Researchers from Skoltech have developed a simple, universal formula that accurately predicts the chemical reactivity of all elements in the periodic table 88% of the time. The new model augments the classic concept of electronegativity — an atom’s tendency to attract electrons — with a counterbalancing tendency to preserve its own electron density. The findings will aid in designing new materials, such as corrosion-resistant alloys for nuclear reactor pipes. The study was published in Nature Communications and supported by a grant from the Russian Science Foundation.

Some chemical elements, such as tungsten, react with only a handful of others. In contrast, oxygen and fluorine form stable compounds with nearly every element in the periodic table. For over two centuries, chemists have sought a simple, intuitive explanation for this behavior.

The leading contender is the concept of electronegativity, as defined by two-time Nobel laureate Linus Pauling. An element’s electronegativity reflects how strongly its atoms attract, or how easily they donate, electrons. This property can be derived from experimentally measured energies of chemical bonds.

“You can often predict which elements will react by looking at the difference in their electronegativities: a larger difference means a reaction is more likely,” explains Distinguished Professor Artem R. Oganov, head of the Material Discovery Laboratory at Skoltech and co-author of the study.

“While this model’s simplicity is appealing, its logic suggests that any pair of elements should form a stable compound due to their unequal electronegativities, with some combinations just being more reactive than others. But this is clearly wrong. Many elements just don’t react with each other at  all,” Oganov notes.

“Furthermore, while the model elegantly explains the high reactivity of strongly electronegative elements like fluorine, it also predicts that highly electropositive alkali metals, such as cesium, should readily react with almost everything — which they do not,” he adds.

Evidently, a competing force counteracts an element’s tendency to attract or donate electrons. When strong enough, this factor renders a compound energetically unfavorable and thus unstable. Attempts to introduce such a factor have been made for intermetallic compounds by Dutch scientist Andries Rinse Miedema.

The rationale behind Miedema’s destabilizing factor is this: Besides electronegativity, elements differ in their atomic electron density. When a compound forms, the electron densities at the boundaries between the atoms must equalize. The greater the initial disparity in electron densities, the more energy their redistribution costs. So, while a difference in electronegativities stabilizes a potential compound and drives a reaction, a difference in electron densities has the opposite effect.

“Proposed in the 1970s, Miedema’s model was quite successful for metals but later fell into relative obscurity. Its equations included needlessly complex factors and became only even more elaborate over time,” Oganov explains. “I realized that this model could be stripped down to be both simpler and more universal. Sometimes in science, removing unnecessary complexity not only retains accuracy but also broadens a model’s applicability.”

The newly published model is strikingly simple, describing each element with just two parameters: electronegativity and resistance to electron density change. Remarkably, this is sufficient to correctly predict the formation of arbitrary chemical compounds across the entire periodic table 88% of the time.

The model is also more universal in another sense: while Pauling’s scale was formulated for diatomic molecules with single bonds and was difficult to apply to solids, the new model is designed for solids from the outset and can also describe molecules.

Thanks to the stabilizing term (the revised electronegativity), the model correctly attributes high reactivity to oxygen, chlorine, and other electronegative elements. It also explains the paradox that despite their record low electronegativity, alkali metals do not form compounds with most elements. These elements have large atoms with only one valence electron available for bonding, resulting in a very low average electron density. This increases the destabilizing factor in the equation.

The researchers hypothesize that under high pressure, as atoms are compressed, their electron densities will increase, reducing the impact of the destabilizing factor. Meanwhile, as they showed in a previous work, electronegativity differences become more pronounced, boosting the stabilizing factor. Ultimately, this could push more elements — perhaps all of them — to react with each other at sufficiently high pressures.

According to Oganov, the new model has immediate practical applications: “Among the cutting-edge nuclear reactor designs today are lead-cooled fast reactors. These use molten lead instead of water or liquid sodium to carry heat from the active zone of the reactor. A key challenge is that, unlike sodium, molten lead slowly corrodes iron at very high temperatures. Our model suggests that to increase corrosion resistance it will help to add chromium, carbon, and ideally, tungsten or rhenium — as components of steel or of coatings. It is striking that such a simple model can produce such nontrivial conclusions.”