Accelerating Non-Empirical Structure Determination of Ziegler–Natta Catalysts with a High-Dimensional Neural Network Potential

Abstract

The determination of catalyst nanostructures with first-principles accuracy using genetic algorithms (GA) is very demanding due to the cubic scaling of the computational cost of density functional theory (DFT) calculations. Here, we demonstrate, for the case of Ziegler–Natta MgCl2/TiCl4 nanoplates, how this structure determination can be accelerated by employing a high-dimensional neural network potential (HDNNP) of essentially DFT accuracy. First, when building HDNNPs for MgCl2/TiCl4 clusters with computationally tractable sizes, we found that the structural diversity in the training set is crucial for obtaining HDNNPs reliably describing the large variety of structures generated by GA. The resulting HDNNPs dramatically accelerated the structure determination while yielding results consistent with DFT. Subsequently, we developed a multistep adaptive procedure to construct a HDNNP for MgCl2/TiCl4 clusters consistent in size and TiCl4 coverage with experiments where prior DFT results were scarcely collected. The structure determination and analyses underline the importance of system size and composition in order to predict some experimentally known facts such as the surface morphology and population of isospecific sites.

Deciphering the Role of Internal Donors in Shaping Heterogeneous Ziegler–Natta Catalysts Based on Nonempirical Structural Determination

“…Visual analysis of the four most stable structures of each system (Figure ) shows significant differences among compositions. As stated in our previous studies, − bare MgCl 2 structures majorly exposed long {100} surfaces, more energetically stable than {110}, resulting in mostly trapezoidal nanoplates. Due to stronger adsorption on the {110} surface as the mononuclear species, the addition of TiCl 4 increased the exposure of short {110} terraces, as can be seen in 19MgCl 2 /4TiCl 4 and 19MgCl 2 /9TiCl 4 .…”

“…In this study, we selected 19MgCl 2 /4TiCl 4 /5ID systems as the main target of structure determination based on the following considerations. First, experimental observations indicate that the lateral dimension of the primary particles is at least 2–3 nm, corresponding to approximately 50 MgCl 2 units . However, the addition of donor molecules significantly increased the computational cost, making the structure determination for such a large system infeasible with our available computational resources.…”

“…First, experimental observations indicate that the lateral dimension of the primary particles is at least 2−3 nm, corresponding to approximately 50 MgCl 2 units. 44 However, the addition of donor molecules significantly increased the computational cost, making the structure determination for such a large system infeasible with our available computational resources. Nonetheless, it was reported that important conclusions, such as structural reconstruction and diversification due to chemisorption, are insensitive to the system size, except for extremely small systems below 10 MgCl 2 .…”

“…In our previous studies, structure determination of MgCl 2 nanoplates capped with TiCl 4 molecules was performed by combining a GA for global search and DFT for local geometry optimization, , while a parallel work, where high-dimensional neural network potentials were used to accelerate the structure determination, allowed the exploration of structures with size and coverage comparable to the real system . These results showed the interdependence between the structure and adsorption: the adsorption preference and quantity of TiCl 4 directly affected the exposed surfaces of MgCl 2 .…”

Collaboration on Machine-Learned Potentials with IPSuite: A Modular Framework for Learning-on-the-Fly

“…Typically, ML potentials are evaluated based on their energy and force metrics for a test data set generated a priori or during the LotF iterations. However, some more advanced methods have been developed to evaluate models based on their ability to run geometry optimization 39 or accurately reproduce inter-and intra-atomic force contributions. 40 In practice, the development of new methods and models for each of these components in the MLP fitting workflow is often tied to a specific research group and therefore tightly integrated with a specific model architecture.…”