49 research outputs found
An improved lower bound for the maximal length of a multivector
A new lower bound for the maximal length of a multivector is obtained. It is
much closer to the best known upper bound than previously reported lower bound
estimates. The maximal length appears to be unexpectedly large for -vectors,
with n>2, since the few exactly known values seem to grow linearly with vector
space dimension, whereas the new lower bound has a polynomial order equal to
n-1 like the best known upper bound. This result has implications for quantum
chemistry
Generalization of the concepts of seniority number and ionicity
We present generalized versions of the concepts of seniority number and
ionicity. These generalized numbers count respectively the partially occupied
and fully occupied shells for any partition of the orbital space into shells.
The Hermitian operators whose eigenspaces correspond to wave functions of
definite generalized seniority or ionicity values are introduced. The
generalized seniority numbers (GSNs) afford to establish refined hierarchies of
configuration interaction (CI) spaces within those of fixed ordinary seniority.
Such a hierarchy is illustrated on the buckminsterfullerene molecule
Une algèbre pour comprendre les structures électroniques des atomes et des molécules
5 pages, écris pour l'année mondiale de la chimieBibliothèque Tangente 43, (Editions Pole, Paris, 2012), p. 52-57. ISBN : 2-84884-120-6 EAN : 9782848841205 ISSN : 2263-4908 version édulcorée publiée dans Tangente Sup 61, Juillet 2011, (Editions Pole, Paris) p. 8-11 ISSN : 1291-4932Cet article de vulgarisation propose une présentation simple de l'Algèbre de Grassmann et du principe d'exclusion de Pauli puis quelques exemples de ce que cela permet de comprendre sur la structure électronique des atomes et des molécules
A Conjecture on Antisymmetrized Geminal Power Wavefunctions
We conjecture that ``Antisymmetrized Geminal Power'' wave functions, and, in
particular, those of extreme type in Coleman's terminology (i.e. with all
geminal coefficients equal), can always be rewritten as antisymmetrized
products of geminals orthogonal to each other. We prove this conjecture in
simple cases and provide numerical evidence that it holds true in more
complicated examples. Establishing the validity of this conjecture is important
as it questions the physical interpretation of AGP wavefunctions
A Fast Algorithm for the Construction of Integrity Bases Associated to Symmetry-Adapted Polynomial Representations. Application to Tetrahedral XY4 Molecules
Invariant theory provides more efficient tools, such as Molien generating
functions and integrity bases, than basic group theory, that relies on
projector techniques for the construction of symmetry--adapted polynomials in
the symmetry coordinates of a molecular system, because it is based on a finer
description of the mathematical structure of the latter. The present article
extends its use to the construction of polynomial bases which span possibly,
non--totally symmetric irreducible representations of a molecular symmetry
group. Electric or magnetic observables can carry such irreducible
representations, a common example is given by the electric dipole moment
surface. The elementary generating functions and their corresponding integrity
bases, where both the initial and the final representations are irreducible,
are the building blocks of the algorithm presented in this article, which is
faster than algorithms based on projection operators only. The generating
functions for the full initial representation of interest are built recursively
from the elementary generating functions. Integrity bases which can be used to
generate in the most economical way symmetry--adapted polynomial bases are
constructed alongside in the same fashion. The method is illustrated in detail
on XY4 type of molecules. Explicit integrity bases for all five possible final
irreducible representations of the tetrahedral group have been calculated and
are given in the supplemental material associated with this paper
Improving Guess Geminals for the Geminal Mean Field Configuration Interaction Method
The purpose of this letter is to show that a rotation of Hartree-Fock
canonical orbitals which minimizes the lowest eigenvalues of a configuration
interaction calculation limited to the mono-excitated configurations from a
given orbital allows one to construct a better starting guess for the geminal
mean field configuration interaction method
Contributions of the electronic spin and orbital current to the CoCl4(2-) magnetic field probed in polarised neutron diffraction experiments
International audiencePolarised neutron diffraction experiments conducted at 4.2 K on CsCoCl crystals have been analysed by using a -dimensional model Hilbert space made of \abin -electron wave functions of the CoCl molecular ion. Two spin-orbit mixing coefficients and several configuration interaction coefficients have been optimized by fitting calculated magnetic structure factors to experimental ones, to obtain the best ensemble density operator that is representable in the model space. A goodness of fit, , less then has been obtained for the first time for the two experimental data sets available. In the present article, the optimized density operators are used to calculate the magnetic field densities that are the genuine observables probed in neutron diffraction experiments. Density maps of such observables are presented for the first time and numerical details are provided. The respective contributions of spin density and orbital current to the magnetic field density are analyze
Electrons as an environment for nuclei within molecules: a quantitative assessment of their contribution to a classical-like molecular structure
Molecular structure is often considered as emerging from the decoherence
effect of the environment. Electrons are part of the environment of the nuclei
in a molecule. In this work, their contribution to the classical-like
geometrical relationships often observed between nuclei in molecular systems is
investigated. Reduced density matrix (RDM) elements are evaluated from
electron-nucleus wave functions. The computational results show that the
electrons play a role in the localization of the nuclei around specific
geometries. Although the electronic environment alone cannot explain molecular
symmetry-broken isomers, it can contribute to their dynamical stability by
reducing off-diagonal RDM elements.Comment: Theoretical Chemistry Accounts: Theory, Computation, and Modeling,
Springer Verlag, In pres