Hydrocarbon Adsorption on Carbonate Mineral Surfaces: A First

Article pubs.acs.org/JPCC

Hydrocarbon Adsorption on Carbonate Mineral Surfaces: A FirstPrinciples Study with van der Waals Interactions Vagner A. Rigo,† Cigdem O. Metin,‡ Quoc P. Nguyen,‡ and Caetano R. Miranda*,† †

Centro de Ciências Naturais e Humanas (CCNH), Universidade Federal do ABC (UFABC), Santo André, SP, Brazil Department of Petroleum and Geosystems Engineering, The University of Texas at Austin, Austin, Texas 78712, United States

‡

S Supporting Information *

ABSTRACT: In this work, we study the adsorption of hydrocarbon molecules on carbonate surfaces by means of first-principles calculations based on Density Functional Theory (DFT) with and without van der Waals (vdW) corrections. Energetic, electronic, and structural properties have been determined for the adsorption of the representative hydrocarbons (hexane and benzene) on calcite (CaCO3) and dolomite [CaMg(CO3)2] (10−14) dry surfaces. Those hydrocarbons were selected to represent aromatics and alkanes on surfaces, and for each molecule the evaluated properties are similar for both surfaces. Due to the obtained similarities in both surfaces, we have evaluated the vdW corrections only for calcite. Our results suggest that Ca sites are the most energetically favorable for hydrocarbon adsorption on both minerals. This effect is mostly due to the electronic level ordering that leads to charge differences in the possible adsorbed sites (Ca, Mg, and CO3) in the carbonate surfaces. The vdW corrections strengthen the hydrocarbon−surface bond with a corresponding reduction in the bond distance between the benzene and the surface. However, this reduction is not even for all atoms in the molecule, and the angle between the benzene aromatic ring and the surface increases. The energy barrier, for the displacement of the hydrocarbons along the calcite surface, was determined for representative surface direction, using the Nudged Elastic Band method, and adsorption energies for the most stable sites show the same order of magnitude.

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mainly employs classical force field models. For example, Freeman et al.13,14 applied atomistic calculations to study the interactions between mineral, water, and organic molecules (namely, methanol, methanoic acid, methylamine, and dimethyl ether) and also provided comparisons between classical force fields and ab initio methods using the PW9115 functional. Some differences in results obtained by first-principles and classical interatomic potentials have been observed. In those classical simulations, the ab initio data can be used to parametrize the interatomic potential. However, in many cases for ab initio, the dispersion forces are not treated adequately. The inclusion of a dispersion corrected functional to treat the van der Waals interactions at the ab initio level is essential to accurately parametrize a reliable classical model to describe the interaction between molecules and the surface for further modeling of biomineralization and oil exploration processes at larger scales. To the best of our knowledge, our work is the first one to include van der Waals (vdW) corrections on ab initio calculations for carbonaceous surfaces interacting with organic molecules. Benzene and hexane have been chosen as the representative aromatic and alkane adsorbed molecules. The

INTRODUCTION Carbonaceous systems are an abundant material in nature and represent a wide range of physical compounds. They are the main component of minerals rocks, as well as shells and skeletons,1−3 and have a central importance for CO2 exchange in seawater4 and oil accumulation in petroleum fields.5−8 Moreover, calcite (CaCO3) and dolomite [CaMg(CO3)2] represent 90% of sedimentary rocks,5 and in many cases these minerals constitute hydrocarbon reservoirs.6−8 Additionally, most petroleum exploration takes place in carbonaceous oil fields, and a knowledge about the interaction between the hydrocarbon molecules and the mineral surface is desirable.9 The accurate description of the rock−hydrocarbon interaction is an important step to understand the mechanisms and improve the Enhanced Oil Recovery in calcite and dolomite minerals.10−12 One of the most interesting phenomena concerning calcium carbonates is the biomineralization processes, where the interaction between organic molecules and carbonates can drive the mechanism for surface growth. Detailed and accurate information about the molecule−mineral interaction is of central importance to model these systems, and efforts were done to understand this process.2 First-principles calculations represent an important and accurate tool to obtain information about the processes at atomistic level. However, the literature © 2012 American Chemical Society

Received: June 19, 2012 Revised: October 1, 2012 Published: November 2, 2012 24538

dx.doi.org/10.1021/jp306040n | J. Phys. Chem. C 2012, 116, 24538−24548

The Journal of Physical Chemistry C

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were allowed to relax until the forces reached 1 × 10−3 au. For bulk calculations the cell vectors were relaxed until the pressure on the cell reached 0.5 kbar. Initially, the crystalline parameters (atomic positions and cell vectors) of bulk calcite and dolomite were fully relaxed. The hexagonal structure of calcite is shown in Figure 1a and that for

