  A novel approach to predict the atomic densities of amorphous materials is
explored on the basis of Car-Parrinello molecular dynamics (CPMD) in density
functional theory. Despite that determination of the atomic density of matter
is crucial in understanding its physical properties, no such method has ever
been proposed for amorphous materials until now. In our approach, by assuming
that the canonical distribution of amorphous materials is Gaussian
distribution, we generate multiple amorphous structures with several different
volumes by CPMD simulations and average the total energies at each volume. The
density is then determined to be the one that minimizes the averaged total
energy. In this study, this approach is implemented for amorphous silicon
({$a$-Si}) to demonstrate its validity, and we have determined the density of
{$a$-Si} to be 4.1 % lower and its bulk modulus to be 28 GPa smaller than those
of the crystal, which are in good agreement with experiments. We have also
confirmed that generating samples through classical molecular dynamics
simulations produces a comparable result and validates our assumption. The
findings suggest that the presented method is applicable to other amorphous
systems, including those that lack experimental knowledge.
