194 research outputs found
Configuration interaction wave functions: A seniority number approach
This work deals with the configuration interaction method when an N-electron Hamiltonian is projected on Slater determinants which are classified according to their seniority number values. We study the spin features of the wave functions and the size of the matrices required to formulate states of any spin symmetry within this treatment. Correlation energies associated with the wave functions arising from the seniority-based configuration interaction procedure are determined for three types of molecular orbital basis: canonical molecular orbitals, natural orbitals, and the orbitals resulting from minimizing the expectation value of the N-electron seniority number operator. The performance of these bases is analyzed by means of numerical results obtained from selected N-electron systems of several spin symmetries. The comparison of the results highlights the efficiency of the molecular orbital basis which minimizes the mean value of the seniority number for a state, yielding energy values closer to those provided by the full configuration interaction procedure.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de FĂsica de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FĂsica; ArgentinaFil: Torre, Alicia. Universidad del Pais Vasco; EspañaFil: Lain, Luis . Universidad del Pais Vasco; EspañaFil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires. Ciclo BĂĄsico ComĂșn; ArgentinaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico la Plata. Instituto de Investigaciones FisicoquĂmicas TeĂłricas y Aplicadas; Argentin
Entanglement of electrons in interacting molecules
Quantum entanglement is a concept commonly used with reference to the
existence of certain correlations in quantum systems that have no classical
interpretation. It is a useful resource to enhance the mutual information of
memory channels or to accelerate some quantum processes as, for example, the
factorization in Shor's Algorithm. Moreover, entanglement is a physical
observable directly measured by the von Neumann entropy of the system. We have
used this concept in order to give a physical meaning to the electron
correlation energy in systems of interacting electrons. The electronic
correlation is not directly observable, since it is defined as the difference
between the exact ground state energy of the many--electrons Schroedinger
equation and the Hartree--Fock energy. We have calculated the correlation
energy and compared with the entanglement, as functions of the nucleus--nucleus
separation using, for the hydrogen molecule, the Configuration Interaction
method. Then, in the same spirit, we have analyzed a dimer of ethylene, which
represents the simplest organic conjugate system, changing the relative
orientation and distance of the molecules, in order to obtain the configuration
corresponding to maximum entanglement.Comment: 15 pages, 7 figures, standard late
Seniority number in spin-adapted spaces and compactness of configuration interaction wave functions
This work extends the concept of seniority number, which has been widely used for classifying N-electron Slater determinants, to wave functions of N electrons and spin S, as well as to N-electron spin-adapted Hilbert spaces. We propose a spin-free formulation of the seniority number operator and perform a study on the behavior of the expectation values of this operator under transformations of the molecular basis sets. This study leads to propose a quantitative evaluation for the convergence of the expansions of the wave functions in terms of Slater determinants. The non-invariant character of the seniority number operator expectation value of a wave function with respect to a unitary transformation of the molecular orbital basis set, allows us to search for a change of basis which minimizes that expectation value. The results found in the description of wave functions of selected atoms and molecules show that the expansions expressed in these bases exhibit a more rapid convergence than those formulated in the canonical molecular orbital bases and even in the natural orbital ones.Fil: Alcoba, Diego Ricardo. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Oficina de CoordinaciĂłn Administrativa Ciudad Universitaria. Instituto de FĂsica de Buenos Aires; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de FĂsica; ArgentinaFil: Torre, Alicia. Universidad del PaĂs Vasco. Facultad de Ciencia y TecnologĂa. Departamento de QuĂmica FĂsica; España;Fil: Lain, Luis. Universidad del PaĂs Vasco. Facultad de Ciencia y TecnologĂa. Departamento de QuĂmica FĂsica; España;Fil: Massaccesi, Gustavo Ernesto. Universidad de Buenos Aires. Ciclo BĂĄsico ComĂșn; Argentina. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de MatemĂĄtica; ArgentinaFil: Oña, Ofelia Beatriz. Consejo Nacional de Investigaciones CientĂficas y TĂ©cnicas. Centro CientĂfico TecnolĂłgico la Plata. Instituto de Investigaciones FisicoquĂmicas TeĂłricas y Aplicadas; Argentin
Many-body-QED perturbation theory: Connection to the Bethe-Salpeter equation
The connection between many-body theory (MBPT)--in perturbative and
non-perturbative form--and quantum-electrodynamics (QED) is reviewed for
systems of two fermions in an external field. The treatment is mainly based
upon the recently developed covariant-evolution-operator method for QED
calculations [Lindgren et al. Phys. Rep. 389, 161 (2004)], which has a
structure quite akin to that of many-body perturbation theory. At the same time
this procedure is closely connected to the S-matrix and the Green's-function
formalisms and can therefore serve as a bridge between various approaches. It
is demonstrated that the MBPT-QED scheme, when carried to all orders, leads to
a Schroedinger-like equation, equivalent to the Bethe-Salpeter (BS) equation. A
Bloch equation in commutator form that can be used for an "extended" or
quasi-degenerate model space is derived. It has the same relation to the BS
equation as has the standard Bloch equation to the ordinary Schroedinger
equation and can be used to generate a perturbation expansion compatible with
the BS equation also for a quasi-degenerate model space.Comment: Submitted to Canadian J of Physic
Review of biorthogonal coupled cluster representations for electronic excitation
Single reference coupled-cluster (CC) methods for electronic excitation are
based on a biorthogonal representation (bCC) of the (shifted) Hamiltonian in
terms of excited CC states, also referred to as correlated excited (CE) states,
and an associated set of states biorthogonal to the CE states, the latter being
essentially configuration interaction (CI) configurations. The bCC
representation generates a non-hermitian secular matrix, the eigenvalues
representing excitation energies, while the corresponding spectral intensities
are to be derived from both the left and right eigenvectors. Using the
perspective of the bCC representation, a systematic and comprehensive analysis
of the excited-state CC methods is given, extending and generalizing previous
such studies. Here, the essential topics are the truncation error
characteristics and the separability properties, the latter being crucial for
designing size-consistent approximation schemes. Based on the general order
relations for the bCC secular matrix and the (left and right) eigenvector
matrices, formulas for the perturbation-theoretical (PT) order of the
truncation errors (TEO) are derived for energies, transition moments, and
property matrix elements of arbitrary excitation classes and truncation levels.
In the analysis of the separability properties of the transition moments, the
decisive role of the so-called dual ground state is revealed. Due to the use of
CE states the bCC approach can be compared to so-called intermediate state
representation (ISR) methods based exclusively on suitably orthonormalized CE
states. As the present analysis shows, the bCC approach has decisive advantages
over the conventional CI treatment, but also distinctly weaker TEO and
separability properties in comparison with a full (and hermitian) ISR method
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