  We present full quantum mechanical conductance calculations of a quantum
point contact (QPC) performed in the framework of the density functional theory
(DFT) in the local spin-density approximation (LDA). We show that a
spin-degeneracy of the conductance channels is lifted and the total conductance
exhibits a broad plateau-like feature at 0.5*2e^{2}/h. The lifting of the
spin-degeneracy is a generic feature of all studied QPC structures (both very
short and very long ones; with the lengths in the range 40<l<500 nm). The
calculated conductance also shows a hysteresis for forward- and backward sweeps
of the gate voltage. These features in the conductance can be traced to the
formation of weakly coupled quasi-bound states (magnetic impurities) inside the
QPC (also predicted in previous DFT-based studies). A comparison of obtained
results with the experimental data shows however, that while the spin-DFT based
"first-principle" calculations exhibits the spin polarization in the QPC, the
calculated conductance clearly does not reproduce the 0.7 anomaly observed in
almost all QPCs of various geometries. We critically examine major features of
the standard DFT-based approach to the conductance calculations and argue that
its inability to reproduce the 0.7 anomaly might be related to the infamous
derivative discontinuity problem of the DFT leading to spurious
self-interaction errors not corrected in the standard LDA. Our results indicate
that the formation of the magnetic impurities in the QPC might be an artefact
of the LDA when localization of charge is expected to occur. We thus argue that
an accurate description of the QPC structure would require approaches that go
beyond the standard DFT+LDA schemes.
