Nucleus point-charge

Polarization is usually accounted for by computing the interaction between induced dipoles. The induced dipole is computed by multiplying the atomic polarizability by the electric field present at that nucleus. The electric field used is often only that due to the charges of the other region of the system. In a few calculations, the MM charges have been included in the orbital-based calculation itself as an interaction with point charges. 

The exact expression for the dipole moment does n( consider atoms as point charges, but rather as nuclei (eat with a positive charge equal to the atomic number) ar electrons (each with unit negative charge). Atoms wii lone pairs may contribute to the dipole moment, even the atom is neutral, as long as the lone pair electrons a not symmetrically placed around the nucleus. 

Terms up to order 1/c are normally sufficient for explaining experimental data. There is one exception, however, namely the interaction of the nuclear quadrupole moment with the electric field gradient, which is of order 1/c. Although nuclei often are modelled as point charges in quantum chemistry, they do in fact have a finite size. The internal structure of the nucleus leads to a quadrupole moment for nuclei with spin larger than 1/2 (the dipole and octopole moments vanish by symmetry). As discussed in section 10.1.1, this leads to an interaction term which is the product of the quadrupole moment with the field gradient (F = VF) created by the electron distribution. 

The influence of a noncubic electronic charge distribution interacting with a Mossbauer nucleus may be exemplified by using point charges, for which the EFG is easy to calculate. A point charge <7 at a distance r = +y from a... 

The EFG parameters Vzz and described by (4.42a) and (4.42b) do not represent the actual EFG felt by the Mossbauer nucleus. Instead, the electron shell of the Mossbauer atom will be distorted by electrostatic interaction with the noncubic distribution of the external charges, such that the EFG becomes amplified. This phenomenon has been treated by Stemheimer [54—58], who introduced an anti-shielding factor (1 —y 00) for computation of the so-called lattice contribution to the EFG, which arises from (point) charges located on the atoms surrounding the Mossbauer atom in a crystal lattice (or a molecule). In this approach,the actual lattice contribution is given by... 

A second relation between p(r) and 4>(r) may be obtained by noting that the sources of 0(r) are the point charge Ze of the nucleus, located at the origin and the charge distribution due to the N electrons. Treating the charge density —ep(r) of the electrons as continuous, Poisson s equation of electrostatics may be used to write... 

As Fir) is a local maximum at each nucleus in a molecule, if it is plotted along the intemuclear axis z between two bonded atoms, there must be an axial minimum of F(z) (usually positive) at some point zm along that axis. This axial minimum has the interesting property that a point charge Q, placed at zm would feel no electrostatic force in either direction along the intemuclear axis [10,11]. 

For a nucleus at R, the peripheral contribution to the potential 0, due to a spherical density component centered at Rj, consists of a point-charge term and a penetration term. The point-charge term is due to the nuclear charge at Rj and the electronic density within the sphere with radius R, — Ry, centered on Rjt which passes through the nucleus i (Fig. 9.1). The penetration terms are due to the electronic charge outside that sphere. They decay exponentially as the distance Rjj = R, — Rj increases (Hirshfeld and Rzotkiewicz 1974). 

Atomic Levels (positive point charge—nucleus)... 

This chapter is about molecules. A molecule is a collection of nuclei Z., Z/,... at rest (in the Bom-Oppenheimer approximation) in a sea of fast-moving electrons. The nuclei can be identified and thus provide convenient reference marks. Each nucleus found in the molecule, say, Z], can be viewed as the nucleus of a giant atom extending over the entire molecule is surrounded by charges, just as in an ordinary atom, with the difference that motionless positive point charges are now part of its environment. Of course, the electronic content is still described by its stationary density. 

Moreover, because the nuclei are effectively point charges, it should be obvious that their positions correspond to local maxima in tlie election density (and these maxima are also cusps), so the only issue left to completely specify the Hamiltonian is die assignment of nuclear atomic numbers. It can be shown diat diis information too is available from the density, since for each nucleus A located at an electron density maximum Fa... 

In the Gurney-Mott mechanism, the trapped electron exerts a coulombic attraction for the interstitial silver ion. This attraction would be limited to a short distance by the high dielectric constant of the silver bromide. Slifkin (1) estimated that the electrostatic potential of a unit point charge in silver bromide falls to within the thermal noise level at a distance of "some 15 interatomic spacings." The maximum charge on the sulfide nucleus would be 1 e. The charge on a positive kink or jog site after capture of an electron would not exceed e/2. An AgJ would have to diffuse to within the attraction range before coulombic forces could become a factor. 

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