Local Ansatz Research Articles

AB-INITIO CALCULATION OF CORRELATION EFFECTS IN METALLIC LITHIUM

We present an ab initio calculation of the correlation effects in metallic lithium. The calculation is carried out based on the use of local operators (Local Ansatz), where correlations are included as corrections to the Hartree-Fock (HF) ground state. We investigate the strength of longer range correlations and their dependance on distance, which allows us to discuss complementary findings to LDA results. The correlation contributions to the binding energy are extracted. The missing longer range correlations can be estimated. Effects of correlations on the bulk modulus, lattice constant and charge fluctuations are analysed. The structural phases of Li with bcc- and fcc-symmetry are compared.

Temperature-dependent phase separation within the Emery model.

The variational principle of Bogoliubov, combined with a canonical transformation, is used to derive the thermodynamic functions for the hole-doped two-dimensional Emery model of the copper-oxygen planes in high-temperature-superconducting (HTSC) materials. A local ansatz and a transformation optimized for small values of the ratio of the hopping constant to the Coulomb correlation gives the lowest free energy in the neutral case and in the case of moderate doping. The regions of thermodynamic instability in the curves of the chemical potential versus doping, as coexistence regions of phase separation, are determined numerically with use of a Maxwell construction. In the high-doping regime, the coexistence regions are reduced considerably by the condition that the strong-coupling result is the lowest one, better than, e.g., the standard Hartree-Fock solution. The phase diagram of paramagnetic, ferromagnetic, antiferromagnetic, and separated phases is given. The parameter dependence of the maximum temperature of phase separation shows the same tendency as the empirical parameter dependence of the HTSC transition temperatures.

Electronic correlations with inclusion of one-particle operators

When dealing with electronic correlations, the latter are often treated without considering changes in the one-particle density. This is a good approximation in systems in which electronic correlations are sufficiently weak, but it is not justified any longer when they become strong. The treatment of electronic correlations within the local ansatz is generalized by the inclusion of one-particle operators. Nonorthogonalized local operators are used for their description. The generalized scheme allows also for an improvement of self-consistent field calculations by including the effects of a larger basis set via one-particle operators.

Electronic correlations of cubic boron nitride.

We have calculated total and binding energies of zinc-blende-structure boron nitride. Starting from a self-consistent-field ground-state calculation within a finite basis of Gaussian orbitals centered at the different atoms, the electron correlations were treated by applying the local ansatz. The electronic correlations are predominantly short ranged, as was also found for its isostructural compound, diamond. Of specific importance are correlations on the atomic scale. Electrons correlate strongly at the nitrogen atoms. The correlation strength within the B-N bonds and the reduction of the total-atomic-charge fluctuations is discussed in detail. For an agreement between calculated and experimental binding energies, additional basis functions on interstitial sites turned out to be necessary. Without them, correlations in the interstitial regions are too poorly covered. Such an effect should be relevant for all future calculations on open-structure materials. The final results for the binding energy compare well with calculations made within the local-density approximation.

Material properties of low-dimensional charge-transfer salts. I. Charge fluctuations in systems with stronger electronic correlations

We derive the necessary electronic conditions allowing for a coincidence of remarkable charge fluctuations 〈(Δ n i 2 )〉 and strong electronic correlations in quasi one-dimensional synthetic metals. The 〈(Δ n i 2)〉 curves show maxima for localized electrons in the case of on-site (intramonomer) electron densities of 0.5 and 1.5, respectively. The formation of an insulating Mott state with completely suppressed fluctuations is thereby prevented. Only one maximum in the 〈Δ n i 2〉 curve for an on-site density of one is found in the independent-particle limit as well as for weaker correlated electrons. The strength of the interatomic correlations of the conduction electrons is characterized by two quantities, Δ i and Σ i, measuring the reduction of the charge fluctuations in the correlated ground state. The phase diagrams of the quasi-one-dimensional metals are critically discussed. It is shown that electron-electron Umklapp-scattering leads to an enhancement in the charge-density wave response function. The Peierls transition temperature T P is enhanced correspondingly. The many-particle effects are studied by a local ansatz, the modification of T P as a function of the correlation strength by the renormalization group approach. The theoretical findings are compared with available experimental results on organic and organometallic materials.

Why polyacetylene dimerizes — Conclusive results of ab-initio computations

Results of ab-initio computations for a single chain of trans-polyacetylene are reported. Starting from self-consistent field calculations within a Gaussian type orbital basis set, correlations are included by using the Local Ansatz. The dependence of the total energy on dimerization is then analyzed in order to explain the origin of dimerization. The position of the equilibrium dimerization is dominantly determined by atomic correlation effects. Contributions to the exchange energy from nearest neighbor Coulomb interactions play a nonnegligible role concerning the depth of the energy minimum although their strength is strongly reduced in comparison to self-consistent field results. Electron-lattice coupling alone leads only to a marginal dimerization. These findings are in contrast to assumptions often made in connection with soliton theories.

