12,439 research outputs found
A recursive formulation of one‐electron coupling coefficients for spin‐adapted configuration interaction calculations featuring many unpaired electrons
This work reports on a novel computational approach to the efficient evaluation of one-electron coupling coefficients as they are required during spin-adapted electronic structure calculations of the configuration interaction type. The presented approach relies on the equivalence of the representation matrix of excitation operators in the basis of configuration state functions and the representation matrix of permutation operators in the basis of genealogical spin eigenfunctions. After the details of this connection are established for every class of one-electron excitation operator, a recursive scheme to evaluate permutation operator representations originally introduced by Yamanouchi and Kotani is recapitulated. On the basis of this scheme we have developed an efficient algorithm that allows the evaluation of all nonredundant coupling coefficients for systems with 20 unpaired electrons and a total spin of S = 0 within only a few hours on a simple Desktop-PC. Furthermore, a full-CI implementation that utilizes the presented approach to one-electron coupling coefficients is shown to perform well in terms of computational timings for CASCI calculations with comparably large active spaces. More importantly, however, this work paves the way to spin-adapted and configuration driven selected configuration interaction calculations with many unpaired electrons.Deutsche Forschungsgemeinschaft
http://dx.doi.org/10.13039/501100001659Peer Reviewe
Coulomb correlation effects in semiconductor quantum dots: The role of dimensionality
We study the energy spectra of small three-dimensional (3D) and
two-dimensional (2D) semiconductor quantum dots through different theoretical
approaches (single-site Hubbard and Hartree-Fock hamiltonians); in the smallest
dots we also compare with exact results. We find that purely 2D models often
lead to an inadequate description of the Coulomb interaction existing in
realistic structures, as a consequence of the overestimated carrier
localization. We show that the dimensionality of the dots has a crucial impact
on (i) the accuracy of the predicted addition spectra; (ii) the range of
validity of approximate theoretical schemes. When applied to realistic 3D
geometries, the latter are found to be much more accurate than in the
corresponding 2D cases for a large class of quantum dots; the single-site
Hubbard hamiltonian is shown to provide a very effective and accurate scheme to
describe quantum dot spectra, leading to good agreement with experiments.Comment: LaTeX 2.09, RevTeX, 25 pages, 9 Encapsulated Postscript figures. To
be published in Physical Review
Validity of the single-particle description and charge noise resilience for multielectron quantum dots
We construct an optimal set of single-particle states for few-electron
quantum dots (QDs) using the method of natural orbitals (NOs). The NOs include
also the effects of the Coulomb repulsion between electrons. We find that they
agree well with the noniteracting orbitals for GaAs QDs of realistic
parameters, while the Coulomb interactions only rescale the radius of the NOs
compared to the noninteracting case. We use NOs to show that four-electron QDs
are less susceptible to charge noise than their two-electron counterparts.Comment: 11+ pages, 5 figure
Pseudospectral methods for atoms in strong magnetic fields
We present a new pseudospectral algorithm for the calculation of the
structure of atoms in strong magnetic fields. We have verified this technique
for one, two and three-electron atoms in zero magnetic fields against
laboratory results and find typically better than one-percent accuracy. We
further verify this technique against the state-of-the-art calculations of
hydrogen, helium and lithium in strong magnetic fields (up to about T) and find a similar level of agreement. The key enabling advantages
of the algorithm are its simplicity (about 130 lines of commented code) and its
speed (about times faster than finite-element methods to achieve
similar accuracy).Comment: 10 pages, version accepted to MNRA
Electronic structure of rectangular quantum dots
We study the ground state properties of rectangular quantum dots by using the
spin-density-functional theory and quantum Monte Carlo methods. The dot
geometry is determined by an infinite hard-wall potential to enable comparison
to manufactured, rectangular-shaped quantum dots. We show that the electronic
structure is very sensitive to the deformation, and at realistic sizes the
non-interacting picture determines the general behavior. However, close to the
degenerate points where Hund's rule applies, we find spin-density-wave-like
solutions bracketing the partially polarized states. In the
quasi-one-dimensional limit we find permanent charge-density waves, and at a
sufficiently large deformation or low density, there are strongly localized
stable states with a broken spin-symmetry.Comment: 8 pages, 9 figures, submitted to PR
Spin in Density-Functional Theory
The accurate description of open-shell molecules, in particular of transition
metal complexes and clusters, is still an important challenge for quantum
chemistry. While density-functional theory (DFT) is widely applied in this
area, the sometimes severe limitations of its currently available approximate
realizations often preclude its application as a predictive theory. Here, we
review the foundations of DFT applied to open-shell systems, both within the
nonrelativistic and the relativistic framework. In particular, we provide an
in-depth discussion of the exact theory, with a focus on the role of the spin
density and possibilities for targeting specific spin states. It turns out that
different options exist for setting up Kohn-Sham DFT schemes for open-shell
systems, which imply different definitions of the exchange-correlation energy
functional and lead to different exact conditions on this functional. Finally,
we suggest some possible directions for future developments
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