Misleading features of Lewis Dot Representation

Today I had an embarrassing experience when I sat to help my nephew learn Lewis' Dot Representation and realized that I actually don't get it at all. I have a physics background and always thought that the Lewis Structure in chemistry mimics the physical picture, but soon realized that it doesn't.

First of all, the "sockets" where the dots go on Lewis Diagrams do not correspond to actual physical orbitals. They are neither 4-fold symmetric, nor are equivalent (s-orbitals are spherically symmetric, p-orbitals are lobed, etc), so I couldn't give any explanation to my nephew what their physical interpretation is.

Also, I noticed that the rule for filling these "sockets" do not follow the Aufbau rule. For example, in the ground state of carbon, Nature first fills the $\ce{2s}$-orbital and just after that inserts an electron in two of the $\ce{2p}$-orbitals. In contrast, the rules of Lewis' Dot Representation say that C should have a single dot in each of its 4 "sockets", and just after they get exhausted, one starts pairing them. (I wonder how this principle explains compounds like methylene, in which carbon has its $\ce{2s}$-shell pair present... but anyway.)

All of this prompted me to ask, what is the story behind Lewis' Dot Structure and what goals Gilbert Lewis pursued when he introduced it? I guess if I learn this, I'll be able to explain its misleading features and not get embarrassed in front of a 14-year-old.

• The Lewis dot structure is just an electron counting device. It is not intended to indicate anything about the physics of the electrons. – Oscar Lanzi Oct 29 '17 at 19:57
• Carbene exists in both singlet and triplet forms and the singlet carbene’s lone pair can be in either in an s-type or in an $\mathrm{sp^2}$-type orbital. – Jan Oct 30 '17 at 11:35

Lewis dot structures predate the advent of modern quantum theory and quantum chemistry. There is no Schroedinger equation associated with them -- in fact placing a dot on an atom (seems to me that it) violates the concept that electrons must be indistinguishable.

There are no slots, there are no "octet rules". There are only particles, and kinetic and potential energy that depend on their masses and charges. They take a configuration that minimizes the total energy with respect to their location in space.

So my advice is to learn Lewis dot structures as a heuristic device that can be figured out for the purposes of passing General Chemistry and speaking with the vast majority of chemists who have continued to suffer with learning about octet rules, resonance structures, etc. and the "astonishment" when these rules fail. They are hard to learn, because one can not draw on experiences learned about other physical systems that depend on e.g. QM, electrodynamics, etc.

There is a subject known as Valence Bond theory, that uses (spin-adapted) Lewis structures as a basis. But if you knew what went into constructing a proper quantum mechanical valence bond wave function, you might as well say "sure, anything so long as it forms a complete basis." i.e. we might as well talk about molecules being made up of millions of plane waves.

You did mention orbitals: "Orbitals" only arise due to the fact that they are complete bases of Spherical Harmonics and Laguerre Polynomials that were used by Schroedinger to solve the case of the hydrogen-like atom -- a spherically symmetrical system. They do not really apply to molecules, and it is common to use other bases to describe molecules such as Gaussian-Type orbitals, plane waves, etc. Atomic orbitals, molecular orbitals (constructed from linear combinations of AO's) and plane waves have never been observed. Mathematically, orbitals may be complex, and leaves me wondering why we place so much stock in them except as useful complete bases with convenient boundary conditions, e.g. periodic with a unit cell or decaying in the limit of infinite distance. (In contrast, the electron density is real and observable.)

• I thought I remembered something about having been able to observe the orbitals of a water molecule but I could be badly wrong. – Jan Oct 30 '17 at 11:36
• How do we observe molecular orbitals? It's not like they're tiny glass globules attached to the molecule. – Oscar Lanzi Oct 30 '17 at 15:32
• @OscarLanzi In the same way that we have pictural representations of measured atomic orbitals, for example? At least that one is known. – Jan Oct 31 '17 at 6:26
• @Jan I don't think they have been observed, even if there is a paper where they say that they observed them. Even one case would imply that it's possible to observe Psi and Psi*, and I don't see how its possible to observe things that are represented as a + b i and a - b i. – Eric Brown Oct 31 '17 at 12:50

Lewis published his theory in "The Atom and the Molecule". April 1916. J. Am. Chem. Soc., 38, 4 It means that no orbitals and electron density were present. Therefore his arguments were not related to quantum mechanics.

By the way, orbitals can be obtained without any basis set.