Ab initio calculation of the effective valence shell hamiltonian of carbon: Simultaneous treatment of neutral and ion states

The n = 2 effective valence shell hamiltonian, $\text{H}$^v, of carbon is evaluated through second order using ³P Hartree—Fock orbitals (5s4p) with added d functions to provide results within a few percent of the spd convergence limits. The calculated $\text{H}$^v is employed to evaluate the n = 2 valence states of C, C^?, C⁺, C²⁺ and C³⁺ with an average deviation of the 21 excitation energies, ionization potentials and electron affinity from experimental values of 0.32 eV. Three-electron parts of $\text{H}$^v contribute substantially to a number of these excitation energies.     

Photoelectron spectra and their relativistic interpretation for gaseous bismuth trihalides

Photoelectron spectra are reported for BiCl₃, BiBr₃ and BiI₃. Assignments are obtained using the relativistically parameterized extended Hückel (REX) and perturbative Hartree—Fock—Slater methods. The halogen p-bands (4a₁, 1a₂, 4e, and 3e) resemble those in the lighter MX₃ molecules at (M = P? Sb). The bismuth—halogen sigma bond MOs (3a₁ and 2e) suffer a relativistic rehybridization into e_{$\text{1}\text{2}$} > e_{$\text{3}\text{2}$} > e_{$\text{1}\text{2}$}.     

Electric moments,polarizabilities and hyperpolarizabilities for BH(X1Σ+ and CH+ (X1Σ+)

The electric moments and static polarizabilities of BH(1σ²2σ²3σ², X¹Σ⁺) and CH⁺ (1σ²2σ²3σ², X¹Σ⁺) were calculated at the experimental internuclear separation in the LCAO SCF MO approximation. Most of the molecular properties reported in this paper for BH and CH⁺ appear for the first time and should be close to the Hartree—Fock limit. All tensors up to the fourth rank have been included in this study. The isotropy and anisotropy of the α, β and γ tensors are, in atomic units. $\text{α}$ = 22.71, Δα = ?0.26, $\text{β}$ = 55.1, Δβ = ?183.7, $\text{γ}$ = 12428, Δ₁γ = 37895, Δ₂γ = 25120 for BH and $\text{α}$ = 7.73, Δα = 0.39, $\text{β}$ = ?12.4, Δβ = ?11.7, $\text{γ}$ = 344, Δ₁γ = 1515, Δ₂γ = 750 for CH⁺.     

Some properties of the bivariational Hartree–Fock scheme for complex symmetric many-particle operators

The bivariational Hartree–Fock scheme for a general many-body operator T is discussed with particular reference to the complex symmetric case: T^? = T*. It shown that, even in the case when the complex symmetric operator T is real and hence also self-adjoint, the complex symmetric Hartree–Fock scheme does not reduce to the conventional real form, unless one introduces the constraint that the N-dimensional space spanned by the Hartree–Fock functions ? should be stable under complex conjugation, so that ?* = ?α. If one omits this constraint, one gets a complex symmetric formulation of the Hartree–Fock scheme for a real N-electron Hamiltonian having the properties H = H* = H^?, in which the effective Hamiltonian H_eff (1) may have complex eigenvalues ε_k. By using the method of complex scaling, it is indicated that these complex eigenvalues—at least for certain systems—may be related to the existence of so-called physical resonance states, and a simple example is given. Full details will be given elsewhere.     

Perturbation calculation of atomic correlation energies for the first transition period

Results are presented for calculations of Hartree—Fock and correlation energies for the 3dⁿ 4s² and 3dⁿ⁺¹ 4s ground and excited states of the first transition series atoms using second-order Møller—Plesset perturbation theory starting with an unrestricted Hartree—Fock wavefunction.     

A method for obtaining potential parameters for helium from T1 measurements

The temperature dependence of T₁ for ³He gas in the range 0–4°K is calculated for a Lennard-Jones (12,6) potential. The relaxation of the nuclear spins is assumed to be due to a dipolar interaction between the nuclei. A minimum value in the relaxation time, T_1,min, is found to occur at a temperature denoted by T_min. By repeating the calculation for different pairs of values of the potential parameters ? and σ, we have found that for a density of 10^?2 g/cm³,σ²T_min = 13.0?1.12 × 10³ ?σ², T_1,min/σ²(T_min)^{$\text{1}\text{2}$} = 17.4?6.56 × 10² ?σ², with ?, σ, T_min and T_1,min in eV, Å, °K and minutes, respectively. From measurements of T_min and T_1,min, ? and σ can be determined.     

