A CNDO-MO calculation of VCl4

The electronic structure of the tetrahedral molecule VCL₄ is investigated within the CNDO-MO approximations. The metal and ligand valence orbitals, 3d, 4s, 4p; and 3s, 3p; respectively, have been systematically varied in an attempt to minimize the total energy; “optimum” V 4s(χ₄ = 1.10) and 4p(d ³ p ²) orbitals have been established, but V 3d(d ⁿ ) and Cl(-δ) valence orbitals are only seen to favor lower energy for expanded orbitals. Since determining the one-electron molecular orbital level which is occupied by the vanadium lone electron is a major aspect of this investigation, all calculations have been performed in triplicate: calculations assuming the unpaired electron occupies the 3a ₁, 2 _e and 4t ₂ molecular orbital (ground state electronic configurations² A ₁,² E, and² T ₂, respectively). The Hartree-Fock equations have been solved by Roothaan's SCF method for open shells, but off-diagonal multipliers between filled and partly filled molecular orbitals of the same symmetry have been neglected. As a qualitative estimate of the error introduced by this simplification, the pertinent overlap integrals between the eigenfunctions from calculations for the three possible configurations,² A ₁,² E, and² T ₂, are investigated as functions of the component 3d(d ⁿ ) and Cl(-δ) valence orbitals. The overlap integrals from the relevant² A ₁ and² T ₂ calculations are reasonably small, but the neglect of off-diagonal multipliers in calculations on the² E state is found to be a poor approximation. An ordering of the non-filled molecular orbitals in VCl₄ of 4t ₂ < 3a ₁ < 2e < 5t ₂ seems most consistent with the numerous calculations. This suggested ground state electronic configuration of² T ₂ introduces new aspects to the consideration of a (dynamic) Jahn-Teller effect in VCl₄. Experimental data pertinent to the electronic structure of VCl₄ has been briefly summarized, but unfortunately it is inadequate to confirm or deny the present calculations.     

A Mössbauer spectroscopy investigation of the Intergrowth Phases LaSr3Fe3−xMx010−δ (M = Al,Cu)

Iron-57 Mössbauer spectroscopy confirms a high sensitivity of the three-dimensional magnetic ordering temperature (T_Néel) for a series of new intergrowth phases to both oxygen stoichiometry and the partial substitution of iron by copper and aluminium in the Ruddlesden-Popper phase LaSr₃Fe₃0_10?δ. The chemical isomer shifts suggest that significant covalent electron delocalization exists in these phases. Spectra for the paramagnetic phases indicate two distinct iron coordination environments consistent with x-ray and neutron diffraction structure determinations. The Mössbauer spectra at 4.8 K exhibit the overlap of two magnetic hyperfine patterns corresponding to cooperative magnetic order at the iron sites with internal fields of 45 and 27 Tesla for nominal Fe³⁺ and Fe⁴⁺ sites respectively.     

Excited orbitals of sulphur in aliphatic and unsaturated sulphides

The energies of some electron configurations of sulphur in organic sulphides involving 3d and 4s orbitals have been derived by simulating the radial and angular perturbation of the molecular environment on sulphur valence orbitals, with electrostatic potentials. In order to discuss the relevance of the electron configurations in the molecular valence state and the role of the excited orbitals 4s and 3d to bonding, the energies were minimized in respect of size and orientation of sulphur valence orbitals. Interatomic exchange terms were included and the importance of interatomic exchange terms involving the electrons on carbons is discussed. The results are indicative for a negligible participation of 3d and 4s orbitals of sulphur to the ground state of aliphatic and unsaturated sulphides.     

Calculation of Negative Ions of B,C, N,O and F Using Noninteger n Slater Type Orbitals

Combined Hartree‐Fock‐Roothaan calculations have been performed using noninteger n Slater type orbitals for the ground states of the lowest electron configurations 1s²2s²2pⁿ (2 ≤ n ≤ 6) for negative ions of B, C, N, O and F. These results are compared with the corresponding results obtained from the use of integer n Slater type orbitals. All of the nonlinear parameters are fully optimized. The results of calculation of coupling‐projection coefficients, orbital and total energies and virial ratios are presented. It is shown that the noninteger n Slater type orbitals, in general, improve the orbital energies.     

