Many models of chemical bonding have been proposed over the past century


Many models of chemical bonding have been proposed over the past century and a half. The one clear concept that comes from all of these is the importance of the chemical bond, a localised interaction between two neighbouring atoms, but as Philip Ball pointed out (Chemistry World, March 2011, p33), the concept remains fuzzy. However, a rigorous and predictive bond model can be derived from an apparently unlikely source, the ionic model. The model even includes, surprisingly, the covalent bond model of organic chemistry as a special case. 

The ionic model took shape in the early 20th century in order to explain the structures of inorganic crystals. Its flowering was brief; to tackle any but the simplest problems required computational tools that were not then available, and only with the advent of modern computers was it revived by physicists who use it for simulating the structures of complex materials. As chemists, we retired the model to the undergraduate syllabus, otherwise using it only as a place to put chemical structures that did not contain well behaved bonds. The model’s predictive power was limited, its assumption that cation valence electrons are transferred to the anion was unbelievable, and the bonding forces were described in the language of physics (long-range Coulomb potentials) rather than chemistry. There was nothing in the model that suggested the presence of chemical bonds. 

How wrong we were to dismiss this model! When properly developed it is the only model that provides a rigorous definition of a localised chemical bond and assigns it a strength (the bond valence) that correlates quantitatively with the bond length. The model includes a number of rigorous theorems, expressed as simple rules, that relate the lengths of the bonds to the valences and coordination numbers of the ions. These theorems make it one of the more predictive models of structural chemistry. So what is the long-hidden secret of this model? The ionic model’s electric field, which has hitherto been almost completely ignored. 

The simplest way to display the electric field is using the Faraday field lines that we learned to draw in school. If you sketch these for an alternating array of positive and negative charges, you quickly see that the lines that start on a cation all end on the neighbouring anions and vice versa.

Those ions that are linked by field lines are defined as being bonded, and as a bonus, the number of field lines measures the bond’s strength (bond valence). The number of field lines starting on an ion is equal to the charge on the ion (atomic valence) so the sum of the bond valences around an ion is equal to its atomic valence (the valence sum rule). When two ions are brought closer together, they will be connected by more field lines, so the valence of the bond will be larger. 

Correlations between bond valence and bond length, determined by comparing the expected bond valences with observed bond lengths, have been determined for most bond types, so it is possible to validate and analyse a chemical structure by checking whether the sum of the bond valences equals the atomic valence. This is the most widely used feature of the model, but there is much more it can do. A network of ions connected by bonds is equivalent to an electrical circuit which can be solved for the bond valences using the Kirchhoff equations, allowing bond lengths to be predicted with an accuracy of a couple of picometres, even for compounds that do not exist! 

The steric strains in bonds can be analysed, and in favourable cases the crystal structure can be predicted A more physically correct version of the ionic model would replace the point-charges of the ions with neutral atoms consisting of a positive core surrounded by a spherically symmetric valence shell. A bond is formed when the cation and anion valence shells overlap, the valence of the bond being determined by the number of electron pairs in the overlap region. In this version, Faraday field lines run from both ion cores to the bonding electrons in the overlap region. As the bond valence depends only on the number of electron pairs in the bond and not whether they lie closer to the cation or the anion, one can conceptually transfer all the bonding electrons to the anion without changing the bond valence, thus justifying one of the more problematic assumption of the ionic model. 

The valence of a typical bond formed by an ion is called its bonding strength. The valence matching rule states that the most stable bonds are formed between ions having similar bonding strengths. This rule predicts which compounds can be formed and whether they will react with other compounds to yield a better bond match. In short, the bond valence version of the ionic model is a simple but powerful tool for analysing and predicting structures as well as chemical reactivity. It is by no means confined to ionic bonds, it works just as well for any localized bond, even the most covalent. 

I D Brown
Hamilton, Ontario, Canada

Further Reading

I D Brown, The chemical bond in inorganic chemistry, Oxford University Press, 2002 
I D Brown, Chem. Rev.,  2009, 109, 6858 

I write in response to a recent article by Philip Ball (Chemistry World, March 2011, p33). The principle of least action - that everything that occurs in nature does so by minimising the ’action’ - is the most fundamental of all physical principles. This statement from classical mechanics was woven into the fabric of quantum mechanics by the revolutionary work of physicists Richard Feynman and Julian Schwinger and done so at the suggestion of theoretical physicist Paul Dirac. Their work is regarded by physicist Murray Gell-Mann as providing the ’real foundation of quantum mechanics and thus of physical theory.’ Schwinger’s principle of stationary action has been extended to an open system - to an atom in a molecule. Thus the quantum theory of atoms in molecules (QTAIM) and hence the very notion of an atom in a molecule, is rooted in the most fundamental of all physical principles. 

Ball states that the idea embedded in QTAIM, that chemistry may be reduced to the basic principles of physics, ’can be plain wrong’ and gives as an example the following statement: ’Biochemistry [...] is not exhaustively explained by an account of the bonding between the atoms involved.’ People whose ideas are mired in the past are seemingly unaware that they are in the midst of a revolution in the basic ideas of physics. The principle of stationary action now encompasses chemistry, biochemistry and biophysics and will eventually be applied to biology. A living cell is, after all, the most important of all examples of an open system. I only wish I were young enough to experience more of the ever-onward march of the principle of least action in accounting for (perhaps, as suggested by Planck, giving purpose to) the very thrust of nature. 

