The Limited Predictive Power of the Pauling Rules

Abstract

The Pauling rules have been used for decades to rationalise the crystal structures of ionic compounds. Despite their importance, there has been no statistical assessment of the performances of these five empirical rules so far. Here, we rigorously and automatically test all five Pauling rules for a large data set of around 5000 known oxides. We discuss each Pauling rule separately, stressing their limits and range of application in terms of chemistries and structures. We conclude that only 13 % of the oxides simultaneously satisfy the last four rules, indicating a much lower predictive power than expected.

Predicting short-range order and correlated phenomena in disordered crystalline materials

“…Pauling’s original formulations were based on the nature of chemical bonds between ions ( 41 ), a very short-range interaction dictated by quantum mechanics ( 42 ). Thus, it is therefore not unexpected that a disordering mechanism will not violate these fundamental chemical rules.…”

Pauling’s rules for oxide-based minerals: A re-examination based on quantum mechanical constraints and modern applications of bond-valence theory to Earth materials

“…Bonded radii determined for metal atoms match the Shannon (1976) radii for more electropositive atoms, but the match decreases systematically as the electronegativities of the M atoms increase. As a result, significant departures from the radius ratio rule in the analysis by George et al (2020) is not surprising. We offer a modified, more fundamental version of Pauling's first rule and demonstrate that the second rule has a one-to-one connection between the electron density accumulated between the bonded atoms at the bond critical point and the Pauling bond strength of the bonded interaction.…”

“…In addition, Gibbs et al (2013a) found strong evidence that the Pauling bond strength-bond length of a M-O bonded interaction is very similar to the average accumulation of the electron density at the bond critical point (<r(rc)>) between bonded pairs of metal and oxygen atoms. On the basis of the correspondence between equations relating <r(rc)> [<R(M-O)> = 1.46<r(rc)>/r -0.19 ] and <s> [<R(M-O)> = 1.46<s>/r -0.21 ] to bond length, Gibbs et al (2013a) Manuscript #7938R (Correction Date 07/14/2021) Gibbs, Hawthorne, Brown One of our motivations for writing this review paper is to address a recent paper by George et al (2020) entitled "The Limited Predictive Power of the Pauling Rules", which questions the applicability of Pauling's first and second rules in particular, based on a statistical analysis of the success of Pauling's rules when applied to 5000 or so crystal structures in the Inorganic Crystal Structure Database. George et al (2020) make the following comment: "Our work therefore calls for the development of new empirical rules beyond the almost one-century old Pauling rules.…”

“…On the basis of the correspondence between equations relating <r(rc)> [<R(M-O)> = 1.46<r(rc)>/r -0.19 ] and <s> [<R(M-O)> = 1.46<s>/r -0.21 ] to bond length, Gibbs et al (2013a) Manuscript #7938R (Correction Date 07/14/2021) Gibbs, Hawthorne, Brown One of our motivations for writing this review paper is to address a recent paper by George et al (2020) entitled "The Limited Predictive Power of the Pauling Rules", which questions the applicability of Pauling's first and second rules in particular, based on a statistical analysis of the success of Pauling's rules when applied to 5000 or so crystal structures in the Inorganic Crystal Structure Database. George et al (2020) make the following comment: "Our work therefore calls for the development of new empirical rules beyond the almost one-century old Pauling rules. Our analysis and the data set of connectivity and local environment provided is a first step towards building this new theory……".…”

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Since their introduction in 1929, Pauling's five rules have been used by scientists from many disciplines to rationalize and predict stable arrangements of atoms and coordination polyhedra in crystalline solids; amorphous materials such as silicate glasses and melts; nanomaterials, poorly crystalline solids; aqueous cation and anion complexes; and sorption complexes at mineral-aqueous solution interfaces. The predictive power of these simple yet powerful rules was challenged recently by George et al (2020), who performed a statistical analysis of the performance of Pauling's five rules for about 5,000 oxide crystal structures. They This is the peer-reviewed, final accepted version for American Mineralogist, published by the Mineralogical Society of America.The published version is subject to change.

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