Alpha Cluster in Hartree-Fock Calculations

Hartree-Fock (HF) calculations have been performed fcr ¹²C nucleus assuming a trigonal D_3h equilibrium configuration. Different aspects including symmetry, kinds of two-body interactions are investigated. The HF calculations have been carried out using a velocity dependent effective potential of s-wave interaction. The results are compared with previous calculations. In all HF calculations no deviation from axial symmetry is obtained.     

Configuration interaction of Er3+ with a charge transfer configuration in the elpasolite compound Cs2NaErCl6

The discrepancies of the crystal-field analysis in Cs₂NaErCl₆ are lowered by letting the 4f¹¹ configuration interact with a charge transfer configuration enclosing a p electron. 75 levels with a total degeneracy equal to 130 were fitted with a mean deviation of 10.5 cm^?1, compared with 21.4 cm^?1 in the standard model. It is found that: (i) the p electrons involved in the process originate most probably from the six Cl^? ligands; (ii) 14% of the 3p⁶ orbitals are projected onto the central ion coordinate system as an unique orbital with p angular character; (iii) this projected orbital can be coupled with 4fⁿ configurations and handled by tensorial methods; and (iv) the most probable mechanism responsible for the improvement of the crystal-field analysis is a 4f¹¹ 3p⁶-4f¹²3p⁵ interaction. The first configuration represents Er³⁺ surrounded by six Cl^? ligands, whereas in the second one, the rare-earth ion and the ligands have gained and lost one electron respectively. The crystal-field analysis enables the estimation of the location of the charge transfer band.     

Radiative lifetimes of 7d, 8d <Superscript>1</Superscript>D<Subscript>2</Subscript> excited states of Hg I

Radiative lifetimes of 7d, 8d ¹ D ₂ excited states of Hg I are measured using pulsed two-photon excitation from the ground [Xe]5d ¹⁰6s ^{2 1} S ₀ mercury state, detecting the decay of the laser-induced fluorescence. The results are compared with theoretical values, obtained by means of a Hartree-Fock single configuration method, taking into account electron configuration interaction. The radiative lifetime value dependence on the effective principal quantum number for the nd ¹ D ₂ series is analyzed and compared with the quantum defect dependence. Received 25 February 2000 and Received in final form 26 July 2000     

Calculation of X-ray and Auger transition rates, lifetimes, X-ray wavelengths, and fluorescence yields of variously ionized silicon atoms

X-ray and Auger transition rates, X-ray wavelengths, and fluorescence yields are calculated for variously ionized silicon atoms with configurations 1s2s^m2pⁿ, m=0-2, n=1-6. The calculation has been performed using the Hartree-Fock atomic model. Intermediate coupling and configuration interaction have been taken into account. The energies and widths are found to be strongly affected by configuration mixing. The results from the present calculation have been compared with those available in the literature. The theoretical K_α hypersatellite and satellite spectra fall into several well-separated regions, corresponding to each of the possible number of spectator electrons in the 2s and 2p shells. The dependence of radiative rates and fluorescence yields on the number of spectator electrons is also investigated.     

Ab initio rotation-vibration energies of H3O+

For the H₃O⁺ molecular ion 47 points on the ground electronic state potential energy surface have been computed by configuration interaction calculations including all possible single and double excitations that can be generated from a canonical set of rather accurate Hartree-Fock SCF molecular orbitals. Combining these points with a set of 14 previously published points that were calculated in exactly the same way gives a good coverage of the surface. An analytic potential function has been fitted that involves all the vibrational coordinates to these points, and this involves the least squares optimization of the values of 13 parameters in the potential function. Using the nonrigid invertor Hamiltonian with this surface the low lying rotation-vibration energies have been calculated; it is hoped that these results will be of use in the search for the spectrum of H₃O⁺. The equilibrium bond length is found to be 0.978 Å, the equilibrium HOH bond angle is 111.6°, and the inversion barrier is 712 cm^?1.     

Structural analysis and crystal-field calculations of Nd^3＋ in Gdx Lu1-x TaO4（x = 0.85） polycrytalline

The crystal structural parameters of Nd 3+-doped rare earth orthotantalate Gd x Lu 1 x TaO 4(x = 0.85) are determined by applying the Rietveld refinement to its X-ray diffraction,and its emission and excitation spectra at 77 K are analysed.The relativistic model of ab initio self-consistent DV-Xα method,which is applied to the cluster NdO 8 in Gd x Lu 1 x TaO 4,and the effective Hamiltonian model are used to investigate its spin-orbit and crystal-field parameters.The free-ions and crystal-field parameters are fitted to the experimental energy levels at 77 K with a root-mean-square deviation of 14.92 cm 1.According to the crystal-field calculations,96 levels of Nd 3+ are assigned.Finally,the fitting results of free-ions and crystal-field parameters are compared with those already reported for Nd 3+:YAlO 3.The results indicate that the free-ion parameters are similar to those of the Nd3+ in Gdx Lu1-x TaO4 and YAlO 3 hosts,and the crystal-field interaction of Nd3+ in Gdx Lu1-x TaO4 is stronger than that in YAlO 3.     

