DFT Calculations with van der Waals Interactions of Hydrated Calcium

Article pubs.acs.org/JPCA

DFT Calculations with van der Waals Interactions of Hydrated Calcium Carbonate Crystals CaCO3·(H2O, 6H2O): Structural, Electronic, Optical, and Vibrational Properties Stefane N. Costa,† Valder N. Freire,† Ewerton W. S. Caetano,*,‡ Francisco F. Maia, Jr.,§ Carlos A. Barboza,∥ Umberto L. Fulco,∥ and Eudenilson L. Albuquerque∥ †

Departamento de Física, Centro de Ciências, Universidade Federal do Ceará, Caixa Postal 6030, Campus do Pici, 60455-760, Fortaleza, Ceará, Brazil ‡ Instituto Federal de Educaçaõ , Ciência e Tecnologia do Ceará, Avenida 13 de Maio 2081, Benfica, 60040-531 Fortaleza, Ceará, Brazil § Departamento de Ciências Exatas e Naturais, Universidade Federal Rural do Semi-Á rido, Campus Mossoró, 59900-000 Mossoró, Rio Grande do Norte, Brazil ∥ Departamento de Biofísica e Farmacologia, Universidade Federal do Rio Grande do Norte, 59072-970 Natal, Rio Grande do Norte, Brazil S Supporting Information *

ABSTRACT: The role of hydration on the structural, electronic, optical, and vibrational properties of monohydrated (CaCO3·H2O, hexagonal, P31, Z = 9) and hexahydrated (CaCO3·6H2O, monoclinic, C2/c, Z = 4) calcite crystals is assessed with the help of published experimental and theoretical data applying density functional theory within the generalized gradient approximation and a dispersion correction scheme. We show that the presence of water increases the main band gap of monohydrocalcite by 0.4 eV relative to the anhydrous structure, although practically not changing the hexahydrocalcite band gap. The gap type, however, is modified from indirect to direct as one switches from the monohydrated to the hexahydrated crystal. A good agreement was obtained between the simulated vibrational infrared and Raman spectra and the experimental data, with an infrared signature of hexahydrocalcite relative to monohydrocalcite being observed at 837 cm−1. Other important vibrational signatures of the lattice, water molecules, and CO32− were identified as well. Analysis of the phonon dispersion curves shows that, as the hydration level of calcite increases, the longitudinal optical−transverse optical phonon splitting becomes smaller. The thermodynamics properties of hexahydrocalcite as a function of temperature resemble closely those of calcite, while monohydrocalcite exhibits a very distinct behavior. biogenic carbonate minerals.3 The complex interactions occurring between CO2, rocks (mainly carbonates), and water play a central role on the carbon cycle.2 Since the CO2-related acidification of the oceans is linked with their saturation state in respect to calcium carbonate,1 a fundamental knowledge of the CaCO3 phases is of paramount importance, as well as their structural transitions. Rhombohedral calcite (Figure 1, top left, hexagonal representation), orthorhombic aragonite, and hexagonal vaterite are the anhydrous crystalline carbonates. Calcite is stable at atmospheric pressure, aragonite is thermodynamically stable under pressure and can be retained to ambient conditions (it is the high-pressure carbonate polymorph), but the stability of vaterite is not well-established. Within a broad

1. INTRODUCTION Rising atmospheric carbon dioxide (CO2) concentrations over the past two centuries have led to a major concern about the long-term fate of anthropogenic CO2 in the atmosphere and oceans of our planet Earth.1 Changes in atmospheric CO2 concentration are accompanied by related variations in the carbon content of others reservoirs like dissolved CO2 and carbonate, carbonate minerals, and reduced carbon, as stated by Lennie et al.2 Carbonate minerals form the greatest proportion of the Earth’s mineral carbon reservoir, the dominant phase being calcite (CaCO3), which acts as a buffer for long-term cycling of CO2 between atmosphere, oceans, and solid Earth. In addition to the anhydrous Ca-bearing carbonates calcite, aragonite, and dolomite, vaterite and the metastable monohydrocalcite (CaCO3·H2O) and hexahydrocalcite (CaCO3· 6H2Oikaite) are of considerable interest due to their role as precursors of stable carbonate minerals. Besides, amorphous calcium carbonate is an important precursor to geologic and © XXXX American Chemical Society

Received: May 30, 2016 Revised: June 27, 2016

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DOI: 10.1021/acs.jpca.6b05436 J. Phys. Chem. A XXXX, XXX, XXX−XXX

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The Journal of Physical Chemistry A

functional theory (DFT) calculations at the generalized gradient approximation (GGA) level.4 On the one hand, the metastable monohydrocalcite upon dehydration or at higher temperature transforms into the calcite and aragonite water-free modifications,5 while on the other hand the metastable hexahydrocalcite (ikaite) transforms rapidly to calcite and vaterite at ambient temperature.2 Because of its promising industrial use (plastic, rubbers, papers, paints, etc),6 implant applications,7−9 and confinement features of excitons in Si@calcite and calcite@SiO2 spherical core−shell quantum dots,10 pioneer DFT calculations at the LDA and GGA levels of the structural, electronic, and optical properties of the calcite polypmorph were performed,10 soon followed by the works of Hossain et al.11 and Brik.12 In the case of aragonite, the stimulus for the investigation of its poorly known electronic and optical properties13 came from the need to understand the white florescence properties of scallop shells fired at 100−500 °C.14 Finally, the structural properties of vaterite was object of intense debate15−21 (by the way, a recent work also casts doubts on the crystal structure of aragonite22), and only a single paper has been published investigating its electronic states and optical absorption.23 Indeed, many of the previously reported structures for vaterite were ruled out recently,19−21 leaving only two structures consistent with Raman, NMR, and XRD measurements: hexagonal P3221 and monoclinic C2 unit cells. A survey of published experimental and theoretical lattice parameters and measured or calculated energy band gaps of these anhydrous crystalline CaCO3 polymorphs is shown in Table 1.

