Coupled-Hartree-Fock calculations of susceptibilities and magnetic shielding constants

Coupled Hartree-Fock calculations on the susceptibilities X and magnetic shielding constants σ are reported for the title molecules. Very large gaussian basis sets have been used in order to come sufficiently close to the Hartree-Fock limit. The basis set dependence of X and σ is discussed. In addition the applicability of two methods (maximum of X [20] and closure relations [21, 22]) for the prediction of the best gauge origins is investigated.

For C₂H₂, C₂H₄ aand C₂H₆ accurate theoretical results for the complete tensors of X and σ are given for the first time. For ethylene antishielding of σ _yy ^C is observed and illustrated by means of the induced electric currents.     

Heavy fermions in transition metals and transition-metal oxides

Heavy-fermion formation in transition metals and transition-metal oxides is reviewed and compared to observations in canonical f-derived heavy-fermion systems. The work focuses on the dynamic susceptibilities which reveal a characteristic temperature and frequency dependence and which can be unambiguously determined via nuclear magnetic resonance and electron-spin resonance measurements as well as via quasielastic neutron-scattering studies. Different routes to heavy-fermion behaviour are discussed, amongst them Kondo systems, frustrated magnets, and electronically correlated systems close to a metal-insulator transition. From a theoretical point of view, utilizing dynamical mean-field theory, we show that dynamic susceptibilities as calculated for the Hubbard model and for the periodic Anderson model look qualitatively rather similar. These different theoretical concepts describe an universal behaviour of the temperature dependent dynamic susceptibility.Received: 15 May 2003, Published online: 9 September 2003PACS: 71.27.+a Strongly correlated electron systems; heavy fermions - 71.30.+h Metal-insulator transitions and other electronic transitions - 76.60.-k Nuclear magnetic resonance and relaxation - 76.30.Kg Rare-earth ions and impurities     

Semi-empirical calculations of the magnetic properties of condensed hydrocarbons

Coupled Hartree-Fock perturbation theory is used to calculate the non-local contribution to ¹H chemical shifts and magnetic susceptibilities of alternant benzenoid, alternant non-benzenoid and non-alternant conjugated hydrocarbons. It is shown that the agreement between theory and experiment is satisfactory. For the calculation of the coupled first-order orbitals a simplified iterative procedure is proposed.     

Spin-wave spectrum of a two-dimensional itinerant electron system: Analytic results for the incommensurate spiral phase in the strong-coupling limit

We study the zero-temperature spin fluctuations of a two-dimensional itinerant-electron system with an incommensurate magnetic ground state described by a single-band Hubbard Hamiltonian. We introduce the (broken-symmetry) magnetic phase at the mean-field (Hartree-Fock) level through a spiral spin configuration with characteristic wave vector Q different in general from the antiferromagnetic wave vector Q _AF, and consider spin fluctuations over and above it within the electronic random-phase (RPA) approximation. We obtain a closed system of equations for the generalized wave vector and frequency dependent susceptibilities, which are equivalent to the ones reported recently by Brenig. We obtain, in addition, analytic results for the spin-wave dispersion relation in the strong-coupling limit of the Hubbard Hamiltonian and find that at finite doping the spin-wave dispersion relation has a hybrid form between that associated with the (localized) Heisenberg model and that associated with the (long-range) RKKY exchange interaction. We also find an instability of the spin-wave spectrum in a finite region about the center of the Brillouin zone, which signals a physical instability toward a different spin- or, possibly, charge-ordered phase, as, for example, the stripe structures observed in the high-T _c materials. We expect, however, on physical grounds that for wave vectors external to this region the spin-wave spectrum that we have determined should survive consideration of more sophisticated mean-field solutions. Received 15 September 2000     

Spin susceptibilities and the theory of itinerant-electron antiferromagnetism

This article investigates the equilibrium states of antiferromagnetic itinerant-electron systems in the Hartree-Fock approximation. As a result, the spin susceptibilities are determined in the random phase approximation. The lowlying collective excitations are then obtained by finding the poles of these susceptibilities.

We start by giving a brief review of the Hartree-Fock procedure and by indicating how the susceptibilities are obtained. The density matrix approach, where the ground state is interpreted as that minimizing the energy, is used throughout. Using an effective Coulomb interaction of the Hubbard type we consider two distinct systems: a one-band system with an incommensurate spin density wave in its ground state, and a many-band simply commensurate model for f.c.c. manganese.