Spin-orbit coupling and crystal-field splitting in the electronic and optical properties of nitride quantum dots with a wurtzite crystal structure

We present an sp ³ tight-binding model for the calculation of the electronic and optical properties of wurtzite semiconductor quantum dots (QDs). The tight-binding model takes into account strain, piezoelectricity, spin-orbit coupling and crystal-field splitting. Excitonic absorption spectra are calculated using the configuration interaction scheme. We study the electronic and optical properties of InN/GaN QDs and their dependence on structural properties, crystal-field splitting, and spin-orbit coupling.     

Approximate SCF calculations on the [Mn(H2O)6]2+ complex with a minimal basis set

In the restricted Hartree-Fock scheme approximate SCF-LCAO calculations have been performed for the [Mn(H₂O)]₆ ²⁺ complex using a minimal basis set consisting of nine Slater-type orbitals of the manganese ion and four Slater-type orbitals of the water molecule. The 1s, 2s and 2p orbitals of the manganese ion and the 1s orbital of the oxygen atom are treated as frozen core orbitals. In evaluating the different parts of the Hartree-Fock operators we used a two-centre approximation for the multicentre integrals. A new aspect of the calculations is the use of the Hartree-Fock orbital energies of the free water molecule as a first approximation for the corresponding orbital energies of the complex. The calculations have been done for the ground states and six excited states of the complex with symmetry T _h and also for the ground states of two distorted complexes. From the resulting eigenvectors we calculated the hyperfine interaction of the valence electrons of the central ion with the protons of the water molecules for three different geometries. The excited states give two different ways of finding values of 10 Dq and the Racah parameters B and C. The results are encouraging.     

A measurement of the Λ-doubling transition frequencies for SH in its second rotational level

Large-scale configuration interaction calculations of the potential energy surface of Li₃ are described. The major prediction which emerges is that triangular configurations are more stable than linear ones, with the ²B₂ and ²A₁ states having different equilibrium geometries but essentially the same energies. It is found that the most stable linear configuration is symmetric, unlike the prediction of restricted Hartree-Fock calculations. A fit of our calculated surface to a semi-empirical LEPS function is presented.     

Hyperfine-structure and isotope-shift measurements in the 6s 5d↔6p 5d transitions of Ba I in the far-red spectral region

Measurements of the hyperfine structures in the 6p5d ¹ D ₂,³ D ₁ and³ F _{2, 3, 4} states of¹³⁵Ba and¹³⁷Ba, and isotope-shifts in several far-red transitions between the 6s 5d and 6p 5d configurations, as well as the transition 6s ^{2 1} S ₀→6s6p ³ P ₁ at 7,911 Å have been performed using high-resolution laser spectroscopy on a collimated atomic beam of natural barium. An analysis of the magnetic-dipole interaction in the 6p 5d configuration using effective one- and two-body hyperfine operators is presented. In particular the contact interaction was studied with respect to the correlation between the two valence electrons. Effects of strong configuration interaction were found. From a King-plot analysis of the isotope shift term- andJ-dependence of the field shift have been evaluated for the transitions between the 6s 5d and 6p 5d configurations. Relativistic Hartree-Fock (RHF) calculations have been performed of electron densities at the nucleus for six different configurations in Ba I and Ba II. The RHF calculations reproduce the experimental King-plot slopes quite well, while the absolute values, of the changes in electron density at the nucleus for the studied transitions, are found to be 9% lower than the results derived from a muonic experiment.     

