Jeries A. Rihani
(I) THE NOTION OF HALF-FILLED AND COMPLETELY-FILLED ORBITALS
To begin with, let us assume that the nuclei of the elements, including their corresponding atomic structure, beyond element 118 are experimentally synthesizable. Let us further assume that the extrapolated Aufbau Principle also holds and applies in the order shown below without any exception:
1s<2s<2p<3s<3p<4s<3d<4p<5s<4d<5p<6s<4f<5d<6p<7s<5f<6d<7p<8s<5g<6f<7d<8p<9s
NOTE: In element 118, which is the last in the seventh row, all the orbitals up to 7p are completely filled. The filling of the next sequence of orbitals in the order of 8s<5g<6f<7d<8p, as shown above, constitute the extrapolated eighth row. Orbital 9s, however, represents the beginning of the ninth row. Beyond element 120, according to Burkhard Fricke and Wikipedia, the proximity of the electron shells makes placement in a simple table problematic. However, Pekka Pyykk� stated, in his article "Is The Periodic Table All Right?", that in spite of some irregularities and anomalies, the Madelung mnemonic up to Z = 172 still holds and is surprisingly good even in that range. Eric Scerri reveals around 20 of these anomalies in his article "The Trouble With The Aufbau Principle" but all are located in the rows preceding the eighth.
Now, If the previous stated assumptions (stated at the beginning) were granted then we could perhaps argue that since the periodic table of the elements in its extended form must continue to be an exact reflection of the electron configurations of all the elements, including the newly synthesized ones, it must also reflect our detailed understanding of the way the atomic orbitals (at the ground state) tend to become either half-filled or completely-filled orbitals (as a result of seeking lowest possible energy levels). For example, at certain appropriate instances or occasions, the d-orbital, within any relevant electron period (electrons in orbitals very close in energy levels like 7s<5f<6d<7p or 8s<5g<6f<7d<8p), chooses to receive an electron from the s-orbital within the same period in order to satisfy this tendency (as in the electron configurations of Cr, Cu, Mo, Ag, Au, Uuu?, Uhu?). By comparison, the f-orbital, in seeking to satisfy the same tendency in similar occasions, chooses to receive this required electron from the d-orbital, its closest in energy level within the same period (as in the electron configurations of Eu, Yb, Am, No, Uqp?, Upb?).
(II) REACHING THE ENERGY LEVELS OF THE EIGHTH ELECTRON PERIOD AND BEYOND
In the light of this presentation for the d & f orbitals, what are our expectations for the g-orbital in the period 8s<5g<6f<7d<8p? Specifically, if the g-orbital is to follow a similar pattern in seeking lowest possible energy, should it receive its 'occasional electron' from d or from, its closest, the f? And in proceeding even further, when h's turn comes along in the advanced period 10s<6h<7g<8f<9d<10p, should the h-orbital, in seeking the same again, pick its 'occasional electron' from d, from f, or from, its closest, the g?
For now, we can put aside the question regarding h and focus on g alone. In fact it is too early to deal with h and perhaps even not possible but we can probably assume that finding an answer for g may help us extrapolate and predict the answer for h (theoretically at least)*.
(III) SEABORG'S EXTENDED PERIODIC TABLE VERSES MINE
The above nonrelativistic approach to the question regarding g led to two extrapolations or choices (Seaborg's and mine) and, at this stage, we do not know which choice is correct (that is if any). Thus, if g should behave in a similar manner as f and must (in certain instances or occasions) acquire its 'occasional electron' from d, there was no objection to that because it was assumed that d had one electron available to offer as was illustrated in the extended periodic table that was suggested by (Glenn T. Seaborg). On the other hand, if neighboring f constituted a better alternative donor than d (because neighboring f, according to Madelung energy-ordering mnemonic, was closer to g in energy level) then it was necessary to propose a different extension than Seaborg's and probably like that suggested by (Jeries A. Rihani). It must be emphasized, however, that accepting any of these two choices depends on whether the 'occasional electron' is available in either of the two probable electronic configurations and which, of course, is still wanting to be verified experimentally.
