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.     

Unrestricted hartree-fock cluster analysis of F and F A centres in some alkali halides

The optical absorption energies and nearest-neighbour ground state hyperfine interaction constants are evaluated for F centres in lithium and potassium halides, and for FA(Li) centres in KC1 and KBr. For these defects, the electron-ion interaction includes self-consistent unrestricted Hartree-Fock treatment of nearest-neighbour ions, in terms of Gaussian-localized atomic orbital basis functions. The results, with the exception of FA-centre hyperfine constants, are qualitatively correct.     

MCHF+BP Approaches of Hyperfine Interaction Constants in 45SII

Multi-configuration Hartree-Fock and configuration interaction calculations of hyperfine structure constants for 3d^{2 3}P states of ScII are reported. It is very important to consider core polarization (especially spin polarization) and core-core correlation as well as valence correlation for accurate calculation of hyperfine constants. The relativistic correction (through Breit-Pauli approximation) as well as finite-nuclear-mass and fnite-nuclear-size-corrected values of the hyperfine constants for ScII are in good agreement with the most accurate experimental values and better than other ab initio theoretical results.     

Doppler-free spectroscopy of the 8s state of Cs

Doppler-free two-photon spectroscopy and ion detection in a thermionic diode were used to measure the hyperfine splitting and absolute term energy of the 8S state of Cs. The results, a=219.3(2) MHz for the magnetic dipole coupling constant, and E(8S)=24317.1499(4) cm^-1 for the term value of the c.g. of the 8S state relative to the c.g. of the ground state, agree well with earlier, less precise measurements. The hyperfine coupling also agrees well with a recent relativistic Hartree-Fock calculation.     

Theoretical investigations of the spin Hamiltonian parameters for LiF:Mn

The spin Hamiltonian (SH) parameters (g factor, the hyperfine structure constant A as well as the superhyperfine parameters A′ and B′) for LiF:Mn²⁺ are theoretically investigated from the perturbation formulas of these parameters for a 3d⁵ ion under ideal octahedra. The related molecular orbital coefficients and the unpaired spin densities of the fluorine 2s, 2pσ and 2pπ orbitals are quantitatively determined from the cluster approach in a uniform way. The calculated SH parameters show good agreement with the experimental data. The results are discussed.     

Magnetic hyperfine anomaly in muonic193Ir

The nuclear decay of the 5/2⁺ 139 keV state to the 3/2⁺ ground state was observed in muonic¹⁹³Ir. The hyperfine splitting of the 3/2⁺ state and 5/2⁺ state was determined to be 640±100 eV and 1280±160 eV, respectively. The ground state splitting is about twice that of a point nucleus, an anomaly never observed this large. This is mainly due to the different radial distribution of spin and orbital magnetization of a d_3/2 proton configuration for which these contributions nearly cancel to zero in the magnetic moment. But calculations including configuration mixing and coupling to a vibrating or a deformed core show deviations. The groundstate anomaly is in line with that observed by the Mössbauer technique.     

Studies of local phase transition behavior for Co2+ in CsCaCl3 crystals from EPR data

In this paper, we establish the calculation formulas ofg factorsg _∥,g _⊥ and the hyperfine structure constantsA _∥,A _⊥ for 3d⁷ ions in tetragonal octahedral field from a cluster approach. In these formulas, besides the configuration interaction, the covalency effect due to the admixture between d electrons of 3d⁷ ion and the p electrons of ligands is considered. The parameters used in these formulas (except the core polarization constantsk in the calculation ofA _i) can be obtained from optical spectra of the studied crystal. From these formulas, the local release (or elongation) factork, which is introduced to characterize the release effect of impurity-ligand bond along C₄ axis at the cubic to tetragonal phase transition, is estimated for CsCaCl₃:Co²⁺ crystal by calculating the electronic paramagnetic resonance (EPR) parametersg _i andA _i . These EPR parameters are therefore explained reasonably and the results are discussed.     

On the reduction of the Dirac equation to non-relativistic form: the dipole-dipole interaction in the hydrogen atom

Finite nucleus models are used in the calculation of the dipole-dipole part of the second-order hyperfine energy in the ground state of the hydrogen atom. The results are used as a guide to bring the non-relativistic calculation for a point nucleus into agreement with the relativistic calculation. This necessitates the introduction of delta function operators in the dipole-dipole operator and the zeroth-order hamiltonian. It is concluded that the reduction of the Dirac equation to non-relativistic form is valid for the hyperfine interaction up to order mc ²α⁶.     