inclusion of vdW corrections in ab initio methods can improve the description of these systems,3,16 particularly the long-range weak dipole−dipole interaction, as well as provide a fully electronic description for the interface of hydrocarbon molecules and mineral surfaces, which can be used to improve the force fields based on first-principles calculations. We choose the (10−14) surface of the hexagonal calcite structure in our study. This surface is charged neutral and exhibits both Ca atoms and carbonate groups and has been reported in the literature as the most stable one using different theoretical methods: classical force fields17−19 and also by ab initio calculations using the Density Functional Theory (DFT) with both plane waves20 and a Local Combination of Numerical Orbitals (LCAO).21 Other calcite terminations (more energetic) have also been recently considered in the literature: {11−20} and {10−10}.22 An extensive experimental work using ultrathin films by Archibald et al.23 suggests that other orientations would also be favorable as a function of organic surface modification, but the (10−14) surface was experimentally found to be the most stable. The (10−14) surface has also been considered as the most common for dolomite, based on classical force fields including a shell model for polarization.24,25 However, using the same methodology and considering different surface terminations, Titiloye et al.18 reported the {10−10} and {11−20} surfaces as the most stable for dolomite. Pokrovsky et al.26 experimentally showed that the calcite and dolomite surface speciation change as a function of pH. The authors showed that for a given NaCl concentration and CO2 pressure the CaOH2+ is favorable for the calcite surface at low pH, and CaCO3− groups are favorable at high pH. They also reported similar results for dolomite in both cases, Ca or Mg, at the surface. In this work, we first present the calcite and dolomite bulk properties, followed by the calculated properties (energetics, structural, and kinetics) for hydrocarbon adsorption on calcite and dolomite (10−14) surfaces. The effect of vdW interactions on these properties is elaborated, followed by the results on the adsorption and kinetics effects of hydrocarbons on carbonaceous surfaces. Our main goal is to understand the adsorption of representative hydrocarbon molecules on carbonaceous surfaces by first-principles calculations including the vdW dispersion forces, comparing the most used standard functional (PW9127) with the most reliable vdW corrected one for a large number of atoms.

Figure 1. Hexagonal crystal structure of calcite and dolomite and (10− 14) surface of calcite. Side view of calcite (a) and dolomite (b). The unit cell vectors are shown. Considering a cleaved (10−14) surface, we present a side view along [42−1] (c) and [010] (d) directions and an overview (e) of the irreducible cell of the calcite (10−14) surface. The blue and dark balls represent the Ca and Mg atoms. The red and yellow represent the O and C atoms, respectively.

dolomite in Figure 1b. The surfaces were constructed by cleaving the bulk calcite and dolomite in the hexagonal form along the (10−14) surface, and they contain the same number of metal atoms (Ca/Mg) and carbonate groups (CO3) to keep the total charge neutral. Since we are using periodic boundary conditions, surfaces are represented by a finite number of CaCO3 or CaMg(CO3)2 layers. The optimal surface thickness was determined by checking the changes in geometry and energy as a function of the number of layers, for 3, 4, 5, and 6 layers. For these geometries, only atoms in the bottom layer were fixed to simulate the bulk part, while the remaining atoms were allowed to relax. Geometries with two fixed bottom layers were also evaluated. These results for a surface composed by a total of three layers do not show significant differences compared to the other ones, with geometry and energy deviations lower than 1%. We adopted the model with three layers (one of them fixed) to study the interactions of hydrocarbons with calcite and dolomite surfaces. To avoid interaction between the periodic images, we have used a vacuum of at least 11 Å in the simulations.

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METHODS Calculations without vdW Dispersion. Our calculations were based on density functional theory,27,28 using the Perdew and Wang (PW91)29 approximation to the exchange and correlation energy term. This functional is a common choice for calcite and was used to parametrize classical potentials.13,14 Ultrasoft pseudopotentials29 were used to describe the core− valence electron interaction, and the valence electrons are described by plane wave expansions with an energy cutoff of 544 eV. This cutoff value was tested with a calculation using 680 eV, giving a small difference of approximately 5 meV in adsorption energy. The gamma centered Monkhost−Pack method30 was used for the Brillouin-zone sampling integration. For the minimal supercell, a total of seven inequivalent k-points were used, while the isolated hydrocarbons were simulated at the gamma point only. The geometry optimizations were performed using the bfgs minimization algorithm as implemented in the QUANTUM ESPRESSO package.31 Structures 24539



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avoid the interaction between periodic images. The gamma point was used for the Brillouin zone sampling integration, and an energy cutoff of 1088 eV was applied.

Figure 1c,d shows the irreducible unit cell of the calcite surface along the [42−1] and [010] directions, respectively. Figure 1e presents the top view of the (10−14) surface, where the lines show the irreducible unit cell (just one layer). In the adsorption process, we used a geometry composed by two surface irreducible unit cells (a 2 × 1 supercell, according to Figure 1e). In this calculation, we used a surface model with 20 atoms per layer, amounting to 60 atoms. For adsorbed benzene, a total of 72 atoms were used. Considering a benzene molecule lying parallel to this calcite surface geometry model, the closest distance between the molecule and its own image due to the periodic boundary conditions is 5.80 and 3.25 Å along the two periodic directions, according to the coordinate system depicted in Figure 1e (for vdW calculations we used a larger supercell, see below). We have done calculations using a large supercell (3 × 2), to check the size effects of the supercell. Comparing the results of the minimal cell (2 × 1) with the large one (3 × 2), we obtained adsorption energy changes of approximately only 10 meV for the evaluated sites. For hexane adsorption, we used three different geometries: (i) a (2 × 1) geometry (similar to benzene adsorption) for top sites and a (ii) (3 × 1) and (iii) (2 × 2) surface for hexane adsorption. Those geometries were used to consider the nonsymmetric alignments of hexane on the surface. These supercells contain 80, 110, and 140 atoms, respectively. To determine the energy barriers involved in diffusion of both benzene and hexane on the calcite surface, we have used the Nudge Elastic Band (NEB) method.32 The first NEB image represents the most stable adsorption site for each hydrocarbon on the calcite surface. The energy barriers were obtained along the periodic directions along the surfaces, namely, [42−1], [48−1], and [010]. Calculations were converged until all forces were less than 0.05 eV/Å. Calculations Including vdW Dispersion. To take into account the van der Waals dispersion forces, we used the DFT with the Dispersion-Corrected Atom-Centered Potentials model (DCACP).16 This model introduces London dispersion forces applied as an atom-electron potential, and this is included in the system in a self-consistent way using a nonlocal form, similar to that applied for pseudopotentials. We adopt the actual methodology to be a consistent way to obtain the electronic properties of the systems, to evaluate the bond formations between the molecules and the surface for a van der Waals calculation with more than a hundred atoms. It was shown that this methology is superior to the standard atom− atom corrections; for example, using DCACP Lin et al. showed that the description of liquid water can be improved over other vdW corrections that just include an atom−atom potential,33 and recently, an accurate potential for water has been fitted using DCACP results.34 With this method, we applied the vdW correction to all atoms in the calcite surface, except for Ca. A similar procedure was used by Aeberhard et al., for molecules containing sulfur, where the inclusion of vdW in C, O, and H atoms provides satisfactory results.35 This is in agreement with Lin et al. where they showed that the vdW is most relevant for molecules composed by C, O, and H atoms.36 The vdW dispersion calculations were performed with the CPMD package, 37 using the BLYP38,39 approximation for the exchange-correlation energy term and Troullier−Martins pseudopotentials.40 This functional is the most transferable one considering the DCACP methodology and provides the best results, compared with other functionals.41 The computational supercell was doubled with respect to the minimal one to

