Hyperfine structure in low-lying levels of PtII,AuII and BiII

Far UV lines in the spectra of PtII, AuII and BiII emitted by a hollow-cathode lamp exhibit Fabry-Perot patterns, which are used for determining the hyperfine structure of the low-lying levels of these three spectra and the isotopic shifts in five lines of PtII. The experimental data are compared with those computed through the relativistic Dirac-Fock method. The effect of spin polarisation is discussed. In the case ofd electrons the Hartree-Fock method with spin polarisation is used for explaining the large ratio between the spin polarisation and relativistic effects.     

Effects of electron correlation and relativistic effects in X-ray diffraction

Atomic scattering factors for the first row transition metal atoms cobalt and nickel have been evaluated using non-relativistic and ‘relativistic-corrected’ configuration interaction wavefunctions in the |αLSM _LM_S〉 representation. Relaxing the constraints imposed by the Hartree-Fock model results in a very small reduction of the atomic scattering factor at small momentum transfer with a negligible change at higher momentum transfer. Better agreement with the relativistic Hartree-Fock atomic scattering factors at small momentum transfer is obtained when theLS-dependent relativistic effects are included in the Breit-Pauli approximation.     

Relativistic pseudopotentional incorporating core/valence polarization and nonlocal effects

A relativistic pseudopotentional (RPP) for use in ab initio molecular electronic structure calculations is derived in the context of the relativistic effective core potential (REP) method of Lee et al. The resulting atom-specific RPP has salient features of the REP imbedded within it while retaining the form of a functional that is dynamically defined at runtime when used in calculations on molecules. The RPP is determined from Dirac-Fock wave functions for the isolated atom. Outer core two-electron interactions are incorporated into the RPP by means of variable coefficients that are defined in the context of the final molecular wave function. This form permits polarization of the outer core shells analogous to that occurring in all-electron molecular Hartree-Fock calculations while retaining these shells as part of the atomic pseudopotentional. Use of the RPP in post-Hartree-Fock molecular calculations permits the incorporation of core/valence correlation effects.     

Quantum similarity study of atomic density functions: insights from information theory and the role of relativistic effects

A novel quantum similarity measure (QSM) is constructed based on concepts from information theory. In an application of QSM to atoms, the new QSM and its corresponding quantum similarity index (QSI) are evaluated throughout the periodic table, using the atomic electron densities and shape functions calculated in the Hartree-Fock approximation. The periodicity of Mendeleev's table is regained for the first time through the evaluation of a QSM. Evaluation of the information theory based QSI demonstrates, however, that the patterns of periodicity are lost due to the renormalization of the QSM, yielding chemically less appealing results for the QSI. A comparison of the information content of a given atom on top of a group with the information content of the elements in the subsequent rows reveals another periodicity pattern. Relativistic effects on the electronic density functions of atoms are investigated. Their importance is quantified in a QSI study by comparing for each atom, the density functions evaluated in the Hartree-Fock and Dirac-Fock approximations. The smooth decreasing of the relevant QSI along the periodic table illustrates in a quantitative way the increase of relativistic corrections with the nuclear charge.     

Smooth relativistic Hartree-Fock pseudopotentials for H to Ba and Lu to Hg

We report smooth relativistic Hartree-Fock pseudopotentials (also known as averaged relativistic effective potentials) and spin-orbit operators for the atoms H to Ba and Lu to Hg. We remove the unphysical extremely nonlocal behavior resulting from the exchange interaction in a controlled manner, and represent the resulting pseudopotentials in an analytic form suitable for use within standard quantum chemistry codes. These pseudopotentials are suitable for use within Hartree-Fock and correlated wave function methods, including diffusion quantum Monte Carlo calculations.     

Dissociation energy of ekaplutonium fluoride E126F: the first diatomic with molecular spinors consisting of g atomic spinors

Our ab initio all-electron fully relativistic Dirac-Fock (DF) and nonrelativistic (NR) Hartree-Fock (HF) self-consistent field (SCF) calculations predict the superheavy diatomic ekaplutonium fluoride E126F to be bound with the calculated dissociation energy of 7.44 and 10.46 eV at the predicted E126-F bond lengths of 2.03 and 2.18 Angstroms, respectively. The antibinding effects of relativity to the dissociation energy of E126F are approximately 3 eV. The predicted dissociation energy with both our NR HF and relativistic DF SCF wave functions is fairly large and is comparable to that for very stable diatomics. This is the first case, where in a diatomic, an atom has g orbital (l = 4) occupied in its ground state electronic configuration and such superheavy diatomics would have occupied molecular spinors (orbitals) consisting of g atomic spinors (orbitals). This opens up a whole new field of chemistry where g atomic spinors (orbitals) may be involved in electronic structure and chemical bonding of systems of superheavy elements with Z> or =122.     

