260 research outputs found
Fermion -representability for prescribed density and paramagnetic current density
The -representability problem is the problem of determining whether or not
there exists -particle states with some prescribed property. Here we report
an affirmative solution to the fermion -representability problem when both
the density and paramagnetic current density are prescribed. This problem
arises in current-density functional theory and is a generalization of the
well-studied corresponding problem (only the density prescribed) in density
functional theory. Given any density and paramagnetic current density
satisfying a minimal regularity condition (essentially that a von
Weiz\"acker-like the canonical kinetic energy density is locally integrable),
we prove that there exist a corresponding -particle state. We prove this by
constructing an explicit one-particle reduced density matrix in the form of a
position-space kernel, i.e.\ a function of two continuous position variables.
In order to make minimal assumptions, we also address mathematical subtleties
regarding the diagonal of, and how to rigorously extract paramagnetic current
densities from, one-particle reduced density matrices in kernel form
Guaranteed Convergence of a Regularized Kohn-Sham Iteration in Finite Dimensions
The exact Kohn-Sham iteration of generalized density-functional theory in
finite dimensions witha Moreau-Yosida regularized universal Lieb functional and
an adaptive damping step is shown toconverge to the correct ground-state
density.Comment: 3 figures, contains erratum with additional author Paul E. Lammer
The choice of basic variables in current-density functional theory
The selection of basic variables in current-density functional theory and
formal properties of the resulting formulations are critically examined. Focus
is placed on the extent to which the Hohenberg--Kohn theorem,
constrained-search approach and Lieb's formulation (in terms of convex and
concave conjugation) of standard density-functional theory can be generalized
to provide foundations for current-density functional theory. For the
well-known case with the gauge-dependent paramagnetic current density as a
basic variable, we find that the resulting total energy functional is not
concave. It is shown that a simple redefinition of the scalar potential
restores concavity and enables the application of convex analysis and
convex/concave conjugation. As a result, the solution sets arising in
potential-optimization problems can be given a simple characterization. We also
review attempts to establish theories with the physical current density as a
basic variable. Despite the appealing physical motivation behind this choice of
basic variables, we find that the mathematical foundations of the theories
proposed to date are unsatisfactory. Moreover, the analogy to standard
density-functional theory is substantially weaker as neither the
constrained-search approach nor the convex analysis framework carry over to a
theory making use of the physical current density
Non-perturbative calculation of orbital- and spin effects in molecules subject to non-uniform magnetic fields
External non-uniform magnetic fields acting on molecules induce non-collinear
spin-densities and spin-symmetry breaking. This necessitates a general
two-component Pauli spinor representation. In this paper, we report the
implementation of a General Hartree-Fock method, without any spin constraints,
for non-perturbative calculations with finite non-uniform fields. London atomic
orbitals are used to ensure faster basis convergence as well as invariance
under constant gauge shifts of the magnetic vector potential. The
implementation has been applied to an investigate the joint orbital and spin
response to a field gradient---quantified through the anapole moments---of a
set of small molecules placed in a linearly varying magnetic field. The
relative contributions of orbital and spin-Zeeman interaction terms have been
studied both theoretically and computationally. Spin effects are stronger and
show a general paramagnetic behaviour for closed shell molecules while orbital
effects can have either direction. Basis set convergence and size effects of
anapole susceptibility tensors have been reported. The relation of the mixed
anapole susceptibility tensor to chirality is also demonstrated
Kohn-Sham theory with paramagnetic currents: compatibility and functional differentiability
Recent work has established Moreau-Yosida regularization as a mathematical
tool to achieve rigorous functional differentiability in density-functional
theory. In this article, we extend this tool to paramagnetic
current-density-functional theory, the most common density-functional framework
for magnetic field effects. The extension includes a well-defined Kohn-Sham
iteration scheme with a partial convergence result. To this end, we rely on a
formulation of Moreau-Yosida regularization for reflexive and strictly convex
function spaces. The optimal -characterization of the paramagnetic current
density is derived from the -representability conditions.
A crucial prerequisite for the convex formulation of paramagnetic
current-density-functional theory, termed compatibility between function spaces
for the particle density and the current density, is pointed out and analyzed.
Several results about compatible function spaces are given, including their
recursive construction. The regularized, exact functionals are calculated
numerically for a Kohn-Sham iteration on a quantum ring, illustrating their
performance for different regularization parameters
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