  Proximity induced superconductivity with a clean interface has attracted much
attention in recent years. We discuss how the commonly-employed electron
tunneling approximation can be hybridized with first-principles calculation to
achieve a quantitative characterization starting from the microscopic atomic
structure. By using the graphene-Zn heterostructure as an example, we compare
this approximated treatment to the full \textit{ab inito} anisotropic
Eliashberg formalism. Based on the calculation results, we discuss how
superconductivity is affected by the interfacial environment.
