Chemistry Reference
In-Depth Information
an explicit nonlocal density functional
308,310,313,317-322
applicable at all separa-
tions, which shows great promise for including dispersion forces in standard
DFT calculations. TDDFT response functions have also been used in the frame-
work of symmetry-adapted perturbation theory to generate accurate binding
energy curves of van der Waals molecules.
323
One can also use Eq. [63] for bond lengths.
324,325
In fact, Eq. [63]
provides a KS density functional that allows bond breaking without artificial
symmetry breaking.
309
In the paradigm case of the H
2
molecule, the binding
energy curve has no Coulson-Fischer point, and the bond dissociation
correctly gives two isolated H atoms. Unfortunately, while simple approxima-
tions provide correct results near equilibrium and at infinite bond lengths, they
produce an unphysical repulsion at large, but finite separations. This repulsion
can be traced back
309
to the lack of double excitations in any adiabatic
f
XC
.
Study of the basis set convergence of
E
XC
has also revealed an obvious flaw in
the ALDA kernel at short distances.
306
Further research is needed to find accurate XC kernels. One method
307
that can be used to test these new kernels is to examine the uniform electron
gas because the frequency-dependent susceptibility can be found easily with
the well-known Lindhard function. Different approximate XC kernels may
thus be tested,
326
and their results can be compared to results from highly
accurate Monte Carlo simulations.
Strong Fields
We now turn our attention to the nonperturbative regime. Due to
advances in laser technology over the past decade, many experiments are
now possible where the laser field is stronger than the nuclear attraction.
11
The time-dependent field cannot be treated perturbatively, and even solving
the time-dependent Schr ยจ dinger equation in three dimensions for the evolution
of two interacting electrons is barely feasible with present-day computer
technology.
327
Wave function methods are prohibitive for more than a few electrons in
the regime of (not too high) laser intensities where the electron-electron inter-
action is still important. TDDFT is essentially the only practical scheme avail-
able
328-334
for dealing with many electrons in these kinds of time-dependent
fields. There exists a host of phenomena that TDDFT might be able to predict
including: high harmonic generation, multiphoton ionization, above-threshold
ionization, above-threshold dissociation, etc., but these predictions will be
possible only if accurate approximations are available.
With the recent advent of atto-second laser pulses, the electronic time
scale has become accessible experimentally. Theoretical tools needed to ana-
lyze the dynamics of excitation processes on the atto-second time scale will
consequently become more and more important to scientists studying such
fast processes. An example is the time-dependent electron localization