Figure 1. (top left) Calcite unit cell in the hexagonal representation. (top right) Hexahydrocalcite (ikaite) monoclinic unit cell. (bottom) Monohydrocalcite hexagonal unit cell. Blue dashed lines indicate hydrogen bonds. Lattice parameters are shown at the edges of each unit cell.

picture, various experimental works have shown that calcium carbonate exists in five different phases, and their structural transitions were examined through state of the art density

Table 1. Experimental Lattice Parameters and Main Energy Band Gaps of the Anhydrous Crystalline Calcium Carbonates Calcite,a Aragonite, and Vaterite reference Zhang and Reeder38 Effenberg et al.28 this work (DFT, GGA+TS) Baer et al.48 (measured) Skinner et al.49 (calculated) Medeiros et al.10 (calculated) Brick12 (calculated) Hossain11 (calculated) reference Dickens and Bowen50 Bevan et al.22 Medeiros et al.13 (calculated) reference Meyer51 McConnel52 Sato and Matsuda53 Bradley et al.54 Le Bail et al.16 Demichelis et al.18 Demichelis et al.19 Medeiros et al.23 (calculated) a

calcite unit cell/SG R3̅c/rhombohedral R3̅c/rhombohedral R3c̅ /rhombohedral Eg (eV) 6.0 ± 0.35 4.4 ± 0.2 (LDA, D → Z) 4.95 (LDA, D → Z), 5.07 (GGA, D → Z) 5.023 (GGA, K → Γ, M → Γ) 5.07 (GGA, M → Γ) aragonite unit cell/SG Pmcn/orthorhombic P1̅/triclinic Eg (eV) 3.956 (LDA, X → Γ), 4.229 (GGA, X → Γ) vaterite unit cell/SG Pbnm/orthorhombic P6322/hexagonal P63/mmc/hexagonal P6322/hexagonal Ama2/orthorhombic P3221/hexagonal C2/monoclinic Eg (eV) 4.68 (LDA, Γ → Γ), 5.07 (GGA, Γ → Γ)

a, b, c (Å) 4.989, 4.989, 4.989 4.9896, 4.9896, 4.9896 4.990, 4.990, 4.990

α, β, γ (deg) 90, 90, 120 90, 90, 120 90, 90, 120

a, b, c (Å) 4.9598, 7.9641, 5.7379 5.7394, 4.9616, 7.9700

α, β, γ (deg) 90, 90, 90 90.004, 90.012, 90.001

a, b, c (Å) 4.13, 7.15, 8.48 7.135, 7.135, 8.524 4.13, 4.13, 8.49 7.135, 7.135, 8.524 8.7422, 7.1576, 4.1265 7.1239, 7.1239, 25.3203 12.2454, 7.1971, 9.3052

α, β, γ (deg) 90, 90, 90 90, 90, 120 90, 90, 120 90, 90, 120 90, 90, 90 90, 90, 120 90, 115.16, 90

The calculated lattice parameters of calcite are shown as well. B


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The Journal of Physical Chemistry A Two theoretical studies on the hydration and structural properties of ikaite and monohydrocalcite were performed recently by Demichelis et al.24,25 using the DFT formalism. In the first,24 the thermodynamics of water incorporation into calcium carbonate during the formation of its hydrates revealed a failure of pure-DFT, hybrid Hartree−Fock/DFT, and DFTD2 approaches to reproduce the energetics of the hydration process, notwithstanding the good accuracy in the prediction of their structural properties. In the second,25 minimum total energy geometries of the hydrated calcite crystals were obtained considering the PBE0 hybrid exchange-correlation functional and a long-range dispersion correction to take into account oxygen−oxygen interactions. They did not, however, assess the electronic, optical, and vibrational properties of the hydrated crystals. It is our intention to fill this gap by presenting the results of DFT computations for both the monohydrated and hexahydrated crystals of CaCO3, predicting their electronic band structures and partial densities of states, optical absorption curves, infrared and Raman spectra, phonon dispersion relations, and thermodynamic properties. Our main objective, as a matter of fact, is to elucidate how the presence of water molecules inside these calcium carbonate crystals modify their physical properties in comparison to anhydrous calcite.