Idle spin behavior of the shifted hexagonal tungsten bronze type compounds FeIIFeIII2F8(H2O)2 and MnFe2F8(H2O)2

Fe^IIFe^III₂F₈(H₂O)₂ and MnFe₂F₈(H₂O)₂, grown by hydrothermal synthesis ($\text{P ? 200}\text{MPa}\text{, T = 450}\text{or}\text{380°}\text{C}$), crystallize in the monoclinic system with cell dimensions (Å): a = 7.609(5), b = 7.514(6), c = 7.453(4), β = 118.21(3)°; and a = 7.589(6), b = 7.503(8), c = 7.449(5), β = 118.06(3)°, and space group $\text{C2}\text{m}\text{, Z = 2}$. The structure is related to that of $\text{WO}{}_3\text{·}\text{1}\text{3}\text{H}{}_2\text{O}$. It is described in terms of perovskite type layers of Fe³⁺ octahedra separated by Fe²⁺ or Mn²⁺ octahedra, or in terms of shifted hexagonal bronze type layers. Both compounds present a weak ferromagnetism below T_N (157 and 156 K, respectively). Mössbauer spectroscopy points to an “idle spin” behavior for Fe^IIFe^III₂F₈(H₂O)₂: only Fe³⁺ spins order at T_N, while the Fe²⁺ spins remain paramagnetic between 157 and 35 K. Below 35 K, the hyperfine magnetic field at the Fe²⁺ nuclei is very weak: H_hf = 47 kOe at T = 4.2 K. For MnFe₂F₈(H₂O)₂, Mn²⁺ spin disorder is expected at 4.2 K. This “idle spin” behavior is due to magnetic frustration.     

The rate constants of the gas-phase reactions K + Cl ⇆ K+ + Cl− and KCl + M ⇆ K+ + Cl− + M from measurements in atmospheric pressure flames

Mass spectrometric studies of the ions present in H₂/O₂/N₂ flames with potassium and chlorine added have demonstrated that ionization can occur in the forward steps of K + Cl ? K⁺ + Cl^? (II), KCl + M ? K⁺ + Cl^? + M (IV), where M is any third body. Variations of [K⁺] with time in these systems have been measured and establish that the rate coefficients (in ml molecule^?1 s^?1) of the ion-producing steps are k₂ = 5 × 10^?10T^{?$\text{1}\text{2}$} exp(?10 500/T) and k₄ = 2.2 × 10⁷T^?3.5 × exp(?60 800/T). Coefficients for ion-ion recombination have been obtained from k₂ and k₄ using the equilibrium constants of (II) and (IV) and are k_?2 = 1.7 × 10^?9T^{?$\text{1}\text{2}$} and k_?4 = 1.1 × 10^?17T^?3, with each one in the ml molecule^?1 s^?1 system of units. Replacement of the N₂ in one of these flames with sufficient Ar to maintain the temperature constant leaves the measured k₂ and k_?2 unchanged, but lowers the observed k₄ and k_?4. This confirms that ion-recombination in the backward step in (II) is a two-body process, whereas in (IV) it is termolecular.     

Emission spectra of supersonically cooled methyldiacetylene cations

The ā²E → X?²E (Σ= + $\text{1}\text{2}$, - $\text{1}\text{2}$) electronic transitions of rotationally/vibrationally cooled CH₃CCCCH^- cation, as well as the d₁-/d₃-/d₄-substituted species, were studied by emission spectroscopy. Ion emission was obtained by electron impact on the neutral species seeded in a helium supersonic free jet. Vibrational frequencies in both electronic states are inferred to within ±1 cm^-1. Spin-orbit splittings are observed and interpreted on the basis of non-linear vibronic couplings. Rotational subbands are observed, yielding rotational and Coriolis parameters as well as rotational temperatures.     

