Creating the Familiar Periodic Table
Electron Orbital Filling  
Joel M Williams
(author's website)
Los Alamos, NM, USA 
(this html version © 2013 by author)

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While the periodic table arrangement is usefully interpreted in columns of similar behavior, it is erroneous to imply that the underlying orbitals are all the same for all the elements in the columns of a block. Sub-orbital information has been excluded! From the standpoint of chemistry, the “rule of eight” would have provided better imagery on which to build an orbital system than was Bohr’s orb turned-sphere. A sphere is useless from a chemical standpoint. Hybridization should not have to occur to explain the simplest of molecules. Simplicity would have the electrons occupying orbital spaces that are similar in shape. Only three orbital types are actually needed to describe the electron packing of the elements. Octahedral, square-planar, and pyramidal coordination complexes of the transition elements follow logically without the need to hybridize. This brief paper describes a rational packing of electrons around a nucleus that ends up mimicking the familiar periodic table when compressed to similar behavior.


Electron Orbitals based on the "rule of eight" and symmetrical packing without e-spin-reversal

The currently accepted electron orbital structure of atoms is a concession to Bohr’s circular orb. To this orb-turned sphere, the modelers added 3 more orbitals, then 5 more, and then 7 more of various shapes. Explanations of everything related to the electron behavior of atoms was forced to fit this accepted model. When the stoic orbitals could not explain observed behavior, as was the case for even simple molecules, the orbital types were “hybridized” to create even more orbital types, e.g., sp, sp2, etc, etc. There was no looking back for models that needed less massaging to explain reality.

From the standpoint of chemistry, the “rule of eight” would have provided far better imagery on which to build an orbital system than was Bohr’s orb which is useless from a molecular standpoint. The image below shows how non-intersecting orbital spaces are implemented utilizing this “rule of eight” concept.

As seen in the image to the right, there can be two opposing units with four-lobes each. When a single electron is in each of the “red” and “blue” sets, they can move counter to one another and thus be “paired”; this special case of the model negates the need for the spherical orbital type of the current spdf model. More electrons can be added until each lobe is occupied. Oxygen is of note, because its 6 electrons can be arranged in two ways that are not too different in energy, thus giving rise to the singlet/triplet phenomenon; something that required more massaging of the spdf model. Thus, this single 8-lobed model incorporates several of the points that must be addressed in the lowest electron loading and does so without the need for several types of orbitals (spherical and hourglass) and without the need to “hybridize”. Unlike Bohr’s orbs which are scaled to fit the observed spectral data, but have no other rationale, a single electron in one of the 4-lobed orbital scales according to simple classical physics motion and electrostatics to produce the observed spectral data.[1] Why do Electrons (Orbitals) Have Discrete Quantum Numbers?,, Joel M Williams

When the number of electrons is too large to be accommodated by the two quartets (8 total lobes), additional orbital space must be occupied. Simplicity would have the next order of orbitals distributed uniformly amongst the 8 occupied lobes. Simplicity would also have the electrons occupying orbital space not too dissimilar in shape. This is not the case with the spdf model which has increasingly more complex spaces. Symmetrical space-filling arrangements of orbitals around the original 8 are shown below.


Only three orbital types with electrons singularly assigned  to each are needed to describe the electron packing of the elements of the periodic table: Cubic (designated M when only 1 electron occupies a four-lobed unit and C when more than 1 does), Anticubic (18 orbitals in neat symmetry), and Sq-faced (for lack of a better term; 24 orbitals with 8 more to get 32 via tetrahedral space). 

Contrast the simplicity of the MCAS orbitals with the complexity of the doubly occupied spdf orbitals with odd-looking do and fo orbitals (linear combinations of "extra" mathematical solutions to the Schrödinger equation to reduce the number of "expected" orbitals to the number actually needed).

MCAS orbitals and the aufbau of the elements

The image below demonstrates how the elements are formed via the MCAS model starting with the smallest (H) at the bottom and building electron numbers upwards. The unlabeled orbitals below indicated elements are those when all the C-orbitals of a period are filled to create the “inert” gas elements. Breaks in the packing of various orbital sets are shown with gaps and markers.

The following discourse describes some of the salient features of the
MCAS aufbau.  