Table 2. Experimental Lattice Parameters of the Hydrated Crystalline Calcium Carbonates Compared with Theoretical Results monohydrocalcite a, b, c (Å) 10.5547, 10.5547, 7.5644 Demichelis et al.24 B3LYP 10.6708, 10.6708, 7.66274 Demichelis et al.24 B3LYP-D2 10.5019, 10.5019, 7.55684 Demichelis et al.24 PBE-D2 10.523, 10.523, 7.5644 Demichelis et al.24 PBE0 10.5653, 10.5653, 7.58709 Demichelis et al.25 PBE0-DC 10.4713, 10.4713, 7.5319 this work PBE+TS 10.495, 10.495, 7.546 hexahydrocalcite reference a, b, c (Å) Swainson and Hammond27 8.7316, 8.2830, (experimental) 10.9629 Demichelis et al.24 B3LYP 8.91496, 8.34926, 11.0177 8.59189, 8.24158, Demichelis et al.24 B3LYP-D2 10.8094 Demichelis et al.24 PBE-D2 8.62682, 8.24987, 10.7875 Demichelis et al.24 PBE0 8.80145, 8.27472, 10.9081 8.6787, 8.2453, Demichelis et al.25 PBE0-DC 10.8300 this work PBE+TS 8.656, 8.251, 10.866 reference Swainson26 (experimental)

2. MATERIALS AND METHODS 2.1. Crystal Structures. The crystallographic data used as input for the calculations were obtained from the works of Swainson for natural monohydrocalcite by means of neutron diffraction,26 and for ikaite considering neutron diffraction on a synthetic deuterated sample at 4 K.27 In the case of calcite, the structural parameters were obtained from the X-ray diffraction measurements of Effenberger et al.28 Tables 1 (for calcite only) and 2 (for the hydrated crystals) summarize the main structural parameters of interest together, as well as the optimized lattice parameters produced by our simulations. For monohydrocalcite (M), we have a primitive centered hexagonal unit cell with space group symmetry P31 and Z = 9 (Figure 1, bottom), while for hexahydrocalcite (H), the unit cell is centered monoclinic with space group C2/c and Z = 4 (see Figure 1, top right). Each calcium atom in the monohydrated crystal is coordinated by six oxygen atoms belonging to four CO32− groups and two oxygen atoms of distinct water molecules. Single hydrogen bonds are formed between all hydrogen atoms of each water molecule and two oxygen atoms of each CO32− group in the unit cell, except for the O1 atom (we follow here the atom numbering proposed by Swainson;26 see Figure 2), which has two hydrogen bonds with H1 (water 1) and H4 (water 2). The monohydrate tridimensional structure can be obtained from the stacking of triangular motifs along the c axis (Figure 2, top, orange lines), each motif containing three CaCO3·H2O formula units disposed in a helicoidal fashion with well-defined chirality. For the ikaite phase, each calcium ion is coordinated by the oxygen atoms of six water molecules and two oxygen atoms from a single CO32− group. Within the unit cell, the water molecules form clusters along the axes a and c (see Figure 2, middle and bottom parts), which are intercalated with layers containing two CaCO3 (neutral) formula units aligned along the b direction. A set of eight strong hydrogen bonds connecting the CO32− groups and the water clusters runs almost parallel to the ac face of the monoclinic unit cell, while other hydrogen bonds stabilize the structure along the b direction. For each CO32−, two oxygen atoms form two

α, β, γ (deg) 90, 90, 120

α, β, γ (deg) 90, 110.361, 90 -,108.264,-,109.368,-,108.706,-,108.485,-,108.90,-,109.094,-

hydrogen bonds each with neighbor water molecules, while the third one forms four hydrogen bonds. All hydrogen atoms of hexahydrocalcite are hydrogen bond donors, and two-thirds of its water molecules have their oxygen atoms acting as hydrogen bond acceptors. 2.2. Computational Approach. The Perdew−Burke− Ernzerhof (PBE) exchange correlation potential29 within the GGA was used in our computations, together with the parameter-free dispersion correction scheme proposed by Tkatchenko and Scheffler30 to describe long-range van der Waals interactions. The CASTEP code31 for electronic structure calculations was employed to perform the geometry optimization procedure for each crystal under study as well as to obtain their structural, electronic, optical, vibrational, and thermodynamics characteristics. CASTEP uses a plane wave basis set and atomic pseudopotentials to evaluate the physical properties of crystals, allowing one to easily improve the quality of the calculations without concern with typical basis set superposition errors found in other codes32 for dissociation energy estimations. The plane wave energy cutoff was set at 880 eV for all systems, and Monkhorst−Pack33 grids of 3 × 3 × 3, 2 × 2 × 2, and 2 × 2 × 1 were chosen to perform reciprocal space integrations for calcite, monohydrocalcite, and hexahydrocalcite, in this sequence, to determine well-converged structures. Norm-conserving GGA pseudopotentials34 were employed to describe the electronic cores C 1s2, O 1s2, and Ca 1s2 2s2 2p6 (so the valence electrons explicitly dealt with are C 2s2 2p2, O 2s2 2p2, and Ca 3s2 3p6 4s2). The geometry optimization of the unit cells to a total energy minimum was performed using the Broyden−Fletcher−Goldfarb−Shanno (BFGS) quasi-Newton scheme, well-known for its stability and efficiency.35 Convergence thresholds were the C


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formalism37), phonon dispersion curves, and thermodynamic properties (entropy, enthalpy, Debye temperature, and free energy).

