Hydrogen effective nuclear charge

A similar model for many-electron atoms has been developed,6 by considering each electron to be hydrogen-like, but under the influence of an effective nuclear charge (Z — Ss)e, in which Ss is called the size-screening constant. It is found that atoms and ions containing only 5 electrons (with the quantum number l equal to zero) and completed sub-groups of... 

As a first approximation, each electron in a many-electron atom can be considered to have the distribution in space of a hydrogen-like electron under the action of the effective nuclear charge (Z—Ss)e, in which 5s represents the screening effect of inner electrons. In the course of a previous investigation,6 values of S5 for a large number of ions were derived. 

It is customary to express the empirical data concerning term values in the X-ray region by introducing an effective nuclear charge Zeff e in the place of the true nuclear charge Ze in an equation theoretically applicable only to a hydrogen-like atom. Often a screening constant S is used, defined by the equation... 

To calculate the energy functions W and W2 it is necessary to evaluate the three integrals Haa, Hab and Sab. It is noted that the variational constant k has the same role as an effective nuclear charge in hydrogenic functions. The normalized functions ls and lsB are therefore of the form... 

As required by (36), the variational parameter k is calculated to vary between k = 2 at R = 0 and k = 1 at R > 5ao- The parameter k is routinely interpreted as either a screening constant or an effective nuclear charge, as if it had real physical meaning. In fact, it is no more than a mathematical artefact, deliberately introduced to remedy the inadequacy of hydrogenic wave functions as descriptors of electrons in molecular environments. No such parameter occurs within the Burrau [84] scheme. 

Use hydrogen and lithium to compare the concepts of nuclear charge and effective nuclear charge. 

Prove that the Is orbital of hydrogen is orthogonal to the 2s orbital. Is this also true if Z, the effective nuclear charge, is different in Is and 2s ... 

The variational function 0 can be provided with more parameters so that the energy can also be minimized with respect to these parameters, whereby a continually improved agreement with the correct energy can be obtained. The introduction of an effective nuclear charge % into the hydrogen functions instead of the nuclear charge i forms one of these extensions. 

Energies of the Hartree orbitals are different from those of the corresponding hydrogen atomic orbitals. For an atom with atomic number Z they can be estimated as -Zeff/n, where the effective nuclear charge experienced by each electron is determined by screening of that electron from the full nuclear charge by other electrons. 

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