I personally think and I could be wrong, that this question is a mixture of very inhomogeneous concepts. There is indeed a correlation between quantum chemistry and solid state physics. Quantum chemistry in the simple formulation evoked in the comments deals mainly with localised states that are not very too far from atomic orbitals, the expansion of the unknown WF is a set of localised orbitals (LCAO). Solid-state physics is concerned with delocalized states. Their difference is a matter if size and the symmetry of the system under study.
In solid-state physics, the most crucial symmetry is translation, and the single-particle translational operator $\hat{T}$ linked to the linear moment operator $\hat{p}=i\hbar \nabla \hat{T}$. The eigenfunctions here are often plane-waves (PW) or a combinaison of PW. $\hat{T}$ produces the band structure and Bloch states by assuming that it commutes with the Hamiltonian. Everything that affects translational symmetry leads directly to chemical localized states : pairwise $U$ Coulomb interactions, defects ...
In the chemical limit, the operator position $\hat{x}$ is important and the symmetries such as rotations or mirrors that commute with the Hamiltonian.
I don't know where this argument about band structure in liquids where there is no translational symmetry comes from.
CFT in solids like transition metal oxides (cupper oxide) is in my opinion more of a chemistry problem, I could go into mathematical details using the hubbard model to show that in this configuration the metal cation has a quasi-atomic structure for the d-orbitals simply because the overlap of the d-orbitals is too small due to impurities compared to the
coulombic interaction $U$.
The number of bonds is not the generator of a band structure but the symmetry of these bonds. Large molecules such as fullerenes $C_{200}$ do not have a band structure but energy levels because there is not enough translational symmetry. The band gap is just due to how this translational symmetry is affected by the potential, but this gap may differ from the splitting responsible for the colors of these oxides due to CFT.
Even if it's not the direct answer to the question I hope it helps