9,529 research outputs found
Ab initio calculations of the dynamical response of copper
The role of localized -bands in the dynamical response of Cu is
investigated, on the basis of {\em ab initio} pseudopotential calculations. The
density-response function is evaluated in both the random-phase approximation
(RPA) and a time-dependent local-density functional approximation (TDLDA). Our
results indicate that in addition to providing a polarizable background which
lowers the free-electron plasma frequency, d-electrons are responsible, at
higher energies and small momenta, for a double-peak structure in the dynamical
structure factor. These results are in agreement with the experimentally
determined optical response of copper. We also analyze the dependence of
dynamical scattering cross sections on the momentum transfer.Comment: 4 pages, 4 figures, to appear in Phys. Rev.
On Nilcompactifications of Prime Spectra of Commutative Rings
Given a ring R and S one of its ideals, we obtain a compactification of the
prime spectrum of S through a mainly algebraic process. We name it the
R-nilcompactification of SpecS. We study some categorical properties of this
construction.Comment: 12 pages, 8 Tikz figure
Exact Maps in Density Functional Theory for Lattice Models
In the present work, we employ exact diagonalization for model systems on a
real-space lattice to explicitly construct the exact density-to-potential and
for the first time the exact density-to-wavefunction map that underly the
Hohenberg-Kohn theorem in density functional theory. Having the explicit
wavefunction-to- density map at hand, we are able to construct arbitrary
observables as functionals of the ground-state density. We analyze the
density-to-potential map as the distance between the fragments of a system
increases and the correlation in the system grows. We observe a feature that
gradually develops in the density-to-potential map as well as in the
density-to-wavefunction map. This feature is inherited by arbitrary expectation
values as functional of the ground-state density. We explicitly show the
excited-state energies, the excited-state densities, and the correlation
entropy as functionals of the ground-state density. All of them show this exact
feature that sharpens as the coupling of the fragments decreases and the
correlation grows. We denominate this feature as intra-system steepening. We
show that for fully decoupled subsystems the intra-system steepening transforms
into the well-known inter-system derivative discontinuity. An important
conclusion is that for e.g. charge transfer processes between localized
fragments within the same system it is not the usual inter-system derivative
discontinuity that is missing in common ground-state functionals, but rather
the differentiable intra-system steepening that we illustrate in the present
work
Exact Kohn-Sham potential of strongly correlated finite systems
The dissociation of molecules, even the most simple hydrogen molecule, cannot
be described accurately within density functional theory because none of the
currently available functionals accounts for strong on-site correlation. This
problem has led to a discussion of properties that the local Kohn-Sham
potential has to satisfy in order to correctly describe strongly correlated
systems. We derive an analytic expression for this potential at the
dissociation limit and show that the numerical calculations for a
one-dimensional two electron model system indeed approach and reach this limit.
It is shown that the functional form of the potential is universal, i.e.
independent of the details of the system.Comment: 17 pages, 3 figures, submitted to JC
Universal Dynamical Steps in the Exact Time-Dependent Exchange-Correlation Potential
We show that the exact exchange-correlation potential of time-dependent
density-functional theory displays dynamical step structures that have a
spatially non-local and time non-local dependence on the density. Using
one-dimensional two-electron model systems, we illustrate these steps for a
range of non-equilibrium dynamical situations relevant for modeling of
photo-chemical/physical processes: field-free evolution of a non-stationary
state, resonant local excitation, resonant complete charge-transfer, and
evolution under an arbitrary field. Lack of these steps in usual approximations
yield inaccurate dynamics, for example predicting faster dynamics and
incomplete charge transfer
Local reduced-density-matrix-functional theory: Incorporating static correlation effects in Kohn-Sham equations
We propose a novel scheme to bring reduced density matrix functional theory
(RDMFT) into the realm of density functional theory (DFT) that preserves the
accurate density functional description at equilibrium, while incorporating
accurately static and left-right correlation effects in molecules and keeping
the good computational performance of DFT-based schemes. The key ingredient is
to relax the requirement that the local potential is the functional derivative
of the energy with respect to the density. Instead, we propose to restrict the
search for the approximate natural orbitals within a domain where these
orbitals are eigenfunctions of a single-particle hamiltonian with a local
effective potential. In this way, fractional natural occupation numbers are
accommodated into Kohn-Sham equations allowing for the description of molecular
dissociation without breaking spin symmetry. Additionally, our scheme provides
a natural way to connect an energy eigenvalue spectrum to the approximate
natural orbitals and this spectrum is found to represent accurately the
ionization potentials of atoms and small molecules
- …