Origin and evaluation of the four-spin operators in magnetic lattices

The four-spin operators are suspected to have a significant amplitude and an impact on the collective properties in spin ladders and magnetic two-dimensional lattices. They originate from cyclic circulation of electrons ~ring currents!. Starting from a simple Hubbard Hamiltonian one may establish their form from a fourth order expansion of quasidegenerate perturbation theory. This form slightly deviates from the generally assumed biquadratic expression. From a quantitative point of view, their amplitude can be assessed from accurate ab initio explicitly correlated wave functions and energies on embedded clusters. The present work shows that symmetry-broken density functional theory calculations may also provide estimates of the fourbody operator amplitudes, but reliable results require the use of a large Fock component in the exchange functiona

Approaches to dealing with high‐sized polynuclear systems with ab initio methods

This contribution sununarizes sorne of the theoretical strategies developed in the recent past to study systems with an increasing size and complexity by means of accurate extended CI calculations. Sorne examples ofthe capabilities of these strategies are also given, conceming the evaluation of magnetic exchange constants, as well as many other effective interaction parameters, such as hopping integrals, on-site Coulomb repulsion, four-body exchange term, ... on 2D and spin-ladder cuprates, polyoxovanadates, as well as polynuclear molecular compound

Accurate ab initio determination of magnetic interactions and hopping integrals in La2-xSrxCuO4 systems

The nature of magnetic interactions and electron transfer processes in La22xSrxCuO4 systems are studied, by means of an ab initio embedded cluster model approach, using a difference dedicated configuration interaction ~DDCI! procedure. For the undoped system, the crucial role played by the ligand to metal charge transfer ~LMCT! configurations in the magnetic process makes necessary the use of an enlarged DDCI space, which explicitly takes account of the relaxation of these LMCT configurations. This procedure allows us to approach the experimental magnetic coupling constant value. In hole-doped systems, the value obtained for the electron transfer integral, t, is of 0.54–0.57 eV. The extra hole, characterized from the nature and occupation of differential natural orbitals, has a strong p character ~approximately 50%! and is essentially localized in CuO2 planes. These results are in agreement with the experimental evidence about these kinds of compounds. Neither the value of t nor the nature of the extra hole are seriously affected by the optimization of the orbitals used in the CI expansion. This suggests that a t – J effective Hamiltonian is an adequate model to study the electronic properties of these system

Analysis of the magnetic coupling in binuclear complexes. II. Derivation of valence effective Hamiltonians from ab initio Cl and DFT calculations

Most interpretations of the magnetic coupling J between two unpaired electrons rest upon simple valence models that involve essentially the ferromagnetic direct exchange contribution, Kab , and the antiferromagnetic effect of the delocalization resulting from the interaction between neutral and ionic determinants, tab , whose energy difference is U. Ab initio valence-only calculations give very poor estimates of J, whatever the definition of the magnetic orbitals, and large CI expansions are required to evaluate it properly. It is, however, possible to define valence effective Hamiltonians from the knowledge of the eigenenergies and the eigenvectors of these accurate CI calculations. When applied to four different complexes, this strategy shows that spin polarization may change the sign of the direct exchange interaction, Kab , and that dynamical correlation results in a dramatic reduction of the effective repulsion U. The present article also shows how Kab , tab , and U effective parameters can be extracted from density functional theory ~DFT! calculations and that the typical overestimation of J in DFT can be attributed to an excessive lowering of the effective on-site repulsio

A general procedure to evaluate many-body spin operator amplitudes from periodic calculations: application to cuprates

International audienc

Analysis of the magnetic coupling in binuclear systems. III. The role of the ligand to metal charge transfer excitations revisited

In magnetic coordination compounds and solids the magnetic orbitals are essentially located on metallic centers but present some delocalization tails on adjacent ligands. Mean field variational calculations optimize this mixing and validate a single band modelization of the intersite magnetic exchange. In this approach, due to the Brillouin’s theorem, the ligand to metal charge transfer LMCT excitations play a minor role. On the other hand the extensive configuration interaction calculations show that the determinants obtained by a single excitation on the top of the LMCT configurations bring an important antiferromagnetic contribution to the magnetic coupling. Perturbative and truncated variational calculations show that contrary to the interpretation given in a previous article C. J. Calzado et al., J. Chem. Phys. 116, 2728 2002 the contribution of these determinants to the magnetic coupling constant is not a second-order one. An analytic development enables one to establish that they contribute at higher order as a correlation induced increase in the LMCT components of the wave function, i.e., of the mixing between the ligand and the magnetic orbitals. This larger delocalization of the magnetic orbitals results in an increase in both the ferroand antiferromagnetic contributions to the coupling constan

