Using the multipole-expansion formalism and recently published millielectron volt-level-accuracy x-ray structure factors, a detailed description of the crystal-bound silicon atom is derived. A 0.5% expansion of the L shell is detected, in addition to the known ∼6% expansion of the M shell. A nonrigid thermal motion of the atom is also found, with the valence charge vibrating with a much reduced amplitude. Strong evidence is also found for a twofold reduction over the theoretical prediction for the magnitude of the anharmonic force constant in the effective one-atom potential. The R factor of our improved model is only 50% that of the best previously published one, and the goodness of fit is close to unity, indicating that the model exhausts the accuracy of the measured data. Deformation and valence-charge-density maps are presented and found to be in good agreement with previous results. Wave-function- and model-specific influences such as wave-function quality and relativistic and exchange-potential effects are also discussed. It is concluded that their influence on the conclusions of the present study is marginal.

• Received 20 March 1991

DOI:https://doi.org/10.1103/PhysRevB.45.646