Enthalpies calculated using VASP (and some other computational methods) have different references than standard references (i.e. the enthalpy of formation of pure substances, like O2 or Pt, is not necessarily zero). This difference makes it difficult to ensure thermodynamic consistency for our mechanisms since we may be mixing experimental gas thermodynamics with computational surface thermodynamics. In order to make the references consistent, we find a correction factor for each element by solving the equation:

\(\underline {\underline {H}}^{expt}_{[M \times N]} = \underline {\underline {H}}^{DFT}_{[M \times N]} + \underline {\underline {x}}_ {[M \times N]} \underline{\mathbf{h}}_{[N]}\)

where M is the number of reference species, N is the number of elements, Hexpt is the experimental standard enthalpies, HDFT is the standard enthalpies calculated using DFT, x is a matrix that describes the composition of the references (each row represents a specie, each column represents an element), and h is the correction for each element.

The equation can be solved using a Least Squares approach. The correction factor can then be added to subsequent species calculated through DFT to ensure consistent references. Referencing is handled by the References.