Calculations of electronic structure of the UF<Subscript>6</Subscript> molecule and the UO<Subscript>2</Subscript> crystal with a relativistic pseudopotential

The influence of relativistic effects on the properties of uranium hexafluoride was considered. Detailed comparison of the spectrum of one-electron energies obtained in the nonrelativistic (by the Hartree-Fock method), relativistic (by the Dirac-Fock method), and scalar-relativistic (using a relativistic potential of the uranium atom core) calculations was carried out. The methods of optimization of atomic basis in the LCAO calculations of molecules and crystals are discussed which make it possible to consider distortion of atomic orbitals upon the formation chemical bonds. The influence of the atomic basis optimization on the results of scalar-relativistic calculations of the molecule UF₆ properties is analyzed. Calculations of the electronic structure and properties of UO₂ crystals with relativistic and nonrelativistic pseudopotentials are fulfilled.     

The electronic structure of oxo-Mn(salen): single-reference and multireference approaches

Using single- and multireference approaches we have examined many of the low-lying electronic states of oxo-Mn(salen), several of which have not been explored previously. Large complete-active-space self-consistent-field (CASSCF) computations have been performed in pursuit of an accurate ordering for the lowest several electronic states. Basis set and relativistic effects have also been considered. For the geometry considered, our best results indicate the ground spin state to be a closed-shell singlet, followed by a pair of low-lying triplet states, with additional singlet states and the lowest quintet state lying significantly higher in energy. Hartree-Fock and density functional theory (DFT) results are obtained and are compared to the more robust CASSCF results. The Hartree-Fock results are qualitatively incorrect for the relative energies of the states considered. Popular density functionals such as BP86 and B3LYP are superior to Hartree-Fock for this problem, but they give inconsistent answers regarding the ordering of the lowest singlet and triplet states and they greatly underestimate the singlet-quintet gap. We obtained multiple Hartree-Fock and DFT solutions within a given spin multiplicity, and these solutions have been subjected to wave function stability analysis.     

Electronic structure and prediction of atomization energy of naked homoleptic uranium hexacarbonyl U(CO)6

Our ab initio all-electron fully relativistic Dirac-Fock and nonrelativistic Hartree-Fock self-consistent field (SCF) calculations predict the octahedral (Oh) uranium hexacarbonyl U(CO)6 to be bound with the calculated atomization energy of 49.84 and 48.76 eV at the predicted U-C bond lengths (assuming the C-O bond distance fixed at 1.17 A) of 2.53 and 2.63 A, respectively. Moreover, our all-electron fully relativistic Dirac-Fock SCF calculations predict U(CO)6 to be lower in energy by 3.90 eV with respect to dissociation into U plus six CO ligands. We predict U(CO)6 (Oh) to be very stable in view of our predicted large atomization energy (approximately 49 eV) and stability (approximately 4 eV) with respect to dissociation into U plus six CO molecules. Innovative techniques should be devised for the synthesis of uranium hexacarbonyl since the usual synthetic methods have failed so far for this naked actinide hexacarbonyl.     

Gaussian basis sets for calculation of spin densities in first-row atoms

Summary The suitability of Gaussian basis sets for ab initio calculation of Fermi contact spin densities is established by application to the prototype first-row atoms B-F having open shell p electrons. Small multiconfiguration self-consistent-field wave functions are used to describe relevant spin and orbital polarization effects. Basis sets are evaluated by comparing the results to highly precise numerical grid calculations previously carried out with the same wave function models. It is found that modest contracted Gaussian basis sets developed primarily for Hartree-Fock calculations can give semiquantitative results if augmented by diffuse functions and if further uncontracted in the outer core-inner valence region.     

Spin polarization of electrons elastically scattered from argon atoms in the Ramsauer-Townsend region

Spin polarization of elastic electron scattering from argon atoms in the Ramsauer-Townsend region (0.1–0.6 eV) is calculated using a relativistic method. Via the energy-angle dependent surfaces, the differential cross section and the spin polarization parametersS, T andU are presented as functions of both the electron energy and the scattering angle. It is shown that the spin polarization effect is significant along a projected curve in the energy-angle plane.     

