  In this study, we address the significant challenge of overcoming limitations
in catalytic efficiency for the oxygen evolution reaction (OER). The current
linear scaling relationships hinder the optimization of electrocatalytic
performance. To tackle this issue, we investigate the potential of designing
single-atom catalysts (SACs) on Mo$_2$CO$_2$ MXenes for electrochemical OER
using first-principles modeling simulations. By employing the Electrochemical
Step Symmetry Index (ESSI) method, we assess OER intermediates to fine-tune
activity and identify the optimal SAC for Mo$_2$CO$_2$ MXenes. Our findings
reveal that both Ag and Cu exhibit effectiveness as single atoms for enhancing
OER activity on Mo$_2$CO$_2$ MXenes. However, among the 21 chosen transition
metals (TMs) in this study, Cu stands out as the best catalyst for tweaking the
overpotential ($\eta_{OER}$). This is due to Cu's lowest overpotential compared
to other TMs, which makes it more favorable for OER performance. On the other
hand, Ag is closely aligned with ESSI=$\eta_{OER}$, making the tuning of its
overpotential more challenging. Furthermore, we employ symbolic regression
analysis to identify the significant factors that exhibit a correlation with
the OER overpotential. By utilizing this approach, we derive mathematical
formulas for the overpotential and identify key descriptors that affect
catalytic efficiency in electrochemical OER on Mo$_2$CO$_2$ MXenes. This
comprehensive investigation not only sheds light on the potential of MXenes in
advanced electrocatalytic processes but also highlights the prospect of
improved activity and selectivity in OER applications.
