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).

Redox reactions of group 5 elements, including element 105, in aqueous solutions

Standard redox potentials E^0(M^z+x/M^z+) in acidic solutions for group 5 elements including element 105 (Ha) and the actinide, Pa, have been estimated on the basis of the ionization potentials calculated via the multiconfiguration Dirac-Fock method. Stability of the pentavalent state was shown to increase along the group from V to Ha, while that of the tetra- and trivalent states decreases in this direction. Our estimates have shown no extra stability of the trivalent state of hahnium. Element 105 should form mixed-valence complexes by analogy with Nb due to the similar values of their potentials E^0(M^3+/M^2+). The stability of the maximumoxidation state of the elements decreases in the direction 103 > 104 > 105.

State-dependent volume isotope shifts of low-lying states of group-IIa and -IIb elements

Results of relativistic multiconfiguration Dirac-Fock calculations with an extended nucleus are used to analyze the volume isotope shifts of the resonance transitions in the group-IIa and -IIb elements as well as in Yb. This is done together with a review of the isotope shift theory, including a critical evaluation and comparison of the semiempirical calculation of volume isotope shifts commonly used today. Electronic factors F_i, proportional to differences of electronic densities over the nuclear volume, are discussed within various approximations and compared with experimental results.

Computing Generators of Free Modules over Orders in Group Algebras

Let E be a number field and G be a finite group. Let A be any O_E-order of full rank in the group algebra E[G] and X be a (left) A-lattice. We give a necessary and sufficient condition for X to be free of given rank d over A. In the case that the Wedderburn decomposition E[G] \cong \oplus_xM_x is explicitly computable and each M_x is in fact a matrix ring over a field, this leads to an algorithm that either gives elements \alpha_1,...,\alpha_d \in X such that X = A\alpha_1 \oplus ... \oplusA\alpha_d or determines that no such elements exist. Let L/K be a finite Galois extension of number fields with Galois group G such that E is a subfield of K and put d = [K : E]. The algorithm can be applied to certain Galois modules that arise naturally in this situation. For example, one can take X to be O_L, the ring of algebraic integers of L, and A to be the associated order A(E[G];O_L) \subseteq E[G]. The application of the algorithm to this special situation is implemented in Magma under certain extra hypotheses when K = E = \IQ.

Predicted properties of the superheavy elements. III. Element 115, Eka-Bismuth

Element 115 is expected to be in group V-a of the periodic table and have most stable oxidation states of I and III. The oxidation state of I, which plays a minor role in bismuth chemistry, should be a major factor in 115 chemistry. This change will arise because of the large relativistic splitting of the spherically symmetric 7p_l/2 shell from the 7P_3/2 shell. Element 115 will therefore have a single 7p_3/2 electron outside a 7p^2_1/2 closed shell. The magnitude of the first ionization energy and ionic radius suggest a chemistry similar to Tl^+. Similar considerations suggest that 115^3+ will have a chemistry similar to Bi^3+. Hydrolysis will therefore be easy and relatively strongly complexing anions of strong acids will be needed in general to effect studies of complexation chemistry. Some other properties of 115 predicted are as follows: ionization potentials I 5.2 eV, II 18.1 eV, III 27.4 eV, IV 48.5 eV, 0 \rightarrow 5^+ 159 eV; heat of sublimation, 34 kcal (g-atom)^-1; atomic radius, 2.0 A; ionic radius, 115^+ 1.5 A, 115^3+ 1.0 A; entropy, 16 cal deg^-1 (g-atom)^-l (25°); standard electrode potential 115^+ |115, -1.5 V; melting and boiling points are similar to element 113.