  We examine whether essence and quantitative aspects of electronic excitation
spectra are correctly captured by an effective low-energy model constructed
from an {\em ab initio} downfolding scheme. A global electronic structure is
first calculated by {\em ab initio} density-functional calculations with the
generalized gradient approximation. With the help of constrained density
functional theory, the low-energy effective Hamiltonian for bands near the
Fermi level is constructed by the downfolding procedure in the basis of
maximally localized Wannier functions. The excited states of this low-energy
effective Hamiltonian ascribed to an extended Hubbard model are calculated by
using a low-energy solver. As the solver, we employ the Hartree-Fock
approximation supplemented by the single-excitation configuration-interaction
method considering electron-hole interactions. The present three-stage method
is applied to GaAs, where eight bands are retained in the effective model after
the downfolding. The resulting spectra well reproduce the experimental results,
indicating that our downfolding scheme offers a satisfactory framework of the
electronic structure calculation, particularly for the excitations and dynamics
as well as for the ground state.
