لخّصلي

Plots in Figure 1 depict the one-electron radial density distribution for pairs of adjacent atoms (ions) within the He-isoelectronic series in its ground-state. Moreover, some of the main elements of each of the plots are presented in Figure 1. The first characteristic is the inability of the electron density to extend the nucleus. This is a direct consequence of the properties of any well-defined wavefunction in quantum mechanics. In Figure 1 there are three zones: Starting from the far-right side in each plot, the first non-overlapping encountered region is filled with the light blue colour and referred to, in this work, as the Light blue zone. The second non-overlapping region is filled in yellow and referred to as the Yellow zone. There is only one overlapping region, which is filled in grey and referred to as the Grey zone. as shown in Figure 1: (a), (b), (c), (d), (e), and (f). The Light blue zone is part of the one-particle radial density distribution of the He atom. On the contrary, the one-particle radial density distribution of the Li^(+1) does not extend to the Light blue zone, as shown in Figure 1 (a). This is a natural consequence of having a greater atomic number than the He atom. According to Coulomb law, the more positive charge in the nucleus, the more attractive force will affect the electronic cloud.
The plots in Figure 1: (b), (c), (d), (e), and (f) also show three regions. The amount of charge shift will cause the K-shell size to significantly shrink as atomic number values rise, as Figure 1(f) illustrates. However, the shrinkage in the orbital size will be compensated by producing a denser electron cloud near the nucleus. This claim can be supported by evaluating the peaks of the D(r)for elements shown in Figure 1. The higher the peak's value, the denser the electronic cloud will be:
[〖D(r)〗max ]He< [〖D(r)〗max ](Li^(+1) )< [〖D(r)〗max ](Be^(+2) ) [r_0 ](Be^(+2) ) >[r_0 ](B^(+3) ) >[r_0 ](C^(+4) ) >[r_0 ](N^(+5) ) >[r_0 ]_(O^(+6) )
Plots Figure 2 and 3 represent three and two dimensions, respectively. The contour plot is produced by slicing the three-dimensional plots of the D(r_1,r_2 ) into definite slices. Then, assign a colour to every single slice. Therefore, the contour plot is a projection of the three-dimensional plots onto a two-dimensional plane defined by r_1 and〖 r〗_2. Eleven colours are assigned to the vertical values of D(r_1,r_2 ). see Figures 4 and 5. For example, D(r_1,r_2 ) for He atom spreads over values around〖 r〗_1=r_2≈2, as shown in Figure 3 (a), while D(r_1,r_2 ) for N^(+5)ion is confined within〖 r〗_1=r_2≈0.5 , as presented in Figure 3(f). This is similar to the pattern observed in the D(r), discussed earlier in the chapter. On the contrary, the steepness, of D(r_1,r_2 ), is higher for atoms with large atomic numbers, as shown in Figure 2. Another way, at high atomic numbers, the nucleus draws the electron cloud inward and toward itself. The observation that the red region of the Li^(+1) ion covers the region from 〖D(r_1,r_2)〗_max down to D(r_1,r_2 )=1.80 and the red region of the N^(+5) ion extends from 〖D(r_1,r_2)〗_max down to D(r_1,r_2 )=11confirms this phenomena.