61st Annual Report on Research 2016

In this project we will investigate the role of support in catalysts using novel quantum-chemical methods. Catalysis is a major tool in the petroleum refining industry, especially concerning the hydrocracking and hydrogenation stages. The new quantum chemistry methods are Becke’05 method proposed by Becke [1] and implemented by our group [2], and the analysis of atomic population of effectively unpaired electrons proposed and implemented by our group [3]. In contrast to mainstream conventional DFT methods, these new methods are capable of describing nondynamic correlation that is prominent in catalytic reactions. In the first year of this PRF grant, we have made progress on the following two fronts. One is the improvement of the computational applicability of our methods. The other is an initial application of our methods to catalysis.

Improvement of applicability of new computational methods

The catalytic processes such as hydrocracking (HC) and hydrodesulfurization (HDS) involve transition-metal centers such as MoS₂ and Co-MoS₂ supported on g-Al₂O₃ and TiO₂surfaces. These are large molecular structures involving many atoms including heavy ones. They are particularly challenging computationally for new DFT methods because the latter have higher computational cost than conventional DFT methods. The reason is that the new methods require the computation of the HF (Hartree-Fock) exchange energy density. Its computation is expensive and complicates the derivation of SCF solution. We originally proposed a general solution based on RI (resolution of identity) previously for this problem. Our RI solution allowed us to achieve the SCF solution for B05 for the first time, but it is still inefficient especially for large systems, and numerically unstable.

Instead of approximating, we have recently developed an algorithm to compute the original integrals directly and exactly. The details will be published elsewhere but the core idea is that the electrostatic potential (ESP) for each basis function pair, is calculated first at each grid point. This scheme scales the same as the normal HF exchange energy with respect to the molecular size and thus scales better than RI for large molecules. Furthermore, it requires much less memory than the original RI scheme.

We compared the performance of the new scheme with that of RI for an SCF calculation with B05 functional for a number of molecules of different sizes with the popular 6-31G** basis set. The timings are for one SCF iteration in seconds. As one can see, the new scheme is faster than RI, and the gain of performance grows as the molecular size increases. The new scheme is also numerically more stable.

Method	Pyrrole	Benzene	Alanine	Naphthalene
New scheme	42	67	79	164
RI scheme	57	98	121	400

To further improve the applicability of our methods, we implemented our code on multicore computers. The figure below shows the parallel efficiency of our implementation on a series of alanine peptides. As one can see, our code scales very well with respect the number of cores, achieving almost linear speed-up for the larger alanines.

Studies on the ethlylene addition to Ni dithiolene reactions

To assess the applicability of our methods for catalytic reactions, we tested our method for the computation of atomic population of effectively unpaired electrons (APEUE) on the ethylene addition to a Ni-S center Ni(edt)₂ (edt=S₂C₂H₂) [4]. We computed the APEUE numbers on various reactants, products and transition states as listed in the reference [4], and compared the numbers of T1 analysis, an index based on a wavefunction method CCSD(T). CCSD(T) is a high-level method and its results are considered reliable. The graph below shows the correlation between the indexes computed with the two methods. As one can see, they correlate rather well. The advantage of our method is that it is computationally much more affordable than CCSD(T) since it is a DFT-based method. This gives us confidence at applying our methods to studying catalysis.

References

 

1. Becke, A.D., Real-space post-Hartree-Fock correlation models. Journal of Chemical Physics, 2005. 122: p. 64101.

2. Liu, F., et al., Comparison of the performance of exact-exchange-based density functional methods. Journal of Chemical Physics, 2012. 137: p. 114104.

3. Proynov, E., F. Liu, and J. Kong, Analysing effects of strong electron correlation within Kohn-Sham Density-Functional Theory. Phys. Rev. A, 2013. 88: p. 032510.

4. Dang, L., et al., Computational studies on ethylene addition to nickel bis(dithiolene). J. Phys. Chem. A., 2012. 116.