  The gravitational radiation driven capture (GR capture) between unequal mass
black holes without spins has been investigated with numerical relativistic
simulations. We adopt the parabolic approximation which assumes that the
gravitational wave radiation from a weakly hyperbolic orbit is the same as that
from the parabolic orbit having the same pericenter distance. Using the
radiated energies from the parabolic orbit simulations, we have obtained the
critical impact parameter ($b_{\rm crit}$) for the GR capture for weakly
hyperbolic orbit as a function of initial energy. The most energetic encounters
occur around the boundary between the direct merging and the fly-by orbits, and
can emit several percent of initial total ADM energy at the peak. When the
total mass is fixed, energy and angular momentum radiated in the case of
unequal mass black holes are smaller than those of equal mass black holes
having the same initial orbital angular momentum for the fly-by orbits. We have
compared our results with two different Post-Newtonian (PN) approximations, the
exact parabolic orbit (EPO) and PN corrected orbit (PNCO). We find that the
agreement between the EPO and the numerical relativity breaks down for very
close encounters ($\it{e.g.}$, $b_{\rm crit} \lesssim 100$ M), and it becomes
worse for higher mass ratios. For instance, the critical impact parameters can
differ by more than $50\%$ from those obtained in EPO if the relative velocity
at infinity $v_{\infty}$ is larger than 0.1 for the mass ratio of
$m_{1}/m_{2}=16$. The PNCO gives more consistent results than EPO, but it also
underestimates the critical impact parameter for the GR capture at $b_{\rm
crit} \lesssim40$ M.