Optical spectra and crystal-field analyses of samarium in the centrosymmetric hexakis(antipyrine)samarium(III) tri-iodide and tri-perchlorate systems

Optical absorption and emission measurements are reported for single crystals of Sm(AP)₆I₃ and Sm(AP)₆(ClO₄)₃ (where AP denotes an antipyrine ligand molecule). Crystal-field energy levels split out of the 4f ⁵ electronic configuration of Sm³⁺ are located and assigned from the locations and polarizations of magnetic-dipole origin (no-phonon) lines observed in the optical spectra. The energy levels are analyzed in terms of a parametric hamiltonian that assumes D _3d crystal-field symmetry at the Sm³⁺ sites. Crystal-field interaction parameters obtained from calculated-versus-experimental energy level fits are reported and compared for the Sm(AP)₆I₃ and Sm(AP)₆(ClO₄)₃ systems. Good data fits are obtained for both systems, and the rank-two and rank-four crystalfield parameters are reasonably well-determined by these fits. The rank-six parameters are less well-determined. The values determined for the rank-four crystal-field parameters are essentially identical for the tri-iodide and triperchlorate systems; however, the magnitude of the rank-two parameter for Sm(AP)₆I₃ is twice that for Sm(AP)₆(ClO₄)₃. Magnetic-dipole line strengths are calculated for absorptive transitions originating from crystal-field levels of the ⁶H_5/2 (ground) multiplet and for emissive transitions originating from the ⁴G_5/2 (excited) multiplet.     

Vibration-rotation effects on the polarizabilities of CH4 and CD4 calculated from an ab initio polarizability surface

A polarizability surface has been calculated for the methane molecule using a Hartree-Fock wavefunction. Coefficients of the surface are given to second order in terms of both symmetry coordinates and internal coordinates. The polarizability is sensitive to bond stretching and angle bending. The effects of nuclear motion on the polarizabilitles of ¹²CH₄ and ¹²CD₄ have been calculated from the coefficients of the surface. Some of the second order coefficients are found to be significant in contributing to the nuclear motion corrections. The ν₃ mode is the dominant contributor to the corrections. The temperature dependences of the mean molecular polarizabilities of ¹²CH₄ and ¹²CD₄ are also calculated. The results suggest that modern methods of measurement could distinguish between the isotopomers CH_4-n D _n (n=0–4) thereby enabling an experimental surface to be obtained.     

Crystal-field splitting of Pr<Superscript>3+</Superscript> ion multiplets in YPO<Subscript>4</Subscript> with allowance for interconfigurational interaction

The crystal-field splitting of the Pr³⁺ ion multiplets is analyzed with regard to the influence of excited opposite-parity configurations 4f ^{(N − 1)}5d and a configuration with charge transfer. Such an approach makes it possible to (i) refine the characterization of the Stark structure of multiplets by 39% compared with the approximation of a weak configurational interaction and (ii) determine the covalence parameters and the parameters of an odd-symmetry crystal field from experimental data for the Stark structure. The covalence parameters thus determined coincide in order of magnitude with the respective parameters calculated for other ligands using microscopic models.     

Anomalies in thermal expansion of DyVO4 induced by quadrupolar ordering

The thermal expansion of the DyVO₄ crystal has been experimentally and theoretically investigated in the range of the Jahn-Teller structural phase transition. The manifestation of totally symmetric magnetoelastic interactions upon this transition has been studied for the first time. It is found that the temperature dependences of the unit-cell and thermal expansion parameters along the nonactive Jahn-Teller direction in the basal plane for the DyVO₄ crystal exhibit characteristic magnetoelastic anomalies at T<T _c due to the ordering of quadrupole moments of Dy³⁺ ions. The magnetoelastic contributions of the totally symmetric ε^α1 and ε^α2 and symmetry-lowering ε^γ modes to the thermal expansion are calculated within the general crystal-field formalism. The total quadrupolar coefficient G ^γ and magnetoelastic coefficient B ^γ are determined from the spectroscopic and spontaneous deformation data. It is demonstrated that the thermal expansion of the DyVO₄ crystal in the tetragonal and orthorhombic phases is well described in the framework of the unified model using a common set of interaction parameters for both phases.     

Crystal-field splitting of the fundamental multiplet of Tb3+ in terbium aluminum garnet

The low-temperature magnetic behaviour of ‘non-Kramers’ ions depends strongly on the low-lying energy levels, particularly for the case of Tb³⁺ in Terbium Aluminum garnet, where two lowest-lying singlets are well separated from upper levels. Calculations of the crystal-field splitting of the fundamental multiplet ⁷F₆ of Tb³⁺ in a field of tetragonal symmetry have been performed and compared to spectroscopy and magnetization experimental results available. A set of five crystal-field parameters is derived and is found sufficient to give a satisfactory agreement between calculation and experimental results, including susceptibility measurements between 1 and 24K reported here.     

Electronic structure and molecular spectroscopic constants of ScN and ScP investigated by several quantum chemistry methods

The electronic structure of the ScN and ScP molecules is a subject of controversy and turns out to be a challenging problem in quantum chemistry. We show that the ground-state electronic structure for both molecules depends critically on the choice of methods used which incorporate different ways of accounting for electron correlation. A parallel ab initio, DFT and TD-DFT study is performed for this purpose and uses sufficiently flexible basis sets able to reproduce accurate electronic structures, as well as correct spectroscopic constants.

