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Modern Lewis Theory

Electrons dance to a subtle & beautiful quantum mechanical tune.
The resulting patterns are both complicated & exquisite.

As chemists we try to understand and exploit the dance.

Our physicist friends attempt to understand the music theory.

Modern Lewis Theory & Stamp Collecting

Introduced by Niels Bohr in 1913, the Bohr model is a quantum physics modification of the Rutherford model and is often referred to the Rutherford–Bohr model. (Bohr had conducted post-doctoral research work with Rutherford in Manchester, UK.) The model's key success lay in explaining (correlating) the Rydberg formula for the spectral emission lines of atomic hydrogen, but as a model/theory of the atom it was clearly not complete...

Greatly simplifying both the history & the science: In 1916 atomic theory bifurcated into physics and chemistry streams, a fork that continues to this day.

In the early years of the 20th century at UC Berkeley under the leadership of G. N. Lewis, chemists were trying to understand structure, bonding & reactivity. Lewis and colleagues were actively debating the new atomic structure ideas, particularly the Rutherford & Bohr atoms, and postulated that the electron shell atomic model gave insights into their chemical problems.

The first Lewis paper to deal with the new structure & bonding ideas was published in the Journal of the American Chemical Society v. 38 (1916) [full paper, scanned version] The Atom and The Molecule. This was just three years after the introduction of the Rutherford-Bohr atomic structure model in which particle-like electrons were deemed to exist in shells around the small dense nucleus: two electrons in the first shell, 8 in the second, 8 in the third, etc.

By way of example, the 1916 paper contains this very modern looking diagram showing the formation of the ammonium ion:

The diagram shows ammonia, NH3, with three "shared electron-pair covalent bonds" and a "lone pair of electrons" on the nitrogen. Plus, there is a "dative/coordinate covalent bond" in the ammonium ion, NH4+. [However, be warned... not all of this paper – with its odd looking cubic atoms, etc. – looks as "present-day" as the diagram above.]

In essence:

Physics    |    Stamp Collecting    |    Lewis Theory

Ernest Rutherford famously said: "All science is either physics or stamp collecting."

Lewis theory is stamp collecting.

Imagine an alien culture trying to understand planet Earth using only a large collection of postage stamps. The aliens would see all sorts of patterns and would be able to deduce the existence of: nations, currencies, pricing strategies, differential exchange rates, inflation, heads of state, postal service operations, missing stamps, etc.

However, the aliens would infer little about the biology of life on our planet, although there would be hints in the stamp data: various creatures & plants, males & females, etc. [Some crucial aspects of biology have associated social & cultural taboos that are never illustrated on stamps.]

So it is with atoms, ions, molecules, molecular ions, materials, etc.

As chemists we see many patterns in chemical structure and reactivity, and we try to draw conclusions and make predictions using these patterns:

This is Lewis theory.

But the Lewis approach is not complete and it only gives hints about the underlying quantum mechanics, a world observed through spectroscopy and understood through mathematics.

Strikingly, the magic numbers of modern Lewis theory are generally (but not exclusively) small positive integers of even parity: 0, 2, 4, 6, 8...

Some examples of the rules & patterns of modern Lewis theory:

It is astonishing how well these physical "balls & sticks" achieve their objective of modeling molecular and network covalent material structure.

The approach can also be modelled in software, where the approach is called molecular mechanics. Atoms and bonds are parametrised in terms of classical force fields.

Lewis theory is very accommodating and is able to 'add-on' those bits of chemical structure and reactivity that it is not very good at explaining itself.

Consider the mechanism of electrophilic aromatic substitution, SEAr:

The diagram above is pure Lewis theory:

Lewis theory is electron accountancy:

Count the electrons & look for the patterns and note the magic numbers.

Lewis theory is numerology:

Lewis theory cannot explain where the magic numbers come from, other than suggesting that the patterns themselves are the reason for the patterns:

"Bromine is below chlorine in the periodic table, therefore Br2 reacts to give Br."

Lewis theory is eclectic: it greedily begs, borrows, steals and assimilates numbers, patterns & ideas from deeper, predictive theories and incorporates them into itself. "Oh, there's a pattern... we'll have that..."