1.    The energetics of adding more electrons than opposing 2 (He) to the 8 Cubic lobes at the lowest (1st) energy level is far greater than starting a new level. This is much like the situation of landing patterns being able to handle only 2 planes and, thus, all others are placed in more distant patterns. Hydrogen is in mid (1/2-filled) position. Helium has 2 “paired” electrons. The partially filled 8-lobed space should provide some additional behavior that is not available to the other “inert” gases whose lobes are completely filled. Note that only H and He have no underlying electron orbital. All periods above the first have a 1st level with a pair of opposing electrons that occupy separate 4-lobed units. Thus, each element above the first period has its eight first level Cubic lobes filled with the equivalent of 1/4-electron. This is what distinguishes H and He from the rest!.

2.    At the 2nd level (period), the first two electrons go into opposing 4-lobed Cubic orbital sets and are thus paired; electron movement is opposite that of those in the first level. Further additions of electrons continue with the filling of one 4-lobed unit first. Thus, B (C2M1), C (C3M1), N (C4M1), O (C4C2), F C4C3) and Ne (C4C4). The C4C0 state (4-unpaired electrons) of carbon, which facilitates tetrahedral bonding, is not the ground state, but an elevated one. The C3C3 state of oxygen provides the second state that allows O2 to have both singlet and triplet states.

3.    Electron filling at the 3rd period follows the scheme of the 2nd. Again the orbitals to be filled are the two 4-lobed Cubic orbital sets; electron movement is opposite that of those in the 2nd level whose orbital spaces are filled symmetrically (C4C4). This contrasts with the current spdf model that has two different types.

4.    At the 4th period, two electrons can be placed oppose one another in the two 4-lobed Cubic orbital sets. Additional electrons, however, can be accommodated in Anticubic orbitals more favorably than adding them to the remaining Cubic orbitals. The image below should help in understanding the filling that gives the “transition series” its properties.

The Anticubic arrangement bands the Cubic alignment symmetrically. The first few electrons will be in one of the 3 bands. Eventually all 18 lobes will be occupied. Since only 10 electrons are added before the remaining Cubic lobes are filled, 8 electrons must be obtained from elsewhere. These are provided by what would have been the previous Cubic electrons of the same level. Favorable energetics are derived when the Anticubic lobes are filled symmetrically: A18 (completely) and A12 (face-deficient). The Anticubic arrangement easily promotes octahedral, square-planar, and pyramidal coordination complexes without hybridizing as required with the spdf model.  

The table below explains the orbital filling further. Spdf fillings in red are non-Madelung[2].

Orbital Filling of Transition Elements – spdf vs MCAS


4s2 3d1



5s2 4d1



6s2 5d1










4s2 3d2



5s2 4d2



6s2 5d2










4s2 3d3



5s1 4d4    (??)



6s2 5d3










4s1 3d5



5s1 4d5



6s2 5d4     (??)










4s2 3d5



5s2 4d5



6s2 5d5










4s2 3d6



5s1 4d7    (??)



6s2 5d6










4s2 3d7



5s1 4d8    (??)



6s2 5d7










4s2 3d8



5s0 4d10



6s1 5d9    (??)


4M2/3A16 (4M0/3A18)








4s1 3d10



5s1 4d10



6s1 5d10










4s2 3d10



5s2 4d10



6s2 5d10









For the transition elements of the 4 period, the A-orbital filling with the MCAS model is fairly straight forward. Unlike the spdf model, where the only way to have 6-unpaired electrons is to shift a 4-s to a 3-d orbital, the MCAS filling is normal to a symmetrical A12. The symmetrical A12 has one electron missing from each face. The absence of 6-unpaired electrons indicates that this configuration has six 3-electron sub-orbital sets. While the Nickel ground state is standard with 4M2/3A16, it reconfigures to 4M0/3A18 for the tetrahedral Ni(CO)4 with bonding through a now vacant C-orbital. Copper does not follow the pattern as completing the Anticubic orbitals (3A18) with electron pairing provides a lower energy state than pairing an electron in the 4M orbitals. Silver and gold follow suit, in higher periods, with each having a primary valence of 1. Note that each of these has only one of the Cubic sets occupied! These elements are also unique in having fully occupied sub layers. The MCAS Cubic orbitals of Cu, Ag, and Au provide a donor(one electron in a high-energy tetrahedral orbital)-receptor(vacant tetrahedral orbital hole) network that is unrivaled. They, thus, conduct electricity (flowing electrons) nicely.  

A word about the energy of “added” electrons. Internally packed electrons are not easily removed as they are part of a larger structure that would require reordering of others. Thus, while an electron may be “added”, in the sense that one more is needed to balance the nuclear charge, it is not necessarily of higher energy than all of those “added” before it as related to the previous element! Indeed, the “last electron added” is a common misconception produced by the drop-in, aufbau method of the stoic spdf model. Rather, all of an element’s electrons are arranged to give the lowest energy configuration. If one were filling from low-to-high energy, the last electrons loaded would be those in the outermost level! Thus, these are the first removed to form ionic species.