Introduction of the shell structure into the Thomas—Fermi energy density functional for neutral atoms

The Thomas—Fermi energy density functional is constructed for the Na atom using H-like wavefunctions. Minimization of the functional with respect to the Z in the wavefunctions leads to the energy value ot ?166.35 e_O²/a_O, which compares favorably with the Hartree—Fock value of ?161.8 e_O²/a_O.     

Untersuchung der magnetischen Suszeptibilität zum Studium des Bindungsverhaltens von Eisen in V1−xFexO2−xFx

An analysis of the magnetic susceptibility of V_1?xFe_xO_2?xF_x with 0.0026 ? x ? 0.015 in the semiconducting M₁-phase yields a magnetic moment of 5.03 μ per Fe³⁺ ion. Deviations from the Curie-Weiss behavior above T = 120°K are due to the existence of current carriers n, in the V⁴⁺-conduction band. The very high effective mass ($\text{m}{}_{\mathrm{<mtext>e</mtext>}}\text{? 100 m}{}_0$) of the carriers can be explained by the spin polarization cloud which they carry along. A comparison between the activation energy determined from the average slope of the log n vs T^?1 curve and from electric conductivity measurements implies an activated hopping mobility of the charge carriers.This hopping mobility is due to the onset of the Anderson localization resulting from disorder which is induced by the foreign (Fe³⁺, F^?)-ions. Mössbauer-spectroscopic measurements also confirm a reduction of the localized 3d-electrons of the Fe³⁺-cation in V_1?xFe_xO_2?xF_x above T = 120°K.     

On the validity of using the TKR sum rule to place zero angle electron impact spectra on an absolute scale

The use of the Thomas—Kuhn—Reiche (TKR) sum rule to place electron impact spectra on an absolute scale is only rigorously correct if the observed intensities can be extrapolated to their first Born zero momentum transfer limit. This note investigates the error involved in using the TKR sum rule at zero scattering angle instead of zero momentum transfer. By considering an expansion of the generalized oscillator strength at zero angle it is shown that the first order correction to the TKR sum rule can be written as ($\text{1}\text{3}\text{k}{}^2$)[|E_o|?($\text{4}\text{5}$)$\text{V}$_ee] for target systems randomly oriented in space where k² is the incident electron energy and |E_o| and $\text{V}$_ee are the magnitude of the total electronic energy and the electron—electron repulsive energy of the ground state of the target system respectively. Estimates based on Hartree—Fock calculations indicate a 0.27% error in the use of the TKR sum rule for F and 0.79% for Ar at an incident electron energy of 25 keV.     

Magnetic susceptibility of Co4+(d5) in octahedral and tetrahedral environments

Measurements of magnetic susceptibility on compounds containing stoichiometric Co⁴⁺ are reported. The compound Ba₂CoO₄ has the Co⁴⁺(d⁵) ion at a tetrahedral site and displays a susceptibility of the expected magnitude for $\text{S =}\text{5}\text{2}$. The compounds Ba₃Co₂CO₉ and BaCoO₃ have the Co⁴⁺ at an octahedral site and show a susceptibility expected for low spin, $\text{S =}\text{1}\text{2}$. For the low spin case significant deviations from Kotani's calculated susceptibility were observed. Improvement of the theory was made through incorporation of the effects of distortion from perfect octahedral symmetry and the inclusion of higher electronic configurations above t⁵₂ in the ²T₂ ground state. A case of low spin Ni in octahedral environment is also reported.     

Unusual effects of anisotropic bonding in Cu(II) and Ni(II) oxides with K2NiF4 structure