Theoretical study of the TiC molecule: clarification of the ground state

The electronic structure of the TiC molecule was examined using three types of multi-reference single- and double-excitation configuration interaction (MRSDCI) calculations with highly extended basis sets. Multi-reference coupled pair approximation (MRCPA) was applied after the MRSDCI calculations that included core—valence and core—core correlation in addition to the valence correlation (v-c-c CI). From the results of the most accurate calculation with MRCPA (v-c-c CPA) it was concluded that a ¹Σ⁺ state is the ground state, despite previous calculations that suggested a ³Σ⁺ state with a ¹Σ⁺ state lying only slightly above it. The ¹Σ⁺ state is more highly correlated than the ³Σ⁺ state, and it was found that use of a size-consistent method is necessary to predict the relative stability accurately. The study evaluated the spectroscopic constants and considered the effect of the core (Ti 3p) correlation on these parameters. By taking the core correlation effect into account, the estimation of the dissociation energy (D _e) was improved dramatically; D _e obtained through v-c-c CPA was 4.457eV for the ¹Σ⁺ ground state, which agrees well with the experimental value (the latest being 4.35 ± 0.31 eV).     

Structure calculations in18O nucleus

A multishell Hartree-Fock calculation for¹⁸O nucleus has been done with the Tabakin and Hamada-Johnston interactions followed by pairing correlations and angular momentum projection. TheB(E2) transition rates have been reproduced with an effective charge of 1.5e for protons and 0.5e for neutrons, but the fit to energy levels is poor. An approximate alternative formalism has then been developed which casts the eighteen-particle problem into a two-valence nucleon problem. The two valence nucleons interact through the RPA-type oscillation modes of the core. Calculations with the two interactions mentioned above have reproduced roughly the uncorrelated projected Hartree-Fock spectrum. Lastly, the excited band spectra of¹⁸O have been examined in the TDA approach followed by band mixing.     

Ab initio SCF and limited CI calculations of the d-d transitions in cobalt oxide

Ab initio calculations using an extended set of gaussian-type orbitals have been performed for the CoO₆ ^10- cluster in the Hartree-Fock approximation and with a limited configuration interaction. The results have been compared with those of crystal-field theory. CoO is found to be a very ionic system with localized d-electrons. The excited d-states may be described using a simple configuration interaction scheme, which is found to be almost equivalent to a crystal-field parameterized configuration interaction built on Hartree-Fock results. Localization and delocalization phenomena in openshell systems have been discussed.     

Elastic scattering of an electron by the negative lithium ion

In the framework of the many-body theory, the differential and total cross sections of elastic scattering of slow electrons by the negative lithium ion Li⁻ are obtained. Calculations are performed both in the Hartree-Fock single-particle approximation and with regard to many-electron correlations, which take into account the dynamic polarization of the core. Features observed in the behavior of the phases and cross sections for p and d partial waves are associated with resonance scattering of electron waves. Considering the dynamic polarization of the core by an incident electron heightens the diffraction character of the scattering. The real process is compared with particle scattering in models with a repulsive potential.     

Absolute sign of the Mu* hyperfine parameters in diamond

Standard μSR experiments in diamond have shown that the relative sign of the hyperfine parameters of the anisotropic Mu^* state is negative (A _‖/A _⊥<0). We report an experimental determination of theabsolute sign of the Mu^* hyperfine parameters by studying the transferred muon polarization during the thermally-activated transition from the isotropic Mu state to Mu^*. The results demonstrate that the isotropic part of the Mu^* hyperfine interaction is negative. In a nitrogen-poor diamond, both the Mu disappearance rate and the enhancement of the Mu^* signals are well-described by a single Arrhenius law.     

Radially dependent antishielding factor γ(r) of the Sc3+ ion in the solid state

We report the results of our calculation of γ(r), the radially dependent antishielding factor of Sc³⁺ ion in the crytalline environment. Watson sphere model is used to approximately represent the crystal potential. Differential equations resulting from non-orthogonal Hartree-Fock perturbation theory are solved to obtain perturbations to core electron states. Contribution to γ(r) from electron self-consistency effect has been evaluated by using the latter wave-functions in the many-body expression of Schmidtet al.     

