Weak and Strong Electron-correlation

In both molecules and solids the electron-correlation effects may be strong or weak. Let us consider an example of a H2 molecule. For the two electrons involved, Heitler and London [150] suggested the following correlated ground-state wavefunction 

A very different ansatz apphes when the opposite limit holds, i. e. when the kinetic-energy gain due to spreading an electron over both atoms dominates the mutual electron repulsions. The molecular-orbital theory describes the two electrons within the independent electron approximation and the bonding molecular orbital of an H2 molecule is 

The solids with weak and with strong correlations require different methods of treatment. For example, when the correlations are weak, a wavefunction of independent electrons, i.e. a self-consistent field (SCF) or Hartree-Fock (HF) wavefunction seems a good starting point for the implementation of correlation corrections. In a solid, the molecular orbitals are replaced by crystalline (Bloch) orbitals. The latter are solutions of the SCP(HF) equations (4.57). 

The practical methods of post-HF calculations for solids were discussed during the workshop Local correlation methods from molecules to crystals [156]. Computational strategies were considered and new developments suggested in this area of research (the texts of invited speaker talks are published on an Internet site [156]). In particular, it was stated that the development of post-HF methods for crystals is essentially connected with the progress in the localized Wannier-function (LWF) 

In order to calculate the correlated ground state jiZ o) and its energy o, we split the many-electron Hamiltonian JI into 

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