The periodic table is an icon. But chemists still can’t agree on how to arrange it

One hundred fifty years after Russian chemist Dmitri Mendeleev published his system for neatly arranging the elements, the periodic table it gave birth to hangs in every chemistry classroom in the world and is one of the field’s most recognizable symbols. But the solid squares and familiar patterns of today’s table mask one of its fundamental characteristics: “the” periodic table does not exist.

It’s been mutable from the beginning. Not only has it grown as new elements have been discovered; it has also added columns and changed shape as we’ve gained new understanding of the elements’ properties and their relationships to one another. And scientists are still debating its optimum configuration.

Some believe chemical properties should dictate how the elements line up on the periodic table. Others think a more fundamental principle is needed, like electronic configuration or simply atomic number. Partisans are clashing over which elements belong in group 3, where helium should go, and how many columns the periodic table should have. They follow a long line of chemists and physicists who have worked and reworked the elements into a semblance of order.

“What I find interesting about the current debate is there are people who insist on there being one right table,” says Michael D. Gordin, a Princeton University historian who has written about Mendeleev, Julius Lothar Meyer, and other creators of early periodic tables. “It would have struck people like Mendeleev and Lothar Meyer as weird.” Gordin says the periodic table pioneers understood their tables to be a reflection of natural laws but recognized that different tables could represent those laws in different ways. That might be hard to imagine for those of us used to seeing the familiar shape of the table on our coffee mug or shower curtain.

Setting the table

Mendeleev wasn’t the first to recognize patterns in the elements, nor was he the first to try to depict those patterns in a diagram. Chemist Johann Wolfgang Döbereiner, for instance, identified triads of elements with shared properties in 1829. Today we’d recognize these as members of the same group or column of the periodic table, like chlorine, bromine, and iodine.

Geologist Alexandre-Émile Béguyer de Chancourtois published a kind of periodic table in 1862 in which the elements spiraled up a cylinder according to atomic weight. Each column of elements shared properties.

Mendeleev published his table, which he called a “periodic system,” in 1869. It included all 56 elements then known, and if you squint, it has a somewhat similar shape to the periodic table we see today, only tipped 90° on its side. Mendeleev arranged the elements in order of increasing weight and broke them into rows such that elements in each column shared valence, the number of other atoms they combined with, as well as other properties.

What made Mendeleev’s table special was his recognition that the periodic system was strong enough to predict undiscovered elements, which he left holes for, and even their properties. Lothar Meyer was independently working on an almost identical table, but Mendeleev beat him to publication by a few months and secured his place in history.

One can trace today’s controversies over how the periodic table should look to the discovery of quantum mechanics and atomic numbers. Mendeleev ostensibly organized his table by increasing atomic weight, but he gave chemical properties a deciding vote. For example, tellurium is slightly heavier than iodine, but Mendeleev put tellurium first because it has the same valence as oxygen, sulfur, and other elements in its group. Tables have retained that ordering. Mendeleev didn’t know that tellurium has one fewer proton—and thus is one atomic number less—than iodine, which explains why they each belong where they do. “When you get atomic number, it provides logic” to the periodic table, Gordin says.

Along with protons came the discovery of electrons and the quantum-mechanical idea of atomic orbitals. These findings provided a whole new kind of logic for the periodic system. Although the organization of Mendeleev’s system didn’t change, scientists could now see that it was electronic structure that largely dictated elements’ properties and explained why members of the same group were similar. The Madelung rule, or aufbau principle, that dictates that electrons fill the 1s orbital first and then the 2s and the 2p and so on, further explained how the elements were ordered.

That brings us to the tables we see today, which don’t look that different from the versions famed chemist Glenn T. Seaborg drew in the 1940s. Seaborg moved the f-block elements—also called the lanthanide and actinide series—out of the main table to leave them floating below. This decision is generally understood as a concession to convenience; if those elements were in line with the others, the table would be too wide to fit on a standard sheet of paper or the type would be too small to read.