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RESULTS Bulk Properties. Calcite and dolomite have a hexagonal crystalline form (shown in Figure 1). Considering calcite, we have obtained optimized unit cell vectors presented in Figure 1a as: a = b = 5.042 Å and c = 17.220 Å (3.415*a). With the inclusion of vdW, these values are a = b = 5.121 Å and c = 17.512 Å (3.419*a). The slight increase in the lattice parameters with vdW is in agreement with the DCACP theory.36 Quantum chemistry calculations by Villegas-Jiménez et al.42 with a Gaussian basis using RHF/6-31G(d,p) level give a Ca−O bond length of 2.37 Å, which is very close to our calculated value of 2.38 Å using the PW91 functional. Comparing this result with vdW ones, they show deviations of only about 1% for bulk calcite. In Table 1, we summarize our Table 1. Calcite and Dolomite Structural Parameters Obtained in This Work from First-Principles Calculations (Without and With van der Waals) and Compared with Other Methods and Experimental Values calcite unit cell vectors

PW91

B3LYP45

van der Waals

EXPT43

a (Å) c (Å) c/a bond length C−O Ca−O

5.042 17.220 3.4151

5.049 17.343 3.4350

5.122 17.512 3.4191

4.9880 17.0680 3.4220

1.305 2.430

1.29 2.36

1.298 2.381 dolomite

unit cell vectors

PW91

B3LYP46

EXPT44

a (Å) c (Å) c/a

4.833 16.022 3.3153

4.838 16.276 3.3640

4.8069 16.0020 3.3290

results compared with experimental43,44 and other theoretical values based on different functionals.45,46 These values show a deviation close to 1% compared with experimental values, as well as our calculations without and with vdW. We have also determined the structural properties of bulk dolomite. It can be clearly observed from Figure 1b that the geometry for the dolomite crystal is similar to that for the calcite crystal. The main difference between the calcite and dolomite structures comes from the substitution of a Ca atom for a Mg atom in dolomite (Figure 1b), keeping only Ca atoms in calcite (Figure 1a). This creates a slight difference in the lattice parameters of the two minerals. Our first-principles calculations for dolomite also show a very good agreement with the experimental values. The electronic properties of the bulk calcite and dolomite are here analyzed and appear in Figure S1a−c in the Supporting Information. Results with and without vdW in bulk electronic structure do not present any changes and are presented in Figure S2a,b in the Supporting Information. Hydrocarbon Adsorption. For hydrocarbon adsorption on calcite and dolomite, a critical point in our study is to determine the most favorable sites where adsorption can occur. To determine some possibilities, we analyze the charge density slice of a calcite surface of a three-layer surface, as described in 24540



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the Methods section. For surfaces, the charge density profiles do not show deviations between the vacuum exposed layer and the surface inner layer, as shown in Figure S3 in the Supporting Information To evaluate the energetic properties for different adsorption sites, we adsorb the hydrocarbons on nonequivalent sites on calcite and dolomite. As we present along the paper, the calcite and dolomite show similar adsorption characteristics, and we incorporated vdW interactions only for calcite. The adsorption energies (Eads) of the hydrocarbons on the surface systems were obtained by the equation Eads = E(surface + H) − Esurface − E H

