Ab initiocalculation of the macroscopic dielectric constant in silicon

We perform a first-principles calculation of the static dielectric constant of Si in the framework of density-functional theory. The only essential approximation used in this work is the local-density approximation (LDA): norm-conserving pseudopotentials and large plane-wave basis sets are used, numerical roundoff and convergence errors are kept below 1%. The present calculation gives for the first time the ‘‘exact’’ value of the macroscopic dielectric constant at the LDA level. The theoretical value of ${\epsilon }_{\infty }$ is 12% higher than experiment.