Seaborg included 15 elements in his f-block. That doesn’t make a lot of sense from an electronic configuration point of view, since the f orbitals hold only 14 electrons. But many tables—including the table on the website of the International Union of Pure and Applied Chemistry (IUPAC), which has the last word on naming elements and molecules—share this feature. It’s a way of avoiding one of the most controversial questions about the periodic table: What elements belong in group 3? No one disputes scandium and yttrium. But which elements come below those two? Lanthanum and actinium? Or lutetium and lawrencium?

Group decision

Today there’s no standardization in the periodic tables found in classrooms, labs, and textbooks. Some avoid the group 3 question and use a 15-element f-block. Others put La and Ac in group 3, and still others have Lu and Lr, with the remainder of the f-block floating below.

IUPAC has convened a working group to make a definitive recommendation one way or the other. One motivation for forming the task group, according to IUPAC’s website, is to clear up confusion among students and teachers about which table is correct.

Philip Ball, a science writer and member of the working group, says the debate comes down to a fundamental question of whether physics or chemistry shapes the table. Put another way, he says the group is debating whether to side with the quantum physics that determines elements’ electronic configurations or with the way elements behave chemically.

On the side of chemical behavior is Guillermo Restrepo, a mathematical chemist at the Max Planck Institute for Mathematics in the Sciences. Restrepo takes a historical view of how the table should be organized. He points to Mendeleev and his contemporaries, who found their periodic systems by studying elements’ properties, often through their binding behavior. “At the core of the periodic system, what you have is chemistry,” Restrepo says, “and you need chemical reactions.”

Restrepo and colleagues analyzed some 4,700 binary compounds containing 94 elements to determine how chemical reactions inform the periodic system (MATCH Commun. Math. Comput. Chem.2012, 68,417). The molecules could consist of more than one atom but only two elements. The researchers created a map that groups elements near those that form similar compounds. For example, fluorine, chlorine, and the other halogens sit next to each other because they all bind to similar elements.

Restrepo says this similarity landscape shows that lanthanum is more similar to scandium and yttrium than lutetium is, so it should be in group 3. But the analysis doesn’t provide a good answer about Lr versus Ac. Restrepo says the problem is there isn’t much data on how Lr and Ac bind to other entities. While there are tens of thousands of compounds one can use to study the similarities of Sc, Y, La, and Lu, Ac provides only about 70 data points, and Lr, fewer than 40, according to Restrepo.

Eric Scerri, a philosopher of science at the University of California, Los Angeles, and the chair of the IUPAC task group, disagrees. He believes Sc, Y, Lu, and Lr should be the group 3 elements. Scerri thinks a focus on chemical or physical properties is misguided. He compares it to early botanists’ classification of flowers by their color or petal number.

“You’ve got to go for something fundamental,” Scerri says, like electronic configuration. “Just to amass properties is never going to give you a definitive answer.”

Not that electronic configuration is perfect either, as Scerri will tell you. Exceptions have been made for some elements in the periodic table in terms of how their orbitals are filled, like copper. By the periodic table’s logic, all d-block elements should have filled s orbitals. But copper defies that logic. It should have the electron configuration [Ar] 3d⁹ 4s². Instead, its 4s atomic orbital remains unfilled, and one electron goes in its 3d shell, leading to the configuration [Ar] 3d¹⁰ 4s¹, which is more stable.

Scerri does prefer electronic configuration to what he calls “gross physical characteristics” for organizing the table. But he sees an even simpler logic to solve the group 3 problem: arrange by atomic number. If Scerri has his way, we’ll all have to get used to a newly arranged table.

Going wide

“My suggestion is simply this,” Scerri says. “Represent the periodic table in a 32-column format.”

Scerri calls 32 columns a more natural form for the periodic table and attributes the current dominance of 18 columns to convenience only. A 32-column table uses the atomic numbers as its logical foundation. Not only would it solve the group 3 question, but Scerri says 32 columns would be more correct because it puts the f-block in its rightful place: inside the table rather than floating below for convenience.