where Esurface and E(surface+H) are the total energies of the pristine surface and of the surface plus adsorbate, respectively, and EH is the total energy of the isolated adsorbate. Benzene Adsorption. A benzene molecule was placed in different nonequivalent sites above the surfaces. For the initial configurations with the benzene aromatic ring parallel to the surface (hole sites), all benzene carbon atoms are at the same distance from the calcite surface. The adsorption of benzene on calcite can occur above either a Ca atom or a carbonate group. For the dolomite surface, the benzene adsorption can also occur above a Mg site. Top sites (where just one benzene C atom is closest to the surface) and bridge sites (sites with a C− C bond of benzene above the surface sites) were also considered. An overview of representative geometries is schematically presented in Figure 2, where the Ca_hole_a and Ca_hole_b, CO3_hole_a and CO3_hole_b represent hole configurations. The Top_a and Top_b sites represent top configurations. Finally, Ca_bridge and CO3_bridge represent the bridge sites. The hole, top, and oblique geometries considering a Mg site (not shown) correspond to similar configurations presented for Ca sites in Figure 2. Table 2 presents the adsorption energies for benzene adsorbed on the calcite and dolomite surfaces. The Ca_hole_b adsorption site represents the most stable one for a benzene molecule on the calcite (10−14) surface with an adsorption energy of −0.13 eV. The Ca_bridge site has an adsorption energy of −0.11 eV. Adsorption on a CO3 surface site is less favorable compared to adsorption on Ca sites. The most stable adsorption site on a CO3 group is the CO3_hole geometry, where CO3_hole_a and CO3_hole_b have an adsorption energy of −0.06 and −0.08 eV, respectively. Top configurations (Top_a and Top_b) have an adsorption energy close to zero. This adsorption energy value (around 0.1 eV) is of the same order as obtained for HCA organic molecules adsorbed on calcite using DFT calculations with Local Density Approximation (LDA) functional.47 Figure 3a−d shows the optimized adsorption geometry and charge density maps on slices along the benzene and calcite surface, for benzene adsorbed on calcite over Ca_hole_b and CO3_hole sites, respectively. Energetically, Ca_hole_b is the most stable site, and CO3_hole_b is a representative case for adsorption on a CO3 site. After the optimization of forces and energies, the Ca_hole_b configuration shows a small displacement from the initial fully planar configuration. In particular, the angle formed between the benzene aromatic ring and the surface is approximately 15° in the Ca_hole_b geometry (Figure 3a). The benzene with Ca_hole_a geometry (not shown) presents an angle of 9° with the surface. The charge density maps of the region between the surface Ca and benzene C atoms on the Ca_hole_b (Figure 3b) and

Figure 2. Representation of benzene adsorption sites on the calcite (10−14) surface (similar to the dolomite (10−14) surface, where the Mg sites are analogous to the presented Ca ones). The site labels are (a) Ca_hole_a, (b) Ca_hole_b, (c) Top_a, (d) Top_b, (e) Ca_bridge, (f) CO3_bridge, (g) CO3_hole_a, and (h) CO3_hole_b. The blue balls represent the Ca atoms, and the ticks represent the carbonate groups.

Table 2. Adsorption Energies for a Benzene Molecule Adsorbed on Calcite and Dolomite (10−14) Surfaces Eads (eV) configuration

calcite (DFT)

calcite (DFT + vdW)

dolomite (DFT)

Ca_hole_a Ca_hole_b Top_a Top_b Ca_bridge CO3_bridge CO3_hole_a CO3_hole_b Mg_bridge Mg_top_a Mg_hole_a Mg_hole_b

−0.11 −0.13 −0.00 −0.01 −0.11 −0.02 −0.06 −0.08 -

−0.34 −0.33 −0.05 −0.13 −0.23 −0.08 −0.20 −0.23 -

−0.15 −0.13 −0.02 −0.05 −0.11 −0.03 −0.05 −0.07 −0.06 −0.01 −0.07 −0.08

the CO3_hole_b (Figure 3d) configurations show that the interaction between the calcite surface and the benzene molecule is stronger for adsorption on a Ca site, compared to adsorption over a CO3 group. The low charge density along 24541



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Figure 3. Geometry details (a) and slice on surface charge density (b) for a benzene adsorbed on the calcite (10−14) surface at Ca_hole_b and geometry (c) and surface charge density slice (d) for CO3_hole_b configuration on calcite. The figures present only one surface layer; however, the calculations were carried out using three layers. The distances are in Å, and the scale for surface charge density slices is linear between 0 and 0.1 electrons/bohr2.

the surface and benzene in Figure 3b shows that even at the most stable benzene site on calcite (Ca_hole_b) the binding between the aromatic hydrocarbon and the surface is weak. For benzene adsorption on the dolomite (10−14) surface, in addition to the adsorption sites presented in Figure 2, we also evaluated geometries with the benzene above a surface Mg atom. In this way, hole and bridge configurations above the Mg atom were considered. Table 2 shows the adsorption energies for all evaluated benzene−dolomite surface systems. The Ca_hole_a site is the most stable, with adsorption energies of −0.15 eV. The Mg_hole_b site shows a lower adsorption energy considering adsorption over a surface Mg atom (−0.08 eV). The Mg_hole_a site is similar to the Mg_hole_b, differing by a rotation of the benzene molecule on the surface. The adsorption on a carbonate group represents the less stable configuration. In Figure 4a,b, we present the geometry and charge density map for the Ca_hole_a adsorption site on dolomite. This is the most stable site for benzene adsorption on dolomite. In this configuration the benzene carbon atom closest to the surface Ca atom shows a bond length of 3.31 Å. This distance is shorter than that for Ca_hole_b on calcite (3.53 Å). This is an indication of a slight stronger binding of benzene to the dolomite surface, compared to the calcite surface. The charge density map along the surface Ca atom supports this and the closest benzene carbon atom on dolomite (Figure 4b), where isolines suggest a higher charge density between them, compared to the calcite−benzene system (Figure 3b). The bond lengths for benzene adsorbed on both surfaces are greater than those for methanoic acid on calcite (10−14), around 2.21 and 3.01 Å, computed using a classical potential.48 Figure 4c−f shows the geometries and charge density maps for CO3_hole_b and Mg_hole_a geometries. As we can see in Figure 4c,e, the respective distances from the surface increase for benzene above the CO3_hole and Mg sites, as compared to adsorption above the Ca atom (Figure 4a). The charge density

Figure 4. Benzene adsorbed on the dolomite (10−14) surface. The geometry and charge density slice are presented for Ca_hole_a site (a) and (b), CO3_hole_a (c) and (d), and Mg_hole_a (e) and (f), respectively. The distances are in Å, and the scale for charge density slices is the same as Figure 3.

