New algorithms for exploring reduced potential energy surfaces (RPES) have the potential to solve some persistent remaining problems in transition state identification, such as the tendency for eigenvector-following and dimer algorithms to repeatedly discover the same transition states. We outline the RPES framework and some advantages of these new algorithms. We then show how an RPES framework can be used to resolve another long-standing challenge: structure–property relationships for isolated sites on amorphous catalysts. By retaining only the peripheral degrees of freedom in a cluster model, and with the reaction coordinates adiabatically optimized, we can systematically generate a series of isolated site models with varying activity. We do this by combining the RPES framework with a sequential non-linear programming algorithm. The algorithm systematically generates a family of low energy sites with varying reactivity and thereby exposes structural differences between highly active and inactive sites on the catalyst surface. We demonstrate this algorithm on a 2D model energy surface, on a simplified ‘chemical’ model, and lastly for ethene polymerization on the Phillips catalyst (Cr/SiO₂). The novel approach for understanding catalysts on amorphous supports exemplifies how the powerful RPES framework can enable calculations that were previously intractable.