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 $n$-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 Cs$_3$CoCl$_5$ crystals have been analysed by using a $4$-dimensional model Hilbert space made of \abin $n$-electron wave functions of the CoCl$_4^{2-}$ 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, $\chi^2$, less then $1$ 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