Stationary perturbation theory for atoms with two open shells in the Hartree-Fock approximation

Within the Hartree-Fock method, we have obtained equations of stationary “coupled” perturbation theory for multielectron systems with two open shells of different symmetry types (Huzinaga method) in the orbital representation. Corrections to the Hartree-Fock orbitals were determined in the form of expansions in unperturbed orbitals, which were calculated in the LCAO approximation in a basis of Slater-type atomic orbitals. Using an optimized basis set of atomic orbitals, we calculated the static polarizability for a number of atoms with two open shells. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 6, pp. 726–730, November–December, 2007.     

Hartree-fock equations for atoms with two open shells

We have formulated the Hartree-Fock equations for multielectron systems with two open shells (the Huzinaga method) in terms of the density matrix in the LCAO approximation. In order to solve the Hartree-Fock equations, in the algebraic approximation we have obtained expressions for the derivatives of the energy with respect to the density matrix elements and the nonlinear atomic orbital parameters (the orbital exponents). We discuss the question of calculating the open shell parameters (the vector coupling coefficients) in the configurations s¹p^N and s¹d^N within the Huzinaga method. We have calculated the energy for a series of atoms with two open shells in these configurations. Using rather narrow basis sets of Slater-type atomic orbitals), we have obtained energy values close to the results of a numerical solution of the Hartree-Fock equations with sufficiently high accuracy of the virial ratio. __________ Translated from Zhurnal Prikladnoi Spektroskopii, Vol. 74, No. 2, pp. 145–152, March–April, 2007     

Mössbauer effect study of the hyperfine fields and isomer shift of ordered Fe−Co alloys

The influence of Co concentration on the⁸⁷Fe hyperfine magnetic field and isomer shift in ordered and disordered FeCo alloys in the composition range (34–70) at .% is studied. It is shown that the model which assumes an additivity of the hyperfine field perturbation from solutes in the first two nearest neighbour shells of Fe nucleus very well describes the experimental data.     

DFT calculation of geometrical structure and electronic absorption spectra for neutral,mono-, and diprotonated forms of Risperidone (Risperdal)

Vertical electronic transitions to singlet valence states of an antipsychotic drug, Risperidone (Risperdal), in its neutral, mono-, and diprotonated forms have been calculated within the time-dependent density functional theory using the PBE0 hybrid functional with the 6–31+G^* basis set. The results of the computations show that the lowest-energy allowed π–π^* electronic excitation is affected by protonation effects, the spectral shifts of this transition being potentially useful to individuate the different forms of risperidone     

SU(3) coupling schemes for odd-odd nuclei in the interacting boson – fermion – fermion model with both odd proton and odd neutron in natural parity orbits

The SU^BFF(3) dynamical symmetry limits of interacting boson – fermion – fermion model are identified and they are appropriate for heavy deformed odd – odd nuclei for configurations with both the odd proton and odd neutron occupying all the natural parity orbits in the corresponding valence shells. There are three symmetry limits and their correspondence with two quasi-particle (proton-neutron) Nilsson configurations is established; one of the limits mixes both Nilsson n_z's and Λ's and other two limits mix only Nilsson Λ's. The ¹⁹¹Ir (d,t) ¹⁹⁰Ir single nucleon transfer spectroscopic strengths are well described by one of the symmetry limits that mixes only Nilsson Λ's. Received: 22 June 1998     

Point defects in FeAl

Summary Point defects in annealed B2-phase FeAl samples in the range 47–53 at.% Fe were studied using⁵⁷Fe M?ssbauer spectroscopy. Spectra were analyzed using local environment models according to which point defects in atomic shells close to probe atoms induce shifts in the nuclear monopole interaction. For well-annealed samples, better results were obtained assuming only the presence of Fe_Al antisite and V_Fe vacancy defects, and not of Al_Fe antisite defects. Monopole interactions of⁵⁷Fe probes on the Fe and Al sublattices having no defects in the first two shells were about +0.27 and −0.03 mm s⁻¹, respectively, with respect to Fe in alpha-Fe metal. The shifts induced by Fe_Al and V_Fe defects in the first shells of Fe probes on the Fe and Al sublattices were −0.15 and −0.24 mm s⁻¹, respectively, and, in the second shells, +0.06 and +0.011 mm s⁻¹. In addition to structural defects needed to accommodate deviations from stoichiometry, annealed samples were found to contain several percents of Fe_Al and V_Fe defects due to lattice disorder, with greater disorder in Fe-deficient alloys. Paper presented at the ICAME-95, Rimini, 10–16 September 1995.     

Early Universe with Variable Gravitational and Cosmological Constants

Einstein field equations are considered in zero-curvature Robertson–Walker (R–W) cosmology with perfect fluid source and time-dependent gravitational and cosmological “constants.” Exact solutions of the field equations are obtained by using the ’gamma-law' equation of state p = (γ − 1)ρ in which γ varies continuously with cosmological time. The functional form of γ (R) is used to analyze a wide range of cosmological solutions at early universe for two phases in cosmic history: inflationary phase and Radiation-dominated phase. The corresponding physical interpretations of the cosmological solutions are also discussed.     

