Photophenomena are frequently
divided into photophysics, when the photoprocess ends with the same molecules
with which it started, and photochemistry, when the photoprocess ends with
different molecules. This is illustrated by the cartoon in Fig. 1. An example of a
typical photophysical process would be beginning at one S 0 minimum, exciting to
the singly-excited S 1 state, and reverting to the same S 0 minimum. In contrast, an
example of a typical photochemical process would be exciting from one S 0 minimum to an S 1 excited state, followed by moving along the S 1 surface, through
avoided crossings, conical intersections, and other photochemical funnels, to end up
finally at the other S 0 minimum. State-of-the-art LR-TD-DFT does a reasonable job
modeling photophysical processes but has much more difficulty with photochemical processes. The main reason is easily seen in Fig. 1 – namely, that
MBPT Insights About and Corrections to TD-DFT
3
reluctance to use DFT for describing excited states has even given way as linear
response (LR-) time-dependent (TD-) DFT has become an established way to
calculate excited-state properties of medium size and large molecules. One of the
strengths of TD-DFT is that it is formally an exact theory. However, as in traditional
DFT, problems arise in practice because of the need to make approximations.
Of course, from the point of view of a developer of new methods, when people
are given a little then they immediately want more. As soon as LR-TD-DFT was
shown to give reasonably promising results in one context, many people in the
modeling community immediately wanted to apply LR-TD-DFT in a whole range
of more challenging contexts. It then became urgent to explore the limits of
applicability of approximate TD-DFT and to improve approximations in order to
extend these limits. Much work has been done on this problem and there are many
success stories to tell about LR-TD-DFT. Indeed, many of the chapters in this book
describe some of these challenging contexts where conventional LR-TD-DFT
approximations do work. In this chapter, however, we want to focus on the cutting
edge where LR-TD-DFT finds itself seriously challenged and yet progress is being
made. In particular, what we have in mind are photochemical applications where
interacting excited states of fundamentally different character need to be described
with similar accuracy and where bonds may be in the process of breaking or
forming. The approach we take is to introduce a hybrid method where manybody perturbation theory (MBPT) corrections are added on top of LR-TD-DFT.
We also use the tools we have developed to gain some insight into what needs to be
included in the TD-DFT exchange-correlation (xc) functional in order for it to
describe photochemical problems better.
Applications of LR-TD-DFT to photochemistry are no longer rare. Perhaps the
earliest attempt to apply LR-TD-DFT to photochemistry was the demonstration that
avoided crossings between formaldehyde excited-state curves could indeed be
described with this method [2]. Further hope for photochemistry from LR-TDDFT was raised again only a few years later [3, 4], with an example application to
the photochemistry of oxirane appearing after another 5 years [5, 6]. Casida
et al. [7] provides a recent review of the present state of LR-TD-DFT applied to
photochemistry and where some of the difficulties lie.
Let us try to focus on some key problems. Photophenomena are frequently
divided into photophysics, when the photoprocess ends with the same molecules
with which it started, and photochemistry, when the photoprocess ends with
different molecules. This is illustrated by the cartoon in Fig. 1. An example of a
typical photophysical process would be beginning at one S 0 minimum, exciting to
the singly-excited S 1 state, and reverting to the same S 0 minimum. In contrast, an
example of a typical photochemical process would be exciting from one S 0 minimum to an S 1 excited state, followed by moving along the S 1 surface, through
avoided crossings, conical intersections, and other photochemical funnels, to end up
finally at the other S 0 minimum. State-of-the-art LR-TD-DFT does a reasonable job
modeling photophysical processes but has much more difficulty with photochemical processes. The main reason is easily seen in Fig. 1 – namely, that
MBPT Insights About and Corrections to TD-DFT
3