All pertinent definitions and associated notation are collected and concisely summarized in this section. We follow existing definitions and notations from the gas-phase chemistry literature where possible. Throughout this work, we assume that all thermochemical quantities are evaluated at 0 K, consistent with computational chemistry methods. For simplicity and readability, we drop the temperature in the equations below and only indicate if a quantity is evaluated at a different temperature. However, the definitions hold at all temperatures, and all mathematical relationships are valid as long as all quantities are evaluated at a consistent temperature. We also note that the existing computational catalysis literature may use different terms and contains many ambiguities. Thus, the definitions and notation below are inconsistent with some prior studies in computational catalysis, but are largely consistent with the gas-phase literature. Table summarizes all the quantities used in this review. We provide a notation for a single species whenever possible and a linear algebra notation for a set of species (e.g., full mechanism). The general notation uses a ∆ for all relative quantities, with the subscript on the ∆ indicating whether it is a formation f or reaction enthalpy r. The subscript on the H indicates the identity of the species, while the superscript on the H denotes the method used. We introduce another subscript A on the ∆ that indicates whether the enthalpy is relative to a non-standard set of anchor species. For example "∆ A H * CO where A = [CH 4 , H 2 O, H 2 , Pt(111)]" would fully specify an enthalpy of *CO adsorbed on Pt(111) anchored to the DFT energies of CH 4 , H 2 O, and H 2 and Pt(111). By definition, ∆ A H of the an-chor species A are zero in this local thermochemical network. The specification of the subscript on the ∆ is critical when reporting enthalpies of adsorbed species relative to non-standard anchors since, as shown later, the absolute values of the enthalpies vary widely with different anchor species. In this work, we reserve the name of formation enthalpies to its agreed upon definition by the chemistry community. Only enthalpies that are relative to the standard IUPAC anchors, either directly or indirectly, and, thus, are appended to the global thermochemical network are called enthalpies of formation.