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

Abstract

In this work, we have computed the exfoliation energy (the energy required to separate a single layer from the bulk structure), the interlayer distance, and the thermodynamic state functions for representative layered inorganic minerals such as Brucite, Portlandite, and Kaolinite, while leaving the more classical 2D transition-metal dichalcogenides (like MoS 2 ) for future work. Such materials are interesting for several applications in the field of adsorption and in prebiotic chemistry. Their peculiar features are directly controlled by the exfoliation energy. In materials without cations/anions linking different layers, the interactions keeping the layers together are of weak nature, mainly dispersion London interactions and hydrogen bonds, somehow challenging to deal with computationally. We used Hartree–Fock (HF) and density functional theory (DFT) approaches focusing on the role of dispersion forces using the popular and widespread Grimme’s pairwise dispersion schemes (-D2 and -D3) and, as a reference method, the periodic MP2 approach based on localized orbitals (LMP2). The results are highly dependent on the choice of the scheme adopted to account for dispersion interactions. D2 and D3 schemes combined with either HF or DFT lead to overestimated exfoliation energies (about 2.5 and 1.7 times higher than LMP2 data for Brucite/Portlandite and Kaolinite) and underestimated interlayer distances (by about 3.5% for Brucite/Portlandite). The reason is that D2 and D3 corrections are based on neutral atomic parameters for each chemical element which, instead, behave as cations in the considered layered material (Mg, Ca, and Al), causing overattractive interaction between layers. More sophisticated dispersion corrections methods, like those based on nonlocal vdW functionals, many body dispersion model, and exchange-hole dipole moment not relying on atom-typing, are, in principle, better suited to describe the London interaction of ionic species. Nonetheless, we demonstrate that good results can be achieved also within the simpler D2 and D3 schemes, in agreement with previous literature suggestions, by adopting the dispersion coefficients of the preceding noble gas for the ionic species, leading to energetics in good agreement with LMP2 and structures closer to the experiments.

Ab initio description of oxygen vacancies in epitaxially strained $$\hbox {SrTiO}_{{3}}$$ at finite temperatures

“…In particular, the creation of apical oxygen vacancies was found to be energetically most favourable for most of the investigated ’s and the formation energy differences between apical and equatorial ’s were also of the order of 0.01 eV. Moreover, analogous results were obtained by (i) considering the presence of long-range dispersion interactions 67 – 70 and (ii) employing other exchange-correlation DFT functionals like the popular local density approximation (LDA 71 ) and the recently proposed meta-GGA functional SCAN 72 , 73 (Supplementary Fig. 1 ).…”

Reconstruction of a 2D layer of KBr on Ir(111) and electromechanical alteration by graphene

“…A 12 × 12 × 12 K-point grid was used to sample the Brillouin zone of the iridium bulk and the K-point grid was proportionally resized for all the following calculations. We chose not to add any dispersion correction, consistently with our previous investigations [ 56 – 57 ], because these corrections often overestimate the adsorption energies on metallic substrates [ 58 – 59 ]. The process of geometry optimization was stopped when the total energy and the forces converged under thresholds of 1 × 10 −4 Ry and 1 × 10 −3 Ry/bohr, respectively.…”

Ab Initio Computational Study on Fe2NiP Schreibersite: Bulk and Surface Characterization

“…the Grimme's D2 correction modified for solid systems, where van der Walls radii (R0) are rescaled by 1.05 (1.3 for H atoms); 42 • D*0 correction, i.e. the D* correction where the C6 coefficients for the transition metals Fe and Ni are set to 0; 43 • D*n correction, i.e. the D* correction where the C6 coefficients for the transition metals Fe and Ni are set to the values of the preceding noble gas (Argon); 43 • D3 Grimme's correction 44 with Becke-Johnson (BJ) damping.…”

“…the D* correction where the C6 coefficients for the transition metals Fe and Ni are set to 0; 43 • D*n correction, i.e. the D* correction where the C6 coefficients for the transition metals Fe and Ni are set to the values of the preceding noble gas (Argon); 43 • D3 Grimme's correction 44 with Becke-Johnson (BJ) damping. 45 The cutoff energy of plane waves (which control the accuracy of the calculations) was set to 500 and 1000 eV, in order to check the stability of the basis set when the cell volume of the bulk is free to relax.…”