maps of CO3_hole (Figure 4d) and Mg_hole_a (Figure 4f) configurations do not show isolines between the benzene and the dolomite surface, indicating low adsorption energy. Considering calculations without vdW, the most stable site on calcite (Ca_hole_b) and on dolomite (Ca_hole_a) presents an adsorption energy difference of 20 meV. This small difference in adsorption energy suggests a similar bond strength for a benzene molecule on both surfaces. On the basis of this result, we only use the calcite surface to study the effects of vdW interactions and to find the energy barriers for hydrocarbon displacement on these surfaces. When we include the vdW interactions in the systems, by means of DCACP calculations for adsorbing surfaces, the energetic preference for adsorption over Ca sites is preserved. As a general trend, the vdW interactions increase the adsorption energies for all sites and reduce the bond length between the benzene and the surface. The hole sites on Ca atoms were found to be the most stables ones, regardless of vdW interactions. The Ca_hole_a configuration is the most stable for benzene adsorption with vdW interactions (adsorption energy of −0.34 eV), while the Ca_hole_b is the most stable without vdW calculations. These results represent an increase of more than 60% in the adsorption energy, by comparing the calculations without and with vdW correction for these sites. A similar increase in the adsorption energy (more than 60%) is obtained for adsorption on the CO3_hole site. In this case, the vdW results provide an adsorption energy of −0.20 eV. 24542



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analysis (Figures 5b, e, and h) indicates a pronounced modification for benzene adsorption on Ca (Figure 5b), compared to adsorption on Mg (Figure 5e) and CO3 sites (Figure 5h), respectively. These results are in agreement with the observed bond between a benzene and Mg and Ca isolated cations.50 The metal atom−benzene bond is explained in terms of the charge rearranging after adsorption. Additionally to the atomic structure information, we have also studied the electronic structure for Ca_hole_a, Mg_hole_a, and CO3_hole_b pristine and adsorbed sites. The Projected Density of States (PDOS) and orbital population (by means of Löwdin population analysis) were considered. The benzene molecule has a similar total orbital population after adsorption on Ca_hole_a, Mg_hole_a, and CO3_hole_b dolomite surface sites, 29.52, 29.52, and 29.53 electrons, respectively. Those charges provide us a qualitative indication that the adsorbed benzene loses electrons when compared with the isolated molecule (30 valence electrons). This is in agreement with the benzene interaction with isolated Mg and Ca cations.50 The PDOS for the adsorbed sites on the pristine surface (Figure 6a) indicates that the Highest Occupied Molecular Orbital (HOMO) is composed by a sharp oxygen p-orbital, and the conduction level contains a major contribution from 3d and 4s Ca orbitals. A closer inspection of the position of the first

Considering adsorptions on a Ca atom or a CO3 group, the Ca site kept as the most stable when the vdW correction was included. Considering only the Ca_hole_a and Ca_hole_b sites, without vdW interactions the Ca_hole_b site is the most stable for benzene adsorption on a Ca atom. When the vdW correction is included, the most stable sites are the Ca_hole_a. Indeed, according the Figure 2, the Ca_hole_a and Ca_hole_b sites differ by a rotation of the benzene on the surface, and in this way we can consider these as equivalent sites, where the first one corresponds to the global energy minimum (Ca_hole_a). The hydrocarbon adsorption on the dolomite surface provides information concerning the Ca, Mg, and CO3 adsorption sites. The adsorption energies suggest an increase in the stability for hydrocarbon adsorption on a Ca site, compared to Mg and CO3 ones, where the adsorption on Mg is slightly more favorable than on a CO3 site. The benzenes adsorbed on Ca_hole_a, Mg_hole_a, and CO3_hole_b sites are used to understand the differences within carbonate surface adsorption. Figures 5a−i show the structure (as balls and sticks,

Figure 5. Geometry as balls and sticks, slice on charge density difference, and geometry as vdW radii representation for a benzene on the dolomite surface, on Ca_hole_a (a), (b), and (c); Mg_hole_a (d), (e), and (f); and CO3_hole_b (g), (h), and (i) configurations, respectively. The yellow and red balls in carbonates represent C and O atoms, respectively, and dark and cyan (light gray) balls represent the Mg and Ca atom, respectively. The same linear scale is used in all charge difference slices and presents positive (light) and negative (dark) values between 0 and 0.01 electrons/bohr2. The charge density difference is obtained as ρ = ρ(Surface+H) − ρSurface − ρH, where ρ(Surface+H), ρSurface, and ρH represent the surface plus adsorbate, the surface, and the adsorbate charge density, respectively.

Figures 5a, d, and g), the charge differences (Figures 5b, e, and h), and the structure considering the van der Waals radii (Figures 5c, f, and i) for each different chemical species.49 The vdW spheres from the molecule and surface touch each other only for Figure 5c (adsorption on Ca) and do not overlap with the neighbor surface sites in any case. The charge difference

Figure 6. Ca, Mg, and outermost O projected electronic density of states for the (a) pristine and (b) benzene directly adsorbed dolomite surface. The Fermi level is at zero energy. 24543