Hartree–Fock self-consistent field method for atoms with two open shells of identical symmetry

A generalization of the Roothaan–Bagus method (Roothaan–Hartree–Fock atomic theory) on atoms with open shells of identical symmetry is given. Using orbital exponents of Slater-type atomic orbitals optimized with high accuracy by methods for the minimization of the first and second orders, energy values for atoms with two open s-type shells are calculated within the limits of the Roothaan–Hartree–Fock atomic theory.     

H<Superscript>+</Superscript><Emphasis Type="Bold">and He</Emphasis><Superscript>2+</Superscript> impact single and double ionization of lead

H⁺ and He²⁺ impact single and double ionization cross sections of ground state lead atoms have been calculated in the binary encounter approximation. Calculations of direct double ionization cross sections have been performed in the modified double binary encounter model. The accurate expressions of σ_ΔE (cross-section for energy transfer ΔE) and Hartree-Fock velocity distributions for the target electrons have been used throughout the calculations. Contributions to double ionization from Auger effect following ionization of inner shells have been considered in the present work. Our H⁺ impact single and double ionization cross sections are in good agreement with the experimental observations. In calculations of He²⁺ impact cross sections, the present theoretical approach shows limited success in the experimentally investigated region (50–350 keV amu^-1).     

Calculation of open p-shell atoms in the algebraic approach of the Hartree–Fock method

Highly precise calculations of analytical Hartree–Fock orbitals and energies have been performed within the limits of the Roothaan–Hartree–Fock atomic theory (Roothaan–Bagus method) for all open p-shell atoms of the Periodic Table. They were calculated in an algebraic approach using Slater-type atomic orbitals (AOs) as basis functions. Nonlinear parameters (orbital exponents) of AOs were optimized with exceptional accuracy by second-order methods. As a result, it was possible to satisfy exactly the virial relation (10^–14–10^–17) with calculated atomic term energies being close to the Hartree–Fock limit.     

Fluctuating Electric Field Gradients at 111Cd in Ice

¹¹¹Cd–PAC measurements have been made using the high specific activity of ¹¹¹In in the methanol–water mixtures of various concentrations at the room temperature. These experiments revealed that the perturbation factors 〈A ₂ G ₂〉 (integrated over two mean lives τ_N) do not follow the dependence of the macroscopic viscosity η. The observed dynamic character of the PAC spectra in ice is explained by the mobility of orientational and ionic defects. The activation energy for the diffusion process was determined to be E _a =0.35(1) eV. This revised version was published online in September 2006 with corrections to the Cover Date.     

Stark Broadening of F III Lines in Laboratory and Stellar Plasma

Using a semiclassical approach, we have considered electron-, proton-, and ionized helium-impact line widths and shifts for the F III 2p^{3 4}S^o-3s ⁴P resonant line. Moreover, for 10 F III multiplets where the full semiclassical perturbation approach is not applicable in an adequate way due to the lack of reliable atomic data, electron-impact line widths have been calculated within the modified semiempirical approach. Results are obtained as a function of temperature for perturber density of 10¹⁷ cm⁻³. The theoretical data obtained have been used to consider the influence of Stark broadening for A-type star atmosphere conditions. __________ Published in Zhurnal Prikladnoi Spektroskopii, Vol. 72, No. 3, pp. 412–415, May–June, 2005.     

A new method of quantization of classical solutions

The stochastic quantization method of Parisi and Wu is used to derive exact equations for the correlators of quantum fluctuations around the classical solution in the massless φ ⁴ theory. The equations obtained are then solved in the lowest orders of perturbation theory, and the first correction to the free propagator of a quantum fluctuation is calculated. Pis’ma Zh. éksp. Teor. Fiz. 63, No. 5, 381–386 (10 March 1996) Publsihed in English in the original Russian journal. Edited by Steve Torstveit.     

TDPAC studies of111mCd in calciproteins: Calmodulin and parvalbumin

TDPAC measurements of the 150–247 keV gamma-ray cascade in¹¹¹Cd have been performed at room temperature on Calmodulin (CaM) and Parvalbumin (Pa) labelled with radioactive^111mCd. The anisotropy of the coincidence counting rate shows a time-dependent behaviour, typical of two different nuclear quadrupole interactions (NQI) in CaM. The NQI parameters indicate the presence of two distinct metal-binding sites, presenting non-equivalent local electric charge structure. In Pa samples, only one NQI is observed and the measured electric field gradient (EFG) value agrees well with the large one obtained in CaM.     

