Ionization potentials relativistic effects

The total energy in ab initio theory is given relative to the separated particles, i.e. bare nuclei and electrons. The experimental value for an atom is the sum of all the ionization potentials for a molecule there are additional contributions from the molecular bonds and associated zero-point energies. The experimental value for the total energy of H2O is —76.480 a.u., and the estimated contribution from relativistic effects is —0.045 a.u. Including a mass correction of 0.0028 a.u. (a non-Bom-Oppenheimer effect which accounts for the difference between finite and infinite nuclear masses) allows the experimental non-relativistic energy to be estimated at —76.438 0.003 a.u. ... 

Table 4.2 Nonrelativistic (NR) and relativistic (R) ionization potentials A p and electron affinities AEp (positive values and in eV), relativistic effects Ap and relativistic enhancement factors y for the Group 11 elements of the periodic table.

Besides these many cluster studies, it is currently not knovm at what approximate cluster size the metallic state is reached, or when the transition occurs to solid-statelike properties. As an example. Figure 4.17 shows the dependence of the ionization potential and electron affinity on the cluster size for the Group 11 metals. We see a typical odd-even oscillation for the open/closed shell cases. Note that the work-function for Au is still 2 eV below the ionization potential of AU24. Another interesting fact is that the Au ionization potentials are about 2 eV higher than the corresponding CUn and Ag values up to the bulk, which has been shown to be a relativistic effect [334]. A similar situation is found for the Group 11 cluster electron affinities [334]. 

Schwerdtfeger, P. (1991) Relativistic and Electron Correlation Contributions in Atomic and Molecular Properties. Benchmark Calculations on Au and Au2. Chemical Physics Letters, 183, 457 163. Neogrady, P., Kello, V., Urban, M. and Sadlej, A.J. (1997) Ionization Potentials and Electron Affinities of Cu, Ag, and Au Electron Correlation and Relativistic Effects. International Journal of Quantum Chemistry, 63, 557-565. 

Energy levels of heavy and super-heavy (Z>100) elements are calculated by the relativistic coupled cluster method. The method starts from the four-component solutions of the Dirac-Fock or Dirac-Fock-Breit equations, and correlates them by the coupled-cluster approach. Simultaneous inclusion of relativistic terms in the Hamiltonian (to order o , where a is the fine-structure constant) and correlation effects (all products smd powers of single and double virtual excitations) is achieved. The Fock-space coupled-cluster method yields directly transition energies (ionization potentials, excitation energies, electron affinities). Results are in good agreement (usually better than 0.1 eV) with known experimental values. Properties of superheavy atoms which are not known experimentally can be predicted. Examples include the nature of the ground states of elements 104 md 111. Molecular applications are also presented. 

Like copper, silver and gold have a single s electron outside the completed d shell, but in spite of the similarity in electronic structures and ionization potential, the chemistries of Ag, Au, and Cu differ more than might be expected. There are no simple explanations for many of the differences although some of the differences between Ag and Au may be traced to relativistic effects on the 6s electrons of the latter. The covalent radii of the triad follow the trend Cu < Ag Au, i.e., gold has about the same or a slightly smaller covalent radius than silver in comparable compounds, a phenomenon frequently referred to as relativistic contraction (c/. lanthanide contraction). 

To conclude the analysis of the approximations noted, it is possible to state that, from the point of view of chemical applications, they represent very subtle effects. The experience shows that if ab initio calculations are in disagreement with experiment, it is in most cases not due to the approximations noted. As will be shown in next chapters, the crucial point in ab initio calculations is the basis set effect and, if the calculations are at the SCF level, also the correlation energy. The only exceptional case we shall meet in this book concerns ionization potentials for core electrons in molecules containing heavy atoms. Here the relativistic effects are very important. 

Relativistic effects on the valence electrons are already evident by comparing the electropositive character of Fr and Ra with that of their preceding homologues. The ionization potentials of both elements are not lower than those of their homologues Cs and Ba, respectively, as expected by extrapolation, but the ionization potential of Fr is about the same as that of Cs and the ionization potential of Ra is somewhat higher than that of Ba. The influence of relativistic effects on the properties of the actinides is evident also from the tendency of the heavier actinides to form lower oxidation states. For example, Es already prefers the oxidation state Es2+. 

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