An improved impulse approximation treatment of the “allowed” weak and analogue electromagnetic transitions in 12C

Weak and electromagnetic transitions between the ¹²C ground state and 1⁺ members of the T = 1 isomultiplet are studied in the framework of the impulse approximation. Uncertainties due to the nuclear configuration mixing and radial effects are examined, the former in the framework of the Cohen-Kurath and Migdal models, and the latter in the density-dependent Hartree-Fock approach. Within the uncertainties of the models, the weak and electromagnetic observables at low momentum transfer (≦ 0.5 fm^?1) are reasonably well reproduced. The inelastic electron scattering from factor at higher momentum transfer shows strong deviations from the impulse approximation estimates.     

Sub-Doppler laser absorption spectroscopy of the AΠi − XΣ (1, 0) band of CN: Measurement of the N hyperfine parameters in AΠ CN

Measurements of multiple rotational lines in the (1, 0) band of the A²Π_i − X²Σ⁺ “red” system of the cyanogen radical (CN) at sub-Doppler resolution are reported. The CN radical was produced by 193 nm photodissociation of NCCN (ethane dinitrile) and detected with a Ti:sapphire ring laser operating near 10 900 cm⁻¹. The sample was exposed to a weak, frequency-modulated probe beam and a strong, counterpropagating bleach laser beam. Demodulated probe laser signals display absorption and dispersion features derived from Doppler-free saturation of the hyperfine components as the laser scans across the central region of a Doppler-broadened rotational line spectrum. Hyperfine-resolved transition frequencies were combined with known ground-state X²Σ hyperfine term values to determine A²Π state hyperfine term values, which were analyzed in terms of an effective Hamiltonian for the A²Π state. All the expected hyperfine and ¹⁴N quadrupolar parameters were determined and their values analyzed in terms of a simple molecular orbital picture of the bonding in the radical. Higher sensitivity obtained with 400 kHz amplitude modulation of the bleach laser and additional phase-sensitive detection allowed hyperfine splittings in some rotational lines of ¹³C¹⁴N to be observed in natural abundance. Excited state hyperfine splittings were determined for a selection of rotational states, but not enough to determine the ¹³C hyperfine parameters.     

Polarized electron capture by3He2+ at 20–28 keV

Nuclear polarization was measured by means of beam foil spectroscopy for a³He⁺ ion produced by an electron capture process of a³He²⁺ from a polarized sodium atom in an incident energy range from 20 to 28 keV. Assuming that a polarized electron of a sodium atom is predominantly captured to the 3d orbital of a³He⁺ ion andcascades down to the 1s ground state via the 2p orbital, an alignment factorA ₀ ^col (L=2) for the 3d orbital of a³He⁺ ion was extracted by comparing the observed initial sodium polarization andfinal nuclear polarization. The observedA ₀ ^col (L=2) showed a less pronounced energy dependence andwere qualitatively reproduced by the theoretical calculation.     

Rotational Analysis of the ÃA1-X?A1 Band System of Yttrium Dicarbide, YC2

The 000-000 and 3¹₀ bands of the 775-nm electronic transition of YC₂(òA₁←X?²A₁) have been studied at high resolution, using the laser-induced fluorescence from a supersonic jet expansion. Three types of experiment have been carried out. First, the complete rotational and hyperfine structures of the two bands were recorded. To measure the small asymmetry splittings in the K=2 levels of the X?²A₁ state, portions of the b-type 3¹₀ band were then recorded in the presence of a weak static electric field. Finally, a number of pure rotational transitions between the K=0 levels of the ground state were recorded by pump/probe microwave optical double resonance. A few small rotational perturbations occur in the upper electronic state but, omitting the perturbed lines, the combined data sets could be modeled using an effective Hamiltonian operator appropriate for the rotation, electron spin, and hyperfine structure of a rigid asymmetric top molecule. The molecule is confirmed as being “T-shaped,” where the Y atom is bonded to the side of a C₂ group; the rotational constants determined are for the òA₁, 3¹ level, A=1.76128, B=0.189949, C=0.170056 cm⁻¹, and for the X?²A₁, v=0 level, A=1.742731, B=0.201947, C=0.181285 cm⁻¹. Allowing for electron orbital corrections to the rotational constants, the geometrical structures are found to be òA₁ state, r (Y-C)=2.2795 Å, r (C-C)=1.2630 Å, ∠C-Y-C=32.17°; X?²A₁ state, r (Y-C)=2.1946 Å, r (C-C)=1.2697 Å, ∠C-Y-C=33.63°. A molecular orbital diagram is given for the states of YC₂ and the interpretation of the electron spin and hyperfine parameters is discussed.