The first of these is such that the band structure and resulting susceptibilities can be obtained explicitly. The spin-wave energies and wave-vectors are found by a careful, small energy and momentum transfer, expansion of these susceptibilities for the case of a parabolic band. The spin-wave damping, which is shown to arise from spin-wave decay into quasiparticle quasihole pairs, is also obtained for this band structure.

For the case of f.c.c. manganese the antiferromagnetic bands are obtained from a realistic 9-band paramagnetic model by using a many-band generalization of the Hubbard interaction. The enhanced spin susceptibilities are calculated, using the tetrahedral Brillouin zone integration method, and are presented along with their associated collective excitations. The results obtained are discussed with particular reference to the many-band effects. These effects are shown to be very much dependent on the particular form of interaction used.     

Compensation temperatures,magnetic susceptibilities and phase diagrams of a mixed ferrimagnetic ternary system on the Bethe lattice

Compensation behaviors, magnetic susceptibilities and the phase diagrams of the ternary system of the type ABC consisting of Ising spins σ = 1/2, S = 3/2 and m = 5/2 in the presence of a single-ion anisotropy are studied on the Bethe lattice within the framework of the exact recursion relations. Both ferromagnetic and antiferromagnetic exchange interactions are considered. The exact expressions for sublattice magnetizations and magnetic susceptibilities are obtained, and then thermal behaviors of the sublattice magnetizations, total magnetization, magnetic sublattice susceptibilities and total susceptibility are investigated. We find that the system only undergoes a second order phase transition for the different and same bilinear nearest-neighbor exchange interaction parameters, but displays compensation behaviors for only different bilinear interaction parameters. We also present the phase diagrams for the different and same bilinear nearest-neighbor exchange interaction parameters. A comparison is made with the other ternary system of the type ABC consisting of different spin values.     

Problems and prospects for an AB-Initio Hartree-FockPerturbed-Cluster treatment of local defects in ionic solids

Abstract

This paper presents a new theoretical technique for the study of defects in crystals. The methods is based on an ab-initio Hartree-Fock perturbed-cluster (PC) scheme¹. A prerequisite for this technique is the availability of a model for the host, perfect crystal, that must be obtained with the same Hamiltonian and the same computational conditions (basis set, accuracy etc.). This information is provided by CRYSTAL, an ab-initio periodic Hartree-Fock code².     

Electronic structure of Mott insulators

Mott insulators are identified here with ordinary magnetic insulators. The insulating gap, local moment, and effective spin hamiltonian aspects are qualitatively explained by means of a novel set of solutions of the Hartree-Fock equations. The apparent conflict between Bloch's theorem and localized-electron phenomenology is thereby resolved in an elementary manner. This Hartree-Fock approach also sheds considerable light on the physical mechanisms responsible for the associated metal-insulator (Mott) and other related phase transitions, as observed in V₂O₃ and several other materials. With some generalizations and refinements, this theoretical picture is shown to also account semiquantitatively for a number of detailed properties of NiO and CoO, two of the most extensively studied Mott insulator materials. A wide variety of experimental data for NiO is surveyed in order to determine reasonable values for its effective Hubbard hamiltonian parameters, suitably generalized for the 3d electrons. The problems of formally deriving effective spin hamiltonians for macroscopic magnetic insulator systems are also carefully examined. The old non-orthogonality catastrophe is fully resolved by means of a degenerate (open-shell) analogue of the linked cluster perturbation expansion of Brueckner and Goldstone. Although many quantitative issues remain, these results indicate that there is now a reasonably adequate conceptual understanding of the Mott insulating state.     

Low-field magnetic properties of anhydrous NiCl2

Results are reported for the low-field magnetic susceptibilities and the low temperature isothermal magnetization of anhydrous NiCl₂. The theoretical analysis, based on a molecular field model, leads to precise values for certain of the magnetic parameters.     

