Performance of the Empirical Dispersion Corrections to Density Functional Theory: Thermodynamics of Hydrocarbon Isomerizations and Olefin Monomer Insertion Reactions

Most of the commonly used approximate density functionals have systematic errors in the description of the stability of hydrocarbons. This poses a challenge for the realistic modeling of reactions involving hydrocarbons, such as olefin polymerization. Practical remedies have been proposed, including the application to usual black-box DFT of additional empirical correction CR(-6) terms for the van der Waals interaction (termed DFT-D), or introducing additional pseudopotentials that introduce some medium-to-long-range attraction (C-Pot). In this Article, we use the DFT-D scheme as realized in our BOptimize package to evaluate the performance of a range of commonly used DFT functionals (combinations of xPBE, B88, OPTX with LYP and cPBE GGAs and hybrids) for the modeling of the thermodynamics of reactions of the growth of common polyolefins. We also review and reproduce some of the previously done benchmarks in the area: alkane branching and relative stability of C12H12 and C10H16 isomers. In addition to the common DFT methods, computations with correlated wave function methods (MP2) and the new functionals B97-D and M06-L were performed. The performance of the special density functionals B97-D and M06-L is, in general, similar to the best DFT-D corrected regular functionals (BPBE-D and PBE-D). The results show that (1) the DFT-D correction is sufficient to describe alkane branching, but its performance depends on the parametrization; (2) inclusion of the correction is essential for a proper description of the thermodynamics of reactions of polymer growth; and (3) not all approximate density functionals perform effectively for the description of hydrocarbons even with the correction. The C-Pot method for the B3LYP functional shows quantitatively correct results for our test cases. The enthalpies of hydrocarbon reactions were analyzed in terms of the repulsion characteristics of a given DFT method. PBE is the least repulsive, while OLYP is the most. However, there are cases where the failure of a DFT method cannot be correlated with its repulsive character. A striking example is the performance of B3LYP and BLYP for caged molecules with small carbocycles, such as the [D3d]-octahedrane. The stability of [D3d]-octahedrane is underestimated by the B3LYP, BLYP, and B97-D functionals, but not by DFT methods that contain either B88 exchange or LYP correlation functionals separately. While DFT-D cannot amend the performance of the former functionals for the octahedrane, C-Pot for B3LYP does.

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