Hartree-Fock perturbation theory for systems with one-particle perturbation

The Hartree-Fock perturbation theory for theN-electron system with a one-particle perturbation is rederived using the resolvent operator formalism. It is shown that the second-order contribution to the total energy can be expressed in a compact form using a properly defined effective one-particle operator. Relations of the Hartree-Fock perturbation theory with both the many-body theory and the regular Hartree-Fock formalism are discussed.     

Calculation of spin-density matrix by diagrammatic perturbation theory

A diagrammatic perturbation-theory method for direct calculation of spin-density matrix of open-shellN-electron systems described by the restricted Hartree-Fock one-particle functions is formulated. The formulae correct up to the second order of perturbation theory (second order in correlation effects) are presented. Their generalization to account for infinite summations of dominant correlation effects is simple, realized by making use of the so-called coupled cluster approach.     

Theoretical study of the photoelectron spectra of gaseous Cu3Cl3

Ab initio calculations have been performed to interpret the photoelectron spectrum of gaseous cuprous chloride, Cu₃Cl³. Density functional calculations revealed Cu₃Cl₃ to be a planar cyclic D_3h molecule. Koopmans' theorem and two-hole/one-particle calculations with canonical Hartree-Fock orbitals were used to interpret the vertical ionization energies. These were compared with similar calculations using B3LYP Kohn-Sham orbitals. The results confirm the claim by Casida that Kohn-Sham orbitals mimic Dyson orbitals.     

Improved uncoupled Hartree-Fock perturbation theory

Various uncoupling schemes used in the first-order Hartree-Fock perturbation theory are compared. The analysis and extraction of the most important terms in the coupled Hartree-Fock perturbation scheme leads to a definition of the new functional for the determination of the first-order perturbed orbitals. This new functional represents an alternative uncoupling scheme for the first-order Hartree-Fock perturbation theory. Some special cases of real and pure imaginary perturbations and also the connections with previously proposed uncoupling schemes are discussed.

The uncoupling procedure proposed in this paper is illustrated by electric dipole polarizability calculations for some Be- and Ne-like atomic systems. The results obtained are almost as good as those calculated by using coupled Hartree-Fock perturbation theory.     

Explicit approximate relation between reduced two- and one-particle density matrices

A class of approximation of the two-particle density matrix d₂ resembling the Hartree-Fock dependence on the one-particle density matrix d₁ is suggested. The integral relation between d₂ and d₁ is exactly maintained. An optimal choice is performed by means of the Pauli principle. The smallness of the error when applied to Coulomb systems, is qualitatively discussed. Extended Thomas-Fermi theory, as recently introduced by the authors is shortly outlined for the case of Coulomb interaction.     

Systematic study of small BN clusters

We performed a systematic investigation of the small B_xN_y (x + y? 6) clusters using the ab initio Hartree-Fock scheme plus second-order perturbation theory. The nature of the potential energy surface extrema are analyzed through analytical total energy second derivatives. Ionization potentials, binding energies and the stability against some possible reaction mechanisms are calculated. Based on these results we propose that the growing process for these clusters is mainly due to the successive incorporation of BN molecules. A discussion of some mass spectrometry experimental results is also presented. Received 2 October 2000     

Properties of the t-J model in the dynamical mean field theory: One-particle properties in the antiferromagnetic phase

We study the one-particle properties of the t-J model within the framework of Vollhardt's dynamical mean field theory. By introducing an AB-sublattice structure we explicitly allow for a broken symmetry for the spin degrees of freedom and are thus able to calculate the one-particle spectral function in the antiferromagnetic phase. We observe surprisingly rich structures in the one-particle density of states for T < T _N at finite doping up to 15%. These structures can be related to the well known results for one single hole in the Néel background. We are thus able to establish the relevance of this at a first sight academic limit to physical properties of the t-J model with a finite density of holes in the thermodynamical limit.     

