  We study the convergence of the derivative expansion in HAL QCD method from
the finite volume analysis. Employing the (2+1)-flavor lattice QCD data
obtained at nearly physical light quark masses $(m_\pi, m_K) \simeq (146, 525)$
MeV and the physical charm quark mass, we study two representative systems,
$\Omega\Omega$ and $\Omega_{ccc}\Omega_{ccc}$ in the $^1S_0$ channel, where
both systems were found to have a shallow bound state in our previous studies.
The HAL QCD potentials are determined at the leading-order in the derivative
expansion, from which finite-volume eigenmodes are obtained. Utilizing the
eigenmode projection, we find that the correlation functions are dominated by
the ground state (first excited state) in the case of $\Omega\Omega$
($\Omega_{ccc}\Omega_{ccc}$). In both $\Omega\Omega$ and
$\Omega_{ccc}\Omega_{ccc}$, the spectra obtained from eigenmode-projected
temporal correlators are found to be consistent with those from the HAL QCD
potential for both the ground and first excited state. These results show that
the derivative expansion is well converged in these systems, and also provide a
first explicit evidence that the HAL QCD method enables us to reliably extract
the binding energy of the ground state even from the correlator dominated by
excited scattering states.