3. RESULTS AND DISCUSSION 3.1. Unit Cell Optimization. The optimized unit cells for calcite, monohydrocalcite, and hexahydrocalcite are shown in Tables 1 and 2. For calcite, our simulations achieved a lattice parameter practically identical to the experimental measurements28,38 (4.990 Å vs 4.9896 and 4.989 Å). In the case of monohydrocalcite and hexahydrocalcite, our data are as accurate as the theoretical calculations of Demichelis et al.24,25 using pure (PBE) and hybrid (B3LYP, PBE0) exchange-correlation functionals with and without dispersion correction terms (D2, DC). For monohydrocalcite, our lattice parameters were a bit smaller (−0.57% for a and b, −0.24% for c) than the neutron diffraction data (for Demichelis et al.25 the PBE0-DC values were −0.79% and −0.43%, respectively), and the same behavior was observed for hexahydrocalcite, with our a, b, and c parameters, respectively, being 0.87%, 0.39%, and 0.88% smaller than those measured by Swainson and Hammond.27 This must be contrasted with the results obtained using the PBE0-DC approach: 0.61%, 0.45%, and 1.21%, in the same a, b, c order. For the β angle, our simulations led to a value of ∼109°, 1.27° smaller than the diffraction measurements, while Demichelis et al.25 have found 108.3° (B3LYP), 109.4° (B3LYP-D2), 108.7° (PBE-D2), 108.5° (PBE0), and 108.9° (PBE-DC). Overall, one can confirm that DFT simulations nowadays can reproduce very accurately the structural features of crystals with noncovalent interactions if van der Waals forces are adequately taken into account. Figure 3 shows how the unit cell total energy varies if we change the lattice parameters a, b, and c separately for the Figure 2. Monohydrocalcite (top) and hexahydrocalcite (middle, bottom) atom labeling. The triangular motifs of monohydrocalcite are indicated by the orange lines.

following: total energy variation smaller than 0.5 × 10−5 eV/ atom, maximum ionic force per atom smaller than 0.1 × 10−1 eV/Å, maximum ionic displacement smaller than 0.5 × 10−3 Å, and maximum crystal stress component smaller than 0.2 × 10−1 GPa, with a convergence tolerance window of two optimization steps. The unit cell volume was allowed to vary along the optimization process using a finite basis set correction term. For the self-consistent field (SCF) calculations at each geometry optimization step, the following convergence tolerances were adopted: total energy variation per atom smaller than 0.5 × 10−6 eV, electronic eigen energy variation smaller than 0.2875 × 10−6 eV, with a convergence tolerance window of three SCF steps. A Pulay density mixing scheme36 was employed to generate new starting charge densities at each SCF cycle. The final valence electron populations for each unit cell were 64 for calcite, 360 for monohydrocalcite, and 160 for hexahydrocalcite (so the monohydrocalcite calculations were the computationally most expensive), with two electrons per unit cell and per valence band. After the geometry optimization procedure, the following physical properties were obtained for all the crystals: optimized lattice parameters, unit cell total energy as a function of the lattice parameters near the equilibrium, electronic band structures, partial densities of states, optical absorption, vibrational spectra (infrared absorption and Raman scattering, within the linear response

Figure 3. Unit cell total energy of anhydrous (A), monohydrated (M), and hexahydrated (H) calcite as a function of the lattice parameters for independent variations of a, b (hexahydrated crystal only), and c.

hexagonal anhydrous (A), hexagonal monohydrated (M), and monoclinic hexahydrated (H) forms of calcite (but relaxing the internal atomic coordinates) with respect to the optimized parameters a0, b0, and c0. We define the variations Δa = a − a0, Δb = b − b0, and Δc = c − c0 and the corresponding relative D


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The Journal of Physical Chemistry A deviations Δa/a, Δb/b, and Δc/c. One can note in Figure 3 that the energy curves for the hexagonal crystals (anhydrous and monohydrated calcite) follow a parabolic pattern with larger concavity for the variation of a than for c, indicating that the unit cell must be much more compressible along this direction. Indeed, experimental measurements38 report a volume compressibility of 9350 GPa for calcite along c and 2420 GPa along a, confirming such expectation. In the hexahydrated form the total energy variation, as we modify the c parameter, follows a parabolic shape whose concavity is the largest, followed by b and a, in respective order, a result that can be related to the presence of a large number of strong hydrogen bonds almost aligned to the c axis (see Figure 2, bottom). This result is consistent with experimental data for ikaite compressibility,39 which shows a larger compressibility along the a direction. 3.2. Electronic Structure. In Figure 4 one can see the Kohn−Sham electronic band structures and partial densities of