In the ab initio methodology, results have been obtained with methods such as Hartree-Fock (HF), M?ller-Plesset perturbation theory (MPn), direct configuration interaction (CI), quadratic configuration interaction (QC), coupled cluster configuration interaction (CC), complete active space self-consistent field (CASSCF) and multireference configuration interaction (CIPSI) methods. In the DFT methodology, various ‘pure’ and ‘hybrid’ density functionals are used and the corresponding results are compared to sophisticated ab initio methods and to available experimental data.

All the methods used show that the ground state of both molecules is ¹Σ⁺, but two electronic structure natures, ¹Σ⁺ open-shell or ¹Σ⁺ closed-shell, are competitive and depend on the method employed. All the ab initio methods based on a single determinant wavefunction suffer seriously in predicting clearly the exact nature of the ground state or its correct structural and spectroscopic parameters. However, the ab initio methods based on a multiconfigurational wavefunction appear to be successful in describing correctly, within one shot, the electronic structure and the molecular spectroscopic constants. The ground state, particularly for the ScN molecule, presents an unusual electronic structure: the presence of degenerate determinants, quasidegeneracy with other states and one avoided crossing in the region around the equilibrium distances. The bonding of the ground state is a two open-shell ¹Σ⁺ state described as a π double bond and a Σ dative bond; the real triple bond ¹Σ⁺ state, i.e. closed-shell state, is found to lie higher in energy. The potential energy curves of the lowlying electronic states, the derived electronic structures and various molecular spectroscopic constants are presented and discussed for each method employed.     

Electron impact single ionization of copper

Electron impact single ionization cross sections of copper have been calculated in the binary encounter approximation using accurate expression for σ _ΔE as given by Vriens and Hartree-Fock momentum distribution for the target electron. The BEA calculation based on the usual procedure does not show satisfactory agreement with experiment in this case but a striking modification is found to be successful in explaining the experimental observations. The discrepancy is linked with the ionization of the 3d ¹⁰ electrons and probably effective single ionization does not take place from 3d shell of copper leading to smaller values of experimental cross sections.     

Lifetimes of metastable levels in Ar II

We report on a calculation of five lifetimes of metastable levels in Ar II, obtained with a relativistic Hartree-Fock method in which most of the intravalence correlation is represented within a configuration interaction scheme while core-valence correlation is described by a core-polarization model potential with a core-penetration corrective term. The quality of the calculation has been assessed through an experimental determination of the radiative lifetime of the metastable 3d ⁴F_9/2 level. The experiment was performed with a laser probing technique on a stored ion beam at the CRYRING of Stockholm.Received: 16 January 2004, Published online: 30 March 2004PACS: 31.10. + z Theory of electronic structure, electronic transitions, and chemical binding - 32.70.Cs Oscillator strengths, lifetimes, transition moments     

Study of valence states of the CO2 molecule by (e, 2e) momentum spectroscopy

The (e, 2e) technique has been used to measure the binding energy spectrum and the momentum distribution of the electrons in the CO₂ molecule outer orbitals. The innermost valence states 2σ_u and 3σ_g have been localized 2 eV away from each other and evidence of configuration interaction involving 3σ_g has been found. The electron momentum distributions for the various orbitals show poor agreement with the square of the Hartree-Fock wave function Fourier transform.     

Coupled ab initio potential energy surfaces for the two lowest 2A′ electronic states of the C2H molecule

Realistic two-valued potential energy surfaces for the reaction C(³P) + CH(X²Π) → C₂ + H have been constructed from a set of high level ab initio data describing the first two ²A′ electronic states of the C₂H system. These states have linear equilibrium configurations, known as the X ²Σ⁺ and A²Π states, and are coupled by a conical intersection. They lead to the formation of C₂(X¹Σ⁺ _g) and C₂(a³Π_u) considering an adiabatic dissociation process. The ab initio calculations are of the multireference configuration interaction variety and were carried out using a polarized triple-zeta basis set. Using the ab initio adiabatic energies and the matrix elements of the dipole moment, a 2 × 2 diabatic representation of the electronic Hamiltonian was built. Each element of this Hamiltonian matrix was expressed within the double many-body expansion (DMBE) scheme which is based, in this case, on the extended Hartree-Fock approximate correlation energy model (EHFACE). The analytical adiabatic potential energy surfaces are then obtained as the eigenvalues of this matrix, and display correctly the Σ/Π conical intersection. Moreover, the non-adiabatic couplings given by our analytical model are compared with the ab initio ones, and good qualitative agreement is observed.