  We derive the semiclassical Kirzhnits expansion of the D-dimensional
one-particle density matrix up to the second order in $\hbar$. We focus on the
two-dimensional (2D) case and show that all the gradient corrections both to
the 2D one-particle density and to the kinetic energy density vanish. However,
the 2D Kirzhnits expansion satisfies the consistency criterion of Gross and
Proetto [J. Chem. Theory Comput. 5, 844 (2009)] for the functional derivatives
of the density and the noninteracting kinetic energy with respect to the
Kohn-Sham potential. Finally we show that the gradient correction to the
exchange energy diverges in agreement with the previous linear-response study.
