Relativistic ionization potentials

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.

Figure 4.5 Nonrelativistic (NR) and relativistic (R) ionization potentials and electron affinities of the group 11 elements. Experimental (Cu, Ag and Au) and coupled cluster data (Rg) are from Refs. [4, 91, 92].

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. 

The above considerations need relativistic correction at v c, which may be performed in a straightforward manner. More importantly, Eq. (10) assumes that the ionization process is direct, i.e., once a state above the ionization potential is reached, ionization occurs with a certainty. Platzman [25] points out that in molecules, this is not necessarily so and superexcited states with energy exceeding the ionization potential may exist, which will dissociate into neutral fragments with a certain probability. For example, in water in the gas phase, ionization occurs with a sharp threshold at the ionization potential (I.P.) = 12.6 eV, but only with an efficiency of 0.4. Beyond the I.P., the ionization... 

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). 

The diatomic ThO has been detected in the vapor phase over a mixture of Th and Th02 at high temperatures and a D of -9.00 eV, an ionizational potential of 6.0 eV and a R value of 1.8403 angstrom are estimated for ThO (18, 28-29). Ab initio DF SCF calculations in which each molecular spinor (MS) is expressed as a linear combination of (4-component) atomic spinors (LCAS) ( ) as well as the corresponding non-relativistic limit (NRL) calculations were performed for the ground state of ThO at five internuclear separations viz 3.077, 3.477, 3.877, 4.277 and 4.677 au. 

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. 

We comment first on the last point. As we have learned in Chapter 1 the relativistic energies are large for inner shells and their values increase with the atomic number. This trend is reflected in the relativistic corrections. For example, for the inner-shell ionization potentials the relativistic corrections are 0,1 for CH, 0,8... 

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