Four-spin cyclic exchange in spin ladder cuprates

The four-spin cyclic exchange term Jring of three spin-ladder cuprates (SrCu2O3, Sr2Cu3O5, and CaCu2O3) has been calculated from ab initio quantum chemistry calculations. For the first two compounds, a non-negligible cyclic exchange is found, aproximately 20% of the magnetic coupling across the rungs, J⊥, and always larger than the value obtained for two-dimensional La2CuO4 system. In the case of CaCu2O3, the Jring value is quite small, due to the folding of the Cu-O-Cu rung angle, but the Jring/J⊥ ratio is also 0.2 as in the two other system

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

Comprendre et traiter la corrélation électronique dans les atomes et les molécules

On visualise les différentes formes de la corrélation électronique dans l'atome (radiale, angulaire, entre sous-couches ou entre couches), et montre à quelles conditions (grâce à quels types d'orbitales atomiques) sont calculables ces diverses formes de l'énergie de corrélation. Après avoir traité de la corrélation électronique interatomique à longue portée, on s'attache à montrer que la corrélation moléculaire interne à la couche de valence consiste à imposer un ordre de charge et un ordre de spin sur le squelette moléculaire en atténuant les fantastiques fluctuations de charge et de spin qu'autorisait la description Hartrce-Fock. Il est enfin suggéré, analyses à l'appui, que le rôle essentiel des bases étendues dans les calculs moléculaires (des orbitales de polarisation en particulier) consiste à corréler les situations ioniques instantanées (au sens de la théorie Valence-Bond). Un modèle très simple est proposé pour évaluer l'effet de bases étendues sur l'énergie de liaison

Foundation of Heisenberg Hamiltonians for systems with several active electrons per centre : acetylene and polyines

A non-empirical Heisenberg Hamiltonian had been proposed for conjugated π systems from ab initio calculations on ethylene, and proved to be very efficient. Its theoretical foundation from the full Hamiltonian was evident from the concept of effective Hamiltonian and the use of Quasi-Degenerate-Perturbation Theory (QDPT), as shown by Anderson. When one wants to define a Heisenberg Hamiltonian for systems bearing two active electrons in two orthogonal Atomic Orbitals per centre, as in polyines, one may try to derive it from an accurate calculation on acetylene. The QDPT procedure does not converge, and it is shown that the direct use of the Bloch and des Cloizeaux definitions lead to ill-behaved effective Hamiltonians, which deviate strongly from a Heisenberg structure, and give erroneous results on C3H2 . A modified definition of the effective Hamiltonian is proposed, which recovers the form of a Heisenberg Hamiltonian and proves to give a reasonable spectrum of C3H2.Un Hamiltonien de Heisenberg non empirique, proposé pour des systèmes π conjugués à partir de calculs sur l'éthylène, s'était révélé très performant. Son fondement théorique découlait de façon évidente de l'Hamiltonien total, grâce à la Théorie des Perturbations Quasi Dégénérées (QDPT), comme l'a montré Anderson. Si on veut, de la même façon, définir un Hamiltonien de Heisenberg pour des systèmes comportant deux électrons actifs dans deux Orbitales Atomiques orthogonales par centre comme dans les polyines, on peut extraire l'information d'un calcul poussé sur l'acetylène. Le développement QDPT ne converge pas, et la simple application des définitions de Bloch et des Cloizeaux donne des Hamiltoniens effectifs mal conditionnés, très éloignés de la structure de Heisenberg; leur transfert à l'homologue C3H2 donne de mauvais résultats. Nous définissons un autre Hamiltonien effectif qui a bien l'allure d'un Hamiltonien de Heisenberg et qui conduit à un spectre raisonnable pour C3H2