58 research outputs found
A theoretical study of linear beryllium chains: full configuration interaction.
International audienceWe present a full configuration interaction study of Be(N) (N=2,3,4,5) linear chains. A comparative study of the basis-set effect on the reproduction of the energy profile has been reported. In particular, the 3s1p, 4s2p, 4s2p1d, 5s3p2d, and 5s3p2d1f bases were selected. For the smallest chains (i.e., Be(2) and Be(3)), smaller basis sets give dissociative energy profiles, so large basis set is demanded for the reproduction of equilibrium minima in the structures. For Be(4) and Be(5) linear chains, the energy profiles show a minimum also by using the smallest basis sets, but the largest ones give a much stronger stabilization energy. For all the structures, two spin states have been studied: the singlet and the triplet. It is shown that the energy separation of the two states, in the equilibrium region, is small and decays exponentially with respect to the number of atoms in the chain. Finally an interpolative technique allowing for the estimation of the long-chain parameters from shorter ones is presented
Spin partition
The Total Position Spread (TPS) tensor, defined as the second moment cumulant
of the position operator, is a key quantity to describe the mobility of
electrons in a molecule or an extended system. In the present investigation,
the partition of the TPS tensor according to spin variables is derived and
discussed. It is shown that, while the spin-summed TPS gives information on
charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that
provides information about spin fluctuations. The case of the hydrogen
molecule is treated, both analytically, by using a 1s Slater-type orbital, and
numerically, at Full Configuration Interaction (FCI) level with a V6Z basis
set. It is found that, for very large inter-nuclear distances, the partitioned
tensor growths quadratically with the distance in some of the low-lying
electronic states. This fact is related to the presence of entanglement in the
wave function. Non-dimerized open chains described by a model Hubbard
Hamiltonian and linear hydrogen chains H n (n â„ 2), composed of equally spaced
atoms, are also studied at FCI level. The hydrogen systems show the presence
of marked maxima for the spin-summed TPS (corresponding to a high charge
mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be
associated to the presence of a Mott transition occurring in this region. The
spin-partitioned TPS tensor, on the other hand, has a quadratical growth at
long distances, a fact that corresponds to the high spin mobility in a
magnetic system
An application to Heisenberg spin chains
The spin partition of the Total Position-Spread (TPS) tensor has been
performed for one-dimensional Heisenberg chains with open boundary conditions.
Both the cases of a ferromagnetic (high-spin) and an anti-ferromagnetic (low-
spin) ground-state have been considered. In the case of a low-spin ground-
state, the use of alternating magnetic couplings allowed to investigate the
effect of spin-pairing. The behavior of the spin-partitioned TPS (SP-TPS)
tensor as a function of the number of sites turned to be closely related to
the presence of an energy gap between the ground-state and the first excited-
state at the thermodynamic limit. Indeed, a gapped energy spectrum is
associated to a linear growth of the SP-TPS tensor with the number of sites.
On the other hand, in gapless situations, the spread presents a faster-than-
linear growth, resulting in the divergence of its per-site value. Finally, for
the case of a high-spin wave function, an analytical expression of the
dependence of the SP-TPS on the number of sites n and the total spin-
projection Sz has been derived
Solution to the Thomson problem for Clifford tori with an application to Wigner crystals
In its original version, the Thomson problem consists of the search for the
minimum-energy configuration of a set of point-like electrons that are confined
to the surface of a two-dimensional sphere () that repel each other
according to Coulomb's law, in which the distance is the Euclidean distance in
the embedding space of the sphere, {\em i.e.}, . In this work, we
consider the analogous problem where the electrons are confined to an
-dimensional flat Clifford torus with . Since the
torus can be embedded in the complex manifold , we
define the distance in the Coulomb law as the Euclidean distance in
, in analogy to what is done for the Thomson problem on the
sphere. The Thomson problem on a Clifford torus is of interest because
super-cells with the topology of Clifford torus can be used to describe
periodic systems such as Wigner crystals. In this work we numerically solve the
Thomson problem on a square Clifford torus. To illustrate the usefulness of our
approach we apply it to Wigner crystals. We demonstrate that the equilibrium
configurations we obtain for a large numbers of electrons are consistent with
the predicted structures of Wigner crystals. Finally, in the one-dimensional
case we analytically obtain the energy spectrum and the phonon dispersion law
Full configuration interaction calculation of singlet excited states of Be3
The full configuration interaction (FCI) study of the singlets vertical spectrum of the neutral beryllium trimer has been performed using atomic natural orbitals [3s2p1d] basis set. The FCI triangular equilibrium structure of the ground state has been used to calculate the FCI vertical excitation energies up to 4.8 eV. The FCI vertical ionization potential for the same geometry and basis set amounts to 7.6292 eV. The FCI dipole and quadrupole transition moments from the ground state are reported as well. The FCI electric quadrupole moment of the Xâ3A1âČ ground state has been also calculated with the same basis set (Îzz = â2.6461âa.u., Îxx = Îyy = â1/2Îzz). Twelve of the 19 calculated excited singlets are doubly excited states. Most of the states have large multiconfigurational character. These results provide benchmark values for electronic correlation multireference methods. (4eĂ6MO)CAS-SDCI values for the same energies and properties are also [email protected]
A simple position operator for periodic systems
International audienceWe present a position operator that is compatible with periodic boundary conditions (PBC). It is a one-body operator that can be applied in calculations of correlated materials by simply replacing the traditional position vector by the new definition. We show that it satisfies important fundamental as well as practical constraints. To illustrate the usefulness of the PBC position operator we apply it to the localization tensor, a key quantity that is able to differentiate metallic from insulating states. In particular, we show that the localization tensor given in terms of the PBC position operator yields the correct expression in the thermodynamic limit. Moreover, we show that it correctly distinguishes between finite precursors of metals and insulators
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