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Figures 7c−f show the charge density maps for the Ca_hole_b geometry at different positions, respectively. These maps correspond to vertical slices in the geometries shown in Figure 7a,b. In Figure 7c,d, the slices were obtained in the Ca position without and with vdW, respectively. The inclusion of vdW interaction enhances the charge transfer between the Ca atom and the benzene, increasing the surface− benzene binding. We remind that the vdW forces are not included in the Ca atoms. This procedure has been used by Aeberhard et al., where the inclusion of vdW in O, C, and H atoms results in a satisfactory description of a molecular system.35 A similar result was observed for a slice in the oxygen position and the benzene (Figures 7e,f). All observed effects on charge transfer, adsorption energy, and bond length deviations obtained with vdW correction indicate some improvement on the description of the molecule−surface interaction. Considering the adsorption on the CO3_hole_b site, we also obtained an increase in the strength of the surface−benzene bond after the inclusion of vdW, as presented in Figure S4a−d in the Supporting Information. Hexane Adsorption. The fully relaxed hexane (C6H14) molecule shows a long axis (8.183 Å) and a short axis (1.429 Å). Some rotations along these molecular axes define different sites of adsorption on surfaces. Figure 8 presents the evaluated alignments of the hexane molecule with respect to the calcite surface for some rotations along the hexane axes, similarly for

empty state for Ca, Mg, and O surface sites reveals that the Mg3s and O-2p orbitals are located 0.05 and 0.6 eV above the Ca4s peak, respectively. The pristine PDOS indicates that the Ca orbital would be the first available during the benzene−surface interaction followed by the Mg one. In Figure 6b, the PDOS for Ca, Mg, and O surface absorbed sites are shown. For Ca PDOS, a reduction in the intensity of the first 4s peak is observed with respect to the pristine surface. Considering the Mg PDOS, intensity peak reduction on the first empty 3s and 3p orbitals is also observed compared to the pristine surface (Figure 6a). The empty d orbitals for Ca and Mg are not significantly affected. Our results for vdW dispersion forces indicate a reduction in the bond distance between the benzene molecule and the calcite surface and an increase in the adsorption energy. This is in agreement with the DCACP method16 that slightly increases the electron density between the surface and the adsorbing molecule. However, this bond length reduction does not have a systematic deviation from the calculations without vdW interactions. Figure 7a,b shows the representative bond lengths for Ca_hole_b sites, without and with vdW, respectively. The bond length displays a slight reduction, and the angle formed by the benzene aromatic ring and the surface increases as the vdW dispersion forces are taken into account.

Figure 7. Geometry and charge density slices for the Ca_hole_b configuration, without and with van der Waals, in the left and right side, respectively. We present geometrical details (in Å for distances and degrees for angles) obtained without (a) and (b) with van der Waals and charge density slice between the Ca surface atom and the most close benzene C atoms for calculation (c) without and (d) with van der Waals. A slice between a surface O atom and closest benzene C atom is presented (e) without and (f) with van der Waals correction. The same linear scale for charge density slices is presented for all pictures and shows values between 0 and 0.06 electrons/bohr2.

Figure 8. Representation of hexane adsorption sites on the calcite (10−14) surface. The evaluated Mg adsorption sites on dolomite are analogous to the presented Ca ones where the vertical aligned Ca atoms (blue) represent alternate positions for Ca or Mg in the dolomite case. The site labels are (a) Ca_top, (b) CO3_top, (c) sideon_Ca_[010], (d) end-on_Ca_[010], (e) side-on_[42−1], (f) endon_[42−1], and (g) end-on_CO3_[42−1]. 24544



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energy of −60 meV, and the adsorption on the carbonate groups represents the less stable configurations, with adsorption energy of −20 meV for end-on_CO3_[42−1] and unbound for CO3_top configuration. Figure 9a shows the geometry of the end-on_Ca_[010] configuration on the calcite surface (most stable site). The

dolomite, where the Mg sites were also considered. The most representative orientations are the top, end-on, and side-on alignments. The top sites are evaluated with the hexane above a Ca and a CO3 group on the calcite surface. These sites are named as Ca_top and CO3_top. For the dolomite surface, the hexane above a Mg site (Mg_top) is considered in addition to Ca_top and CO3_top. As the surface periodical directions are not identical with respect to the atomic sites, there are two representative orientations of the end-on and side-on surface positions above the surface. Figure 8 presents different orientations for hexane above the calcite surface. Only one calcite surface layer is presented, and the vertical aligned Ca atoms in Figure 8 indicate the successive position of Ca and Mg atoms in the dolomite case. When the long axis of hexane is oriented along the [42−1] direction, the hexane molecule can adsorb over both Ca and Mg atoms. Due to these geometrical details, we denote sideon_[42−1] and end-on_[42−1] as the sites on which the hexane long axis is oriented along the [42−1] direction on the surfaces. In addition, in the [42−1] direction, the adsorption of the hexane above a CO3 site was considered in the endon_CO3_[42−1] configuration as a representative case for adsorption on the carbonate group. The adsorption of the hexane molecule with the long axis along the [010] direction of the surfaces was done over the line of consecutive Ca atoms, considering the side-on and end-on orientations (named as side-on_Ca_[010] and endon_Ca_[010] configurations). The adsorption above Mg sites (dolomite case) is evaluated in the end-on_Mg_[010] configuration. The evaluation of these configurations completely characterizes the hexane adsorption on calcite and dolomite. Table 3 presents the values of adsorption energies for the adsorption of hexane on calcite and dolomite. For the

Figure 9. Optimized geometry and charge density map for a hexane molecule adsorbed on a calcite surface on end-on_Ca_[010] configuration without van der Waals (a) and (c), respectively, and with van der Waals corrections (b) and (d), respectively. In (a) the geometry presented corresponds to the calcite surface; however, the hexane on the same site of dolomite shows a similar geometry. The bond lengths are presented (in Å) for calcite (outside of parentheses) and dolomite (inside parentheses). The charge density map (c) represents the adsorption on calcite, where the adsorption on dolomite shows qualitatively identical results. The scale is linear between 0 and 0.08 electrons/bohr2.

