Nuclear charge defined

A question which has been keenly argued for a number of years is the following if it were possible continuously to vary one or more of the parameters determining the nature of a system such as a molecule or a crystal, say the effective nuclear charges, then would the transition from one extreme bond type to another take place continuously, or would it show discontinuities For example, are there possible all intermediate bond types between the pure ionic bond and the pure electron-pair bond With the development of our knowledge of the nature of the chemical bond it has become evident that this question and others like it cannot be answered categorically. It is necessary to define the terms used and to indicate the point of view adopted and then it may turn out, as with this question, that no statement of universal application can be made. 

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... 

Whether zinc is a main-group or transition metal depends, of course, on one s definition of transition metal and main-group metal. Those who classify zinc as a main-group metal cite its (almost) exclusive oxidation number of +2 in compounds (but see Section 2.06.15.2) and the absence of a partially filled r/ shell in the metal and its compounds. Those who classify zinc as a transition metal usually note its much greater effective nuclear charge, polarizing power and its limited, but well defined, coordination chemistry. 

Schwartz50, 51 pointed out that the binding energy of a core electron is essentially equal to the potential felt at the core due to the nuclear charge and all the other electrons in the system. Chemical shifts can be related to a valence electron potential , < val, defined as... 

By = xiytZi) and spin coordinates of individual electrons, n represents the number of electrons in the molecule. For many cases it is appropriate to include nuclear charges as well and to define a molecular charge distribution Q (R) ... 

The Hellmann-Feynman theorem offers a convenient way to highlight the main features of chemical binding. By choosing the nuclear charges as parameters, it becomes possible to define the binding of each individual atom in a molecule without having recourse to an explicit partitioning of that molecule into atomic subspaces. 

The general result for the nuclear charge radius and the Darwin-Foldy contribution for a nucleus with arbitrary spin was obtained in [9]. It was shown there that one may write a universal formula for the sum of these contributions irrespective of the spin of the nucleus if the nuclear charge radius is defined with the help of the same form factor for any spin. However, for historic reasons, the definitions of the nuclear charge radius are not universal, and respective formulae have different appearances for different spins. We will discuss here only the most interesting cases of the spin zero and spin one nuclei. 

In equation (A.77) is defined the atomic orbital population P,-. Summing all of the P, that belong to the same atom, I, yields the atomic population / [equation (A.78)]. The net charge qj on atom I is just the difference between the nuclear charge Zi and the atomic population,... 

The first term in the square bracket in this equation is the electric monopole moment, which is equal to the nuclear charge, Ze. The second term in the square bracket is the electric dipole moment while the third term in the square bracket is the electric quadmpole moment. For a quantum mechanical system in a well-defined quantum state, the charge density p is an even function, and because the dipole moment involves the product of an even and an odd function, the corresponding integral is identically zero. Therefore, there should be no electric dipole moment or any other odd electric moment for nuclei. For spherical nuclei, the charge density p does not depend on 0, and thus the quadmpole moment Q is given by... 

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