Chemistry Reference
In-Depth Information
In fact, TDDFT yields predictions for a huge variety of phenomena that
can largely be classified into three groups: (1) the nonperturbative regime, with
systems in laser fields so intense that perturbation theory fails, (2) the linear
(and higher order) regime, which yields the usual optical response and
electronic transitions, and (3) back to the ground state, where the fluctuation-
dissipation theorem produces
ground-state
approximations from TDDFT
treatments of excitations.
Overview
This chapter focuses primarily on the linear response regime. Through-
out, we emphasize the difference between small molecules (atoms, diatomics,
etc.) and the larger molecules that are of greater practical interest, where
TDDFT is often the only practical first-principles method that can be used.
We use naphthalene (C
10
H
8
) as an example to show how the selection of
both the basis set and the exchange-correlation (XC) functional affects com-
puted excitation energies and oscillator strengths. Small molecules are some-
what exceptional because they usually exhibit high symmetry that prevents
strong mixing of the Kohn-Sham (KS) states due to configuration interaction,
and also because basis set requirements are often exacerbated for small sys-
tems. Naphthalene is large enough to avoid these effects; reasonably accurate
gas-phase experiments exist and correlated wave function calculations are still
possible for such a molecule.
We will use atomic units (
e
2
¼
h
¼
m
e
¼
1) throughout this tutorial, so
that all energies are in hartrees (1E
h
'
27
:
2eV
'
627
:
5 kcal
=
mol) and dis-
529
˚
) unless otherwise noted. For brevity, we drop com-
ma's between arguments wherever the meaning is clear. In DFT and TDDFT,
there is a confusing wealth of acronyms and abbreviations. Table 1 is designed
to aid the readers' navigation through this maze.
The content of this review is organized as follows. The second and
third main sections cover the basic formalism of the theory that is needed
to understand where it comes from, why it works, and where it can
be expected to fail. The fourth section focuses on details of implementation,
especially basis-set selection, while the fifth section is devoted to perfor-
mance and analyzing the sources of error in the basis-set limit. In the sixth
section, we examine a few atoms in microscopic detail: Because we know
the
exact
ground-state Kohn-Sham potential in such cases, we can assess
the performance of TDDFT. The seventh section covers the many attempts
that go beyond standard functionals approximations and highlights where
such nonstandard functionals are needed. The eighth section covers topics
outside the usual linear response approach to excitations, including
ground-state functional derived from TDDFT, challenges for strong fields,
and transport through single molecules. The last section summarizes this
tutorial/review.
tances in bohr (
'
0
:
