  Derivation of low-energy effective models by a partial trace summation of the
electronic degrees of freedom far away from the Fermi level, called
downfolding, is reexamined. We propose an improved formalism free from the
double-counting of electron correlation in the low-energy degrees of freedom.
In this approach, the exchange-correlation energy in the local density
approximation (LDA) is replaced with the constrained self-energy corrections
defined by the sum of the contribution from eliminated high-energy degrees of
freedom, Sigma H and that from the frequency-dependent part of the partially
screened interaction, Delta Sigma L. We apply the formalism to SrVO3 as well as
to two iron-based superconductors, FeSe and FeTe. The resultant bandwidths of
the effective models are nearly the same as those of the previous downfolding
formalism because of striking cancellations of Sigma H and Delta Sigma L. In
SrVO3, the resultant bandwidth of the effective low-energy model is 2.56 eV (in
comparison to LDA: 2.58 eV, full GW approximation: 2.19 eV). However, in the
non-degenerate multi-band materials such as FeSe and FeTe, the momentum
dependent self-energy effects yield substantial modifications of the band
structures and relative shifts of orbital-energy levels of the effective
models. The FeSe model indicates a substantial downward shift of the x2-y2
orbital level, which may lead to an increase in the filling of the x2-y2
orbital above half filling. It suggests a destruction of the orbital selective
Mott phase of the x2-y2 orbital in agreement with the experimental absence of
the antiferromagnetic phase.
