Gas‐Phase Thermodynamics as a Validation of Computational Catalysis on Surfaces: A Case Study of Fischer–Tropsch Synthesis

Abstract

Density functional theory has become a valuable tool to study surface catalysis. However, due to the scarcity of clean and reliable experimental data on surfaces, the theoretical methods employed to explore heterogeneous catalytic mechanisms are usually less well validated than those for gas-phase reactions. We argue herein that gas-phase reactions and the corresponding surface reactions are related through the Born-Haber cycle and computational catalysis on surfaces will be less meaningful if gas-phase behavior cannot first be suitably determined. In this contribution, we have constructed a set of gas-phase reactions relevant to the Fischer-Tropsch synthesis as a case study. With this set, we have tested the validity of the widely used PBE and B3LYP functionals and found that neither of them are capable of describing all kinds of gas-phase reactions properly, such that some surface reactions may be biased falsely against the others. Significantly, XYG3, which is a double-hybrid functional that includes Hartree-Fock-like exchange and many-body perturbation correlation effects, presents a significant improvement for all of the gas-phase reactions, holding promise for further development for surface catalysis.

The XYG3 type of doubly hybrid density functionals

“…There exist many benchmarking calculations, as well as practical applications, for the xDH functionals. The results have been intensively compared with those from other DFT methods and WFT methods.…”

“…In the followed sections, we will discuss the theoretical background of the DH functionals, briefly reviewing the adiabatic connection (AC) formalism, coordinate scaling relations, and Görling–Levy (GL) perturbation theory . General performance of the DH functionals will then be summarized, not only for energies, but also for structures. In particular, we will present the fractional charge behaviors of the DH functionals, examining the SIEs, the delocalization errors and the deviation from the linearity condition, as well as their effects on the predicted ionization potentials, electron affinities and fundamental gaps, providing a theoretical rationale for the observed good performance of the xDH functionals.…”

Analytic derivatives for the XYG3 type of doubly hybrid density functionals: Theory, implementation, and assessment

“…With the help of eqs. (40)(41)(42)(43)(44), and by directly differentiating eq. (12) with respect to parameter x, we have…”

“…(6). [24,[36][37][38][39][40][41][42][43][44][45][46] In fact, both XYG3 [24] and XYGJ-OS [40] use B3LYP to generate the orbitals and density. In such a way, XYG3 or XYGJ-OS shares with B3LYP the terms of T s , V ext , and E J , which are the large quantities in the total electronic energy of eq.…”

“…A new type of functionals that have been put forward recently is the so‐called doubly hybrid (DH) functional where the name suggests that not only the DFA exchange is hybridized with HF‐like exchange, but also the DFA correlation is hybridized with the Møller–Plesset theory to the second order (MP2)‐like nonlocal correlation. Numerical assessments demonstrated that even greater accuracy can be achieved with the DH functionals, especially for some difficult cases associated with the traditional DFA functionals, such as predictions of reaction barrier heights and nonbonded interactions …”