states of anhydrous calcite (top), monohydrocalcite (middle), and hexahydrocalcite (bottom) near their main band gaps (see also Figure S1 in the Supporting Information for a more detailed description of the band structures in the −3.0−8.0 eV energy range). Considering the hexagonal representation for the first Brillouin zone, anhydrous calcite exhibits indirect band gaps of 5.12 eV (M → Γ transition from valence band to conduction band), 5.19 eV (nearly the transition K → Γ), and 5.20 eV (nearly the transition H → Γ) and a direct gap of 5.17 eV (transition M → M). The top of the valence band and the bottom of the conduction band are dispersive, with the former originating mainly from the CO32− groups, mostly from the O 2p states, while the latter has some contribution from Ca 4s states mixed with O 2p orbitals. At the Γ point, the valence band of calcite is very flat, while the conduction band has some curvature, indicating that the effective masses of holes are much larger than the electron masses. The calculated energy band gaps found here, however, must be considered with a grain of caution, as it is well-known that DFT approximations tend to underestimate their values in comparison with the experimental data. Trends of qualitative behavior are more relevant than numerical figures when one analyzes DFT gap predictions.40,41 Looking now at the monohydrocalcite band structure (Figure 4, middle), the first contrast that can be observed relative to the anhydrous form is that the uppermost valence bands are much flatter, notwithstanding the absence of water contributions to them (they originate mainly from the O 2p CO32− groups, as occurred for anhydrous calcite). This means that the structural rearrangement of the calcium carbonate formulas inside the unit cell when the water molecules enter in the structure is the main factor behind the flattening of the valence energy levels. The same effect can be observed also for the lowermost conduction bands, which, however, preserve some degree of dispersion near to the Γ point. Electronic states with significant contribution of the water molecules can be observed at the bottom of the conduction band and for the valence bands below −1.0 eV (by the way, the 0 eV level was adjusted to be the top of the valence band for all crystals under study). The monohydrated form of calcite has two very close indirect band gaps, 5.53 eV (transition A → Γ) and 5.60 eV (transition K → Γ), which are 0.3−0.4 eV than the gaps found for calcite. In comparison with the monohydrated crystal, hexahydrated calcite has a much simpler electronic band structure near the main band gap (Figure 4, bottom). The uppermost valence band is formed by only two flat bands very close to each other, with significant contribution from the O 2p states of water. Below it, a set of many valence bands can be seen between −1.5 and −0.75 eV, originated mainly from O 2p states of water and the CO32− groups. Thus, the water effects on the electronic states of hydrocalcite are much stronger and direct, and not mostly related to structural changes as we observed for monohydrocalcite. The lowermost conduction band has a large dispersion near to the Γ point minimum, with a direct band gap of 5.14 eV, which is of the same order of the anhydrous calcite crystal. We note that the present results describing the electronic structure of the hydrated forms of calcite cannot be compared to any previously published data, as we have no knowledge of similar calculations (or any measurements) for these systems being reported in the literature. 3.3. Optical Absorption. The optical absorption due to electronic transitions calculated for polycrystalline samples of

Figure 4. Kohn−Sham band structures (left) and partial densities of states (right) of anhydrous (A) calcite (top), monohydrated (M) calcite (middle) and hexahydrated calcite (bottom). E


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tions (3 A2u + 10 Eu + 8 Eg + 3 A2g + 2 A1u + 1 A1g, point group D3d). On the one hand, the normal modes A2u (A1g) and the double degenerate Eu (Eg) are infrared (Raman) active modes, while the normal modes A1u and A2g are silent. Monohydrocalcite, on the other hand, has 213 normal modes with two irreducible representations, E and A (142 E + 71 A, point group C3), both infrared and Raman active, while hexahydrocalcite exhibits 135 normal modes with irreducible representations Bu, Au, Ag, and Bg (34 Bu + 32 Au + 33 Ag + 36 Bg, point group C2h), the Bu and Au (Ag and Bg) normal modes being active for infrared (Raman) absorption, the two spectroscopic techniques, infrared and Raman, being complementary and exhaustive for the vibrational analysis of CaCO3·6H2O crystals. The vibrational spectra will be presented here considering the wavenumber range divided into four windows, namely (from now on in this section, all wavenumbers are given in cm−1): (a) low-frequency modes, with the lattice modes between 0 and 500, as depicted in Figure 6 (7) for the infrared (Raman) spectrum;

anhydrous calcite and its hydrated forms is shown in Figure 5. One must consider here that the obtained curves are only an

Figure 5. Calculated optical absorption of calcite and its hydrated forms. (inset) Close-up of the optical absorptions near to the main band gaps of the structures. The solid lines are tangent to the absorption curves and reveal the band gaps for each crystal.

approximation, as they assume an identification with the Kohn−Sham eigenvalues with quasiparticle energies. In the case of semiconductors, there is a computational demonstration42 (made by direct comparison between GW and DFT band structures) that the differences between Kohn−Sham eigen energies and the true excitation energies can be corrected by a rigid shift of the conduction band. So, the absorption spectra obtained from our calculations must reflect the real absorption curves just by applying a rigid translation along the energy axis. For calcite, the absorption onset occurs at 5.1 eV, nearly at the same energy found for hexahydrocalcite, while monohydrocalcite has its optical absorption curve starting to rise at ∼5.6 eV (see the inset of Figure 5). For both the anhydrous and monohydrated crystals, the absorption onset is initially smooth and then becomes very sharp after an energy increase of 0.1 eV above the main band gap, while for hexahydrocalcite we see a slow absorption increase with energy, followed by a decrease with a minimum at ∼5.5 eV, probably related to the low electronic density of states in the conduction band between 5.1 and 5.5 eV (see Figure 4, bottom). As the photon energy increases, one can observe that the calcite absorption spectrum exhibits a wide absorption band between 5 and 20 eV, followed by a gap between 20 and 25 eV and another absorption band between 25 and 32 eV. For monohydrocalcite, the optical absorption is intense between 5.6 and 10 eV and has a very sharp maximum at nearly 12 eV. It practically disappears above 15 eV but increases again forming a band between 23 and 27 eV. Hexahydrocalcite, on the other hand, has an initial absorption band with many peaks between 5 and 17 eV and a secondary band between 25 and 28 eV. In a nutshell, it seems that the presence of water molecules leads to an overall decrease of the optical absorption in the simulated energy range. 3.4. Infrared and Raman Spectra. After optimizing the geometries of anhydrous calcite and its hydrated forms, we calculated the infrared and Raman spectra for each structure. Calcite has 27 normal modes with six irreducible representa-

Figure 6. DFT-calculated infrared spectra of anhydrous (A), monohydrated (M), and hexahydrated (H) calcite in the 0−500 cm−1 wavenumber range.

