Self-consistent calculation of Compton profiles, X-ray structure factors, and band structure for silicon

The electron distribution in silicon. A comparison between experiment and theory

“…Excellent agreement with experiment is also obtained for the calculations of Zunger (1980), Zunger & Cohen (1979), Heaton & Lafon (1981), Wang & Klein (1081) and Stukel & Euwema (1970;KSG, S1-RHF and KSG-RHF sets). The calculation by Dovesi et al ( 1981) predicts the correct topography of Ap and pv~a, but consistently underestimates the magnitude of the features.…”

“…We compare twelve calculations of structure factors, either for the total electron density, or for the valence density. These are taken from Yin & Cohen (1982), Dovesi, Causa & Angonoa (1981), Wang & Klein (1981 ), Heaton & Lafon (1981 ), Zunger (1980), Zunger & Cohen (1979), Tejedor & Verges (1979), Chelikowsky & Cohen (1974) and Stukel & Euwema (1970). These publications report varying numbers of structure factors, and in the cases of Tejedor & Verges (1979) and Chelikowsky & Cohen (1974) only valence density structure factors.…”

“…A systematic difference is also seen in the S1 set of Stukel & Euwema (1970), where I Foxpl is uniformly less than I F,.oorl-Such errors prevent us from making strong conclusions based on agreement indices alone. Based on the R factors in Table 4, three sets by Stukel & Euwema (1970) and those by Heaton & Lafon (1981) and by Wang & Klein (1981) stand out from the rest. The Hartree-Fock calculation of Dovesi et al (1981) is noticeably inferior, as it substantially overestimates all key low-angle reflections, while underestimating the important 222 reflection by 40%.…”

The electronic charge distribution in crystalline silicon: comparison of ab initio theory and experiment

“…While the second approximation could be partially circumvented by adding the core structure factors to the pseudo-valence structure factors, this procedure ignores core-valence orthogonality and leads to systematic errors noted by Spackman (1986). All-electron calculations, which treat core and valence wavefunctions on equal footing (Raccah, Euwema, Stukel & Collins, 1970;Wang & Klein, 1981;Dovesi, Causa & Angonoa, 1981;Heaton & Lafon, 1981;Weyrich, 1988;Methfessel, Rodriguez & Andersen, 1989;Polatoglou & Methfessel, 1990), are free from such complications. However, some of them involve independent approximations such as perturbation theory (Bertoni et al, 1973) or the use of small basis sets (Dovesi et al, 1981;Heaton & Lafon, 1981).…”

“…All-electron calculations, which treat core and valence wavefunctions on equal footing (Raccah, Euwema, Stukel & Collins, 1970;Wang & Klein, 1981;Dovesi, Causa & Angonoa, 1981;Heaton & Lafon, 1981;Weyrich, 1988;Methfessel, Rodriguez & Andersen, 1989;Polatoglou & Methfessel, 1990), are free from such complications. However, some of them involve independent approximations such as perturbation theory (Bertoni et al, 1973) or the use of small basis sets (Dovesi et al, 1981;Heaton & Lafon, 1981). Recent developments in understanding correlation effects in the density functional theory (Ceperley & Alder, 1980;Perdew & Zunger, 1981) and in numerical strategies (see, for example, Wei & Krakauer, 1985;Bernard & Zunger, 1989) now make highly precise calculations on simple crystals straightforward.…”