We have calculated the quasiparticle energy of the occupied surface st
ates of the H-Si(111)1x1 surface. The electron self-energy operator is
expanded to first order in the screened Coulomb interaction in the GW
approximation. The results explain the data from recent high-resoluti
on angle-resolved photoemission spectroscopy. Comparison of the quasip
article surface-state energies with those from local-density-functiona
l eigenvalues shows that the self-energy corrections are very large, t
ypically two to three times larger than the corrections found in previ
ous calculations on other semiconductor surface systems. We have also
performed a frozen-phonon study of the stretching mode of the Si-H bon
d. As observed in several recent experiments and theoretical studies,
a large anharmonicity is found.