Quantum Chemistry and Superconductors

Book chapter, 2017

Thirty years after the discovery of high temperature (HT) superconductivity (SC), no by all accepted theory exists. The Bardeen, Cooper, Schrieffer (BCS) model, hewed into the Bloch theory for metals, is unfit for local systems such as cuprates and organic superconductors. In this chapter, we will use a theory that dates back to Landau and Pekar, but we will avoid the effective mass approach by using a total free energy model, as designed for electron transfer problems by Marcus and Jortner. A diffusion equation is used to derive the resistivity in the local case. The original definition of Hubbard U by Mott as a metal-to-metal (or molecule-to-molecule) charge transfer energy will be updated by including the neglected negative terms. It will be shown that the absorption at 2 eV in the cuprates is indeed due to Cu–Cu charge transfer, identical to the Hubbard U or Mott transition. The model accounts for bond-length fluctuations due to occupancy of d-orbitals (extended over the ligands), or in the molecular case the ? orbitals, and this makes it necessary to make a distinction between adiabatic and vertical Hubbard U. Uvert = 1.5–3 eV while Uad may be a few hundred times smaller. Organic SC in aromatic hydrocarbons will be shortly reviewed and found consistent with the general model. Finally, we will discuss SC in tungsten bronzes discovered in 1964 by Matthias.