Electronic states elements of molecular quantum mechanics

Electronic States Elements of Molecular Quantum Mechanics... 

Extensive DFT and PP calculations have permitted the establishment of important trends in chemical bonding, stabilities of oxidation states, crystal-field and SO effects, complexing ability and other properties of the heaviest elements, as well as the role and magnitude of relativistic effects. It was shown that relativistic effects play a dominant role in the electronic structures of the elements of the 7 row and heavier, so that relativistic calculations in the region of the heaviest elements are indispensable. Straight-forward extrapolations of properties from lighter congeners may result in erroneous predictions. The molecular DFT calculations in combination with some physico-chemical models were successful in the application to systems and processes studied experimentally such as adsorption and extraction. For theoretical studies of adsorption processes on the quantum-mechanical level, embedded cluster calculations are under way. RECP were mostly applied to open-shell compounds at the end of the 6d series and the 7p series. Very accurate fully relativistic DFB ab initio methods were used for calculations of the electronic structures of model systems to study relativistic and correlation effects. These methods still need further development, as well as powerful supercomputers to be applied to heavy element systems in a routine manner. Presently, the RECP and DFT methods and their combination are the best way to study the theoretical chemistry of the heaviest elements. 

As stated, the most important concept in molecular quantum similarity is the electron density. The idea of the electron density as the ultimate molecular descriptor is founded on the basic elements of quantum mechanics. It is the alldetermining quantity in DFT, and it holds a close relation to the wave function. It is therefore appropriate in this context to raise the question of whether the electron density can really be considered as the all-determining entity in quantum similarity studies. Clear indications of this conclusion were described by Flandy and are attributed to Wilson,although initial ideas can also be traced back to Born" and von Neumann." The electron density p(r) has several important features. First, integrated over all space, it gives the number of electrons ... 

In Section 11.6 we saw that the ability of metals to conduct heat and electricity can be explained with molecular orbital theory. To gain a better understanding of the conductivity properties of metals we must also apply our knowledge of quantum mechanics. The model we will use to study metallic bonding is band theory, so called because it states that delocalized electrons move freely through bands formed by overlapping molecular orbitals. We will also apply band theory to certain elements that are semiconductors. 

Relativity adds a new dimension to quantum chemistry, which is the choice of the Hamiltonian operator. While the Hamiltonian of a molecule is exactly known in nonrelativistic quantum mechanics (if one focuses on the dominating electrostatic monopole interactions to be considered as being transmitted instantaneously), this is no longer the case for the relativistic formulation. Numerical results obtained by many researchers over the past decades have shown how Hamiltonians which capture most of the (numerical) effect of relativity on physical observables can be derived. Relativistic quantum chemistry therefore comes in various flavors, which are more or less well rooted in fundamental physical theory and whose relation to one another will be described in detail in this book. The new dimension of relativistic Hamiltonians makes the presentation of the relativistic many-electron theory very complicated, and the degree of complexity is far greater than for nonrelativistic quantum chemistry. However, the relativistic theory provides the consistent approach toward the description of nature molecular structures containing heavy atoms can only be treated correctly within a relativistic framework. Prominent examples known to everyone are the color of gold and the liquid state of mercury at room temperature. Moreover, it must be understood that relativistic quantum chemistry provides universal theoretical means that are applicable to any element from the periodic table or to any molecule — not only to heavy-element compounds. 

The first two lines in Table 11.6, the bond energies, are required to relate the calculations to the standard states of the elements as the zero of reference. The bond energies in molecular mechanics are just that because of the formalism. But the so-called bond energies in the quantum mechanical calculation also include the energies of the formation of the atoms from the nuclei and the electrons, and hence these numbers are very much larger. 

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