43 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
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
Density-Wavefunction Mapping in Degenerate Current-Density-Functional Theory
We show that the particle density, , and the paramagnetic
current density, , are not sufficient to determine
the set of degenerate ground-state wave functions. This is a general feature of
degenerate systems where the degenerate states have different angular momenta.
We provide a general strategy for constructing Hamiltonians that share the same
ground state density, yet differ in degree of degeneracy. We then provide a
fully analytical example for a noninteracting system subject to electrostatic
potentials and uniform magnetic fields. Moreover, we prove that when
is ensemble -representable by a mixed
state formed from degenerate ground states, then any Hamiltonian
that shares this ground state density pair must have at
least degenerate ground states in common with . Thus, any
set of Hamiltonians that shares a ground-state density pair
by necessity has at least have one joint ground state
A local tensor that unifies kinetic energy density and vorticity dependent exchange-correlation functionals
We present a kinetic energy tensor that unifies a scalar kinetic energy
density commonly used in meta-Generalized Gradient Approximation functionals
and the vorticity density that appears in paramagnetic
current-density-functional theory. Both types of functionals can thus be
subsumed as special cases of a novel functional form that is naturally placed
on the third rung of Jacob's ladder. Moreover, the kinetic energy tensor is
related to the exchange hole curvature, is gauge invariant, and has very
clearcut -representability conditions. The latter conditions enable the
definition of effective number of non-negligible orbitals. Whereas quantities
such as the Electron Localization Function can discriminate effective
one-orbital regions from other regions, the present kinetic energy tensor can
discriminate between one-, two-, three-, and four-or-more orbital regions
Revisiting density-functional theory of the total current density
Density-functional theory requires an extra variable besides the electron
density in order to properly incorporate magnetic-field effects. In a
time-dependent setting, the gauge-invariant, total current density takes that
role. A peculiar feature of the static ground-state setting is, however, that
the gauge-dependent paramagnetic current density appears as the additional
variable instead. An alternative, exact reformulation in terms of the total
current density has long been sought but to date a work by Diener is the only
available candidate. In that work, an unorthodox variational principle was used
to establish a ground-state density-functional theory of the total current
density as well as an accompanying Hohenberg-Kohn-like result. We here
reinterpret and clarify Diener's formulation based on a maximin variational
principle. Using simple facts about convexity implied by the resulting
variational expressions, we prove that Diener's formulation is unfortunately
not capable of reproducing the correct ground-state energy and, furthermore,
that the suggested construction of a Hohenberg-Kohn map contains an irreparable
mistake