Consider Hückel aromaticity which has a sound molecular orbital theory foundation. Aromaticity is predicted by the 4n+2 π-electron rule, giving the number π-electrons associated with aromaticity as: 2, 6, 10, 14, 18...

The way Hückel aromaticity is often invoked in chemical education is pure Lewis:

"Benzene has three double covalent bonds, hence three π–bonds, hence 6 π–electrons... which is one of the magic Hückel aromatic numbers (2, 6, 10, 14...) so benzene is aromatic":

Liar, liar, Pants on Fire

Lewis theory is also naughty... it tells fibs!


Consider the Period 2 diatomic molecular species: fluorine, oxygen and nitrogen, F2,, O2, & N2.

Every school student (and the biologist who drew the diagram below) 'knows' that:

        Fluorine has a single covalent bond:  F–F
        Oxygen has a double covalent bond:  O=O
        Nitrogen has a triple covalent bond:  N≡N

But this is a lie... a damnable lie.

Dioxygen is actually a diradical that can exist in singlet & triplet states. Ground state triplet oxygen is paramagnetic and liquid oxygen attracted to the poles of a magnet:

Ground state triplet oxygen, O2, should be represented as: •O–O• or ↿O–O↿.

Thus, there is no  F2     O2     N2   pattern. Dioxygen simply does not fit the Lewis pattern.

This inconvenient fact is simply ignored by Lewis theory and many Lewis theory centric textbooks because the Lewis analysis is just so pretty... even though the diradical structure of O2, is inevitable in the molecular orbital description of dioxygen.

Madelung's Rule

Another example of naughty Modern Lewis theory: Madelung's Rule.

Madelung's rule states that atomic orbitals fill with electrons with the sequence: n + , where n is the principal quantum number and  is the subsidiary quantum number. The rule is used to explain orbital filling and why the 4s orbital has a lower energy than the 3d orbital, and thus it invoked to explain 'why' the periodic table its characteristic appearance.

Madelung's rule is just so beautiful. The pattern is so convincing.

But in actuality, Madelung's is only a rather crude "rule of thumb" with many exceptions. When examined closely, it fails with a third of the transition elements. There are many quantum mechanical subtleties to atomic structure: nuclear screening, electron repulsion, spin-orbit coupling, relativistic effects, etc. The greater the number of electrons [as with the heavier transition elements] the more considerations there are... and the more over-simple rule breaks down.

Madelung's Rule looks like (and smells like) authentic quantum mechanics with its use of principle & subsidiary quantum numbers, but it is actually stamp collecting and not very good stamp collecting at that. Madelung's Rule makes over simple predictions about patterns of electronic structure... but the predictions often turn out to be inexplicably incorrect. Yet, within Madelung's Rule the logic looks so beautiful, so pretty, so perfect!

And Yet... And Yet... And Yet...

Modern Lewis theory works remarkably well with the lighter main group elements – and thus nearly all organic chemistry employs – which is why modern Lewis theory is taught to school and university students the world over.

The approach works less and less well as the number of electrons increases.


Consider the pattern:

Now zoom out slightly:

The right hand side "does not fit the pattern" of the first image. Is an anomaly?

Zoom out a bit more and the anomaly seems to disappear:

Or does it? There is a purple patch on the upper right hand side does not seem to fit the pattern and so may be anomaly:

But zooming right out we see that everything is part of a larger regular pattern:

(Thanks Digital Flowers at DryIcons)

When viewing the larger scale the overall pattern emerges and everything becomes clear. Of course, the Digital Flowers pattern is trivial, whereas the interactions of electrons and positive nuclei are astonishingly subtle, more like this:

On close inspection, Roy Lichtenstein's Girl Crying looks like a regular pattern of dots, but zoom out and the full complex picture emerges.

This situation is like learning about chemical structure and reactivity using Lewis theory.

First we learn about the Lewis octet and how atoms lose & gain electrons so that they have 8 electrons in their valence shell – magic number 8 – and we come to believe that the pattern of chemical reactivity can be explained in terms of the very useful Lewis octet model.

