  To quantify charge transport through molecular junctions fabricated using the
conducting probe atomic force microscopy (CP-AFM) platform, information on the
number of molecules $N$ per junction is absolutely necessary. $N$ can be
currently obtained only via contact mechanics, and the Young's modulus $E$ of
the self-assembled monolayer (SAM) utilized in the key quantity for this
approach. The experimental determination of $E$ for SAMs of CP-AFM junctions
fabricated using oligophenylene dithiols (OPDn, $1 \leq n \leq 4$) and gold
electrodes turned out to be too challenging. Recent measurements (Z. Xie et al,
J. Am. Chem. Soc. 139 (2017) 5696) merely succeeded to provide a low bound
estimate ($E \approx 58\,$GPa). It is this state of affairs that motivated the
present theoretical investigation. Our microscopic calculations yield values $E
\approx 240 \pm 6\,$GPa for the OPDn SAMs of the aforementioned experimental
study, which are larger than those of steel ($ E \approx 180 - 200\,$GPa) and
silicon ($E \approx 130 - 185\,$GPa). The fact that the presently computed $E$
is much larger than the aforementioned experimental lower bound explain why
experimentally measuring $E$ of OPDn SAM's is so challenging. Having $E \approx
337 \pm 8\,$GPa, OPDn SAMs with herringbone arrangement adsorbed on fcc (111)Au
are even stiffer than Si$_3$N$_4$ ($E \approx 160 - 290\,$GPa).
