How big is an atom? On the order of angstroms, researchers agree, but putting an exact number on a given element is trickier. For ions and molecules, even more.
Answers have been offered from a variety of empirical sources, with everything from compressibility and crystal structure to optical refraction and electrical polarity used to quantify what is known as the Van der Waals radius – named after the researcher who theorized finite molecular size in gases. Researchers have also turned to quantum mechanics and computation, computing electron wave functions – the probability clouds that surround atoms – and using a sensible limit value to mark an atomic limit.
A team at the University of Oregon, USA, has now proposed a new measure: the electric field that surrounds each atom. Led by Christopher Hendonthey have developed a software package to calculate this electric field, which occurs under the net influence of the atom’s nucleus and electrons, and quantify its distribution in space.
For neutral, non-interacting atoms, the charge of the electrons balances the nucleus and eliminates the electric field beyond. Using their field-based method, the team’s calculations were in line with established values. “We match close to the accepted Van der Waals radii,” says Hendon. “It’s good common sense.”
Joner is there, in Hendon’s words, the model “really takes a turn for the interesting”, as illustrated for the case of Mg2+. Under the conventional measure of electron density, this cation is more compact than its neutral counterpart, due to its lack of external electrons. However, the image of the electric field shows an increase in size. This is because the nuclear charge is no longer completely shielded by the electrons, so the field can penetrate further into space.
The advantage of this approach, according to Hendon, is that it corresponds to the region that the ion affects, which may be more relevant than the region it occupies, especially when choosing materials for applications. The result for Mg2+, he suggests, can explain why magnesium ion batteries do not work well. “Magnesium sticks to everything … It does not move so easily, unlike other ions.”
Even for anions, the model draws surprising conclusions, not least when comparing elements. Under the field-based model, a Br– ion turns out to be bigger than me–and F– is even larger. This reversal occurs because the extra electron on a bromide ion has its field limited by the larger nucleus. “You basically dilute the negative charge with more positive species,” Hendon explains.
Santiago Alvarez, an electronic structure expert at the University of Barcelona, Spain, warns against overly literal interpretation. “To compare with a macroscopic situation, would we define the size of a magnet as the degree of any cut-off of its magnetic field?” he asks.
Alvarez, who has also worked on quantifying atomic size, points out that the electric field is just one way through which nearby atoms can interact, with Pauling repulsion, orbital dispersion and spin-spin interactions like others. And he highlights complications that can occur when atoms form bonds: “How could we apply Fes radius3+ [calculated by Hendon’s team as approximately 4.2Å]to species such as FeO45- anion, in which the oxygen atoms are barely 1.90Å from the iron core? ‘
Hendon would like to emphasize that his approach should complement, not replace, the existing ones. “Van der Waal’s radii are backed up by experimental data. This has been extremely valuable.”
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