Theory of magnetic susceptibilities and N.M.R. chemical shifts in terms of localized quantities

A method based on Individual Gauge for Localized (molecular) Orbitals (IGLO) proposed recently has been applied to a study of the magnetic susceptibilities and the chemical N.M.R. shifts of the molecules N₂, HCN, CO, C₂H₂, CO₂, N₂O, O₃, FNO and OF₂. Large basis sets have been used and the results are presumed to be close to the Hartree-Fock limit. The agreement with experiment is fair as far as reliable experimental data are available (both for the isotropic shifts and the anisotropies), although it seems that the present calculations overestimate somewhat the paramagnetic contributions. Possibly correlation effects, neglected so far, play a rôle here. Ozone is a quite exceptional molecule in several respects; it is van Vleck paramagnetic, there is extreme antishielding of the nuclei and the dependence of both χ and σ on small changes of the geometry is fantastic.     

Critical behavior of a mixed ferrimagnetic ternary alloy on the Bethe lattice

The critical behavior of the mixed Ising model of the type AB _p C_1−p ternary alloy consisting of spins σ = 1/2, S = 1, and m = 3/2 is investigated on the Bethe lattice by using the exact recursion relations. The exact expressions for the magnetizations and magnetic susceptibilities are found, and the thermal behaviors of the magnetizations and susceptibilities are studied. The magnetizations and susceptibilities have also been investigated as functions of the crystal-field interaction or single-ion anisotropy. The phase diagram has been constructed according to which the system always undergoes a second-order phase transition for the coordination number q ≤ 3 and second-and first-order phase transitions for q > 3; hence, the system has a tricritical point. The system also exhibits reentrant behaviors. The text was submitted by the authors in English.     

Magnetism in Rh clusters under hydrostatic deformations

The magnetic behavior of rhodium clusters Rh_N (N = 4-38) under hydrostatic deformations was investigated. The starting cluster structures were obtained from an evolutionary search algorithm applied to a Gupta potential. The spin-polarized electronic structure and related magnetic properties were calculated using a self-consistent spd tight-binding Hamiltonian within the unrestricted Hartree-Fock approximation. The magnetic behavior was analyzed in terms of the interdependence between the geometrical parameters and the electronic structure. Anomalous magnetic effects were found in some cases. Received 5 August 2002 / Received in final form 10 January 2003 Published online 4 March 2003 RID="a" ID="a"e-mail: berlanga@dec1.ifisica.uaslp.mx     

Temperature dependence of the coefficient of self-diffusion in liquids

The effect of the hydrogen bonding on the magnetic anisotropy of o-halogenobenzoic acids and some derivatives of phenol, namely 2-aminophenol, 2,3-dimethylphenol and 2-methyl-3-bromophenol, is studied. These molecules are of known crystal structures. The crystal susceptibilities (x ₁, x ₂ and x ₃) of each compound were measured. From these measurements and the molecular orientation, the principal molecular susceptibilities (K ₁, K ₂ and K ₃) have been calculated. The observed magnetic data are interpreted in the light of the structures of these molecules and their hydrogen bonding systems.     

Third-order diamagnetic susceptibilities of hydrogenlike atoms

We develop a method for calculating diamagnetic susceptibilities based on higher-order perturbation theory for the wave function and energy of the excited states of the hydrogen atom with degeneracy of arbitrary multiplicity. We derive analytical expressions for third-order matrix elements in the spherical states |nlm〉 with fixed principal quantum number n and magnetic quantum number m. The formulas for the susceptibilities of doubly degenerate levels are represented in the form of radical-fractional relationships containing polynomials in the principal quantum number. We establish the existence of a monotonic interdependence between the absolute values of susceptibilities of the first three orders. We also present the results of numerical calculations for the states with n⩽6 and m⩽3 mixed by the field. Finally, for Rydberg states with large n and small m we detect the existence of a discontinuity in the interdependence of the susceptibilities at the boundary between the doublet and equidistant parts of the spectrum of diamagnetic sublevels with opposite parities. Zh. éksp. Teor. Fiz. 116, 838–857 (September 1999)     

Experimental and theoretical lifetimes in Yb III

Lifetimes of three levels belonging to the configuration 4f ¹³5d with J = 1 in Yb III have been measured for the first time using the time-resolved laser-induced fluorescence method. Experimental transition probabilities have been deduced for the transitions between the levels studied and the ground state. The comparison of the experimental lifetimes with theoretical data, deduced within the relativistic Hartree-Fock (HFR) approach, underlines the dramatic importance of an adequate consideration of core-polarization effects in the theoretical model and the sensitivity of one of the lifetime values to small correlation effects. Received 2 April 2001     

Influence of the carbon substitution on the critical current density and AC losses in MgB<Subscript>2</Subscript> single crystals

