Charles Janet's left-step periodic table  is the most widely used alternative to the traditional depiction of the periodic system. It organizes elements according to an idealized orbital filling (instead of valence). For example, the elements Sc to Zn are shown as a 3d block implying orbital occupancy (Ar)4s23dx, although it is now known that Cr actually has orbital occupancy (Ar)4s13d5 and Cu has (Ar)4s13d10.
This form of periodic table is congruent with the order in which electron shells are ideally filled according to the Madelung rule, as shown in the accompanying sequence in the left margin (read from top to bottom, left to right). The experimentally determined electron configurations of the elements differ from the configurations predicted by the Madelung rule in twenty instances.
Left to right: s-, f-, d-, p-block in the common periodic table presentation; for sufficiently high principal quantum numbers, these blocks fill out in the order of s, p, d, and f. The left-step periodic table is organized according to a reversal of this order, so that the true order is maintained through a proper reading.
Compared to the common layout, the left-step table has these changes:
Helium is placed in group 2 (not in group 18).
Groups 1 and 2 (the s-block), including elements 119 and 120 in extended period 8, are moved to the right side of the table.
The s-block is shifted upwards one row, and all elements not in the s-block are now one row lower than in the standard table. For example, most of the fourth row in the standard table is the fifth row in this table.
In the result, the order is still consistently by atomic number (Z), 1–120.
Paul Giguère's 3-D periodic table consists of four connected billboards with the elements written on the front and the back. The first billboard has the group 1 elements on the front and the group 2 elements at the back, with hydrogen and helium omitted altogether. At a 90° angle the second billboard contains the groups 13 to 18 front and back. Two more billboards each making 90° angles contain the other elements.
Ronald L. Rich has proposed a periodic table where elements appear more than once when appropriate. He notes that hydrogen shares properties with group 1 elements based on valency, with group 17 elements because hydrogen is a non-metal but also with the carbon group based on similarities in chemical bonding to transition metals and a similar electronegativity. In this rendition of the periodic table carbon and silicon also appear in the same group as titanium and zirconium.
ADOMAH (Valery Tsimmerman, 2006)
The ADOMAH periodic table reflects electron configurations of atoms.
The ADOMAH table is an adaptation of the left step table. Each strictly vertical column of the table has the same value of the principal quantum number n. For example, n = 3 for Fe. Each block of elements has the same value of the secondary quantum number l. For example, l = 2 for Fe. Each element entry together with all preceding elements corresponds to the electron configuration of that element (with 20 exceptions out of 118 known elements). For example, the electron configuration of Fe is determined by starting at H, which is 1s1, and counting in atomic number order. This gives a configuration of 1s2 2s2 2p6 3s2 3p6 4s2 3d6 or, in short form, [Ar] 4s2 3d6.
The four blocks of the Adomah table can be rearranged such that they fit, equidistantly spaced, inside a regular tetrahedron. The latter, in turn, fits into a cube.
A chemists' table ("Newlands Revisited") with an alternative positioning of hydrogen, helium and the lanthanides was published by EG Marks and JA Marks in 2010.
Variants of the classical layout
From Mendeleev's original periodic table, elements have been basically arranged by valence (groups in columns) and the repetition therein (periods in rows). Over the years and with discoveries in atomic structure, this schema has been adjusted and expanded, but not changed as a principle.
Mendeleev's 1871 periodic table in VIII columns. Nowadays, roughly spoken, pairs of Reihen are shown as grouplabels A, B (for example: Reihen 4, 5 are written as period 3 and groups (columns) IA–VIIIA, IB–VIIIB).
H. G. Deming used the so-called long periodic table (18 columns) in his textbook "General Chemistry", which appeared in the USA for the first time in 1923 (Wiley), and was the first to designate the first two and the last five main groups with the notation "A", and the intervening transition groups with the notation "B".
The numeration was chosen so that the characteristic oxides of the B groups would correspond to those of the A groups. The iron, cobalt, and nickel groups were designated neither A nor B. The noble-gas group was originally attached (by Deming) to the left side of the periodic table. The group was later switched to the right side and usually labeled as group VIIIA.
In the research field of superatoms, clusters of atoms have properties of single atoms of another element. It is suggested to extend the periodic table with a second layer to be occupied with these cluster compounds. The latest addition to this multi-story table is the aluminium cluster ion Al− 7, which behaves like a multivalent germanium atom.
Spiral periodic table (Robert W Harrison)
The Ring Of Periodic Elements (TROPE)
Curled ribbon periodic table (J. F. Hyde)
Circular periodic table
Alternative circular periodic table
Spiral periodic table (Jan Scholten)
Mendeleev's Flower (Flower periodic table)
Binary electron shells periodic table
"Stowe" periodic table
"Zmaczynski & Bayley" periodic table
ADOMAH periodic table (V. Tsimmerman)
Pyramidal periodic table
Stowe–Janet–Scerri with 3D electron orbitals
4D Stowe–Janet–Scerri periodic table
^E. R. Scerri. The Periodic Table, Its Story and Its Significance. Oxford University Press, New York, 2006, ISBN0195345673.
^Henry Bent. New Ideas in Chemistry from Fresh Energy for the Periodic Law. AuthorHouse, 2006, ISBN978-1-4259-4862-7.
^Stewart, Philip J. (2009). "Charles Janet: Unrecognized genius of the periodic system". Foundations of Chemistry. 12: 5–15. doi:10.1007/s10698-008-9062-5.
^Benfey's table appears in an article by Glenn Seaborg, "Plutonium: The Ornery Element", Chemistry, June 1964, 37 (6), 12–17, on p. 14.
^Mazurs, E. G. (1974). Graphical Representations of the Periodic System During One Hundred Years. Alabama: University of Alabama Press. p. 111. ISBN978-0-8173-3200-6.
^ The animated depiction of Giguère's periodic table that is widely available on the internet (including here) is erroneous, as it does not include hydrogen and helium. Giguère included hydrogen, above lithium, and helium, above beryllium. See: Giguère P. A. (1966). "The 'new look' for the periodic system". Chemistry in Canada vol. 18 (12): 36–39 (see p. 37).
^Stewart, P. (2018). "Amateurs and professionals in chemistry: The case of the periodic table". In Scerri, E.; Restrepo, G. (eds.). From Mendeleev to Oganesson: A Multidisciplinary Perspective on the Periodic Table. New York: Oxford University Press. pp. 66–79 (76–77). ISBN978-0-190-66853-2.; Leach, M. R. "ADOMAH Periodic Table Glass Cube". Internet Database of Periodic Tables. Retrieved August 1, 2019.
^Marks, E. G.; Marks, J. A. (2010). "Newlands revisited: A display of the periodicity of the chemical elements for chemists". Foundations of Chemistry. 12: 85–93. doi:10.1007/s10698-010-9083-8.
A 1974 review of the tables then known is considered a definitive work on the topic: Mazurs, E. G. Graphical Representations of the Periodic System During One Hundred Years. Alabama; University of Alabama Press, 1974, ISBN0-8173-3200-6.