(b) middle-frequency modes, displaying two distinct lattice modes intervals. The first one, between 500 and 1100, as shown in Figure 8 (9), for the infrared (Raman) spectrum. The second, between 1200 and 1700 (as it can be seen in Figure 10 (11) for the infrared (Raman) spectrum). (c) high-frequency modes, between 2900 and 3400, as illustrated in Figure 12 (13) for the infrared (Raman) spectrum. For high-frequency modes, anhydrous calcite exhibits no infrared absorption lines or Raman intensity lines, so the data are restricted for the monohydrocalcite and hexahydrocalcite cases only. When possible, we will compare the theoretical calculations with the previously reported experimental data of Coleyshaw et al.43 (infrared and Raman) and Tlili et al.44 (micro-Raman measurements) for the hydrated crystals, as well as the Raman measurements (infrared absorption’s theoretical study) for anhydrous calcite performed by De La Pierre et al.45 (Prencipe et al.46). F


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Figure 9. Same as in Figure 7 but in the 500−1100 cm−1 wavenumber range.

Figure 7. DFT-calculated Raman spectra of anhydrous (A), monohydrated (M) and hexahydrated (H) calcite in the 0−500 cm−1 wavenumber range.

wavenumber


Our work is the first one to report simulated vibrational spectra for the hydrated crystals of calcite, which makes it useful to clarify any imprecisions commonly found in traditional methods of normal mode assignment. The normal modes associated with each infrared and Raman peak, depicted in Figures 6−13, are detailed in the Supporting Information of this paper (Tables S1−S6). The following notation in the description of the modes is adopted: TLMtranslational lattice mode, RLMrotational lattice mode, δdeformation, σscissors, ωwagging, ρrocking, τtwisting, νstretching. Some subscripts can be eventually used: outout-of-plane motion, aasymmetric, ssymmetric. 3.4.1. Wavenumber Interval 0−500. Beginning by the lowfrequency window between 0 and 500, the top part of Figure 6 shows the infrared absorption spectra of the anhydrous crystal, with five peaks at 113 (TLM, with irreducible representation Eu), 122 (RLM, A2u), 222 (TLM, Eu), 292 (TLMthe most intense peak, Eu), and 308 (RLM, A2u). The corresponding values calculated by Prencipe et al.46 for the same peaks using


Figure 8. Same as in Figure 6 but in the 500−1100 cm range.

−1

G


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Raman lines, practically in the same wavenumber range observed in our low-wavenumber window’s simulations. For the hexahydrated calcite crystal, the Raman bands are shifted upward to higher frequencies relative to the monohydrocalcite spectra, starting at 155 (TLM, Ag) and ending near 361 (TLM, Bg). The most intense line, originated from a TLM mode, appears at ∼266, being surrounded by other major peaks assigned to TLM, Ag modes at 228, 238, 320, 197, and 341, in order of decreasing intensity. We did not find any experimental data describing the Raman spectrum of ikaite in the low-frequency wavenumber range. 3.4.2. Wavenumber Interval 500−1100. Figure 8 depicts the infrared absorption spectra of calcite and its hydrates in the wavenumber range of 500−1100. For anhydrous calcite, one has only two maxima at ∼835 and 689, assigned to an A2u mode (δout of the CO32− group) and to a doubly degenerate Eu mode (σ CO32−), in respective order. Experimentally, there are two peaks in the infrared spectrum of calcite at 872 and 712 to which our simulations can be matched.46 Looking now to monohydrocalcite (Figure 8, middle), an infrared absorption band between 650 (ρ H2O, σ CO32−) and 889 (ω H2O) can be seen with a separated small peak at 1048 (νs CO32−). The most intense absorption maximum occurs at 859 and is assigned to the wagging motion of water. Secondary maxima occur at 819 (ω H2O), 695 (ρ H2O), and 764 (τ H2O). On the one hand, a comparison with the experimental data available43 allowed us to establish the following correlations with our results: 859 (theory) → 872 (experiment), 695 (theory) → 698 (experiment), 1048 (theory) → 1063 (experiment). The infrared spectrum of ikaite (Figure 8, bottom), on the other hand, has three sets of absorption bands, the first one between 612 and 713, the second between 777 and 860, and the third being formed by two maxima at 934 and 960. A single peak can be observed at 1027 (δ OH, τ H2O, ρ H2O t). The most intense infrared absorption lines appear at: (a) 679 (ω H2O, Bu mode), 612 (ρ H2O, ρ CO32−, Bu), and 654 (ρ H2O, Au) for the first set; (b) 777 (ρ H2O and ω H2O, δout CO32−, Bu) and 837 (ω H2O, Bu) for the second one; (c) 957 for the third (δ OH, Bu). In particular, the absorption peak at 837 seems to correspond to a vibrational signature of hexahydrocalcite in comparison with monohydrocalcite, as it is absent in the latter. Experimental matches 43 are found for the 713 (726 experimental, ρ H2O), 819 (800 experimental, ρ H2O), and 860 (873 experimental, τ H2O) absorption lines. The Raman spectrum for anhydrous calcite between 500 and 1100 (Figure 9) has only two bands, at 689 (Eg double degenerate mode involving the scissors motion of the carbonate ions) and 1061 (A 1g mode due to ν s CO 3 2− ). The corresponding experimental values at 80 K are 712.4 and 1087.1.45 For monohydrocalcite, we find a very intense peak at 1046, assigned to a symmetric stretching of covalent bonds in the carbonate groups, reminiscent of the anhydrous calcite A1g mode. The experimental wavenumbers for this normal mode are 106943 and 1066.44 There is a secondary peak at 819 (ω H2O) and a set of five small maxima at 658 (ρ H2O), 690 (ρ H2O, experiment: 69943 and 69444), 764 (ρ H2O, experiment: 72343 and 71944), 867 (ω H2O), and 886 (ω H2O, experiment: 87643 and 87344). In the case of ikaite, a strong Ag band at 1052 (experimental values: 107043 and 107244), again related to a symmetric C−O bond stretchings also observed for anhydrous calcite, has a shoulder corresponding to the normal mode at 1069 (Ag, δ OH), and a secondary maximum at 926 (Ag, δ OH, experiment: 87343). Other peaks occur at 688 (Ag, ρ H2O,