NOTE: In 1984, I made two layouts, on independent sheets of paper, for two different extended periodic tables corresponding to the two different possible answers for g suggested above. And instead of including both versions in the appendix of the two studies published by The Royal Scientific Society in Amman, Jordan, I included only mine. I was hoping that someday my extended form might draw the attention of somebody interested in the same issue and perhaps initiate some sort of a debate in order to resolve the issue. This debate never materialized and the issue still stands unresolved. Presently, however, it has been approached as follows:
The proponents of the two extrapolated extensions just presented based their extensions on the presumption that the heavier elements of the eighth period must necessarily follow the previous notions and patterns set by the lighter elements of the preceding periods without any exception. By this presumption they ignored taking into account the following:
a) The relativistic effects which in the heavier elements, compared to the lighter elements, become more imminent and more significant.
b) The crowded effects of the many extra shells or subshells in the heavier elements and how they energetically overlap and become partially occupied and how, at this stage, the calculations involved can only give approximate or incomplete results because of the extreme complexity of the situation. Actually, when the orbitals become about equal in energy levels, the electron shells overlap in such a way that the block concept no longer applies and the positioning of the elements become very difficult. For that reason, many elements in the 8th period are predicted to have mix characteristics not of one specific group but of several (Read Eric Scerri's article, "Cracks In The Periodic Table", published by Scientific American in 2013).
c) The theoretical studies in 1971 by Burkhard Fricke and later by Pekka Pyykk� revealed in theoretical detail how several of the super heavy elements get displaced from the Madelung energy-ordering mnemonic and how the spin-orbit coupling effects come significantly into play and reduce the validity of the orbital approximations substantially. In other words, these super-heavy displacements are expected to divert the periodic table away from its normal flow and may, eventually, disqualify and discredit my long held perception that assumed, based on (Timothy Stowe's) ingenius tabulation, that the periodic table, in spite of some casual irregularities, may continue to flow along its familiar path and may at the end reach a final 3D bilateral symmetry constituting a finale or an end to the periodic table (Timothy Stowe's Extended).
(IV) PYYKKO'S RELATIVISTIC AND COMPUTER MODELING APPROACH
Pekka Pyykk� of the University of Helsinki, Finland, in a paper presented at the 150th anniversary of "Weltkongress Chemie" at Karlsruhe, Germany, covered all of the above issues in his relativistic approach to extension. He, as an expert in relativity and quantum chemistry, used computer modeling (as Burkhard Fricke did before him) and applied the Dirac-Fock calculations on atoms and ions to calculate the positions and relative placements of the elements 119 up to 172 in the different blocks of the Periodic Table, and found that these elements did not exactly follow the Madelung energy-ordering mnemonic or exactly the notion of half-filled or completely-filled orbitals and showed, after taking into account the lower and higher spin-orbit split components of 8p and 9p, that the exterior shell-filling sequence for the period of elements 119-172 should roughly follow the order shown below:
Note that this exterior energy order incorporates new factors and, therefore, is different from the corresponding one in the extrapolated Aufbau Principle (i.e. 8s<5g<6f<7d<8p), and suggests an extension very different from the extensions we indicated previously. Thus, by showing the effect of spin orbital splitting at this super heavy atomic stage, which is highly significant, Pekka Pyykk� predicts and expects the exterior shell-filling sequence to fill up in the following order:
1) two spaces for 8s [for Z = 119 & 120]
2) eighteen spaces for 5g [for Z = 121,122, ...138]
3) the first two spaces for 8p(1/2) [for Z = 139 & 140]
4) fourteen spaces for 6f [for Z = 141,142, ...154]
5) ten spaces for 7d [for Z = 155,156, ...164]
6) two spaces for 9s [for Z = 165 & 166]
7) the first two spaces for 9p(1/2) [for Z = 167 & 168]
8) the rest of four spaces for 8p(3/2) [for Z = 169,170, ...172]
And to study Pyykk�'s Extended Periodic Table, which is the most recent, and compare it with the others, you need to go here (Pekka Pyykk�) or here:
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*Reaching the h-block stage is highly improbable and it seems likely the periodic table may reach an end at a much earlier stage either at atomic number 120 or 170.
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