2,772 research outputs found
Efficient Algorithm for Asymptotics-Based Configuration-Interaction Methods and Electronic Structure of Transition Metal Atoms
Asymptotics-based configuration-interaction (CI) methods [G. Friesecke and B.
D. Goddard, Multiscale Model. Simul. 7, 1876 (2009)] are a class of CI methods
for atoms which reproduce, at fixed finite subspace dimension, the exact
Schr\"odinger eigenstates in the limit of fixed electron number and large
nuclear charge. Here we develop, implement, and apply to 3d transition metal
atoms an efficient and accurate algorithm for asymptotics-based CI.
Efficiency gains come from exact (symbolic) decomposition of the CI space
into irreducible symmetry subspaces at essentially linear computational cost in
the number of radial subshells with fixed angular momentum, use of reduced
density matrices in order to avoid having to store wavefunctions, and use of
Slater-type orbitals (STO's). The required Coulomb integrals for STO's are
evaluated in closed form, with the help of Hankel matrices, Fourier analysis,
and residue calculus.
Applications to 3d transition metal atoms are in good agreement with
experimental data. In particular we reproduce the anomalous magnetic moment and
orbital filling of Chromium in the otherwise regular series Ca, Sc, Ti, V, Cr.Comment: 14 pages, 1 figur
Hilbert space renormalization for the many-electron problem
Renormalization is a powerful concept in the many-body problem. Inspired by
the highly successful density matrix renormalization group (DMRG) algorithm,
and the quantum chemical graphical representation of configuration space, we
introduce a new theoretical tool: Hilbert space renormalization, to describe
many-electron correlations. While in DMRG, the many-body states in nested Fock
subspaces are successively renormalized, in Hilbert space renormalization,
many-body states in nested Hilbert subspaces undergo renormalization. This
provides a new way to classify and combine configurations. The underlying
wavefunction ansatz, namely the Hilbert space matrix product state (HS-MPS),
has a very rich and flexible mathematical structure. It provides low-rank
tensor approximations to any configuration interaction (CI) space through
restricting either the 'physical indices' or the coupling rules in the HS-MPS.
Alternatively, simply truncating the 'virtual dimension' of the HS-MPS leads to
a family of size-extensive wave function ansaetze that can be used efficiently
in variational calculations. We make formal and numerical comparisons between
the HS-MPS, the traditional Fock-space MPS used in DMRG, and traditional CI
approximations. The analysis and results shed light on fundamental aspects of
the efficient representation of many-electron wavefunctions through the
renormalization of many-body states.Comment: 23 pages, 14 figures, The following article has been submitted to The
Journal of Chemical Physic
The influence of orbital rotation on the energy of closed-shell wavefunctions
The orbital dependence of closed-shell wavefunction energies is investigated by performing doubly-occupied configuration interaction (DOCI) calculations, representing the most general class of these wavefunctions. Different local minima are examined for planar hydrogen clusters containing two, four, and six electrons applying (spin) symmetry-broken restricted, unrestricted, and generalised orbitals with real and complex coefficients. Contrary to Hartree-Fock (HF), restricted DOCI is found to properly break bonds and thus unrestricted orbitals, while providing a quantitative improvement of the energy, are not needed to enforce a qualitatively correct bond dissociation. For the beryllium atom and the BH diatomic, the lowest possible HF energy requests symmetry-broken generalised orbitals, whereas accurate results for DOCI can be obtained within a restricted formalism. Complex orbital coefficients are shown to increase the accuracy of HF and DOCI results in certain cases. The computationally inexpensive AP1roG geminal wavefunction is proven to agree very well with all DOCI results of this study
Excitation, two-center interference and the orbital geometry in laser-induced nonsequential double ionization of diatomic molecules
We address the influence of the molecular orbital geometry and of the
molecular alignment with respect to the laser-field polarization on
laser-induced nonsequential double ionization of diatomic molecules for
different molecular species, namely and . We
focus on the recollision excitation with subsequent tunneling ionization (RESI)
mechanism, in which the first electron, upon return, promotes the second
electron to an excited state, from where it subsequently tunnels. We show that
the electron-momentum distributions exhibit interference maxima and minima due
to the electron emission at spatially separated centers. We provide generalized
analytical expressions for such maxima or minima, which take into account
mixing and the orbital geometry. The patterns caused by the two-center
interference are sharpest for vanishing alignment angle and get washed out as
this parameter increases. Apart from that, there exist features due to the
geometry of the lowest occupied molecular orbital (LUMO), which may be observed
for a wide range of alignment angles. Such features manifest themselves as the
suppression of probability density in specific momentum regions due to the
shape of the LUMO wavefunction, or as an overall decrease in the RESI yield due
to the presence of nodal planes.Comment: 11 pages revtex, 2 figure
Preparation of an Exciton Condensate of Photons on a 53-Qubit Quantum Computer
Quantum computation promises an exponential speedup of certain classes of
classical calculations through the preparation and manipulation of entangled
quantum states. So far most molecular simulations on quantum computers,
however, have been limited to small numbers of particles. Here we prepare a
highly entangled state on a 53-qubit IBM quantum computer, representing 53
particles, which reveals the formation of an exciton condensate of photon
particles and holes. While elusive for more than 50 years, such condensates
were recently achieved for electron-hole pairs in graphene bilayers and metal
chalcogenides. Our result with a photon condensate has the potential to further
the exploration of this new form of condensate that may play a significant role
in realizing efficient room-temperature energy transport
Molecular phases in coupled quantum dots
We present excitation energy spectra of few-electron vertically coupled
quantum dots for strong and intermediate inter-dot coupling. By applying a
magnetic field, we induce ground state transitions and identify the
corresponding quantum numbers by comparison with few-body calculations. In
addition to atomic-like states, we find novel "molecular-like" phases. The
isospin index characterizes the nature of the bond of the artificial molecule
and this we control. Like spin in a single quantum dot, transitions in isospin
leading to full polarization are observed with increasing magnetic field.Comment: PDF file only, 28 pages, 3 tables, 4 color figures, 2 appendices. To
appear in Physical Review B, Scheduled 15 Feb 2004, Vol. 69, Issue
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