The equation-of-motion method offers advantages in the calculation of
properties of large structural models, of the kind recently developed
for a-Si (10(4) or more atoms). Originally developed for calculating d
ensities of states, it has been shown to be adaptable to a wide variet
y of other purposes, including the study of localization, conductivity
and the Hall effect. Recently we Have shown how it may be used to cal
culate linear optical properties as a function of frequency. Here we p
resent new calculations for a-Si and a-Si:H, using various structural
models. The method may be further extended to evaluate nonlinear optic
al coefficients chi((2))(omega) and chi((3))(omega); we are applying i
t to the study of chi((3))(omega) for crystalline and amorphous silico
n. A conventional approach to this problem, such as calculating eigens
tates, would be totally impractical.