Effective nuclear charge density

The calculated nuclear quadrupole coupling constants (NQCCs) of in artemisinin 9a and some of its derivatives and the effects of charge density due to the nature of ligands on the NQCC of were described. All calculations were performed at the HF/3-21G level <2005MI366>. 

While d is proportional to the s-electron density at the nucleus, valuable information about the d (and other) electrons can still be obtained from this parameter due to screening effects. That is, the addition of a d electron reduces, via screening, the effective nuclear charge felt by the s electrons thereby leading to an expansion of the s-electron cloud and a decrease in the electron density at the nucleus. A measurement of 8 thus reflects to some extent the entire electron distribution surrounding the nucleus, giving information about both the atom and its bonding characteristics. 

Two coupled first order differential equations derived for the atomic central field problem within the relativistic framework are transformed to integral equations through the use of approximate Wentzel-Kramers-Brillouin solutions. It is shown that a finite charge density can be derived for a relativistic form of the Fermi-Thomas atomic model by appropriate attention to the boundary conditions. A numerical solution for the effective nuclear charge in the Xenon atom is calculated and fitted to a rational expression. 

Cullity, B. D. Elements ofX-ray Diffraction, 2nd ed., Addison-Wesley Reading, Massachusetts, 1978. The effective nuclear charge is defined as the actual nuclear charge felt by a particular valence electron. It is expressed as Zgff = Z —c, where Z is the nuclear charge for the atom and a is the screening constant. This latter term corresponds to the number of core electrons, and the effectiveness of the orbitals to shield core electron density. 

Based on Eq. 3, the factors that govern the oscillation frequency (and the observed color) are electron density (size/shape of the nanostructures. Figure 6.11), the effective nuclear charge of the nuclei, and the size/shape of the charge distribution (polarization effects, strongly affected by the dielectric constant of the metal). As you might expect, further effects toward the resonance frequency/intensity are... 

If there is a halogen atom bonded directly to the transition metal atom a relatively low specific intensity for the molecule results (2, 30, 52,109). The explanation is probably that the halogen atom increases the effective nuclear charge of the central atom and lowers the energy of the d orbitals. This removes some electron density from the orbitals of the carbonyl groups and thus decreases the specific intensity. The effect has even been claimed to be additive for some types of derivatives (109). It has been established that the specific intensity is related to the inductive character of the halogen atom and decreases in the order I > Br > Cl. In some cases, a linear relationship appears to exist (52). Extending these ideas, Nesmeyanov et al. 107)... 

The term Lamb shift of a single atomic level usually refers to the difference between the Dirac energy for point-like nuclei and its observable value shifted by nuclear and QED effects. Nuclear effects include energy shifts due to static nuclear properties such as the size and shape of the nuclear charge density distribution and due to nuclear dynamics, i.e. recoil correction and nuclear polarization. To a zeroth approximation, the energy levels of a hydrogen-like atom are determined by the Dirac equation. For point-like nuclei the eigenvalues of the Dirac equation can be found analytically. In the case of extended nuclei, this equation can be solved either numerically or by means of successive analytical approximation (see Rose 1961 Shabaev 1993). 

The restricted density functional approximation- —restrict the one-electron functions to superposition of the effective nuclear charge on the nuclei ... 

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