Relativistic effects in physics and chemistry of element 105. [Part] I.

A detailed study of the electronic structure and bonding of the pentahalides of group 5 elements V, Nb, Ta, and element 105, hahnium (and Pa) has been carried out using relativistic molecular cluster Dirac-Slater discrete-variational method. A number of calculations have been performed for different geometries and molecular bond distances. The character of the bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It is shown that hahnium is a typical group 5 element. In a great number of properties it continues trends in the group. Some peculiarities in the electronic structure of HaCl_5 result from relativistic effects.

Relativistic effects in physics and chemistry of element 105. [Part] II.

Relativistic self-consistent charge Dirac-Slater discrete variational method calculations have been done for the series of molecules MBr_5, where M = Nb, Ta, Pa, and element 105, Ha. The electronic structure data show that the trends within the group 5 pentabromides resemble those for the corresponding pentaclorides with the latter being more ionic. Estimation of the volatility of group 5 bromides has been done on the basis of the molecular orbital calculations. According to the results of the theoretical interpretation HaBr_5 seems to be more volatile than NbBr_5 and TaBr_5.

Relativistic effects in physics and chemistry of element 105. [Part] III.

Electronic structures of MOCl_3 and MOBr_3 molecules, where M = V, Nb, Ta, Pa, and element 105, hahnium, have been calculated using the relativistic Dirac-Slater discrete variational method. The character of bonding has been analyzed using the Mulliken population analysis of the molecular orbitals. It was shown that hahnium oxytrihalides have similar properties to oxytrihalides of Nb and Ta and that hahnium has the highest tendency to form double bond with oxygen. Some peculiarities in the electronic structure of HaOCl_3 and HaOBr_3 result from relativistic effects. Volatilities of the oxytrihalides in comparison with the corresponding pentahalides were considered using results of the present calculations. Higher ionic character and lower covalency as well as the presence of dipole moments in MOX_3 (X = Cl, Br) molecules compared to analogous MX_5 ones are the factors contributing to their lower volatilities.

Theoretical evidence for quasi-molecular structure at small internuclear distances in elastic ion-atom scattering

The potential energy curve of the system Ne-Ne is calculated for small internuclear distances from 0.005 to 3.0 au using a newly developed relativistic molecular Dirac-Fock-Slater code. A significant structure in the potential energy curve is found which leads to a nearly complete agreement with experimental differential elastic scattering cross sections. This demonstrates the presence of quasi-molecular effects in elastic ion-atom collisions at keV energies.

Inclusive probability calculations for the K-vacancy transfer in collisions of S{^15+} on Ar

Using the single-particle amplitudes from a 20-level coupled-channel calculation with ab initio relativistic self consistent LCAO-MO Dirac-Fock-Slater energy eigenvalues and matrix elements we calculate within the frame of the inclusive probability formalism impact-parameter-dependent K-hole transfer probabilities. As an example we show results for the heavy asymmetric collision system S{^15+} on Ar for impact energies from 4.7 to 16 MeV. The inclusive probability formalism which reinstates the many-particle aspect of the collision system permits a qualitative and quantitative agreement with the experiment which is not achieved by the single-particle picture.

Multiple vacancy inclusive probabilities for the scattering system 16 MeV S{^16+} on Ar

To evaluate single and double K-shell inclusive charge transfer probabilities in ion-atom collisions we solve the time-dependent Dirac equation. By expanding the timedependent wavefunction in a set of molecular basis states the time-dependent equation reduces to a set of coupled-channel equations. The energy eigenvalues and matrix elements are taken from self-consistent relativistic molecular many-electron Dirac-Fock-Slater calculations. We present many-electron inclusive probabilities for different final configurations as a function of impact parameter for single and double K-shell vacancy production in collisions of bare S on Ar.

Interatomic potential structures in highly ionized scattering systems

The interatomic potential of the ion-atom scattering system I^N+-I at small intermediate internuclear distances is calculated for different charge states N from atomic Dirac-Focker-Slater (DFS) electron densities within a statistical model. The behaviour of the potential structures, due to ionized electronic shells, is studied by calculations of classical elastic differential scattering cross-sections.

Electronic structure of UF_5

Non-relativistic and relativistic self-consistent Hartree- Fock-Slater and Dirac-Slater models have been used to calculate one-electron energy levels and ionization energies for UF_5. The calculations were performed in an assumed structure of C_4v symmetry with the uranium atom at the center of mass of the molecule. The spacing and level ordering are compared with earlier results obtained with the MS X\alpha method using the muffin-tin approximation. Connections with the multiphoton isotope separation scheme of UF_6 are discussed.