Correlation energies in distorted 3<Emphasis Type="Italic">d</Emphasis>-<Emphasis Type="Italic">t</Emphasis><Subscript>2g</Subscript> perovskite oxides

Using an effective low-energy Hamiltonian derived from the first-principles electronic structure calculations for the narrow t _2g bands of YTiO₃, LaTiO₃, YVO₃, and LaVO₃, we evaluate the contributions of the correlation energy E _c to the stability of different magnetic structures that can be realized in these distorted perovskite oxides. We consider two approximations for E _c that are based on regular perturbation theory expansion around a nondegenerate Hartree-Fock ground state. One is the second order of perturbation theory, which allows comparing the effects of local and nonlocal correlations. The other is the local t-matrix approach, which allows treating some higher-order contributions to E _c . The correlation effects systematically improve the agreement with the experimental data and additionally stabilize the experimentally observed G- and C-type antifer-romagnetic (AFM) structures in YVO₃ and LaVO₃, although the absolute magnitude of the stabilization energy is sensitive to the level of approximations and is somewhat smaller in the t-matrix method. The nonlocal correlations additionally stabilize the ferromagnetic ground state in YTiO₃ and the C-type AFM ground state in LaVO₃. Among two inequivalent transition-metal sites in the monoclinic structure, the local correlations are stronger at the sites with the least distorted environment. Limitations of the regular perturbation-theory expansion for LaTiO₃ are also discussed. The text was submitted by the authors in English.     

Ab initio many-body treatment of the electronic structure of metals

We propose and apply a combination of an ab initio (band-structure) calculation with a many-body treatment including screening effects. We start from a linearized muffin-tin orbital (LMTO) calculation to determine the Bloch functions for the Hartree one-particle Hamiltonian, from which we calculate the static susceptibility and dielectric function within the standard random phase approximation (RPA). From the Bloch functions we obtain maximally localized Wannier functions, using a method proposed by Marzari and Vanderbilt. Within this Wannier basis all relevant one-particle and unscreened and screened Coulomb matrix elements are calculated. This yields a multi-band Hamiltonian in second quantization with ab initio parameters, for which screening has been taken into account within the simplest standard approximation. Then, established methods of many-body theory are used. We apply this concept to a simple metal, namely lithium (Li). Here the maximally localized Wannier functions turn out to be of the sp³-orbital kind. Furthermore, only the on-site contributions of the screened Coulomb matrix elements are relevant, and a generalized, four-band Hubbard model is justified. The screened on-site Coulomb matrix elements are considerably smaller than the band width because of which it is sufficient to calculate the selfenergy in weak-coupling approximation. We compare results obtained within the screened Hartree-Fock approximation (HFA) and within the second-order perturbation theory (SOPT) in the Coulomb matrix elements for Li and find that many-body effects are small but not negligible even for this simple metal.     

Zero-time one-particle states in quantum field theory

In the framework of the weakly-coupledP()₂-models we construct perturbation approximations of vectors of a dense set of the state space, especially vectors of the one-particle state subspace, by polynomials of zero-time fields acting on the vacuum state, with rigorous control of the remainders.     

Ab initio SCF and limited CI calculations of the d-d transitions in cobalt oxide

Ab initio calculations using an extended set of gaussian-type orbitals have been performed for the CoO₆ ^10- cluster in the Hartree-Fock approximation and with a limited configuration interaction. The results have been compared with those of crystal-field theory. CoO is found to be a very ionic system with localized d-electrons. The excited d-states may be described using a simple configuration interaction scheme, which is found to be almost equivalent to a crystal-field parameterized configuration interaction built on Hartree-Fock results. Localization and delocalization phenomena in openshell systems have been discussed.     

Bloch enhancement of electric field gradient in Fe and Cu host alloys

The Bloch enhancement factor α(k _f ) of the electric field gradient has been evaluated for the half-filledd-core Fe host metal and completely filledd-core Cu host metal in single orthogonalized plane wave (OPW) approximation. For this purpose the radially-dependent antishielding factors,γ(r) have been calculated in non-orthogonal Hartree-Fock perturbation theory (NHFPT). The results show that the contributions of antishielding to α(k _f ) from the plane wave-plane wave part and the core part of the OPW state are individually large but opposite in sign and thereby lead to partial cancellation. The net effect of antishielding on α(k _f ) is found to be − 5.6% in Fe and 14% in Cu.     

Remarks on the quantum field theory in lattice space. II

We consider a strong-coupling approach to ⁴-meson theory as formulated in a lattice space which is of simple cubic type having lattice constanta and total volumeV. Self-adjointness and regularity of the Hamiltonian are established. The strong-coupling perturbation series are examined for the cases with and without mass renormalization. The series for ground state and one-particle state as well as for their energies are shown to converge when the coupling constant is sufficiently large, say > _c (sufficient condition). The bounds _c we have found increase with the total volumeV and/or the cut-off momentuma ^–1. Some other features of the strong-coupling perturbation theory are also discussed.     