Valence bond studies of AH2 molecules

Minimal basis set (STO) molecular orbital and valence-bond calculations are reported for the³ B ₁ and¹ A ₁ states of CH₂. The open-shell molecular orbital calculations used the Roothaan formulation. The valence-bond calculations used the Prosser-Hagstrom biorthogonalisation technique to evaluate the cofactors required in using Löwdin's formulae. Optimisation of geometry and orbital exponents in the molecular orbital calculation on the³ B ₁ state gave a geometry of R_C-H=2.11 a.u. and H-C-H=123.2 °. The energy obtained was ?38.8355 a.u. The molecular orbital and valencebond calculations are compared. In the valence-bond calculations the variation with bond-length and bond-angle of the configuration energies was studied. Valence bond “build-up” studies are also reported. Valence-bond calculations using hybrid orbitals instead of natural atomic orbitals showed that the perfect-pairing approximation is not as good for CH₂ as BeH₂. The nature of the lone-pair and bonding orbitals is found to be significantly different between the³ B ₁ and¹ A ₁ states. In the³ B ₁ state the 2s and 2p orbitals are fairly equally mixed between both types of orbital. However in the¹ A ₁ state the bonding orbitals have mainly 2p character and the lone pair orbitals have mainly 2s character. As was found for H₂O, the bonding hybrid orbitals do not follow the hydrogen nuclei as the bond angle varies but continue to point approximately in their equilibrium directions.     

M?ssbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

The electrostatic contribution to the M?ssbauer isomer shift of mercury for the series HgF _n (n?=?1,?2,?4) with respect to the neutral atom has been investigated in the framework of four- and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the M?ssbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF _n (n?=?1,?2,?4), relevant for the isomer shift, is on the order of 50?ppm with respect to absolute densities. Contrary to previous studies of the ⁵⁷Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF _n (n?=?1,?2,?4). Projection analysis shows the expected reduction of the 6s _1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s _1/2 orbital due to increasing effective charge of the mercury atom, which explains the non-monotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around +2 for HgF₄ at the DFT level, far from the formal charge +4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF₂ and square-planar HgF₄ molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r _e = 2.007 ? and ?? _e = 513.5?cm^?1.     

Experimental and theoretical cross sections for photoionization of metastable Xe*. (6s 3 P 2, 3 P 0) atoms near threshold

Using high resolution laser photoelectron spectrometry we have determined absolute cross sections σJ ₀ J ₁ and the electron angular distribution parameter for one photon ionization of metastable Xe^*(6s ³ P _J0, J ₀ = 2, 0) atoms to the resolved Xe₊ (² P _J1, J ₁ = 3/2, 1/2) ion states at several wavelengths near threshold. For comparison with the present and future experimental data we have calculated partial cross sections and ß-parameters for photoionization of Xe^*(6s ³ P _J0, J ₀ = 2, 0) and of the analogous alkali atom Cs(6s) over the photoelectron energy range (0–5) eV. We have used both a term-dependent Pauli-Fock (PF) approach and a configuration interaction method involving Pauli-Fock atomic orbitals (CIPF). Through the PF method we include relativistic effects on the atomic orbitals; the CIPF method was designed to take into account the important electron correlation effects which are found to be essential for obtaining good agreement between the theoretical and experimental results.     

Electronic state of Fe used as Mössbauer probe in the perovskites LaMO3 (M=Ni and Cu)

