Angular momentum charge densities

The electron transfer from a partially filled band is obtained by multiplying Nj.j by the fractional occupation of the T band. The purely ionic model is transformed by the latter two equations into a model containing a bonding charge that reproduces the essential features of the electronic structure of NaCl-type compounds when the hybridization is reasonably weak. Whereas the atom and angular-momentum projected densities of states in the unhybridized model arose simply from the T unhybridized bands, they now contain additional parts due to hybridization with the T bands. Dashed lines have been added to complete the hybridized density of states in fig. 58. The number of electrons transferred between the atoms by this interaction is estimated from eq. (68) to be, with UN as example,... 

We often say that an electron is a spin-1/2 particle. Many nuclei also have a corresponding internal angular momentum which we refer to as nuclear spin, and we use the symbol I to represent the vector. The nuclear spin quantum number I is not restricted to the value of 1/2 it can have both integral and halfintegral values depending on the particular isotope of a particular element. All nuclei for which 7 1 also posses a nuclear quadrupole moment. It is usually given the symbol Qn and it is related to the nuclear charge density Pn(t) in much the same way as the electric quadrupole discussed earlier ... 

S magnitude and direction of the spin angular momentum p charge density, Cm"3 (density, gcm ... 

Figure 2.1. Schematic picture illustrating the local probe character in XES for N2 adsorbed on a Ni surface. From the total charge density (gray envelope) valence electrons with p-angular momentum (contour lines) decay into the N Is core hole. From Ref. [3].

In our spherical geometry the states of an electron-hole pair can be classified according to the values of the total angular momentum of the electron and hole. We shall assume that the electron-hole pair occupies the lowest excited state. In this state the total angular momentum is zero, and therefore the function >(r, r) is spherically symmetric and P(r) = P(r). Orienting the 2-axis parallel to the vector dvc, we obtain for the charge density... 

It is also possible to produce a spherically symmetric half-filled subshell, in which each orbital contains only one electron, and the spins are all aligned parallel to each other. This situation arises, for example, in the element Mn, which has five electrons in the d subshell, all five of which have their spins pointing in the same direction. The charge density for the half-filled subshell is spherically symmetric, and it therefore has zero total orbital angular momentum L = 0 and a total spin S = 5/2 (its multiplicity is 25 + 1 = 6). Its ground state is therefore 6S5/2-... 

When two CH2 molecules combine, it seems reasonable to assume the superposition of two identical charge distributions of this kind, with a common Z-axis. An alternative is to assume that the two carbon atoms line up with respective electronic configurations of C(p p+i) and C p p i) as in 7(b)E. The azimuthal distribution of the angular momentum vectors of such a pair is in opposite sense as shown in Figure 20-7(e). The actual distribution of electron density in the ethylene molecule is conjectural. The obvious guess that anti-parallel 2p solutions quench the angular momentum, is favoured, but not confirmed, by chemical intuition. 

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