  We fully implement the Aversa and Sipe sum-over-states formulism and make a
full ab initio band structure analysis of interband and intraband contributions
for the third-order nonlinear optical susceptibilities of bulk silicon. The
band structure and momentum matrix elements were calculated by using the highly
accurate all-electron full potential linearized augmented plane wave method
within the local density approximation. The convergence tests including the
scissor correction with different k-points meshes and empty states were
performed. Both real and imaginary parts of susceptibility were directly
calculated and checked by the Kramers-Kronig relation. The converged results
are compared with other theoretical and experimental ones and in agreement with
the recent ab initio real-time-based calculation. The nonlinear optical
coefficient comes from three parts: the pure interband contribution (Pinter),
the modulation of interband terms by intraband terms (Pmod), and the intraband
contribution (Jintra). For each part, the origin of enhanced peaks is explored
by tracing the sum-over-states process. The interband contribution is found to
be dramatically modulated by the intraband contribution.
