Apparent nuclear charge

The apparent nuclear charge, or the effective nuclear charge, is designated Zeff. For a helium atom Zeff, the charge experienced by each electron, is less than 2. In general,... 

E = me2 Einstein s equation proposing that energy has mass E is energy, m is mass, and c is the speed of light. (12.2) Effective nuclear charge the apparent nuclear charge exerted on a particular electron, equal to the actual nuclear charge minus the effect of electron repulsions. (12.11)... 

The effective nuclear charge is the apparent nuclear charge that the valence electrons experience as the result of shielding by the inner core electrons. As the effective nuclear charge increases, the electrons contained within an orbital feel a stronger attractive force toward the nucleus. The electrons are pulled toward the nucleus, reducing the size of the atomic orbital. 

Fig. 9.51 An electron at a distance rfrom the nucleus experiences a Coulombic repulsion from all the electrons within a sphere of radius rthat is equivalent to a point negative charge located on the nucleus. The effect of the point charge is to reduce the apparent nuclear charge of the nucleus from Ze to Z e.

A variation function with variable orbital exponents in the 1 atomic orbitals making up the LCAOMOs ofEq. (20.3-5) gives Oe = 3.49 eV and re = 73.2 pm with an apparent nuclear charge equal to 1.197 protons (a larger charge than the aetual nuclear charge). A careful Hartree-Fock-Roothaan calculation gives De = 3.64 eV and = 74 pm." If this result approximates the best Hartree-Fock result, the correlation error is approximately 1.11 eV. 

Now our nuclear model suffices. We can build up the atoms for all elements. Each atom has a nucleus consisting of protons and neutrons. The protons are responsible for all of the nuclear charge and part of the mass. The neutrons are responsible for the rest of the mass of the nucleus. The neutron plays a role in binding the nucleus together, apparently adding attractive forces which predominate over the electrical repulsions among the protons. ... 

Much more recently, extremely accurate studies on He-like systems have been reported, including that of Frolov [4] on H and He, an even more precise study of He by Schwartz [5], and computations on the He-like positive ions with nuclear charges Z=3-10 by Frolov and Smith [6]. While these investigations quantitatively reproduced the energy and other properties of He-like systems, the wavefunctions which did so contained thousands of terms, making an understanding of their features less than apparent. The situation corresponds well to an observation made by Mulliken [7] (and resuscitated in a recent paper by Scully et al. [8]) ... 

A second factor which must be considered is the nature of the d orbitals. The size of the d orbitals is inversely related to the effective nuclear charge. Since elective overlap of d orbitals appears necessary to stabilize metal clusters, excessive contraction of them will destabilize the cluster. Hence large charges resulting from very high oxidation states arc unfavorable. For the first transition series, the d orbitals are relatively small, and even in moderately low oxidation states ( + 2 and +3) they apparently do not extend sufficiently for good overlap. 

Most of the quantum chemical calculations of the nuclear shielding constants have involved two classes of solvation models, which belong to the second group of models (n), namely, the continuum group (i) the apparent surface charge technique (ASC) in formulation C-PCM and IEF-PCM, and (ii) models based on a multipolar expansion of the reaction filed (MPE). The PCM formalism with its representation of the solvent field through an ASC approach is more flexible as far as the cavity shape is concerned, which permits solvent effects to be taken into account in a more accurate manner. 

Given the greater nuclear charge of the succeeding elements, however, and these structures become stable. (In the case of erbium the three additional nuclear charges of lutecium are necessary before this particular erbium kernel structure becomes stable.) Thus the following elements derive their properties from the tendency to revert to the stable forms of the key elements. These are called the beta forms, or Ni/3, Pd/3, Er/3, Pt/3, and the subordinate periods are based on these forms, as is apparent in the table, in the same way that the major periods are based on the inert gases. 

From the discussion of Chapter I, it follows that metallic conduction is to be associated with partially filled bands of collective-electron states. Since the s-p bands of an ionic compound are either full or empty, metallic conduction implies partially filled d bands, and collective d electrons imply Rtt < Rc(n,d). From the requirement Rtt < Rc(n4) it is apparent that the metallic conduction in ionic compounds must be restricted either to transition element compounds in which the anions are relatively small or to compounds with a cation/anion ratio > 1. Also Rc(n,d) decreases, for a given n, with increasing atomic number, that is with increasing nuclear charge, and the presence of eQ electrons increases the effective size of an octahedral cation (627) (see Fig. 66) and similarly UQ electrons the size of a tetrahedral cation. It follows that If the cation/anion ratio < 1, MO d electrons are more probable in ionic compounds with octahedral-site cations if the cations contain three or less d electrons MO d electrons are more probable in ionic compounds with tetrahedral-site cations if the cations contain two or less d electrons. 

As Table III indicates, the nature of the substituents in distannanes can influence both the chemical shift (S referenced relative to tetramethyltin) and the direct one-bond coupling constant, J(" Sn-" Sn). The influence of substituents on chemical shifts has been discussed in detail elsewhere (42 a) therefore, an in-depth analysis of the nature of this influence will not be repeated here. However, the influence of substituents on the J(" Sn-" Sn) values deserves some comment 43-44 a-c). In the case of peralkyidistannanes (Table III), it has been proposed that from an apparent linear correlation between J( " Sn-" Sn) and 2cr (the sum of the Taft cr constants of the six alkyl groups bound to the tin atoms), the main factor involved in determining the value of J(" Sn-" Sn) in these compounds is eff) the effective nuclear charge at the tin nucleus 43 a,b). However, an alternative proposal to explain the trend observed in Table III is based on the equation derived by Pople and Santry 45) for the coupling mechanism in a two-body spin system [Eq. (7)]. Here, s(0)... 

Trends in orbital energy and size reflect changes in the principal quantum number and effective nuclear charge. They are seen experimentally in trends in ionization energy (IE) and apparent radius of atoms. 

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