Use of combined Hartree–Fock–Roothaan theory in evaluation of lowest states of K[Ar]4s03d1 and Cr?+?[Ar]4s03d5 isoelectronic series over noninteger n-Slater type orbitals

By using noninteger n-Slater type orbitals in combined Hartree–Fock–Roothaan method, self-consistent field calculations of orbital and lowest states energies have been performed for the isoelectronic series of open shell systems K[Ar]4s ⁰3d ¹ (² D) (Z = 19–30) and Cr⁺[Ar]4s ⁰3d ⁵ (⁶ S) (Z = 24–30). The results of the calculations for the orbital and total energies obtained by using minimal basis-sets of noninteger n-Slater type orbitals are given in the tables. The results are compared with the extended-basis Hartree–Fock computations. The orbital and total energies are in good agreement with those presented in the literature. The results can be useful in the study of various properties of heavy atomic systems when the combined Hartree–Fock–Roothaan approach is employed.     

The ADHM Construction and Non-local Symmetries of the Self-dual Yang–Mills Equations

We construct the most general reducible connection that satisfies the self-dual Yang–Mills equations on a simply-connected, open subset of flat \mathbbR⁴{\mathbb{R}^4}. We show how all such connections lie in the orbit of the flat connection on \mathbbR⁴{\mathbb{R}^4} under the action of non-local symmetries of the self-dual Yang–Mills equations. Such connections fit naturally inside a larger class of solutions to the self-dual Yang–Mills equations that are analogous to harmonic maps of finite type.     

Emission spectroscopy of the A<Superscript>1</Superscript>Π–X<Superscript>1</Superscript>Σ<Superscript>+</Superscript> system of AlH

The high-resolution emission spectrum of the A¹ Π–X¹Σ⁺ transition of AlH was observed in the 18 000–25 000 cm^-1 spectral region using a conventional spectroscopic technique. The AlH molecules were excited in an Al hollow-cathode lamp filled with a mixture of Ne carried gas and a trace amount of NH₃. The emission from the discharge was observed with a plane grating spectrograph and recorded by a photomultiplier tube. In total 163 transition wave numbers belonging to six bands (0-0,1 and 1-0,1,2,3) were precisely measured and rotationally analysed. In the final fit the present data have been combined with available high-resolution measurements of the vibration-rotation bands by White et al. [J. Chem. Phys. 99, 8371 (1993)]. This procedure enabled extracting molecular constants for the A¹ Π and X¹ Σ⁺ states of AlH. A very slight local perturbation has been discovered in the v=1 vibration level of the A¹ Π state at J=5. This was probably caused by the interaction with the a³Π state.     

Borel Summability and Lindstedt Series

Resonant motions of integrable systems subject to perturbations may continue to exist and to cover surfaces with parametric equations admitting a formal power expansion in the strength of the perturbation. Such series may be, sometimes, summed via suitable sum rules defining C ^∞ functions of the perturbation strength: here we find sufficient conditions for the Borel summability of their sums in the case of two-dimensional rotation vectors with Diophantine exponent τ =1 (e.g. with ratio of the two independent frequencies equal to the golden mean).     

Evolution of the population of outer 6s and 5d shells in rare-earth metals

The shifts of the Kα ₁ and Kβ ₁ lines of all rare-earth (RE) metals (from La to Lu) have been measured experimentally by the x-ray shift method. The population of the RE-metal 6s and 5d shells has been determined by comparing the experimental and theoretical shifts obtained within the Dirac-Fock (Koopmans) model. Trivalent metals exhibit a monotonic cross-over from the 6s ^≈25d ^≈1 to 6s ^≈15d ^≈2 configuration with increasing atomic number. Fiz. Tverd. Tela (St. Petersburg) 41, 1361–1362 (August 1999)     

Electrical properties of a solid polymeric electrolyte of PVC–ZnO–LiClO4

The ZnO filler has been introduced into a solid polymeric electrolyte of polyvinyl chloride (PVC)–ZnO–LiClO₄, replacing costly organic filler for conductivity improvement. Ionic conductivity of PVC–ZnO–LiClO₄ as a function of ZnO concentration and temperature has been studied. The electrolyte samples were prepared by solution casting technique. The ionic conductivity was measured using impedance spectroscopy technique. It was observed that the conductivity of the electrolyte varies with ZnO concentration and temperature. The temperature dependence on the conductivity of electrolyte was modelled by Arrhenius and Vogel–Tammann–Fulcher equations, respectively. The temperature dependence on the conductivity does not fit in both models. The highest room temperature conductivity of the electrolyte of 3.7 × 10⁻⁷ Scm⁻¹ was obtained at 20% by weight of ZnO and that without ZnO filler was found to be 8.8 × 10⁻¹⁰ Scm⁻¹. The conductivity has been improved by 420 times when the ZnO filler was introduced into the PVC–LiClO₄ electrolyte system. It was also found that the glass transition temperature of the electrolyte PVC–ZnO–LiClO₄ is about the same as PVC–LiClO₄. The increase in conductivity of the electrolyte with the ZnO filler was explained in terms of its surface morphology.