In the literature of heterogeneous water-splitting catalytic thermodynamic study, the computational hydrogen electrode (CHE) scheme is used in the majority of the cases. In this scheme, either the bare surface without O and OH decoration or a decorated phase chosen from a surface Pourbaix diagram is employed as a starting point in a four-electron reaction loop (FERL) to describe the oxygen evolution reaction (OER) process. The electrode potential that makes every step of this FERL exothermic is defined as the thermodynamic overpotential (eta(OER)(td)) of the OER reaction and is often compared with the experimental overpotential. In this study, we point out that for complex systems where each reaction site can bind multiple species, this widely used scheme could lead to wrong eta(OER)(td). To yield the correct reaction path and eta(OER)(td), one needs to extend the CHE scheme to a full Gibbs free energy landscape scheme, where all of the intermediate states and their possible transitions are laid out and considered. The correct criterion for eta(OER)(td) should not be "there is no trapped intermediate state (TIS) for any single FERL", rather "there is no TIS for the whole reaction landscape". Using transition metal-doped graphene-nitrogen (TMN(4)Gra) (TM = Fe and Co) as examples, we show that these two approaches yield different results.