Geometric constraints present in A₂BO₄ compounds with the tetragonal-T structure of K₂NiF₄ impose a strong pressure on the BO_IIB bonds and a stretching of the AO_IA bonds in the basal planes if the tolerance factor is $\text{t ?}\text{R}{}_{\mathrm{<mtext>AO</mtext>}}\text{√2 R}{}_{\mathrm{<mtext>BO</mtext>}}\text{< 1}$, where R_AO and R_BO are the sums of the AO and BO ionic radii. The tetragonal-T phase of La₂NiO₄ becomes monoclinic for Pr₂NiO₄, orthorhombic for La₂CuO₄, and tetragonal-T′ for Pr₂CuO₄. The atomic displacements in these distorted phases are discussed and rationalized in terms of the chemistry of the various compounds. The strong pressure on the BO_IIB bonds produces itinerant bands and a relative stabilization of localized d_z² orbitals. Magnetic susceptibility and transport data reveal an intersection of the Fermi energy with the d²_z² levels for half the copper ions in La₂CuO₄; this intersection is responsible for an intrinsic localized moment associated with a configuration fluctuation; below 200 K the localized moment smoothly vanishes with decreasing temperature as the d²_z² level becomes filled. In La₂NiO₄, the localized moments for half-filled d_z² orbitals induce strong correlations among the electrons above $\text{T}{}_{\mathrm{<mtext>d</mtext>}}\text{? 200}\text{K}$; at lower temperatures the electrons appear to contribute nothing to the magnetic susceptibility, which obeys a Curie-Weiss law giving a μ_eff corresponding to $\text{S =}\text{1}\text{2}$, but shows no magnetic order to lowest temperatures. These surprising results are verified by comparison with the mixed systems La₂Ni_1?xCu_xO₄ and La_2?2xSr_2xNi_1?xTi_xO₄. The onset of a charge-density wave below 200 K is proposed for both La₂CuO₄ and La₂NiO₄, but the atomic displacements would be short-range cooperative in mixed systems. The semiconductor-metallic transitions observed in several systems are found in many cases to obey the relation $\text{E}{}_{\mathrm{<mtext>a</mtext>}}\text{? kT}{}_{\mathrm{<mtext>min</mtext>}}$, where $\text{? = ?}{}_0\text{exp}\text{(}\text{?E}{}_{\mathrm{<mtext>a</mtext>}}\text{kT}\text{)}$ and T_min is the temperature of minimum resistivity ?. This relation is interpreted in terms of a diffusive charge-carrier mobility with $\text{E}{}_{\mathrm{<mtext>a</mtext>}}\text{? ΔH}{}_{\mathrm{<mtext>m</mtext>}}\text{? kT}$ at T = T_min.     

Self-consistent molecular hartree—fock—slater calculations. IV. On electron densities,spectroscopic constants and proton affinities of some small molecules

The use of the Xα exchange approximation in calculations on small molecules is studied. Electron densities are very similar to Hartree—Fock densities, as judged from density difference maps. The statistical total energy, E_Xα, is used in order to calculate R_eB_e, ω₃ and D_e of a series of diatomic molecules. The agreement with experiment is again similar to that in Hartree—Fock calculations. Proton affinities can also be calculated very well. The Hartree—Fock—Slater and Hartree—Fock models show on the whole very analogous behaviour. These results are obtained by using accurate, unapproximated, potentials and densities.     

Excitation of XeF* by reactions of XeF2 with Ar(3P0,2),Kr(3P2) and Xe(3P2)

The reactions of the lowest metastable states of Ar, Kr and Xe with XeF₂ were studied in a flowing afterglow apparatus; XeF emission (from D²Π_{$\text{1}\text{2}$} and B ²Π⁺ states) was observed in all cases. The total rate constants (cm³ molecule^?1 s^?1) for XeF^* formation were determined as 75 × 10^?11 ? Xe(³P₂);64 × 10^?11 ? Kr(³P₂) and 20 × 10^?11 ? Ar(³P_0,2). The reactions of Ar(³P_0,2) and Kr(³P₂) with XeF₂ also gave ArF^* and KrF^*, respectively. Analysis of these emissions indicates that at least two different mechanisms are operative: reactive quenching by the ionic—covalent curve-crossing mechanism and excitation transfer. The Ar(³P_0,2 + XeF₂ reaction is a sufficiently strong source of XeF(D—X) emission that the main features of the XeF(D²Π_{$\text{1}\text{2}$} ? X²Σ⁺) system could be photographed and tentative assignments of these vibrational bands are given. The XeF(D → B) emission could not be observed and the ratio of the D—X versus the D—B transition probability must be > 1000 : 1.     

Optical absorption spectra of praseodymium acetate complexes in solution

Results of analyses of the solution spectra of Pr³⁺ in the acetates of praseodymium, magnesium, calcium and cadmium complexes are presented. Slater-Condon (F₂, F₄ and F₆), configurational interaction (α,β), spin-orbit (ξ_4f), nephelauxetic ($\text{β}$) bonding (δ) and Judd-Ofelt (T₂T₄ and T₆) intensity parameters are evaluated. Judd-Ofel intensity relationship has been used in the calculation of electric dipole line-strengths. Theoretical evaluation of predicted radiative lifetimes (τ_R) of the electronic excited states ³P₁, ³P₀ and ¹D₂ of Pr³⁺ in four diff been carried out.     