For the first time a comparative study of rhombohedral LaNiO₃ and LaCuO₃ oxides, using ⁵⁷Fe Mössbauer probe spectroscopy (1% atomic rate), has been carried out. In spite of the fact that both oxides are characterized by similar crystal structure and metallic properties, the behavior of ⁵⁷Fe probe atoms in such lattices appears essentially different. In the case of LaNi_0.99Fe_0.01O₃, the observed isomer shift (δ) value corresponds to Fe³⁺ (3d⁵) cations in high-spin state located in an oxygen octahedral surrounding. In contrast, for the LaCu_0.99Fe_0.01O₃, the obtained δ value is comparable to that characterizing the formally tetravalent high-spin Fe⁴⁺(3d⁴) cations in octahedral coordination within Fe(IV) perovskite-like ferrates. To explain such a difference, an approach based on the qualitative energy diagrams analysis and the calculations within the cluster configuration interaction method have been developed. It was shown that in the case of LaNi_0.99Fe_0.01O₃, electronic state of nickel is dominated by the d⁷ configuration corresponding to the formal ionic “Ni³⁺-O²⁻” state. On the other hand, in the case of LaCu_0.99Fe_0.01O₃ a large amount of charge is transferred via Cu-O bonds from the O:2p bands to the Cu:3d orbitals and the ground state is dominated by the d⁹L configuration (“Cu²⁺−O” state). The dominant d⁹L ground state for the (CuO₆) sublattice induces in the environment of the ⁵⁷Fe probe cations a charge transfer Fe³⁺+O⁻(L)→Fe⁴⁺+O²⁻, which transforms “Fe³⁺” into “Fe⁴⁺” state. The analysis of the isomer shift value for the formally “Fe⁴⁺” ions in perovskite-like oxides clearly proved a drastic influence of the 4s iron orbitals population on the Fe−O bonds character.     

Electronic structure and photoluminescence properties of Eu-activated Ca2BN2F

The electronic structure of undoped and luminescence properties of Eu²⁺-doped Ca₂BN₂F have been investigated. First-principles calculations for Ca₂BN₂F show that the valence band is mainly composed of F and N 2p, B 2s and 2p orbitals, while the Ca 4s and 3d are almost empty, indicating that Ca₂BN₂F is a very ionic compound. The valence band close to the Fermi level is dominated by the N 2p states, and the bottom of the conduction band is determined by the Ca 3d and N/B 3s orbitals. The direct energy gap is calculated to be about 3.1 eV, in fair agreement with the experimental data of ∼3.6 eV derived from the diffuse reflection spectrum. Due to the high degree of ionic bonding of the coordinations of Eu with (N, F) on the Ca sites, Ca₂BN₂F:Eu²⁺ shows strong blue emission with a maximum at about 420 nm upon UV excitation in the absorption range of 330-400 nm.     

Effect of the structural change of an iron–iron oxide mixture on the decomposition of trichloroethylene

The effect of the structure of a mixture of industrially produced iron and iron oxide on the decomposition of trichloroethylene (TCE) was investigated by gas chromatography, scanning electron microscopy, Fourier transform infrared spectroscopy, energy dispersive X-ray analysis, X-ray diffractometry, and ⁵⁷Fe-Mössbauer spectroscopy. The concentration of 10 mg L^?1 TCE aqueous solution decreased to 0.41, 0.52, 0.26, and 0.09 mg L^?1 when stirred for 7 days with iron–iron oxide mixtures having mass ratios of 2:8, 3:7, 4:6, and 5:5, respectively. The Mössbauer spectra of the mixtures after leaching were composed of two sextets with respective isomer shifts (δ) and internal magnetic fields (H) of 0.29_±0.01 mm s^?1 and 48.8_±0.1 T, and 0.64_±0.01 mm s^?1 and 45.5_±0.1 T, attributed to the Fe³⁺ species in tetrahedral (T _d) and the Fe²⁺ and Fe³⁺ mixed species (Fe^2.5+) in octahedral (O _h) sites, respectively. Mössbauer spectra of a 3:7 mass ratio iron–iron oxide mixture showed a gradual decrease in the absorption area (A) of zero valent iron (Fe⁰) from 40.6. to 12.6, 13.2, 3.8 2.8, and 1.0_±0.5 % and an increase in A of Fe₃O₄ from 31.8 to 59.4, 71.4, 93.2, 95.6, and 98.0_±0.5 % after leaching with 10 mg L^?1 TCE aqueous solution for 1, 2, 3, 7, and 10 days, respectively. Consistent values of the first-order rate constant were calculated as 0.32 day^?1 for Fe⁰ oxidation, 0.34 day^?1 for Fe₃O₄ production, and 0.30 day^?1 for TCE decomposition, which indicates that the oxidation of Fe⁰ was the rate-controlling factor for Fe₃O₄ production and TCE decomposition. It is concluded from the experimental results that an iron–iron oxide mixture is very effective for the decomposition of TCE.     