Then we encounter phosphorous pentachloride, PCl5, and discover that it has 10 electrons in its valence shell. Is PCl5 an anomaly?

No! just get over it...

The fact is that the pattern generated through the Lewis octet model is just too simple.

Look, PCl5 has five bonding pairs and Lewis theory's VSEPR technique predicts the molecule to have a trigonal bipyramidal geometry with 120° & 90° bond angles, and it does:

The chemist's approach to understanding chemical structure & reactivity is to count the electrons and take note of the patterns.

This is Modern Lewis theory.

A Bit of Philosophy: Realist vs. Antirealist

It is possible to take two positions with respect to a particular theory: realist or antirealist.

An instrumentalist is an anti-realist who simply uses the toolbox of conceptual and mathematical techniques to describe and understand the physical world.

However, the problem goes deeper than this. Chemistry has an educational problem. Many of the structure and reactivity ideas/concepts in chemistry are taught to school and/or university students as if it is real, even though they are not.

Consider how the VSEPR analysis is used to explain/predict the shape of the methane, CH4,, molecule:

"A carbon atom has four electrons in its valence (outer shell). When covalently bonded to four hydrogen atoms, there is a Lewis octet of eight electrons in the carbon's valence shell arranged as four bonding pairs. These four bonding pairs [which can be regarded as negative charge clouds] repel each other to give a perfectly symmetrical tetrahedral molecule with 109.5° bond angles."

The above argument is 100% realist in that it asks us to actually believe that pairs of point like charged particles conveniently arrange themselves in a physical valence shell. The viewpoint is classical mechanical. We only have to study a small amount of quantum mechanics – and to discover that the electron is better considered as a wave – to realise that the VSEPR analysis is utter and complete tosh. BUT VSEPR WORKS!

[What interests your author is how such a ridiculously simple set of rules can possibly work as well as they do.]

So, even though theories are all we have, they should be used but not believed. Do not inhale.

This is crucial, because when tested to the extreme all chemical theories are found wanting, a situation that always confuses the realist. The cynical anti-realist knows model breakdown is inevitable because theories are not real.

Now, chemistry teachers and textbook authors [yes, we are all guilty] are prone to present arguments about the nature of chemical structure and bonding without adding any anti-realist provisos... which confuses students when new facts come along, like PCl5. (But hey, we were confused when we were learning this stuff.)

For example, most of the structure and bonding ideas in textbooks, and this web book is no exception, are expressed in terms of Lewis/VSEPR ideas.

Lewis theory is a fantastic model and it works nearly all the time. In fact, Lewis theory is so good that most chemists can get away with assuming that it is true, that it is real.

Lewis Theory | Quantum Mechanics

Quantum mechanics and Lewis theory are both concerned with patterns. However, quantum mechanics is active and is concerned with the causation of the patterns, whereas Lewis theory is passive and only exploits the observed patterns.

We observe patterns of structure & reactivity behaviour through experiment. Lewis theory looks down on the empirical evidence, identifies patterns in behaviour and classifies the patterns in terms of electron accountancy & magic numbers. Lewis theory gives no explanation for the patterns.

In large part, chemistry is about the behaviour of electrons and electrons are quantum mechanical entities. Quantum mechanics causes chemistry to be the way it is. The quantum mechanical patterns are can be:

Not Lewis Theory

Small diatomic molecules rotate in the gas phase, but the motion is not classical, but quantum mechanical and only a few discrete values are allowed. Consider the rotational spectroscopy of hydrogen chloride, HCl, molecule:

From Libre Texts, Chemistry: Absorption spectrum of hydrogen chloride (HCl) from the n=0 to n=1 vibrational levels. The discrete peaks indicate a quantization of the angular momentum of the molecule. The bands to the left indicate a decrease in angular momentum, whereas those to the right indicate an increase in angular momentum.

This spectrum is also discussed on the Hyperphysics page.

While there is no point in attempting to using any type of classical Lewis theory to help explain the above spectrum, the pattern is exquisitely described using quantum mechanics.

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Timeline of Structural Theory Valence Shell Electron Pair Repulsion

© Mark R. Leach 1999 –

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