# Negative numbers for ionic radii?

I was looking for a good table of ionic radii for an experiment on the van't-hoff factor when I stumbled upon R. D. Shannon, Acta Cryst. 1976, A32, 751.

In table 1, it lists 1 of the ions of carbon with as so:

C +4 1S 2 III .06 -.08

The bold numbers are of concern here. The first number, 0.06 Å is what the paper refers to as the crystal radius, while the second number, -0.08 Å, is referred to as the effective ionic radius. I was also unable to find any good distinction between the two in the paper, except that the radius of $\ce{O^2+}$ for the crystal radius is 1.40 Å, while the effective ionic radius for $\ce{O^2+}$ is 1.26 Å.

I also doubt that this is a typo since it agrees with this statement made later in the paper:

crystal radii differ from traditional radii only by a constant factor of 0.14 [ Å].

• Interestingly $\ce{H+}$ is listed as having both a negative crystal radius as well as a negative effective ionic radius. Only light, highly positively charged ions appear to give negative values ($\ce{H+}$, $\ce{D+}$, $\ce{C^{4+}}$, $\ce{N^{5+}}$). It is likely that these values are calculated in a way which cannot handle the extremely high demand for at least some covalency from these strongly polarising cations, so the model breaks down. – Nicolau Saker Neto Feb 10 '16 at 10:46
• Though I'm not 100% sure about this, the paper seemed to not be a model, but instead was directly measured. I couldn't find a real model anywhere so I can only assume that it must have been directly measured. These values were also not discussed anywhere in the paper as far as I can tell. – purepani Feb 10 '16 at 13:36
• Also, that about negatively charged ions: why are they not affected? – purepani Feb 10 '16 at 14:15
• Is it possible that the radii were measured in referential unit like amu? – Agyey Arya Feb 10 '16 at 16:42
• I'm going to take a much closer look at the paper and then come back to this question. – purepani Feb 11 '16 at 0:31

(There are materials (ferroelectrics) in which the coordinated ion does not completely fill the space allotted. In $$\ce{BaTiO3}$$, the $$\ce{Ti^{+4}}$$ ion is so small that it can shift its position in the octahedral cage of oxygen anions in response to an external electric field.)