Thermodynamic Consistency of the DFT-Predicted Energetics

In general, energies predicted using DFT methods differ from experimental or high-level ab initio data. This is best illustrated when a thermodynamic loop is drawn. Consider the activation of CO on a surface (CO -i- C -i- O ). The thermodynamic cycle for this reaction can be written as 

For the specific example, the heat of the CO activation reaction in gas-phase (CO - C + 0) at 298 K evalnated by the DFT method nsed here, inclnding temperature correction, is 247.3 kcal/mol as compared to 257.1 kcal/mol calcn-lated from [36]. This difference (of 10kcal/mol in this example) makes the DFT calculations inconsistent with high-level ab initio methods nsed to compnte thermodynamic properties in the gas phase. Use of DFT valnes only, without employing literature or ab initio gas-phase thermodynamics, can overcome this inconsistency at the expense of having less accurate thermodynamics with implications for error in energy balances, eqnilibrium conversions, and gas-phase species concentrations. Similarly to enthalpic inconsistency, entropic inconsistency may also exist. 

Generally, a method must be devised to satisfy Equation (8.14), as well as the corresponding equation for entropic consistency. Such a method was first discussed in Ref. [37], based on the number of linearly independent degrees of freedom one has in a miCTokinetic model. As a specific example for entropic consistency, consider the preexponential factors in Table 8.1 that must be thermodynamically consistent. This is accomplished using Equation (8.16) [11]  

Regarding enthalpic consistency, Grabow et al. [38] have proposed a method in which the enthalpy of adsorption is kept as predicted from DFT, and the heat of surface reaction is adjusted to make the mechanism thermodynamically consistent for each thermodynamic loop. The difference between the corrected (A// and the 

DFT-predicted heats of reaction is then distributed over the forward and 

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