Table 3. Adsorption Energies Considering a Hexane Molecule Adsorbed on Calcite and Dolomite (10−14) Surfaces

bond length between the closest hexane C atom and the calcite (dolomite) surface Ca atom is 3.57 Å (3.50 Å). The charge density profiles between the hexane molecule and the surfaces (calcite and dolomite) are similar for the end-on_Ca_[010] configurations. Figure 9c shows the charge density slice to the end-on_Ca_[010] geometry for the hexane molecule on calcite (similar to the dolomite case). This figure shows that the binding between the hexane molecule and the surface is weak as indicated by a low charge density between them. Considering top sites on calcite, like Ca_top and CO3_top, the distance between a closest C atom from hexane to the surface Ca atom or the CO3 group is 3.10 and 3.31 Å, respectively. On the dolomite surface, the distance between the surface and the closest carbon atom in the hexane on Ca_top is 3.58 Å, and the Mg_top site shows a distance of 3.41 Å. The top sites calculated in this work show high adsorption energies, compared to the end-on and side-on adsorption sites. Another interesting observation is at the end-on_[42−1] site on calcite and dolomite. For these configurations we found an adsorption energy of −0.11 eV for calcite and −0.09 eV for dolomite. This difference in adsorption energies is most likely due to the differences between the calcite and the dolomite surface sites. The end-on_[42−1] site on calcite and dolomite occurs on different chemical elements. On calcite the adsorption is on the Ca atom only; however, on dolomite the adsorption is on Ca and Mg atoms. From the adsorption purely

Eads (eV) configuration

calcite (DFT)

calcite (DFT + vdW)

dolomite (DFT)

Ca_top CO3_top Mg_top side-on_Ca_[010] end-on_Ca_[010] end-on_Mg_[010] side-on_[42−1] end-on_[42−1] end-on_CO3_[42−1]

−0. 06 −0.00 −0.09 −0.11 −0.10 −0.11 −0.02

−0.12 −0.09 −0.32 −0.35 −0.30 −0.32 −0.12

−0.04 −0.01 −0.02 −0.07 −0.10 −0.06 −0.09 −0.09 −0.03

adsorption on calcite, the end-on_Ca_[010] and endon_[42−1] configurations are the most stable (Eads = −0.11 eV). This result indicates that the nonequivalent end-on hexane orientations on the calcite surface (along the [010] or [42−1] directions) are energetic degenerates. This result also shows that the two different surface directions do not have any significant effect on the surface−hexane binding. The side-on orientations (side-on_Ca_[010] and side-on_[42−1]) are more energetic by 20 and 10 meV than the end-on ones, respectively. The Ca_top configuration shows an adsorption 24545



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on Ca or Mg surface atoms (Ca_top and Mg_top sites), we found that the adsorption on Ca atoms is more favorable than on Mg atoms as indicated by lower adsorption energies for endon_[42−1] sites on calcite than dolomite. Regarding vdW calculations, the most stable sites with and without vdW do not change (end-on_Ca_[010]). However, the adsorption energy increases by approximately 69% if vdW is taken into account. Figures 9b,d present the geometry and the charge density map, respectively, for the end-on_Ca_[010], hexane adsorbed site on calcite for vdW calculations. As similarly observed for benzene on calcite, the inclusion of vdW reduces the bond length between hexane and the surface and improves the hexane−surface charge transference, compared to that without vdW (Figures 9a,c), respectively. Headen et al.9 have considered an asphaltene molecule adsorbed on the calcite surface by means of computational simulations using a classical force field. The authors reported an optimum calcite−asphaltene bond length of 3.5 Å. This result is far from our result with vdW calculation for hexane (3.27 Å) but closer to that for the benzene (approximately 3.4 Å). However, the authors emphasized the necessity of more accurate calculations due to the presence of different types of atoms in the simulations (a typical difficulty with classical force fields). Our vdW calculations are able to deal with this difficulty and can be used as reference results. Energy Barriers. To better characterize the hydrocarbon− mineral surface energetics, we have also determined the energy barriers involved in the displacement of hydrocarbon molecules along the mineral surface. These energy barriers are important to quantify the energetic cost of hydrocarbon adsorption, migration, and diffusion on these surfaces. Those are crucial parameters for a more realistic description of this kind of system and can be used to derive a classical or semiclassical force field. The energetics of adsorption of the hydrocarbons considered in this work over the calcite and dolomite surfaces presents, in a closer look, important similarities. The first one is that the most stable adsorption site, for all mineral−hydrocarbon combinations, is over a Ca atom. Moreover, the differences in adsorption energies for a given hydrocarbon over the Ca atom of both mineral surfaces are very small, amounting to 40 meV for benzene and 10 meV for hexane. This suggests that energy barriers should qualitatively display the same behavior and be furthermore very close quantitatively. Therefore, we focus on the energy barriers for the displacement of the hydrocarbons over the calcite surface only. To compute the energy barriers, we consider densely sampled nonequivalent paths along the calcite (10−14) surface, as shown in Figure 10. Since the inclusion of the computationally expensive vdW dispersion shifts the adsorption energies up but trends are generally conserved, we initially calculate the barriers with plain GGA and only consider vdW effects, selfconsistently, for the points corresponding to each minimum and maximum energy value along the path. From now on, we will refer to these points (maxima and minima) as extrema. Figure 11 shows the energy barriers to displace the benzene molecule along the [010], [42−1], and [48−1] directions on the calcite surface. The extrema in each curve are labeled and marked by arrows, and energy values for both, GGA and vdW calculations on these points, as well as the corresponding energy differences, are shown in Table 4. As can be seen from these results, the net effect of including vdW interactions is to shift energies up homogeneously, and significant energy

