  We explore the possibility to control the superconducting (SC) transition
temperature at optimal hole doping $T_{c}^{\rm opt}$ in cuprates by tuning the
chemical formula (CF). $T_{c}^{\rm opt}$ can be theoretically predicted from
the parameters of the \textit{ab initio} low-energy effective Hamiltonian (LEH)
with one antibonding (AB) Cu$3d_{x^2-y^2}$/O$2p_{\sigma}$ orbital per Cu atom
in the CuO$_2$ plane, notably the nearest neighbor hopping amplitude $|t_1|$
and the ratio $u=U/|t_1|$, where $U$ is the onsite effective Coulomb repulsion.
However, the CF dependence of $|t_1|$ and $u$ is a highly nontrivial question.
In this paper, we propose the universal dependence of $|t_1|$ and $u$ on the CF
and structural features in hole doped cuprates with a single CuO$_2$ layer
sandwiched between block layers. To do so, we perform extensive \textit{ab
initio} calculations of $|t_1|$ and $u$ and analyze the results by employing a
machine learning method called Hierarchical Dependence Extraction (HDE). The
main results are the following: (a) $|t_1|$ has a main-order dependence on the
radii $R_{\rm X}$ and $R_{\rm A}$ of the apical anion X and cation A in the
block layer. ($|t_1|$ increases when $R_{\rm X}$ or $R_{\rm A}$ decreases.) (b)
$u$ has a main-order dependence on the negative ionic charge $Z_{\rm X}$ of X
and the hole doping $\delta$ of the AB orbital. ($u$ decreases when $|Z_{\rm
X}|$ increases or $\delta$ increases.) We elucidate and discuss the microscopic
mechanism of (a,b). We demonstrate the predictive power of the HDE by showing
the consistency between (a,b) and results from previous works. The present
results provide a basis for optimizing SC properties in cuprates and possibly
akin materials. Also, the HDE method offers a general platform to identify
dependencies between physical quantities.