In a 32-column table arranged by ascending atomic number, lanthanum (atomic number 57) follows barium (number 56) to start the f-block, with actinium below it. That makes lutetium the first element in the third row of the d-block, with scandium and yttrium above it and lawrencium below to form group 3. Strict adherence to atomic number satisfies Scerri’s desire for a fundamental organizing principle and neatly sidesteps questions about chemical or physical properties.

Another table similar to the 32-column version has been proposed, but it uses electronic configuration rather than atomic numbers as its primary guide. French scientist Charles Janet’s left-step periodic table, devised in 1928, isn’t likely to make it into textbooks anytime soon, however. Janet moves the s-block to the right side of the table and includes helium at the top of group 2 because its s orbital, like other elements in that group, is filled.

Most tables place helium atop the noble gases. Scerri thinks helium’s demotion in the left-step table is one reason the table never got more traction, though recent experiments showing helium can form stable bonds help Janet’s argument that it belongs in a group with other reactive, rather than inert, elements.

Regardless, read from top to bottom and left to right, the left-step table more correctly conforms to the Madelung rule, which states that electrons must first fill the lowest-available electron levels before filling higher ones, Scerri says. It has a regularity that current tables don’t: two periods of 2 elements, two of 8 elements, two of 18, two of 32. And when element 121 is discovered, it will begin the g-block and two new periods of 50 elements.

Relative difficulty

The filling order that most chemists are used to might not hold up for much longer, however. Some calculations show the Madelung rule breaks down at higher atomic numbers because of relativistic effects. Electrons in large atoms move so fast that their behavior—and the properties of the atoms they belong to—begin to change.

Fans of relativistic effects will be happy to know there’s a table for them too. Pekka Pyykkö, a theoretical chemist at the University of Helsinki, calculated electron configurations up to element 172 and made a table for them (Phys. Chem. Chem. Phys. 2010, DOI: 10.1039/c0cp01575j). Pyykkö doesn’t bother with the group 3 question. His table leaves a hole under yttrium and has three 15-element rows in an f-block floating beneath the main table. Nor is he so constrained by atomic numbers. For instance, element 164 is followed by elements 139, 140, and then 169. According to Pyykkö’s calculations, 139 and 140 are the first elements with electrons in the 8p orbital.

This table is, of course, largely hypothetical. Scientists have not yet synthesized any elements beyond 118, and while several groups are working to do so, it’s possible we will reach the limits of our abilities to forge new elements well before element 172 or even 139.

“This is open land,” says Peter Schwerdtfeger, a theoretical chemist at Massey University studying superheavy elements. He calls Pyykkö’s calculations a “very good approximation” of the electron configurations but says more calculations are needed to pin down the precise characteristics of these elements. Pyykkö agrees. He too is waiting for more detailed calculations to show how wrong or right his table is.

And there are still other configurations of the elements that scientists are arguing for. Some tables look like rings or spirals. Some are 3-D, with lobes or stacks of element blocks. It seems less likely any of these will challenge the basic shape of the current table.

But Restrepo encourages scientists to think beyond just one table. “There’s a lot of discussion about if this table is good or bad, if this shape is better or worse,” he says. He prefers to focus on the periodic system rather than on the table. In a sense, he says, the system is like a sculpture, and the tables are shadows cast by lights shone from different angles. He says that allows chemists to find the periodic table or tables that are most useful to them, whether they’re looking for new elements or trying to understand properties in detail.

Gordin agrees on historical grounds. The periodic tables of the 19th century, he says, were made “to be flexible.” But he understands the resistance to radically different periodic tables, comparing new periodic tables to Pluto’s demotion from the ranks of planets. “The table you grew up with is the table you like.”

That raises a question about how much scientists and others should worry about these debates. “There’s a little group that argues over which [periodic table] is best,” Ball says. He believes the IUPAC group’s work is important because the current situation, with several competing tables, is confusing. But Ball says there’s no reason to think one table can capture the whole picture. “This notion of periodicity was so important for chemistry when the periodic table was first put forward and in the subsequent decades to make sense of this chaos of elements,” he says.

But today it should be more of a rule of thumb rather than a law of nature, Ball adds, arguing that there’s room for more than one periodic table: “Chemistry is about compromise.”