Young readers are encouraged to read Feynman’s account of the principle of least action given in the second volume of his Lectures on physics  (Addison-Wesley Pub Co, Reading Mass. 1964, Chapter 19). A most readable account of the role of the principle is given in Variational principles in dynamics and quantum theory  by W Yourgrau and S Mandelstam (Dover Pub. Inc., 1968, p162 ff). 

R Bader 
Hamilton, Ontario, Canada 

I am not sure how many people have tried this but the other night I realised that I could spell out my name using elements. In addition to this, I could use each element only once (Ca Lu Md I C K In S O N). It was only when I started going through other people’s names that I realised how unusual this was. Just going through those that received the Nobel prize in chemistry, there have only been four (unless I missed somebody). W Al Th Er He Rn St (1920), Ar Ne W K Ti Se Li U S (1948), He Rb Er Tc Br O W N (1979) and Y V Es C H Au V In (2005). However, the latter uses vanadium twice. I doubt this means I am on track to be a Nobel laureate in circa 2035. Are there any other interesting ones?

C Dickinson 
Limerick, Ireland 

I scanned with some interest the article ’New aromatic coupling’ (Chemistry World, June 2011, p22). The mention of Friedel-Crafts reminded me of an intrinsic difficulty that there was in the teaching of first-year organic chemistry when I entered university 40 years ago.  

We had all been taught about the Friedel-Crafts alkylation at school in A-level, and at university had to be taught that, although Friedel-Crafts acylation was useful in preparative organic chemistry, Friedel-Crafts alkylation was not. I was taught this by Professor F G Holliman at Leeds. Holliman, who as well as being a Cambridge graduate was a native of that town (his parents had a furniture business there) and was an entertaining lecturer. In addressing the point I have mentioned above he wrote in capitals on the board: Friedel-Crafts alkylation: N B G.

Only one student amongst the 60 or so present asked for a clarification of the initials. I have never specialised in preparative organic chemistry and have no idea whether Holliman’s present day counterparts would endorse his very directly expressed view.  

J C Jones FRSC 
Aberdeen, UK 

Reading the unreadable (Chemistry World, May 2011, p72) is something of great importance to many people in the library and archive world - in fact, I gave a presentation on this to my colleagues at the British Library only last month.  

One of the first people to investigate ways of unrolling the Herculaneum papyri was Sir Humphry Davy. When the scrolls were first discovered, the King of Naples sent samples to the other crowned heads of Europe to see if their men of science could devise suitable methods. The scrolls that Davy worked on are now in the British Library’s collection, and one of my colleagues is currently searching the archives to try to find out exactly what Davy tried. 


X-ray cross-section of a Herculaneum scroll

X-ray tomography as a method of virtually unrolling scrolls has been extensively researched by Brent Seales at the University of Kentucky, US. There are two main problems - one is chemical and the other is computational. Every x-ray imaging technique relies on there being a difference in atomic number between the elements forming the image and those forming the background. 

Where you have pigments containing copper or lead, or iron gall ink (containing iron(III)-gallate complexes), the contrast is adequate and it is possible to reconstruct an image. It is even possible to see an image of writing in bone or ivory black ink, as this contains calcium phosphate as well as carbon. However, most ancient papyri are written with pure carbon black ink, so you are looking for carbon on a carbon background. 

LETTERS pic 2-100

Scroll of Herculaneum papyrus

David Jones’ suggestion (in his Last retort  article) of decorating the ink with a contrast agent is interesting; as I have just said, this needs to contain heavy elements in order to work. However, for very good reasons, conservators are reluctant to use any reagent on an ancient artefact that reacts permanently with it and which cannot be removed. Additionally, the scrolls are very tightly wound and stuck together with degraded polysaccharides from the papyrus (see picture), so it is not at all clear that even a gaseous reagent would be able to penetrate the scrolls and be able to be removed again. 

The second drawback to x-ray tomography is computational. In order to get a usable image, the resolution of the system has to be at least 100 m m. Given that the scrolls are about 15cm wide and may be up to 10m long, the number of pixels that has to be recorded is very large, so managing the files and operating on them is beyond the capability of ordinary desktop computers. 

Your mention of diethyl zinc reminds me of the Library of Congress’s fairly unsuccessful attempts to use it as a method of deacidifying books. The trouble with diethyl zinc is that it is terribly reactive and explodes on contact with oxygen and water. After a couple of disastrous fires the Library wisely abandoned the method. You can find more details in Nicholson Baker’s polemical book Double fold  (Random House, 2001). 

B Knight MRSC 
London, UK 

David Jones finishes his Last retort  on Chemical words with a limerick which, he claims, is the only poem in which a chemical name fits perfectly (Chemistry World, June 2011, p72).  

I would draw his attention to an Elizabethan sonnet composed by the physical organic chemist Howard Maskill (Nature, 1981, 294, 606) that goes well beyond that, and should be more widely known: 

To trans, trans-tricyclo[,13]tridecane  
Shall I compare thee to a perfect form of cyclohexane locked with bulky group? 
Or should it be with that bicyclic norm 
Whose ethane bridge 1,5 doth bridge the hoop? 

A Sella FRSC 
London, UK 

We, the Women’s Institute, celebrated 100 years of Marie Curie being awarded the Nobel prize with a 9ft high x 7ft wide clayed board decorated completely with natural materials, mainly individual flower petals (see picture). Well-dressing is virtually unique to Derbyshire originating from approximately 1348 to celebrate pure water during the plague. We thought you might be interested to see our celebration of women in chemistry.


Celebrating women in chemistry

Celebrating women in chemistry

D Noons, Etwall, a small village in Derbyshire, held their Well-Dressing Festival on 21-23 May.
By email