  The effect of doping in the two-dimensional Hubbard model is studied within
finite temperature exact diagonalization combined with cluster dynamical mean
field theory. By employing a mixed basis involving cluster sites and bath
molecular orbitals for the projection of the lattice Green's function onto 2x2
clusters, a considerably more accurate description of the low frequency
properties of the self-energy is achieved than in a pure site picture. The
transition from Fermi-liquid to non-Fermi-liquid behavior for decreasing hole
doping is studied as a function of Coulomb energy, next-nearest neighbor
hopping, and temperature. In particular, the self-energy component Sigma_X
associated with X=(pi,0) is shown to exhibit an onset of non-Fermi-liquid
behavior as the hole doping decreases below a critical value delta_c. The
imaginary part of Sigma_X(omega) then develops a collective mode above E_F,
which exhibits a distinct dispersion with doping. Accordingly, the real part of
Sigma_X(omega) has a positive slope above E_F, giving rise to an increasing
particle-hole asymmetry as the system approaches the Mott transition. This
behavior is consistent with the removal of spectral weight from electron states
close to E_F and the opening of a pseudogap which increases with decreasing
doping. The phase diagram reveals that delta_c = 0.15 ... 0.20 for various
system parameters. For electron doping, the collective mode of Sigma_X(omega)
and the concomitant pseudogap are located below the Fermi energy which is
consistent the removal of spectral weight from hole states just below E_F. The
critical doping which marks the onset of non-Fermi-liquid behavior, is
systematically smaller than for hole doping.