Coupled-cluster-equations for the local ansatz

A new approximation is presented for calculations within the Local Ansatz, a scheme that allows to perform ab-initio correlation calculations for solids. While the approximations made so far when using this method do not give a perfect treatment of long range screening, this modification is able to handle them well. In addition a few more strongly correlated cases than before can be accounted for, although one is still far from treating the strongly correlated limit in general. The approximation consists in solving the complete Coupled-Cluster-equations in the subspace of those local two-particle operators constructed by the Local Ansatz. Such a treatment does not require sizeable additional computational costs as compared with the approximation made so far.

Electronic structure and correlations of high-temperature superconducting compounds.

Calculations on negatively charged planar ${\mathrm{Cu}}_{\mathit{n}}$${\mathrm{O}}_{\mathit{m}}$ clusters are reported. Starting from a self-consistent-field calculation within a good Gaussian-type-orbital basis set, correlations are included using the local ansatz. A charge analysis reveals a Cu 3d occupation in close agreement with calculations in the local-density approximation. The electrons in the formal ${\mathrm{Cu}}_{\mathit{n}}^{2+}$${\mathrm{O}}_{\mathit{m}}^{2\mathrm{\ensuremath{-}}}$ entities are delocalized between Cu and O sites and strongly correlated. Our findings do not agree with the assumption of localized ${\mathrm{Cu}}^{2+}$ spins which is often made in models for these compounds. Spin correlations indicate strong short-range antiferromagnetic order even if electrons are removed. For them, there is no difference between O and Cu sites.

Why polyacetylene dimerizes: Results of ab initio computations.

Results of ab initio computations for a single chain of trans-polyacetylene are reported. Starting from self-consistent-field calculations within a Gaussian-type-orbital basis set, correlations are included by using the local ansatz. The dependence of the total energy on dimerization is then analyzed in order to explain the origin of dimerization. The position of the equilibrium dimerization is dominantly determined by atomic correlation effects. Contributions to the exchange energy from nearest-neighbor Coulomb interactions play a non-negligible role concerning the depth of the energy minimum although their strength is strongly reduced in comparison to self-consistent-field results. Electron-lattice coupling alone leads only to a marginal dimerization. These findings are in contrast to assumptions often made in connection with soliton theories.

The validity of the local approximation in Penning ionization as studied by model calculations

In the theoretical treatment of Penning ionization A* + B→A+ B+ + e− it is standard to describe the nuclear motion in the entrance channel A* + B by a local complex potential. The motivation stems from the conceptual simplicity of the local potential operator compared to the nonlocal formulation and from the necessity to economize in computer time. In all practical calculations the local ansatz has worked well so far. Observed discrepancies between calculated and experimental data have never unambiguously been assigned to a failure of the local approximation. However, a numerical test on its validity by comparing to nonlocal calculations has not been carried out. The present study shows by means of model calculations that Penning ionization can very well be treated within the local theory. It turns out that the coupling to the Rydberg family A+B* is vital for the validity of the local ansatz in situations where the electron energy spectrum extends to small or even zero energy. This finding shows that for practical calculations Penning ionization differs from the related process of collisional detachment even though the formal theory can be written down the same way.

Doping dependence of hole distribution in CuO2 planes of high-Tc superconductors: Local ansatz versus exact results.

The hole distribution within a ${\mathrm{CuO}}_{2}$ plane, a common structural element of high-temperature superconductors, is investigated as a function of doping by holes. The correlated ground state of a three-band Hubbard model is found by making use of a local ansatz which includes local correlations between holes. It is found that doped holes have \ensuremath{\sim}70% oxygen character for the parameters determined from the local-density approximation, in agreement with experimental observations, while hole droplets on oxygen orbitals are formed for large copper-oxygen Coulomb repulsion, ${\mathit{U}}_{\mathit{d}\mathit{p}}$. All our results agree with those obtained from finite-cluster diagonalization.

Effects of electron correlations on energy bands of semiconductors: A projection-technique treatment

A recently developed method based on projection techniques is applied to the computation of electron correlations in excited states of semiconductors. In particular it is shown that the method is able to reproduce the results previously obtained by applying the variational Local Ansatz. The advantages of the present approach are its conceptual simplicity and that it can be applied not only to weakly but also to strongly correlated electronic systems.

