Assessment of density functional approximations for N2 and CO2 physisorption on benzene and graphene

Abstract Experimental isotherms of N2 and CO2 on carbon‐based porous materials and models of the physisorption of gases on surfaces are used to obtain the pore size distribution (PSD). An accurate modelization of the physisorption of N2 and CO2 on the surface of carbon‐based porous materials is important to obtain accurate N2 and CO2 storage capacities and reliable PSDs. Physisorption depends on the dispersion interactions. High precision ab initio methods, such as CCSD(T), consider accurately the dispersion interactions, but they are computationally expensive. Double hybrid, hybrid and DFT‐based methods are much less expensive. In the case of graphene, there are experimental data of the adsorption of N2 and CO2 on graphite that can be used to build the Steele interaction potential of these gases on graphene. The goal is to find out hybrid and/or DFT methods that are as accurate as the CCSD(T) on benzene and as accurate as the experimental results on graphene. Calculations of the interaction energy curves of N2 and CO2 on benzene and graphene have been carried out using the CCSD(T) method and several double hybrid, hybrid, and DFT methods that consider the dispersion interactions. The energy curves on benzene have been compared to the CCSD(T) and the energy curves on graphene have been compared with the Steele energy curves. The comparisons indicate that double hybrids with dispersion corrections and ωB97 based DFT methods are accurate enough for benzene. For graphene, only the PBE‐XDM functional has a good agreement with the Steele energy curves.

1 I. GAUSSIAN 16 The Gaussian 16 (G16RevA.03) code 1 was used to make calculations of N 2 and CO 2 on benzene, but not on graphene. This code has several methods implemented and used in the present work: CCSD(T) 2 , PBE 3,4 , VWN5 5 , PW91 6 , B97D 7,8 , PBE-D2 7 B97D3 7 , B2PLYP-D3 9 and MN15 10,11 and ωB97-XD 12 . The VWN5 method uses the LDA for exchange and correlation effects with the Vosko-Wilk-Nusair (VWN5) parameterization 5 . PBE and PW91 use GGA functionals due to Perdew, Burke and Ernzerhof, 3,4 and to Perdew and Wang,6 respectively. The PBE-D2 and B97D methods include the dispersion corrections according to the DFT-D scheme. PBE-D2 stands for the PBE functional plus the Grimme's D2 dispersion corrections 7 . B97D is a functional proposed by Grimme 7 , based on the B97 functional of Becke 8 and the Grimme's D2 dispersion corrections. It is a reparameterization of the original B97 functional.
The G16 code performs all-electron calculations using gaussian basis sets to expand the wavefunctions. The basis set used for all the methods is the augmented correlation-consistent basis set, aug-cc-pVTZ, of Dunning et al. [13][14][15][16][17] . Basis sets of the aug-cc-pVXZ family contain diffuse functions which are necessary to account for dispersion interactions. The spin restricted calculations (because N 2 , CO 2 and benzene are closed-shell systems) were done self-consistently with a total energy convergence tolerance of 2.72 × 10 −5 eV. The optimizations of the geometries were run until the forces on the atoms were lower than 4.63 × 10 −3 eV/Å and the displacements of atoms were lower than 1.9 × 10 −4Å .
A test of the basis set is provided in Figure 1, where a comparison of CCSD(T) calculations of N 2 interacting with benzene with the para-para orientation on top of the center of the benzene hexagon, done with the aug-cc-pVTZ and aug-cc-pVQZ basis sets is presented.
The counterpoise method was used to calculate the interaction energies in Figure 1. The aug-cc-pVQZ basis set is the largest one. The difference between the aug-cc-pVTZ and aug-cc-pVQZ interaction energies is smaller than 10 −3 eV/molecule in the region near the minimum, and it becomes negligible at larger N 2 -benzene distances. The CCSD(T) interaction energies obtained with the aug-cc-pVQZ basis set are very similar to those obtained using the aug-cc-pVTZ basis set (See Fig. 1), but the computational cost was much higher. Therefore, the aug-cc-pVTZ basis set and the counterpoise method have been selected to make the G16 calculations with all the methods.
The use of aug-cc-pVTZ basis sets, the correction of the BSSE and the value of the self-consistent threshold used mean that the present G16 calculations have a high degree of precision. local van der Waals VV10 kernel (ωB97X-V), respectively. All functionals were treated with the chain-of-sphere approximation for the evaluation of the exchange integrals (RIJCOSX) 24 .
We have checked, for the particular case of N 2 -benzene with the ωB97X-D3BJ functional, that the RIJCOSX treatment introduces negligible differences in geometries and interaction energies when compared to the exact calculation of exchange integrals. Besides, standard defaults in Orca were used, except: (1) SCF convergence criterion was set to 'tightscf",