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Use tex2html_wrap_inline7749 Interaction

Having identified that almost all the exchange and correlation interaction between electrons occurs over a short range, it seems sensible to use the exact Coulomb interaction, i.e. tex2html_wrap_inline7749 at short range, to capture this exchange and correlation as accurately as possible. The exchange and correlation energy can then be written as




and the limit s on an integral describes an integral over the supercell and the limit a describes an integral over all space. The first term describes each electron interacting via the full tex2html_wrap_inline7749 Coulomb interaction with all other electrons within its Wigner-Seitz cell. This is similar to the evaluation of the new Jastrow function described in chapter gif where each electron-electron separation vector is reduced into the Wigner-Seitz cell centred on the electron being considered by subtracting reciprocal lattice vectors from the electron-electron separation vector as illustrated in figure gif. The second term in Eq.(gif) is required to cancel out the contribution from the first term to the Hartree energy. The Ewald interaction still correctly describes the Hartree energy,


Combining Eqs.(gif and gif) produces a general expression for the electron-electron energy


Andrew Williamson
Tue Nov 19 17:11:34 GMT 1996