The DC magnetization and AC complex magnetic susceptibilities were measured for MgB₂ single crystals, unsubstituted and carbon substituted with the composition of Mg(B_0.94C_0.05)₂. The measurements were performed in AC and DC magnetic fields oriented parallel to the c-axis of the crystals. From the DC magnetization loops and the AC susceptibility measurements, critical current densities (J _c were derived as a function of temperature and the DC and AC magnetic fields. Results show that the substitution with carbon decreases J _c ) at low magnetic fields, opposite to the well known effect of an increase of J _c at higher fields. AC magnetic losses were derived from the AC susceptibility data as a function of amplitude and the DC bias magnetic field. The AC losses were determined for temperatures of 0.6 and 0.7 of the transition temperature T _c , so close to the boiling points of LH₂ and LNe, potential cooling media for magnesium diboride based composites. The results are analyzed and discussed in the context of the critical state model.     

Large scale multi-configuration Hartree-Fock calculation of the hyperfine structure of the ground state of vanadium

The hyperfine structure of the ground state of vanadium, ⁵¹VI, is calculated in the nonrelativistic framework of the multi-configuration Hartree-Fock approximation. A configuration state function limiting algorithm is used to make the calculations feasible and to study the influence of core, valence and core-valence correlations in detail. The obtained configuration state function space captures the most important orbital correlations within 2%. Further correlations are included through configuration interaction calculation. The atomic state functions are used to evaluate the magnetic dipole hyperfine factor A and the electric quadrupole factor B. It turns out that the ab initio calculation can not capture the core polarization of the 2s shell. It introduces an error that is higher than the Hartree-Fock approximation. However, the detailed correlations being observed suggest the introduction of a wrong correlation orbital due to the algorithm being used. Neglecting this orbital leads to good agreement with 2% deviation from the experimental values for the A factors.     

The impact of laser field statistics in determination of temperature and concentration by multiplex USED CARS

Experiments have been performed which demonstrate that the ratio of resonant to nonresonant third-order susceptibilities measured in multiplex USED CARS are affected by the time correlation of the pump fields. Comparing the resonant to nonresonant signal ratio obtained with decorrelated fields to the ratio obtained with correlated fields, a relative increase of 2.5 was measured for the nitrogen Q-branch, whereas a corresponding increase of 1.9 was observed for the hydrogen Q(1)-line. To compare our experimental results with theoretical calculations of the spectral shapes, the nonresonant third-order susceptibilities of a number of gases were re-evaluated by calibrating to the nonresonant susceptibility of argon.     

Electronic structure of high-T c superconductors and related compounds

We study a 5-band Hubbard model for the CuO₂ planes in cuprate super-conductors using Hartree-Fock mean-field theory including spiral spin density waves. For the half-filled case we recover a ZSA-like phase diagrambut with an additional new region characterized by strong covalency effects, which we call a covalent insulator region. We also provide a nonperturbative calculation ofJ _eff, the effective in-plane antiferromagnetic interaction, as a function of parameters of the model. We suggest that the high-T _c cuprates are in or very close to the covalent insulator region and within this we show that a consistent explanation of apparently conflicting high energy spectroscopic and magnetic measurements of the high-T _c cuprates can be given.     

Effect of interlayer tunneling on the electronic structure of bilayer cuprates and quantum phase transitions in carrier concentration and high magnetic field

We present a theoretical study of the electronic structure of bilayer HTSC cuprates and its evolution under doping and in a high magnetic field. Analysis is based on the t-t′-t″-J* model in the generalized Hartree-Fock approximation. Possibility of tunneling between CuO2 layers is taken into account in the form of a nonzero integral of hopping between the orbitals of adjacent planes and is included in the scheme of the cluster form of perturbation theory. The main effect of the coupling between two CuO₂ layers in a unit cell is the bilayer splitting manifested in the presence of antibonding and bonding bands formed by a combination of identical bands of the layers themselves. A change in the doping level induces reconstruction of the band structure and the Fermi surface, which gives rise to a number of quantum phase transitions. A high external magnetic field leads to a fundamentally different form of electronic structure. Quantum phase transitions in the field are observed not only under doping, but also upon a variation of the field magnitude. Because of tunneling between the layers, quantum transitions are also split; as a result, a more complex sequence of the Lifshitz transitions than in single-layer structures is observed.