In order to compare the calculated cohesive energy with experiment various correction terms must be added to the solid calculations to account for: (i) Coulomb finite-size effects; (ii) single-particle finite-size effects; (iii) the use of a local pseudopotential; and (iv) zero-point motion. These corrections are discussed in detail in reference [33]. All these corrections are essentially independent of the optimisation of the wavefunction and it therefore suffices to compare directly the VMC and DMC results for the same system. A DMC calculation for the germanium pseudo-atom gave an energy of -103.42 0.03 eV, which is only 0.20 eV below our best VMC result, while for the solid the VMC calculation (without ) gave an energy 0.34 eV above the DMC result. Therefore the VMC cohesive energy, of 3.80 ev per atom, is only 0.14 eV less than the DMC result, of 3.85 eV per atom, which amounts to an error of only 4%. As mentioned earlier we believe that 0.12 eV of the difference in energy between the VMC and DMC results for the solid is due to the incomplete basis set used for the single particle orbitals. If this is corrected for, the VMC cohesive energy differs from the DMC value by only 1%. This indicates that although there is still a significant difference in the VMC and DMC energies, the difference in the atomic energies transfers almost completely into the solid calculations and therefore cancels out of the cohesive energies.

Tue Nov 19 17:11:34 GMT 1996