62nd Annual Report on Research 2017

This is the second annual report for this project for the investigation of 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 and implemented by our group, and the analysis of atomic population of effectively unpaired electrons (APEUE) proposed and implemented by our group.  At the core of hydrocracking and hydrogenation is the catalysis driven by transition-metal centers.  The chemical reactivity of those transition-metal centers is challenging to computational conventional methods, especially density functional theory methods, due to the lack of the treatment of nondynamic correlation.  The implementation of the new methods and their applications provide hope to overcome this challenge.  In the second year, we continue to improve the computational methods and study the applicability of these methods to transition metal compounds.

Improvement of applicability of new computational methods

Improving the computational capability is critical for quantum simulations, especially for catalytic processes.  Hydrocracking and hydrodesulfurization involve transition-metal centers supported on g-Al₂O₃ and TiO₂ surfaces.  These are large molecular structures involving many atoms.  They are particularly challenging computationally for new DFT methods such as B05 and our own KP16/B13 because the new methods needs the HF exchange energy density.  Its computation is expensive and complicates the derivation of SCF solution.  We have recently developed an algorithm to compute the original integrals directly and exactly when we started with this project, and published it recently.

The method scales quadratically with respect to the molecular size and the basis set size O(N²), versus the quardruple scaling O(N⁴) of the conventional scheme with respect to the basis set size.  It is exact for computing the HF exchange energy density, is favored for medium-sized basis sets and can be competitive even for large basis sets. It can also be used as a seminumerical integration scheme to compute the HF exchange energy and matrix on a standard atom-centered grid. Calculations on a series of alanine peptides show that for large basis sets the new scheme can be about six times faster for aug-cc-pvtz basis compared to the conventional scheme.  The graph here shows the computation time versus the size of the peptitdes with aug-cc-pvtz basis.  The series of peptides includes 6, 8, 11, 13, and 16 alanine units.  As one can see, the seminumerical scheme speeds up the computation several times with this large basis set, providing a distinct computational advantage.

Investigation of nondynamic correlation for transition-metal compounds

In the last few years, our group has developed the unique APEUE method to estimate the atomic population of effectively unpaired electrons, which indicates the degree of nondynamic correlation, a crucial aspect of electronic structure for catalysis.  In the first year, we tested our APEUE method on the ethylene addition to a Ni-S center Ni(S₂C₂H₂)₂ to assess the applicability of our methods for catalytic reactions.  We compared with the T1 analysis, an index based on a wavefunction method CCSD(T).  CCSD(T) is a high-level method and its results are considered reliable.  Our results show that both indexes correlate rather well.

This positive initial assessment prompted us to investigate further the applicability of our APEUE method for transition-metal compounds.  To this end, we have started to benchmark with the correlation-consistent composite approach for transition-metals (ccCA-TM-11).  This set is consisted of 193 first-row TM compounds.  The multireference character of those TM complexes were already studied by the same group in a subsequent paper using  T1, %TAE, D1 and C0 of CASSCF.

We have computed the APEUE results for the whole set.  Here we give preliminary analysis of some of the results.  The table here lists the APEUE for the TM atom in two series of molecules containing Ni and Cr.  The APLEUE is on the metal.  The %TAE and T1 results show a decrease trend as more ligands are added to Ni, consistent with them being size inconsistent.  APEUE, on the other hand, shows an increase trend except for Ni(PF3)₄, which is consistent with the analysis for the stretched alkane case.  However, both the CCSD(T)-based methods and the APEUE show the same decrease trend for the Cr series.  This is somewhat surprising and further analysis is needed.

We emphasize that the estimation of the multireference character is very important for the computational study of catalysis.  Wavefunction methods such as CASSCF, MRCI and their variations are required for molecular systems with significant nondynamic correlation, and can only be afforded to a problem of very small size, either being a small molecule or a small region of a molecule.  Therefore, it is desirable to know a priori the degree of the multireference character to estimate the reliability of a single-reference method and to determine if a multireference method needs to be applied.  Our DFT-based APEUE method has tremendous advantage on the current CCSD(T)-based methods in terms of computational efficiency.  Thus, the success of the APEUE method will impact significantly the computational study of catalysis.