Electronic structure and properties of the group 4, 5 and 6 highest chlorides including elements 104, 105, and 106

Results of the Dirac-Slater discrete variational calculations for the group 4, 5, and 6 highest chlorides including elements 104, 105, and 106 have shown that the groups are not identical with respect to trends in the electronic structure and bonding. The charge density distribution data show that notwithstanding the basic increase in covalency within the groups this increase diminishes in going from group 4 to group 6. As a result, E106Cl_6 will be less stable toward thermal decomposition than WCl_6, which is confirmed by an estimated low E106-Cl bond energy. \delta H_form equal to -90.3 ± 6 kcal/rnol is obtained for E106Cl_6 in the gas phase, which is indicative of a very low stability of this compound. The stability of the maximum oxidation state is shown to decrease in the direction E104(+4) > E105(+5) > E106(+6).

Predicted properties of the superheavy elements, II. Element 111, Eka-Gold

The chemical properties of element 111, eka-gold, are predicted through the use of the periodic table, relativistic Hartee-Fock-Slater calculations, and various qualitative theories which have established their usefulness in understanding and correlating properties of molecules. The results indicate that element 111 will be like Au(III) in its chemistry with little or no tendency to show stability in the I or II states. There is a possibility that the 111 - ion, analogous to the auride ion, will be stable.

Finite element method for the accurate solution of diatomic molecules

We present the Finite-Element-Method (FEM) in its application to quantum mechanical problems solving for diatomic molecules. Results for Hartree-Fock calculations of H_2 and Hartree-Fock-Slater calculations of molecules like N_2 and C0 have been obtained. The accuracy achieved with less then 5000 grid points for the total energies of these systems is 10_-8 a.u., which is demonstrated for N_2.

Model calculations on the influence of quantum electrodynamical effects on the chemistry of superheavy elements.

Using a phenomenological model, the influence of quantum electrodynamical effects on the prediction of the chemical behavior of superheavy elements within a relativistic Dirac-Slater calculation was investigated. This influence will be small and nondetectable for elements up to Z = 114. For elements near Z = 164 some changes in the ground state configurations occur but the chemical behavior will not change. Using this heuristic model, it is also possible to calculate elements beyond Z = 175. As an example we have chosen element E184 and are now able to make more valid speculations about the chemical behavior of the element than Penneman and co-workers could.

Relativistic effects in physics and chemistry of element 105. [Part] IV.

Results of relativistic (Dirac-Slater and Dirac-Fock) and nonrelativistic (Hartree-Fock-Slater) atomic and molecular calculations have been compared for the group 5 elements Nb, Ta, and Ha and their compounds MCl_5, to elucidate the influence of relativistic effects on their properties especially in going from the 5d element Ta to the 6d element Ha. The analysis of the radial distribution of the valence electrons of the metals for electronic configurations obtained as a result of the molecular calculations and their overlap with ligands show opposite trends in behavior for ns_1/2, np_l/2, and (n -1 )d_5/2 orbitals for Ta and Ha in the relativistic and nonrelativistic cases. Relativistic contraction and energetic stabilization of the ns_1/2 and np_l/2 wave functions and expansion and destabilization of the (n-1)d_5/2 orbitals make hahnium pentahalide more covalent than tantalum pentahalide and increase the bond strength. The nonrelativistic treatment of the wave functions results in an increase in ionicity of the MCl_5 molecules in going from Nb to Ha making element Ha an analog of V. Different trends for the relativistic and nonrelativistic cases are also found for ionization potentials, electronic affinities, and energies of charge-transfer transitions as well as the stability of the maximum oxidation state.

Calculation of isomer shift in Mössbauer spectroscopy

The approximations normally used in the calculation of the isomer shift are compared with the exact expressions using Dirac-Slater orbitals and a three-parameter Fermi-type nuclear charge distribution. The nonuniformity of the electronic density over the nuclear volume affects the results. Different choices of the nuclear surface thickness t and the radius c in the protonic density P_N (\gamma) also affects the isomer shift differently even though the values are chosen to yield a given value of \delta . The change in the electronic charge density which is caused by the alteration of P_N (\gamma) in the ground state and excited state of the nucleus is discussed using two extrememodels and the possible influence on the observable isomer shift is estimated.

Relativistic molecular calculations of superheavy molecules

Relativistic molecular calculations within the Dirac-Slater scheme have been used in a study of the electronic structure of 6d-metal superheavy hexafluorides. The theoretical results are compared with calculations and measurements of the homolog 4d- and 5d-metal hexafluorides. Large spin-orbit splitting dominates the electronic structure and even has the same order of magnitude as the crystal-field splitting for the valence electrons for the superheavy molecules. Ionization energies have been calculated using a transition state procedure.