The isoelectronic series
As shown in Figure 1, the isoelectronic series are subject to certain regularities which can be described by formulas and numbers.
What strikes in Figure 1 first is that the gradients of the rows from left to right decrease . The decrease happens within the groups. Within these groups, the rows drift nearly parallel. Only at those positions in the periodic table where the switch between main and side groups takes place, the initial value of the isoelectronic series falls; parameter β reflects that. . Furthermore, the structure of the ionization energy in ground state continues in each section. That means that the ionization energies of the elements and their ionized states change consistently in solid proportions to each other.
The first group of isoelectronic series contains of two rows, the second group eight rows, the third and fourth group each contains 18 rows, and finally the fifth and sixth group each contain 32 isoelectronic rows.
As shown before, the gradient of a following group corresponds to a quarter of the previous group. Within each group the gradient of each row rises from left to right. From the second group on, the fine structure 2, 3, 3 of the isoelectronic series can be seen at the start of each pitch group. After these eighth groups, a secondary group follows and it is the one with the same gradient but also with a gap on a value basis. It is parameter β that describes that gap. Not before that the next group, with a reduced gradient, follows.
The first group contains 1 * 2 rows.
The second group contains 1 * 2 and 3 * 2 rows.
The third and fourth group contains 1 * 2 and 3 * 2 and 5 * 2 rows.
The fifth and sixth group contains 1 * 2 and 3 * 2 and 5 * 2 and 7 * 2 rows.
It needs to be investigated whether any rule could be discharged from that . It strikes that the increase of elements in each period is odd and even again by the multiplication with two.