Characteristics of Many-Electron Atoms

Like the Bohr model, the Schrodinger equation does not give exact solutions for many-eleetron atoms. However, unlike the Bohr model, the Schrodinger equation gives very good approximate solutions. These solutions show that the atomic orbitals of many-eleetron atoms resemble those of the H atom, which means we can use the same quantum numbers that we used for the H atom to describe the orbitals of other atoms. 

Nevertheless, the existence of more than one electron in an atom requires us to consider three features that were not relevant in the case of hydrogen (1) the need for a fourth quantum number, (2) a limit on the number of electrons allowed in a given orbital, and (3) a more complex set of orbital energy levels. Let s examine these new features and then go on to determine the electron configuration for each element. 

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Studies of isoelectronic sequences are very useful and fruitful in theoretical, semi-empirical and experimental investigations of atomic spectra. They reveal important regularities and pecularities in the behaviour of various physical characteristics of many-electron atoms and ions, help to identify and classify their energy levels with an optimal coupling scheme, find initial values of semi-empirical parameters, etc. 

The methods of theoretical description of many-electron atoms on the basis of tensorial properties of the orbital and spin angular momenta are well established [14, 18] and enable the spectral characteristics of these systems to be effectively found. The relation between the seniority quantum number and quasispin makes it possible to extend the mathematical tools to include the quasispin space and to work out new modifications of the mathematical techniques in the theory of spectra of many-electron atoms that take due account of the tensorial properties of the quasispin operator. 

The data of atomic spectroscopy are of extreme importance in revealing the nature of quantum-electrodynamical effects. For the investigation of many-electron atoms and ions, it is of great importance to combine theoretical and experimental methods. Therefore, the methods used must be universal and accurate. A number of physical characteristics of the many-electron atom (e.g., a complete set of quantum numbers) may be found only on the basis of theoretical considerations. In many cases the mathematical modelling of physical objects and processes using modern computers may successfully replace the corresponding experiments. In this book we shall describe the contemporary state of the theory of many-electron atoms and ions, the peculiarities of their structure and spectra as well as the processes of their interaction with radiation, and some applications. 

These are the simplest processes in spectroscopy. The principles of spectroscopy will be a recurring theme as we probe the microscopic structure of many-electron atoms and molecules, because spectroscopy remains the most precise and adaptable tool for controlling and measuring the quantum mechanical characteristics of a chemical system. From spectroscopy comes our most precise molecular geometries and successful theories of chemical bonding, as well as many of our most powerful analytical techniques. 

It has not proved mathematically feasible to calculate the electron-electron repulsion that causes this change in orbital-energies for many-electron molecules. It is even difficult to rationalize the qualitative changes in sequence on the basis of the shapes of the 11orbitals. Greater success has been achieved by an approximate method which begins with orbitals characteristic of the isolated atoms present in the molecule, and assumes that molecular orbital wave functions can be obtained by taking linear combinations of atomic orbital wave functions (abbreviated L.C.A.O.). For... 

In fact, there is little reason to believe that s, p, and d orbitals really do exist in the outer shells of many bonded atoms. Remember that these different orbitals arise in the first place from the interaction of the electron with the central electrostatic force field associated with the positive nucleus. An outer-shell electron in a bonded atom will be under the influence of a force field, emanating from two positive nuclei rather than one, so we would expect the orbitals in the bonded atoms to have a somewhat different character from those in free atoms. We can, in fact, throw out the concept of atomic orbital altogether and reassign the electrons to a new set of molecular orbitals that are characteristic of each molecular configuration. This approach is indeed valid, but we will defer a discussion of it until later. For now, we will look at a less-radical model that... 

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