47 research outputs found
Correlation energy functional and potential from time-dependent exact-exchange theory
In this work we have studied a new functional for the correlation energy
obtained from the exact-exchange (EXX) approximation within time-dependent
density functional theory (TDDFT). Correlation energies have been calculated
for a number of different atoms showing excellent agreement with results from
more sophisticated methods. These results loose little accuracy by
approximating the EXX kernel by its static value, a procedure which enormously
simplifies the calculations. The correlation potential, obtained by taking the
functional derivative with respect to the density, turns out to be remarkably
accurate for all atoms studied. This potential has been used to calculate
ionization potentials, static polarizabilities and van der Waals coefficients
with results in close agreement with experiment.Comment: 6 pages, 2 figure
Dynamical effects in X-ray spectra and the final-state rule
The dynamical theory of X-ray spectra due to Nozieres and De Dominicis (ND, 1969) is evaluated here numerically for numerous model systems including cases where the core-hole potential possesses a bound state. It is shown that the resulting emission spectra obey the final-state rule rather accurately. An approximate but analytical derivation of this rule is given which provides insight into the mechanisms leading to the final-state rule. The evaluations are performed with the use of two methods, one based on an integral equation together with a separable core-hole potential and the other based on determinantal wave functions for a finite number (N) of electrons in a box. The equivalence of the two methods is demonstrated both formally and numerically. By comparing them the authors prove the finite-N approach to be accurate already for rather small N. They also show that a separable potential does not give rise to any spurious results but can actually be chosen to yield the same ND spectrum as a local potential. The ND theory of X-ray photoemission spectra is discussed and from calculations of the exponent function α(Ï) for several model systems closely corresponding to simple metals the authors conclude the equivalence of this theory and its asymptotic approximation as far as the extraction of asymmetry indices is concerned. Recent criticism of the major conclusions reached here and in previous work is refuted.(61 refs
The correlation potential in density functional theory at the GW-level: spherical atoms
As part of a project to obtain better optical response functions for nano
materials and other systems with strong excitonic effects we here calculate the
exchange-correlation (XC) potential of density-functional theory (DFT) at a
level of approximation which corresponds to the dynamically- screened-exchange
or GW approximation. In this process we have designed a new numerical method
based on cubic splines which appears to be superior to other techniques
previously applied to the "inverse engineering problem" of DFT, i.e., the
problem of finding an XC potential from a known particle density. The
potentials we obtain do not suffer from unphysical ripple and have, to within a
reasonable accuracy, the correct asymptotic tails outside localized systems.
The XC potential is an important ingredient in finding the particle-conserving
excitation energies in atoms and molecules and our potentials perform better in
this regard as compared to the LDA potential, potentials from GGA:s, and a DFT
potential based on MP2 theory.Comment: 13 pages, 9 figure
Exact-exchange kernel of time-dependent density functional theory: Frequency dependence and photoabsorption spectra of atoms
In this work we have calculated excitation energies and photoionization cross
sections of Be and Ne in the exact-exchange (EXX) approximation of
time-dependent density functional theory (TDDFT). The main focus has been on
the frequency dependence of the EXX kernel and on how it affects the spectrum
as compared to the corresponding adiabatic approximation. We show that for some
discrete excitation energies the frequency dependence is essential to reproduce
the results of time-dependent Hartree-Fock theory. Unfortunately, we have found
that the EXX approximation breaks down completely at higher energies, producing
a response function with the wrong analytic structure and making inner-shell
excitations disappear from the calculated spectra. We have traced this failure
to the existence of vanishing eigenvalues of the Kohn-Sham non-interacting
response function. Based on the adiabatic TDDFT formalism we propose a new way
of deriving the Fano parameters of autoionizing resonances.Comment: 14 pages, 7 figure
Linear density response function within the time-dependent exact-exchange approximation
We have calculated the frequency-dependent exact exchange (EXX) kernel of
time-dependent (TD) density functional theory employing our recently proposed
computational method based on cubic splines. With this kernel we have
calculated the linear density response function and obtained static
polarizabilites, van der Waals coefficients and correlation energies for all
spherical spin compensated atoms up to Argon. Some discrete excitation energies
have also been calculated for Be and Ne. As might be expected, the results of
the TDEXX approximation are close to those of TD Hartree-Fock theory. In
addition, correlation energies obtained by integrating over the strength of the
Coulomb interaction turn out to be highly accurate.Comment: 10 pages, 5 figure