Relativistic corrections to alkali atomg-factors

Relativistic and Breit corrections tog-factors in ground states of alkali atoms, obtained by using a four component non-perturbative formalism and single determinantal wavefunctions constructed from central field Dirac-Fock four-component orbitals, are reported. The results enable a clear assessment on the magnitude of relativistic effects on alkali-atomg-factors. Deviations of our results from experiment further provide estimates on the effect of electron correlation on alkali atomg-factors.     

Relativistic well-tempered gaussian basis sets

The effectiveness of well-tempered Gaussian basis sets has been tested for the atoms He-Ar, Ag, and Xe. It has been found that orbital exponents optimized through the well-tempered scheme for non-relativistic atoms can be carried over to relativistic calculations to produce wavefunctions close to the relativistic Hartree-Fock limit.     

Calculated optical and magnetic properties of hexafluorouranate (V) anion: UF- 6

Our ab initio all-electron Dirac-Fock and the corresponding nonrelativistic limit calculations performed at four U-F bond distances yield for octahedral UF(6) (-) the optimized U-F bond distance of 2.091 and 2.088 A, respectively. We have also performed Dirac scattered wave calculations at the optimized U-F bond distances using the first-order pertubational procedure to obtain the Zeeman and hyperfine magnetic tensors for the octahedral anion UF(6) (-). The calculated isotropic Zeeman tensor of Deltag=-2.87 is in fairly good agreement with the value of Deltag=-2.78+/-0.10 obtained in electron spin resonance experiments on the H(3)O(+)UF(6) (-) adduct and the unpaired electron-spin spends approximately 2.5% of its time on the fluorine 2p(3/2) spinors. The calculated relativistic transition energies of the near-IR and visible absorption bands are also in good agreement with the experimental results. The octahedral uranium hexafluoride anion has a simple crystal field f(1) configuration; however, relativistic four-component wave functions are necessary to interpret correctly the available magnetic data, while a relativistic treatment taking into account double group symmetrized basis functions should suffice for the interpretation of the optical data.     

Electric field effects on the shielding constants of noble gases: a four-component relativistic Hartree-Fock study

Second derivatives of nuclear shielding constants with respect to an electric field, i.e., shielding polarizabilities, have been calculated for the noble gas atoms from helium to xenon. The calculations have been carried out using the four-component relativistic Hartree-Fock method. In order to assess the importance of the individual relativistic corrections, the shielding polarizabilities have also been calculated at the nonrelativistic Hartree-Fock level, with spin-orbit and scalar (Darwin and mass-velocity) effects having been established by perturbative methods. Electron correlation effects have been estimated using the second-order polarization propagator approach. The relativistic effects on the tensor components of the shielding polarizabilities are found to be larger and changing less regularly with the atomic number than for the shielding constant itself. However, there is a partial cancellation of the contributions to the parallel and perpendicular components of the shielding polarizability and as a consequence the mean shielding polarizability is far less affected than the individual components.     

Relativistic effects in kurchatovium chemistry

Using the relativistic multiconfigurational Dirac-Fock method, the first four ionization potentials of Ku, the promotion energies of the atom, and the atomic and ionic radii were calculated. The enthalpy of sublimation of metallic Ku was estimated. Relativistic SCF-X scattering wave Dirac-Slater computations of the tetrachlorides of group IV elements were performed. The lower halides of Ku are predicted to be more stable and less volatile than the respective Hf compounds, due to the ds² p ground state in the Ku atom.     

Configuration interaction methods for improving unrestricted Hartree-Fock spin densities

Limited Configuration Interaction wave functions based on Unrestricted Hartree-Fock natural orbitals are found to be easy to compute and to give much more satisfactory spin densities than are provided by techniques currently in use.     

A semiclassical model of polarisation forces in atomic scattering

Low-energy elastic, differential and integral, collision cross sections for electron scattering from rare gas atoms are calculated using a simplified model treatment of the short-range polarisation forces already applied successfully to helium atoms (De Fazio et al., 1994). Static and exchange contributions to the total interaction are treated exactly, while a global semiclassical model provides a simple procedure for the short-range damping of all the long-range adiabatic terms which asymptotically lead to the polarisation forces. The results are compared with several available experimental findings for Ne and Ar atoms. The higher order terms in the perturbation expansion are found to have little effect on the cross sections and then only at low energies and in the small-angle region.Von Humboldt Stiftung Forschungspreisträger (1992)