CASSAM-CHENAÏ , Patrick

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 generalized seniority numbers (GSNs) afford to establish refined hierarchies of configuration interaction (CI)...

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Cet 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.

Master

We prove a stronger form of the Hohenberg-Kohn theorem.

We show on a analytical case example how the projection method on full Hilbert space converges to Weinstein variance minimization and differs from Ritz variational method.

An expression for the square of the spin operator expectation value, < S^2>, is obtained for a general complex Hartree-Fock (GCHF) wave function and decomposed into four contributions: The main one whose expression is formally identical to the restricted (open-shell) Hartree-Fock expression. A spin contamination one formally analogous to that...

The concept of p-orthogonality (1=< p =< n) between n-particle states is introduced. It generalizes common orthogonality, which is equivalent to n-orthogonality, and strong orthogonality between fermionic states, which is equivalent to 1-orthogonality. Within the class of non p-orthogonal states a finer measure of non p-orthogonality is...

Le problème typique du physicien théoricien, tel qu'il peut être décrit dans certains manuels scolaires, consiste à rendre compte de faits expérimentaux et d'observations à l'aide d'un modèle théorique. L'expérimentateur (qui peut être la même personne) quant à lui valide ou invalide le modèle au moyen de nouvelles expériences. Pour le...

We obtain necessary conditions for coordinate transformations to turn a dynamical system into a Hamiltonian one in canonical coordinates. These equations, restricted to the class of coordinate transformations which act on each coordinate independently, are greatly simplified. However, they are surprisingly successful in defining canonical...

It seems more and more legitimate to think that elementary particles acquire their mass by interacting with the quantum fields of other particles \cite{CMS12,ATLAS12}. In the same way as ''elementary'' entities should be massless, i.e. should transform under translations as the trivial representation, one would expect them to be spinless i.e....

We will present the electron-nucleus effective field configuration interaction method [1], which encompasses as particular cases the best electron-nucleus direct product wave function and the exact full CI electron-nucleus wave function for a given finite basis set. Then, electron-nucleus and electronic correlation energies will be compared...

Prédire un spectre moléculaire, ou inversement, attribuer des raies spectrales observées à une transition quantique entre niveaux d'énergie moléculaires, sont des opérations nécessaires à la pleine exploitation de techniques de détection et de sondage à distance, aussi bien terrestres que spatiales. Pour réaliser de telles opérations, il faut...

The mean field configuration interaction (MFCI) method is a variational approximation method that has been developed to solve the Schrödinger equation for molecular vibrations (VMFCI) and electrons (EMFCI). The Rayleigh-Schrödinger perturbation theory generalized to eigen-operators in non-commutative rings has been proposed to solve the...

In this paper, we extend the critical approach of Boyer-Kassem et al. (Boyer-Kassem, Thomas, Duchêne , Sbastien, Guerci Eric (2016), " Testing quantum-like models of judgment for question order effect " , Mathematical Social Sciences 80: 33-46.) to degenerate quantum models.

The Lewis electron-pair picture pervades all of chemistry and a substantial domain of materials science. "Geminals" are electron-pair quantum states which are used to express approximate solutions of the Schrödinger equation of polyelectronic systems. In quantum chemistry, geminal-based methods are potentially more effective than the...

We know that HF or more generally CASSCF wave functions are invariant under aunitary transformation of the occupied orbitals. This can be taken advantage ofto obtain a "localized" version of a "delocalized" wave function.More generally, the question of determining the set of transformations preserving the structure of awavefunction of a certain...

A perturbation scheme to find approximate solutions of a generalized spectral problem is presented. The spectral problem is generalized in the sense that the ``eigenvalues'' searched for, are not real numbers but operators in a non-commutative ring, and the associated ``eigenfunctions'' do not belong to an Hilbert space but are elements of a...

The Lewis electron-pair picture pervades all of chemistry and a substantialdomain of materials science. "Geminals" are electron-pair quantum states whichare used to express approximate solutions of the Schrödinger equation of polyelec-tronic systems. In quantum chemistry, geminal-based methods are potentially moreeffective than the traditional...

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...

We derive the Hamiltonian corresponding to the Lagrangian of P. W. Higgs, "Brokensymmetries and the masses of gauge bosons", Phys. Rev. Lett. 13, 508 (1964).

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...

We obtain conditions, which when fulfilled, permit to transform the coordinates of a dynamical system into pairs of canonical ones i.e. conjugate with respect to a Hamiltonian. These conditions, restricted to the class of coordinate transformations which act on each coordinate independently, are greatly simplified. However, they are...

We obtain conditions, which when fulfilled, permit to transform the coordinates of a dynamical system into pairs of canonical ones for some Hamiltonian system. These conditions, restricted to the class of coordinate transformations which act on each coordinate independently, are greatly simplified. However, they are surprisingly successful in...