Cost-Effective Quantum Mechanical Approach for Predicting Thermodynamic and Mechanical Stability of Pure-Silica Zeolites

Abstract

Several computational techniques for solid-state applications have recently been proposed to enlarge the scope of computer simulations of large molecular systems. In this contribution, we focused on two of these, namely, HF-3c and PBEh-3c. They were recently proposed by the Grimme’s group, as “low-cost” ab initio-based techniques for electronic structure calculation of large systems and were proved to be effective essentially for organic molecules. HF-3c is based on a Hartree–Fock Hamiltonian with a minimal Gaussian quality basis set, whereas PBEh-3c is a density functional theory (DFT) based method with a hybrid functional and a medium-quality basis set. Both HF-3c and PBEh-3c account for dispersion (London) interactions and are free from the basis set superposition error due to limited basis set size, through several pairwise semiempirical corrections. To the best of our knowledge, despite the promising results on the cost-accuracy side of molecular simulations of organic molecules, these methods have been used only in few cases for solid-state applications. In this contribution, we studied the performance of HF-3c and PBEh-3c for predicting the properties of inorganic crystals to enlarge the applicability of these cheap and fast methodologies. As a testing ground, we have chosen a well-known class of material, e.g., microporous all-silica zeolites. We benchmarked geometries, formation energies, vibrational features, and mechanical properties by comparing the results with literature data from both experiment and computer simulation. For structures, HF-3c is extremely accurate in predicting the zeolites cell volume, albeit we do not include any vibrational contribution, neither zero point nor thermal, on the computed volumes, which may introduce small variations in the predicted values. For the energetic, the relative stability of the zeolites using the DFT//HF-3c approach allows predictions within the experimental error for most of the cases taken into consideration when the experimental enthalpies were corrected back to electronic energies by using the HF-3c thermodynamic contributions computed in the harmonic approximation. This strategy is particularly convenient, as the slow step (geometry optimization) is carried out with the cheapest HF-3c method, whereas the fast step (single point energy evaluation) is carried out with costly DFT methods. In this sense, the use of the DFT//HF-3c approach results to be a promising one to predict the stability and structure of microporous materials. Finally, the HF-3c method predicts the mechanical properties of the zeolite set in reasonable agreement with respect to those computed with the state-of-the-art DFT simulations, indicating the HF-3c method as a possible technique for the mechanical stability screenings of microporous materials.

Exfoliation Energy of Layered Materials by DFT-D: Beware of Dispersion!

“… 10 In the HF-3c-027 approach, the s 8 term of the D3 scheme is scaled by a factor of 0.27. With this refinement, HF-3c-027 gave excellent results in predicting protein and molecular as well as microporous inorganic crystal structures, see refs ( 10 − 12 ). We also employed the recently proposed revised form of the HF-3c-027 method, (HFsol-3c 17 ) specifically tuned for the efficient simulations of crystalline materials.…”

“…Within the HF framework, we also have employed the recently proposed HF-3c method, 9 which has shown to be a cost-effective and reasonably accurate method for studying molecular crystals, 10 simple collagen models, 11 and microporous materials. 12 Furthermore, for all systems, we have tested the hybrid DFT-D//HF-3c approach, in which the energetic is estimated by a single-point energy evaluation at the DFT-D level on the geometry relaxed with a fast revised version of the HF-3c approach. Our theoretical findings are compared with experiments and to previously published theoretical values when available.…”

Modeling phosphorene and $$\hbox {MoS}_{2}$$ interacting with iron: lubricating effects compared to graphene

“…We took into account London dispersion forces by adopting the D2 scheme [29], using the value for the s 6 scaling factor suggested in the original paper ( s 6 = 0.75). This type of dispersion scheme gave very good results for computing not only organic [30][31][32][33][34] but also inorganic materials properties [35,36]. Recent investigations indicate that more modern dispersion correction schemes are also appropriate for simulating the chemisorption of 2D material on metal and ceramic surfaces [37,38].…”

Extending and assessing composite electronic structure methods to the solid state

“…Work is in progress to apply these methods to porous materials 7 and metal-organic frameworks. The accuracy of hybrid composite methods combined with their computational efficiency is ideal for high-throughput screenings.…”

“…Successful applications include protein-ligand binding affinities, 4 large molecular crystals with shortest intermolecular hydrogen contacts, 5 unusual halogen bonding motifs, 6 and screening of zeolite thermodynamics. 7 They are based on the pure Hartree-Fock (HF) method or HF/DFT hybrid functionals with the target of yielding good structures and reasonable energetic properties. The key ingredients are (i) the use of minimal or small-to-medium basis sets expressed in terms of atomcentered Gaussian-type functions and (ii) the combination of three (or two) semiclassical atom-pairwise (or triplewise) corrections to include London dispersion interactions, [8][9][10] to remove the basis set superposition error (BSSE), 11 and to compensate for the basis set incompleteness error (BSIE) through a short-range (SRB) correction.…”