Figure 12. Same as in Figure 6 (excluding anhydrous calcite) but in the 2900−3400 cm−1 wavenumber range.

the B3LYP hybrid functional are (the experimental values are inside the brackets): 129.3 (102), 159.1 (136), 221.5 (223), 286.7 (297), and 293.7 (303), respectively. So our theoretical predictions are in good agreement with the experimental data and surpass the quality of estimates using a more accurate exchange-correlation functional without van der Waals corrections, notwithstanding the fact that PBE is not the most recommended functional to be used to predict vibrational properties (even with dispersion energy added). The infrared spectrum for monohydrocalcite (Figure 6, middle) exhibits a set of broad absorption bands between 120 and 300 with seven peaks worth highlighting. The most intense maximum occurs at ∼273, which corresponds to a TLM mode with irreducible representation E, followed by a secondary TLM peak at 235. Other TLM E modes occur at 124, 168, 180, and 301 cm−1, while a RLM mode appears at 211. For hexahydrocalcite, however, we have a single infrared absorption band with several peaks between 120 and 350, with the most pronounced maximum at 261 (TLM, Bu irreducible representation), followed in intensity by a peak at 275 (TLM, Au) and another one at 250 (TLM, corresponding to two vibrational modes with irreducible representations Bu and Au, in this order). Other relevant maxima of infrared absorptionall with Bu irreducible representationappear in order of intensity at 226 (TLM), 128 (RLM), 168 (TLM), 350 (TLM), 334 (TLM), and 152 (TLM). Moving now to the Raman spectra, one can see, at the top of Figure 7, that anhydrous calcite has only two Raman bands between 0 and 500 located at 160 and 281, being assigned to TLM vibrations with irreducible representation Eg. These estimates are in nice agreement with the experimental values at 80 K: 159 for the first normal mode45 and 286.9 for the second one. Theoretical figures using the B3LYP hybrid functional45 predict the same vibrations at 155.1 and 276.3, respectively. The calcite monohydrate has a set of peaks starting at 82 (TLM, A), whose intensity increases steadily up to 180 (TLM, E), displaying afterward, two very pronounced maxima at 216 (TLM, A) and 224 (TLM, A). It presents also another significant peak at 257 (TLM, E), together with a set of smaller peaks extending up to a last maximum at 332 (TLM, E). Experimental measurements of the Raman spectra of monohydrocalcite43 have demonstrated a sharp peak at 208, which was assigned to a lattice mode matching closely our calculated peak at 216. The same result also has a broad set of H


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The Journal of Physical Chemistry A experiment: 72243 and 71844), 763 (Bg, ρ H2O), 784 (Ag, ω H2O), 825 (Ag, δ OH), and 951 (Ag, ω H2O). One can easily establish a correspondence between some of the monohydrocalcite and ikaite normal modes in this region: 690 (M) → 688 (H), 764 (M) → 763 (H), and 819 (M) → 825 (H). 3.4.3. Wavenumber Interval 1200−1700. The infrared spectra calculated for anhydrous, monohydrated, and hexahydrated calcite in the wavenumber interval of 1200−1700 is presented in Figure 10. The only absorption line for anhydrous calcite occurs at nearly 1374 being originated from a doubly degenerate Eu band resulting from the asymmetric stretch of C−O bonds (experimental value: 140746). The monohydrocalcite crystal has four pronounced absorption peaks at 1373 (νa CO32−), 1454 (νa CO32−), 1484 (ν CO), and 1666 (σ H2O). The most intense peak, at 1373, is exactly the same normal mode responsible for the anhydrous calcite band at 1374 with a small contribution from a secondary vibration at 1376 (νa CO32−). According to Coleyshaw et al.,43 monohydrocalcite has three infrared lines at 1401, 1492, and 1700 that can be related to our calculated peaks at 1373, 1484, and 1666. For the ikaite crystal, however, the monohydrated calcite band at 1373 is shifted upward to 1387 (Bu irreducible representation), with a secondary Au vibration at 1382, both assigned to C−O stretchings, but with contribution from the deformation and scissoring motions of some water molecules. These vibrations can be related to the experimental infrared absorption maxima found at 1425 and 1411, respectively.43 Two small maxima also can be seen at 1594 (Au) and 1631 (Bu), which are due to water wagging oscillations, being matched by experimental infrared absorption bands at 1616 and 1644.43 Considering now the Raman spectra between 1200 and 1700 (Figure 11), the anhydrous calcite crystal exhibits a single maximum at 1405 due to the Eg symmetric doubly degenerate stretching of C−O bonds in the carbonate ion group, 29 cm−1 smaller than the experimental value.46 The monohydrocalcite normal mode at 1373, which gives a prominent absorption band in the infrared spectrum, also contributes to a strong Raman line, with another maximum at 1395 (experimental value: 140344) related to the anhydrous calcite Raman line at 1404. Another pronounced peak occurs at 1454 (νa CO32−, experiment: 148044), followed by a small hump with strongest contribution due to a vibration at 1475 (ν CO, σ H2O). A gap in the Raman spectrum is noted between 1500 and 1640, followed by a set of broad Raman bands with two maxima at 1652 (σ H2O) and 1666 (σ H2O, experiment: 167744), the latter being also observed in the infrared spectrum. Finally, for hexahydrocalcite, one can see two peaks at 1383 (ν CO, Ag irreducible representation) and 1419 (νa CO32−, Bg), a gap, and then a structure with three maxima due to water scissors motions with Ag irreducible representation at 1606, 1636, and 1664. Of these normal modes, the vibration at the 1606 maximum can be related to an experimental maximum at 1620 found by Tlili et al.44 By the way, the Raman band observed at 1664 has exactly the same experimental value. The experimental data of Coleyshaw et al.,43 in contrast, reveals a single maximum at 1483 in the wavenumber range, which is probably due to some lack of resolution in their data. 3.4.4. Wavenumber Interval 2900−3400. The highfrequency interval between 2900 and 3400 is characterized by the absence of any contributions from carbonate group vibrations, and therefore the anhydrous calcite has no spectral features to be seen. The OH stretching modes observed in this

