Fock space estimates

The polarizability of T1 and element 113 has been calculated using the fully relativistic ab initio Dirac-Coulomb Fock-space coupled-cluster method and the finite field procedure. For Tl, the theoretical value is in good agreement with experiment. In group 13, the atomic polarizability increases from A1 to Ga, attains a maximum for In and then decreases towards Tl and furthermore towards element 113. So, element 113 presents the smallest polarizability, which results from the large relativistic contraction and stabilization of the 7pi/2 orbital. These values have then been used to estimate the adsorption enthalpies of Tl and element 113 on polyethylene and teflon surfaces and have shown that the difference of enthalpy attains 6 kJ/mol, which should be enough to separate and identify them. 

One-center expansion was first applied to whole molecules by Desclaux Pyykko in relativistic and nonrelativistic Hartree-Fock calculations for the series CH4 to PbH4 [81] and then in the Dirac-Fock calculations of CuH, AgH and AuH [82] and other molecules [83]. A large bond length contraction due to the relativistic effects was estimated. However, the accuracy of such calculations is limited in practice because the orbitals of the hydrogen atom are reexpanded on a heavy nucleus in the entire coordinate space. It is notable that the RFCP and one-center expansion approaches were considered earlier as alternatives to each other [84, 85]. 

Figure 1. Total nonrelativistic multi-configuration Hartree-Fock energy, relativistic corrections (estimated as the difference between the multi-configuration Dirac-Hartree-Fock and Hartree-Fock energies) and correlation contributions (estimated from correlation energy density functional calculations) for the group 4 elements. The multi-configuration treatments were carried out with the atomic structure code GRASP [78] and correspond to complete active space calculations with the open valence p shell as active space. The nonrelativistic results were obtained by multiplying the velocity of light with a factor of 10 .

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