Electronic charge distributions and correlations in highT c superconducting compounds

Calculations on negatively charged planar Cu n O m clusters are reported. Starting from a self-consistent field calculation within a good Gaussian-type orbital basis set, correlations are included by using the Local Ansatz. A charge analysis reveals that the Cu 3d occupation is 9.5, in close agreement with Local Spin Density calculations. The electrons in the formal ((CuO2)2−) n entities are delocalized between Cu and O sites and strongly correlated. Our findings do not agree with the assumption of localized Cu2+ spins which lead to thet-J model. Spin correlations indicate strong short-range antiferromagnetic order even when additional electrons are removed. For them, there is no difference between O and Cu sites.

Application of projection techniques to the electron correlation problem

By applying projection techniques a unified description of weakly and strongly correlated electronic systems can be given. For that purpose the theory is formulated in Liouville instead of Hilbert space. By introducing an appropriate metric in terms of cumulants it is ensured that all energies are size consistent. An energy expression is derived which is a generalization of Goldstone’s linked cluster theorem for arbitrary Hamiltonians. It is suitable for applying the projection method of Zwanzig and Mori. The equations for the correlation energy within the Local Ansatz and within coupled electron pair approximation CEPA-2 follow straightforwardly from the present theory.

Electronic correlations in polyethylene

Results of a correlation calculation for the ground state of polyethylene, as obtained within the local ansatz, are presented. The starting point is a SCF ground state calculated within a double-zeta basis. For the correlation part, the basis is extended by including a set of polarization functions on each atom. The correlation computations are inexpensive and fast converging. On correcting for finite basis set deficiencies, an estimate of the binding energy is obtained which is very close to experiment. Pair correlation functions are also discussed. These compare well to those obtained previously for small hydrocarbon molecules and diamond, where similar bond patterns occur. The computation scheme itself contains a new feature, which allows for an improved use of the translational symmetry.

Physical picture of electron correlations in three-center four-electron bonds

It is shown that the strong electron correlations of π electrons in the O3 molecule may be well understood in terms of a simple analytic model which is a natural extension of a bond orbital approximation to the case of a three-center bond. Electron correlations are here responsible for the increase of density at the central atom and for enhanced correlations at both terminal ones. This result is confirmed by a numerical calculation of the interatomic correlations by using a local ansatz imposed on a semiempirical selfconsistent field ground state. It is argued that the discussed increase of the bond polarity in the O3 molecule is a universal phenomenon for three-center bonds filled (on the average) by more than one electron per atom, as, for example within the CuO2 planes of Cu based perovskites.

Mixed state quantum mechanics in hydrodynamical form

A newly derive set of quantum fluid dynamical equations appropriate for the description of mixed state dynamics is presented. Based essentially on moments of the Wigner function, the theory presented here uses an expansion of the pseudodistribution function in conjunction with a renormalization technique to obtain a semiclassical approximation for the dynamics of the probability, probability current, and energy densities. Particularly simple equations, ideal fluid dynamics with a nonlocal potential, result from using a local Maxwellian ansatz for the Wigner function. Further, the transformed potential may be easily computed from the fields being convected. Analogies with classical kinetic theory and fluid dynamics are exploited whenever possible.

A time-dependent variational principle and the time-dependent Hartree approximation in hydrodynamical form

A quantum mechanical time-dependent variational principle is generalized using the classical theory of fluids to obtain a variational principle suitable for the fluid dynamical description of mixed state quantum mechanics. A newly derived set of moment equations, in both standard and renormalized form, can be derived with the aid of this principle through minimization of the error in expressing the total derivative of the Wigner function. Coupled systems are studied in the time-dependent Hartree (TDH) approximation using a novel variational principle, and the renormalization procedure used earlier in the examination of single particle dynamics is extended to the TDH analysis. Use of a local Maxwellian ansatz for each particle results in a particularly simple ‘‘two-fluid’’ theory, the TDH/LM approximation, which does not violate the standard and renormalized energy conservation theorems derived earlier for the single particle equations. The fluid dynamical TDH/LM approximation is shown to possess a simple semiclassical interpretation.

Electron correlations in the ground state of silicon.

Ab initio correlations calculations for the ground state and for the binding energy of silicon are presented. As a starting point we use a self-consistent-field ground state as determined within the local-density approximation. Electron correlations are treated by applying the local ansatz. As in the case of diamond the important correlations are predominantly short ranged. They are similar to the ones in small molecules with Si-Si bonds. The contribution of electron correlations to the binding energy is of the order of 25%. The accuracy of the present approach is discussed. A comparison with the results of the local-density approximation is provided.

Two-phonon frequency difference absorption in Si and Ge

We measure the infrared absorption of crystalline silicon and germanium up to the one-phonon Raman frequency for temperatures between 10 and 300 K. We observe several peaks whose strength increases with increasing temperature. Calculations of the absolute two-phonon frequency difference absorption using Weber's adiabatic bond charge model and a local charge transfer ansatz based on phonon-induced bond length distortions to model the dipole moments yield satisfactory agreement with the experimental spectra.