We apply a microscopic formulation to calculate the second harmonic sp
ectra of clean and hydrogenated Si(100) surfaces. We find a trend of t
he surface-allowed Ei resonance as a function of the hydrogen coverage
, which is consistent with experiment. Another resonance at lower ener
gy, recently observed at the clean surface, is also reproduced and exp
lained in terms of transitions across surface states. Its quenching is
clearly demonstrated as a function of hydrogen coverage. Our results
for the energetically more favorable c(4 X 2) structure are in better
agreement with low temperature experimental data than those calculated
for the 2 X 1 reconstruction. We find that the spectra are dominated
by the chi(III perpendicular to)(S) component of the second-order nonl
inear surface susceptibility. [S0031-9007(98)07375-X].