Successful location of tin dopant cations on surface sites of anatase-type TiO2 crystallites evidenced by 119Sn Mössbauer spectroscopic probe and XPS techniques

The present study provides the first experimental evidence for the stabilization of tin dopant cations immediately on the surface of an oxide having a tetragonal structure. ¹¹⁹Sn Mössbauer spectra of the dopant, introduced by air annealing into the bulk of anatase microcrystals, showed that it was located, in the tetravalent state, in somewhat distorted octahedral sites of a unique type. On the contrary, the reduced tin species, formed upon subsequent hydrogen annealing the Sn⁴⁺-doped samples, are found to occupy different sites being characterized by two sets of the isomer shift δ and quadrupole splitting ΔE_Q values (δ_I = 3.25 mm s⁻¹, ΔE_QI = 1.75 mm s⁻¹; and δ_II = 2.85 mm s⁻¹, ΔE_QII = 1.71 mm s⁻¹). Either of them implies both the divalent state of tin atoms and their presence at low-coordination sites that can be assigned to the surface of crystallites. Mössbauer spectra of Sn^4+←2+ daughter ions, formed upon contact with air of Sn²⁺, consist of a symmetrically broadened peak characterized by only slightly different average values of both the isomer shift (<δ> = 0.07 mm s⁻¹) and quadrupole splitting (<ΔE_Q> = 0.50 mm s⁻¹), as compared to the δ and ΔE_Q values for the bulk-located Sn⁴⁺. However, considerable broadening of Sn^4+←2+ doublet components (Γ = 0.97 mm s⁻¹) allows one to suggest that these secondary formed ions remain distributed over the non equivalent sites inherited from their Sn²⁺ precursors. The occurrence of Sn^4+←2+ at surface sites is independently proven by XPS measurements that revealed a greater than 10-fold enrichment with tin of 3–5 nm thick surface layers.     

Molecular geometries and moments from the maximum overlap criterion

The maximized overlap population, defined as Σ_μ≠νP_μνS_μν, and a related quantity, Σ_μ,νP_μνS²_μν are computed for a series of configurations. The extremum of both approximate molecular geometries, the latter with an accuracy suitable for predictive value. The maximum overlap orbitals predict dipole and quadrupole moments that give reasonable agreement with experimental values.     

An investigation of the radial densities in the FeS5−4 cluster as calculated by the multiple scattering X α method

Multiple scattering Xα calculations on the FeS^5?₄ cluster are used to investigate the participation of the radial functions in the bonding mechanisms of the cluster. The total electron density at the iron nucleus is used to interpret Mössbauer isomer shift data and determine the iron isomer shift calibration constant.     

Quantum chemical calculations of the isomer shift in iron(II) complexes of 1,2,4-triazoles with a 1 A 1 ⇔ 5 T 2 spin transition

DFT calculations have been performed to determine the isomer shift for a series of iron(II) clusters with nitrogen-containing ligands which serve as models of coordination units in Fe(II) complexes with 1,2,4-triazoles possessing a ¹ A ₁ ? ⁵ T ₂ spin transition. Good agreement has been found between the theoretical and experimental values of the isomer shift for both low-and high-spin phases. Our calculations confirmed the hypothesis about relationship between the experimentally observed differences in the isomer shift for the low-spin phases of the complexes and variations of the Fe-N mean bond length.     

Picture change error correction in the radial distributions of canonical orbital densities and total electron density of radon atom: the effect of the size of nucleus and the basis set limit

The 2nd order Douglas-Kroll-Hess (DKH2) and the Infinite Order Two Component (IOTC) radial distributions of electron density of canonical Hartree-Fock (HF) orbitals of radon atom are presented. Furthermore, the total electron density is revisited. The picture change error (PCE) correction is investigated by analytical means. The point charge model of nucleus and the Gaussian nucleus model are employed. The basis set is extrapolated by means of including tight s and also p Gaussians within the original triple zeta basis set. It is found that the DKH1 PCE corrected DKH2 total electron and s orbital contact densities are negative for the point charge model of nucleus if tight enough s Gaussians are included in the basis set. It is shown that this failure is caused due to the missing terms of the second order Douglas-Kroll transformation for the DKH2 electron density. PCE is found the most striking in the DKH2/IOTC electron density of s orbitals close to the nucleus. The radial distributions of the 2-component p _1/2 orbital densities are considerably affected by PCE at the nucleus as well. Furthermore, the PCE corrected DKH2/IOTC scalar p orbital densities have a non-zero value of electron density at nucleus and can be considered as an spin-orbit (SO) average of the p _1/2 and p _3/2 orbitals. The d and f orbitals are affected by PCE in the vicinity of the nucleus only little. The PCE corrected DKH2 and IOTC radial distributions of orbital densities are nodeless, which is completely in agreement with the radial distribution of the analytic or numeric DCH orbital densities.     

