Interaction of Aromatic Molecules with Forsterite: Accuracy of the Periodic DFT-D4 Method

Abstract

Density functional theory (DFT) has provided deep atomic-level insights into the adsorption behavior of aromatic molecules on solid surfaces. However, modeling the surface phenomena of large molecules on mineral surfaces with accurate plane wave methods (PW) can be orders of magnitude more computationally expensive than localized atomic orbitals (LCAO) methods. In the present work, we propose a less costly approach based on the DFT-D4 method (PBE-D4), using LCAO, to study the interactions of aromatic molecules with the {010} forsterite (Mg₂SiO₄) surface for their relevance in astrochemistry. We studied the interaction of benzene with the pristine {010} forsterite surface and with transition-metal cations (Fe²⁺ and Ni²⁺) using PBE-D4 and a vdW-inclusive density functional (Dion, Rydberg, Schröder, Langreth, and Lundqvist (DRSLL)) with LCAO methods. PBE-D4 shows good agreement with coupled-cluster methods (CCSD(T)) for the binding energy trend of cation complexes and with PW methods for the binding energy of benzene on the forsterite surface with a difference of about 0.03 eV. The basis set superposition error (BSSE) correction is shown to be essential to ensure a correct estimation of the binding energies even when large basis sets are employed for single-point calculations of the optimized structures with smaller basis sets. We also studied the interaction of naphthalene and benzocoronene on pristine and transition-metal-doped {010} forsterite surfaces as a test case for PBE-D4. Yielding results that are in good agreement with the plane wave methods with a difference of about 0.02-0.17 eV, the PBE-D4 method is demonstrated to be effective in unraveling the binding structures and the energetic trends of aromatic molecules on pristine and transition-metal-doped forsterite mineral surfaces. Furthermore, PBE-D4 results are in good agreement with its predecessor PBE-D3(BJM) and with the vdW-inclusive density functionals, as long as transition metals are not involved. Hence, PBE-D4/CP-DZP has been proven to be a robust theory level to study the interaction of aromatic molecules on mineral surfaces.

Figure 1

Top view (a) and (b) and lateral view (c) and (d) of the optimized structure of the 4 × 3 {010} forsterite surface with the corresponding atomic labels (Mg, O, Si, and M = Fe or Ni). The vacuum region is located along the z-axis.

Figure 2

Hubbard-corrected total and projected density of states, PDOS, and optimized structure of the bulk (PBE/DZP) of forsterite with atomic labels reported on the corresponding atoms.

Figure 3

Optimized structure (PBE/DZP) of benzene adsorbed on the {010} forsterite surface. The colored balls correspond to the following atoms: hydrogen (white), carbon (gray), magnesium (green), silicon (yellow), and oxygen (red). Atomic labels are reported on the corresponding atoms.

Figure 4

Top view and side view of the optimized geometry (PBE/DZP) of benzene coordinated with (a) Fe²⁺ (Benz-Fe²⁺) in quintet state and (b) Ni²⁺ (Benz-Ni²⁺) in triplet state.

Figure 5

Side view and top view of the spin density isosurface (isovalue 0.007 e/A³) of Benz-Fe²⁺ computed in quintet state at PBE/DZP and DRSLL/DZP levels. Spin population and atomic labels are reported.

Figure 6

Side view and top view of the spin density isosurface (isovalue 0.005 e/A³) of Benz-Ni²⁺ computed in triplet state at PBE/DZP and DRSLL/DZP levels. Spin population and atomic labels are reported.

Figure 7

Binding energies of benzocoronene and naphthalene chemisorbed on {010}-fo (singlet state), Fe (quintet state), and Ni-{010}-fo (triplet state) surfaces using different levels of theory (PBE-D4, PBE-D3(BJM), and PBE) with the CP-DZP basis set. The order of the labels corresponds to the order of the bars. Note: Numerical values are reported in the SI.

Figure 8

Binding energies of benzocoronene and naphthalene chemisorbed on {010}-fo (singlet), Fe (quintet), and Ni-{010}-fo (triplet) surfaces using PBE-D4 and DRSLL with the CP-DZP basis set and with the corresponding counterpoise-noncorrected values at the back. The order of the labels of the forsterite surfaces corresponds to the order of the bars. Note: Numerical values are reported in the SI.

Figure 9

Atomic labels and optimized structures of naphthalene and benzocoronene chemisorbed on Ni-{010}-fo (a) and (b) and Fe-{010}-fo (c) and (d). Table of carbon and metal distances (d_cc/mc) between the PAH and the surfaces using PBE and DRSLL. Note: As we are reporting only the geometric parameters and not the energy, we have not included the D3(BJM) and D4 correction (see the Theoretical Methods and Models section).