5.    The transition elements of the 5th period have their 4th level Anticubic orbitals overlaying those of the filled 3rd level Anticubic orbitals. As such, they must coordinate with them; phased oppositely. This adds an additional factor to the aufbau and the likelihood of packing anomalies. The series according to the MCAS model starts like that of the 4th period (Yttrium and Zirconium) with the A12 and A18 symmetry drivers holding (Molybdenum and Silver). Palladium also has the A18 allotment and thus no 5M electrons. Niobium, Ruthenium and Rhodium are problematic for the spdf model. I have presented the MCAS configuration of all three that corresponds to those of the 4th and 6th period transition elements.  

6.    The transition elements of the 6th period have their 5th level Anticubic orbitals overlaying those of the filled 3rd level Anticubic orbitals. With the greater level (energy) separation than that in the 5th period, the aufbau is more similar to that of the 4th period. The electrons in the 4th level Anticubic orbitals now occupy 4th level C or S orbitals (see below). The spdf anomalies are Tungsten and Platinum. The expected MCAS filling is given for both with the knowledge that the Anticubic orbitals can load asymmetrically, although it appears this rarely happens.  

7.    When more electrons must be managed than the Anticubic 18 orbitals can handle, another arrangement of the electrons is necessary. After the 5th Anticubic level is begun in the 6th period, electrons are then added to the 4th level. Now, however, unlike the 18-lobes of the Anticubic configuration of the 4th level that sufficed for the 5th period, a 32-lobed configuration (24 S + 8 C) is required. The image below indicates how this is accomplished.  


8.    A similar situation occurs for the 7th period and the 5th level.


From Orbital Filling to the Familiar Periodic Table

The familiar periodic table is very useful in its simplicity: periods with increasing proton mass in columns of similar chemical behavior. Implicit in its conveyance to newbies, however, is that all of the underlying electrons fit stoic “file cabinets”. This is emphasized by the use of [He], [Ne], [Ar], [Kr], [Xe], and [Rn] as the underlying cores. The foregoing section demonstrates that the packing of electrons around a nucleus is more dynamic and uniform than the spdf model permits. The following set of images indicates what is lost in the compression of the MCAS orbital loadings to the familiar version of the periodic table. The starting image is given again for convenience.  

First, the sub-orbitals that are below any element “labeled” level are removed.

Next, all the “unlabeled” orbitals are removed.


Next, the elements are arranged as they are “filled” with the similar designations aligned over one another.

Now, all the individual levels are compressed to that of the outer most level (period) in the order of their filling – the inverse of the familiar periodic table which emphases the building upwards of the element mass.  


The order is now reversed to reflect the lowest electron packing at the top as traditionally viewed.  


While the periodic table arrangement is usefully interpreted in terms of “blocks” and columns of similar behavior, it is erroneous to indicate that the underlying orbitals are all the same for all the elements in that block.  The sub-orbital information has been excluded! Labile electrons are those of uncompleted sets, thus the facile removal of electrons from the “interrupted set” orbitals indicated at the far left. Once completed, orbital sets are quite stable.


Each element is indicated by the unique orbitals it uses. Think in terms of each possessing all those in the period to its left. Thus, Chromium is characterized by MA, Uranium by MAS, but Tungsten by MSA. Their sub-orbitals may be quite different.


To summarize, the MCAS model yields the periodic table upon compression and does not require all the “hybridizing” that the highly touted spdf model needs to accommodate the chemical materials of our real world.



The Uniquely Different Symmetry of Each Noble Element's Underlying Orbital Filling


Unlike the constant, stoic, spdf "block-filling" of electrons around the nucleus, the MCAS model has the electrons flexibly filling space to minimize overlapping electron orbital density. The following image demonstrates the symmetry of each completely filled level terminating with a noble element. As seen, each noble element has a uniquely different, but highly symmetrical, distribution of electrons, as opposed to the currently taught "solid block filling" of the spdf model. In the MCAS model, an orbital is assigned to each and every individual electron and those orbital lobes are all the same shape. The spdf model has 2 electrons paired in orbitals of ever increasing complexity needed to generate them under the model's assumptions. Pairing in the MCAS model occurs with every orbital having a diametrically oppose orbital and thus requires no spin-reversal parameter.


[1] Why do Electrons (Orbitals) Have Discrete Quantum Numbers?,, Joel M Williams


Additional reference: Modeling the MCAS Way (; shaper image version at