Electronic correlation and effective interactions in small alkali clusters

The crucial importance of correlation effects versus delocalization, and their nature in small Alkali clusters is analysed from an ab-initio point of view through a detailed investigation of the Li₂ dimer. The role of the external correlation (provided by extended basis sets and large Configuration Interaction calculations) is shown to lower the energy of ionic configurations and to increase their weight in the electronic wavefunction, increasing simultaneously the importance of delocalization versus internal correlation within thes-band. Effective interactions are determined from accurate diabatic calculations on dimers and transfered to clusters via an effective hamiltonian spanned bys orthogonal orbitals. Although not including explicitely thep-band, this model provides results in good agreement with abinitio calculations on Lithium clusters.     

Electronic charge density and mean kinetic energy of lithium orbitals in LiH,LiH+, Li2, Li2+, LiH2+, and Li2H+

The electron density near the lithium nucleus in the species LiH, LiH⁺, Li₂, Li₂⁺, LiH₂⁺, and Li₂H⁺ was analyzed by transforming the SCF molecular orbitals into a sum of atomic contribnutions, for both core and valence orbitals. These “hybrid-atomic” orbitals were used to compare: electron densities, orbital polarizations, and orbital mean kinetic energies with the corresponding lithium atom quantities. Core-orbital electron densities at the lithium nucleus were observed to increase by up to 0.5% relative to the lithium atom 1s orbital. Lithium cores also exhibited polarization but, surprisingly, in the direction away from the internuclear region. Similar dramatic changes were seen in the electron densities of the valence orbitals of lithium: The electron density at the nucleus for these orbitals increased two-fold for homonuclear species and twenty-fold for heteronuclear triatomic species relative to the electron density at the nucleus in lithium atom. The polarization of the valence orbital electronic charge, in the vicinity of the lithium nucleus, was also away from the internuclear region. The mean “hybrid-atomic” orbital kinetic energies associated with the lithium atom in the molecules also showed changes relative to the free lithium atom. Such changes, accompanying bond formation, were relatively small for the lithium core orbitals (within 0.2% of the value for lithium atom). The orbital kinetic energies for the lithium valence electrons, however, increased considerably relative to the lithium atom: By a factor of about 2 in homonuclear diatomics, by a factor of 7 in heteronuclear diatomics, and by a factor of 11 in the triatomic species. In summary, the total electronic density (core plus valence) at the lithium nucleus remained remarkably constant for all of the species studied, regardless of the effective charge on lithium. Thus, the drastic changes noted in the individual lithium orbitals occurred in a cooperative fashion so as to preserve a constant total electron density in the vicinity of the lithium nucleus. In all cases, bond formation was accompanied by an increase in the orbital kinetic energy of the lithium valence orbital. We suggest that these two observations represent important and significant features of chemical bonding which have not previously been emphasized.     

Theoretic study of the electronic spectra of neutral and cationic PaO and PaO2

The electronic spectra of neutral PaO and PaO₂ and their mono- (PaO⁺, PaO₂ ⁺) and dications (PaO²⁺, PaO₂ ²⁺) were studied by performing multiconfigurational quantum chemical calculations at the CASSCF/CASPT2 level of theory taking into account spin–orbit coupling. Including the protactinium 7s, 6d, and 5f orbitals as well as selected orbitals of oxygen in the active space, the vertical excitation energies at the ground-state geometries have been computed up to ca. 36,000 cm^?1. The gas-phase electronic spectra at 298 and 3,000 K were evaluated on the basis of the computed oscillator strengths.