Self-consistent perturbation theory

The density matrix form of Hartree-Fock perturbation theory is developed for the case in which the basis functions themselves are perturbation-dependent. Energy expressions are derived, through second order, for both single and double perturbations.

The theory is applied in the calculation of electric dipole polarizabilities and hyperpolarizabilities for atoms (He, Be) and molecules (H₂, LiH), with excellent results. The high computational efficiency of the method is discussed and possibilities of further development are outlined.     

Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented and carried out to order (t/U)⁵ for the one-particle Green function in arbitrary dimension. The spectral weight is expressed as a Jacobi continued fraction and compared with new Monte-Carlo data of the one-dimensional, half-filled Hubbard model. Different regimes (insulator, conductor and short-range antiferromagnet) are identified in the temperature-hopping integral (T,t) plane. This work completes a first paper on the subject (Phys. Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules and higher-order results. In addition, the non half-filled case, infinite resummations of diagrams and the double occupancy are discussed. Various tests of the method are also presented. Received 25 October 1999     

Renormalization beyond the framework of the perturbation theory

By the example of a scalar field model with ϕ⁴ interaction, the possibility of separating the finite parameters beyond the framework of standard (in the interaction representation) perturbation theory is discussed. A scheme of divergence separation for large momenta and their compensation by infinite initial parameters – mass and coupling constant – is examined. The one-particle sector of the diagonal component of the total Hamiltonian admits this procedure. In this case, the energy of the one-particle spectrum has a relativistic form.     

Linear kinetic equation: long-time behavior of one-particle distribution function

We construct asymptotic (long-time) solution of the linear Boltzmann equation using the time-dependent perturbation theory generalized to non-Hermitian operators. We prove that for times much larger than the relaxation time τ₀, t ≫τ₀, one-particle distribution function separates into spatio-temporal and velocity dependent parts, and provide the explicit expression for the long-time solution of the linear Boltzmann equation. Our analysis does not assume that relative density gradients $n^{-1}(\partial / \partial \mathaccent"017E{r}) n$n^{-1}(\partial / \partial \mathaccent"017E{r}) n are small. It relates the hydrodynamic form of the one-particle distribution function to spectral properties of operators involved in linear Boltzmann equation.     

Relativistic calculation of spectra of 2-2 transitions in O- and F-like atomic ions

We have studied theoretically the structure of 1s²2s^n₁2p^n₂ levels in O- and F-like ions with z = 25 ÷ 40. Relativistic perturbation theory is used for the total interelectronic interaction. Allowance is made for Coulomb and relativistic interelectronic interactions. The first order perturbation theory for retardation of the interaction has been calculated fully. The complete calculation has also been made for the nonrelativistic correction in the second order and the Hartree-Fock part of the nonrelativistic correction in the third order. The Hartree-Fock relativistic correction in the second order has been taken into account fully for F-like ions and partially for O-like ions. Corrections to higher orders for z ? 28 have been found empirically and extrapolated to the region z = 29 ÷ 40. For energies of 2-2 transitions, calculation errors for z ? 28 do not exceed 900 cm^-1 and do not increase with z. Typical errors obtained with conventional, more cumbersome calculations are 5000 cm^-1 at z = 30.     

Interaction induced delocalization of two particles: large system size calculations and dependence on interaction strength

The localization length L₂ of two interacting particles in a one-dimensional disordered system is studied for very large system sizes by an efficient and accurate variant of the Green function method. The numerical results (at the band center) can be well described by the functional form L ₂ =L ₁ [0.5+c(U) L ₁ ] where L₁ is the one-particle localization length and the coefficient depends on the strength U of the on-site Hubbard interaction. The Breit-Wigner width or equivalently the (inverse) life time of non-interacting pair states is analytically calculated for small disorder and taking into account the energy dependence of the one-particle localization length. This provides a consistent theoretical explanation of the numerically found U-dependence of c(U). Received 16 September 1998     

Effective hamiltonian of the nuclear moments electronic shielding

An information is given allowing to use the second quantization and the effective operator methods in the ligand field theory. The operator was constructed accounting for the interaction of the multi-shell electronic configurations through a one-particle perturbation V≪R. The expression obtained is believed to be useful in microscopic calculations and phenomenological interpretation of spectroscopic experiments. As an illustration, the effective hamiltonian of the nuclear moments electronic shielding has been deduced. It was found, in particular, that the dipolar part of the hyperfine interaction contributes to the shift of the nuclear g-factor in the systems with the electronic spin S>0.