A scheme, to obtain the weights of resonating Lewis structures from Hückel calculations, is presented and tested against established ab initio methods. In this paper we make use of the fact that the solution of the Schrödinger equation can be written in any base. When the Hückel solution is written in the base of two Lewis structures (resonance contributors), the off-diagonal term of the corresponding Hamiltonian matrix is easily obtained, and can be used to calculate the weights of each resonance contributor.

The formamide resonance is used as a example. Ab initio computations lead to a major structure I at 66% (minor is II at 34%).

Lets write the delocalized state (resonant hybrid) as a linear combination of the Lewis structures (resonant contributors): &Psi_Tot= C_I &Psi_I+ C_II &Psi_II. We can consider &Psi_I and &Psi_II as an orthonormal basis that we use to write an Hamiltonian matrix whose solution is the delocalized state (&Psi_Tot,E_Tot) described at the Hückel level. From this completed Hamiltonian one finds easily C_I and C_II. The weights found with the HL-CI approach are the square of the coefficients (e.g. C_I²). The values we obtain are consistent with those found with the NRT method. More importantly for the educational purpose, they are consistent with the predictable trends.

Note that if I is the lowest resonance structure, the resonance energy is ΔE_I.

This simple scheme creates an additional link between Hückel theory and usual organic chemistry concepts such as Lewis structures and resonance. Because the Lewis structures can be considered as configurations, the scheme can be used to exemplify Configuration Interaction (CI) concepts with meaningful configurations, hence the name "Hückel-Lewis CI" (HL-CI) given for the scheme.