  We compute the superconducting condensation energies Econd of Hg1201 and
Tl2201 cuprates by applying the variational Monte Carlo method to the
two-dimensional Hubbard model, first, with the specific band parameters t' =
-2t" = -0.25t appropriate for these highest-Tc single-CuO2-layer cuprates; t,
t' and t" are the first-, second- and third-neighbor transfer energies,
respectively. In the range of on-site Coulomb energy U of (7\sim10)t with
optimal doping, we succeed in obtaining the bulk-limit Econd values by
extrapolating the results. They sharply increase with increasing U and become
comparable to experimental values when U \approx 9t. Next, Econd values at t' =
-2t" = -0.18t demonstrate that with a fixed U the bulk-limit Econd quickly
increases with a decrease in |t'| = 2t" in the large-|t'| region. Finally, we
argue that the remoteness of the apex oxygen from the planar Cu in the two
cuprates is considered to increase U and bring about the experimental magnitude
of Econd. The present scheme explains the observed correlation between Tc and
t' among cuprates.