Phase diagram and some physical properties of V2O3+x1 (0 ? x ? 0.080)

The magnetic and electric properties of V₂O_3+x were investigated by measurements of magnetic susceptibility, electrical resistivity, magnetotorque, Mössbauer of doped ⁵⁷Fe, and NMR of ⁵¹V, and the results were compared with those of the (V_1?xTi_x)₂O₃ system or highly pressured V₂O₃. The results obtained are as follows: (1) The metallic state shows an antiferromagnetic ordering at T_N (x). The value of T_N for metallic V₂O₃, obtained by interpolation to x = 0, shows the coincidence between V₂O_3+x and the (V_1?xTi_x)₂O₃ system. (2) Magnetic susceptibility of V₂O_3+x is expressed as χ_M(V₂O_3+x) = (1?x)χ_M(V³⁺) + xχ_M(V⁴⁺). χ_M(V⁴⁺) obeys the Curie-Weiss law $\text{(χ}{}_{\mathrm{<mtext>M</mtext>}}\text{(}\text{V}{}^{\mathrm{4+}}\text{) =}\text{0.77}\text{T}\text{+ 17)}$. (3) In the insulating phase, the electrical resistivity ? is expressed as a common equation: $\text{? = 10}{}^{\mathrm{?1.8}}\text{exp}\text{(}\text{E}\text{kT}\text{)}$. This implies that the substitution of Ti or nonstoichiometry (V⁺⁴ + metal vacancies) has little influence on the carrier mobility (or bandwidth). (4) There is a critical length in the c-axis (? 14.01 Å) where the metal-insulator transition takes place. This suggests that the length of the c-axis plays an important role in the metal-insulator transition of V₂O₃-related compounds.     

X-ray study of Hg2Cl2Br2 and HgCl2HgBr2 reactions in solid state

The reactions (I) Hg₂Cl₂(s) + Br₂(g) and (II) HgCl₂(s) + HgBr₂(s) have been investigated by an X-ray method. Both the reactions yield two forms of the mixed halide HgClBr, designated as α-HgClBr and β-HgClBr. The cell parameters of the two are as follows:α-HgClBr: $\text{a = 6.196}\text{A}\text{?}$, $\text{b = 13.12}\text{A}\text{?}$, $\text{c = 4.37}\text{A}\text{?}$, z = 4, ? = 5.91 g/cm³. The powder pattern and cell parameters are similar to that of HgCl₂. Therefore it is probable that the chlorine atoms, in the linear halogenHghalogen molecules of HgCl₂ structure have been replaced by bromines, and since the radius of the bromine atom is larger than that of chlorine, the lattice is larger in this case.β-HgClBr: $\text{a = 6.78}\text{A}\text{?}$, $\text{b = 13.175}\text{A}\text{?}$, $\text{c = 4.17}\text{A}\text{?}$, z = 4, ? = 5.40. These parameters are the same as those reported in the literature for β-Hg(ClBr)₂, and its X-ray powder pattern is similar to HgCl₂. Therefore this phase also has linear halogenHghalogen molecules but the distribution of Cl and Br atoms is perhaps random.Heating the products (I) and (II) up to the melting point increases the amount of α phase and decreases the β phase, whereas crystallization increases the β phase. DTA study has supported the X-ray findings.     

Dissolution of Ca3(AsO4)2 · 2H2O in the system CaOAs2O5H2O at 35, 40, 45 and 50°C and the related thermodynamic data

Calcium arsenate dihydrate is precipitated at pH 7.0 and its dissolution in aqueous solutions at temperatures of 35, 40, 45 and 50°C and a pH of between 3.0 and 8.0 is investigated. The thermodynamic parameters ΔG⁰, ΔS⁰ and ΔH⁰ for the process are evaluated. Temperature dependence of solubility is obtained by the equations ?log K_TCA = $\text{9078.138}\text{T}$ ? 34.0468 + 0.0821421 T