Figure 10. Directions for energy barrier evaluation on calcite, for (a) benzene and (b) hexane adsorption. The paths were chosen so as to have the end points on an equivalent Ca atom. For benzene, paths lie along the nonequivalent [010], [42−1], and [48−1] directions, and for benzene, paths lie along the [010] and [42−1] directions. Hydrocarbons are shown only over the initial point in the path.

differences can be seen. Thus, it is very important to take vdW dispersion effects into account for a proper description of the interaction of the molecules with the surfaces, and this should make a difference in classical and/or semiclassical potentials for MD and MC calculations. For hexane, Figure 12 shows the energy barriers for the displacement along the paths indicated in Figure 10, and energies and energy differences for the GGA and vdW calculations for the points of energy extrema are summarized in Table 5. The results are different from the ones obtained for benzene displacement, where [010] is the direction with the largest barrier. This is due to the presence of a carbonate group along the path: for the [010] direction, hexane is always above Ca atoms. Benzene, in its turn, would diffuse over a carbonate group along its path, hence the different paths for the highest energy barrier. The calculated energy barriers are comparable to the adsorption energy in these systems. A hydrocarbon molecule diffuses along the surface as soon as it has enough energy to desorb, and in typical conditions found in oil wells, thermal energy could supply this activation energy. Hence, diffusion of hydrocarbon molecules is very likely to occur, and it is important to take into account the energy barriers in a semiclassical potential, to provide a better description of the 24546



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Table 5. Energy Values for GGA and vdW Calculations on the Geometries of Hexane, On the Points Labeled in Figure 12a

a

direction

point

EGGA

EvdW

ΔEvdW‑GGA

[010] [42−1]

Ha1 Hb1 Hb2

0.07 0.16 0.16

0.11 0.20 0.20

0.04 0.04 0.04

All energies are given in eV.

hydrocarbon/mineral interaction at hydrocarbon reservoir conditions, for longer time scales.

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CONCLUSIONS We have studied the adsorption of hydrocarbons molecule (benzene and hexane) on calcite and dolomite (10−14) surfaces. These molecules are representative of aromatic and alkane hydrocarbons, and our calculations show that those molecules weakly adsorb on both calcite and dolomite surfaces. Our results suggest that Ca sites are the most energetically favorable for hydrocarbon adsorption on both minerals. This effect is mostly due to the electronic level ordering that leads to charge differences in the possible adsorbed sites (Ca, Mg, and CO3) in the carbonate surfaces. The van der Waals correction increases the stability for those systems. For benzene adsorbed on Ca sites, we obtain an increase in the stability by 0.21 eV (63%) including van der Waals, compared to the calculation result without van der Waals. In addition, the shortest distance between carbon in benzene and the Ca surface atom is 3.12 Å (with vdW) compared with 3.69 Å (without vdW). The angle with respect to the surface increases from 15 to 27° with the inclusion of vdW. For adsorption on carbonate sites, this energy difference is 0.16 eV (67%), and distances between the closest carbon and oxygen atoms were found to be 3.64 Å (vdW) compared with 3.77 Å (without vdW). The vdW corrections resulted in an increase in the hydrocarbon−surface binding and a decrease in the distance between benzene and the surface. Evaluating the hydrocarbon migration on the calcite surface, the highest energy barriers associated with the hydrocarbon displacements on the surfaces are of the same order of the adsorption energies for the most stable sites. Finally, the obtained energy barriers in complement to adsorption energies and geometries including van der Waals interaction point out that this methodology must be taken into account in the evaluated systems. In this way, the comparison and parametrization of classical methods is also an important issue that can be important for studies in biomineralization and to describe the hydrocarbons/mineral rocks interaction in oil fields, providing a more realistic description for those systems.

Figure 11. Energy barriers for benzene displacements along (a) [010] and (b) [42−1] and (c) [48−1] directions on the calcite surface, according to Figure 8a. Labeled arrows mark the points of energy maxima.

Table 4. Energy Values for GGA and vdW Calculations on the Geometries of Benzene, On the Points Labeled in Figure 11a direction

point

EGGA

EvdW

ΔEvdW‑GGA

[010] [42−1]

Ba1 Bb1 Bb2 Bc1 Bc2

0.16 0.07 0.08 0.12 0.13

0.24 0.11 0.13 0.20 0.21

0.08 0.04 0.05 0.08 0.08

[48−1] a

All energies are given in eV.

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ASSOCIATED CONTENT

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AUTHOR INFORMATION

S Supporting Information *

Additional figures showing charge density for bulk, surface, and benzene adsorbed on a dolomite carbonate surface are showed. This material is available free of charge via the Internet at http://pubs.acs.org. Figure 12. Energy barriers for hexane displacements along (a) [010] and (b) [42−1] directions on the calcite surface, as shown in Figure 10b. Labeled arrows mark the points of maxima.

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest. 24547



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ACKNOWLEDGMENTS We acknowledge the financial support of the Advanced Energy Consortium (AEC) and the Brazilian agencies CAPES, FAPESP, and CNPq. The calculations have been partially performed at CENAPAD-SP, CESUP-RS, and UFABC supeŕ D. Coutinhocomputer facilities. We are grateful to Mauricio Neto and Marcos Verı ́ssimo Alves for insightful discussions and the anonymous referees for their comments.

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Hydrocarbon Adsorption on Carbonate Mineral Surfaces: A First

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