wavenumber range are known to be described more accurately employing hybrid exchange-correlation functionals, so differences between our theoretical results and experimental data are expected to be larger. Figure 12 shows the infrared spectrum for monohydrocalcite and hexahydrocalcite only. A quick comparison reveals that hexahydrocalcite has the richest and broadest vibrational structure for infrared absorption, with at least 10 peaks being observed within the 3000−3350 wavenumber range, while monohydrocalcite has six maxima contained in the 3100−3275 range. All modes above 3000 originate from stretchings of the water OH bonds. In the case of monohydrocalcite, on the one hand, the peaks at 3172, 3188 (the most intense), and 3220 are due to νa H2O normal modes, while the peak at 3191 is created by a νs H2O vibration. The maxima at 3099 and 3274, on the other hand, are related to stretchings of a single OH bond. A comparison with the measurements of Colleyshaw et al.43 reveals that our results are somewhat shifted toward smaller wave numbers. Their lowestfrequency absorption band was found at 3236, which seems related to our theoretical absorption band prediction at 3099. At the highest frequency, experiment has an infrared absorption line at 3425, while our calculation predicts a maximum at 3274. For hexahydrocalcite, we have the following maxima due to νa H2O oscillations: 3132 (Bu), 3244 (Bu), and 3307 (Au). Symmetric water stretchings have the most important contributions to the peaks at 3050 (Au), 3195 (Bu), and 3259 (Au), while single OH bond stretchings are associated with the normal modes with infrared absorption at 3027 (Bu), 3219 (Bu), 3296 (Bu), and 3351 (Au), but also with secondary contributions from νa and νs H2O. Again these figures are redshifted with respect to experiment,43 whose smallest (largest) infrared peak wavenumber is 3119 (3543). However, the measurements and the theoretical calculations agree that ikaite’s infrared spectrum is broader and more structured than the spectrum of monohydrocalcite above 3000 cm−1. In comparison with the infrared, the Raman intensities in the 3000−3400 wavenumber interval exhibit a simpler pattern (see Figure 13). On the one hand, the monohydrated form of calcite exhibits a set of five maxima, with the most intense line at 3207, with a shoulder due to a secondary vibration with wavenumber 3220. The other peaks occur at 3099, 3275 (experiment: 3425,43 341644), and 3172. On the other hand, hexahydrocalcite has eight peaks, the most intense being assigned to the Ag normal mode at 3029 (the peak with smallest wavenumber

Figure 13. Same as in Figure 7 (excluding anhydrous calcite) but in the 2900−3400 cm−1 wavenumber range. I


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Figure 14. Normal modes behind the most intense maxima of the infrared spectra for anhydrous calcite (top), monohydrocalcite (middle), and hexahydrocalcite (bottom). The 837 cm−1 normal mode for the hexahydrate is a vibrational signature.

Figure 15. Normal modes behind the most intense maxima of the Raman spectra for anhydrous calcite (top), monohydrocalcite (middle), and hexahydrocalcite (bottom).

approximately replicated by monohydrocalcite and hexahydrocalcite at the wavenumbers 1046 and 1053, in respective order. Animation files of all modes are also provided in the Supporting Information. 3.5. Phonons and Thermodynamic Potentials. Figure 16 shows the phonon band structure of anhydrous calcite (top), monohydrocalcite (middle), and hexahydrocalcite (bottom) in the full 0−3500 cm−1 wavenumber range (left) and zoomed in in the 0−200 cm−1 interval (right). The acoustic sum rule correction was applied to produce these results. Phonon dispersion in anhydrous calcite is more pronounced, while the phonon bands for the hydrated forms are flatter, the hexahydrated crystal exhibiting more bands within the range of

in the range, possibly associated with the experimental value 312044), being followed in intensity by a maximum due to an Ag vibration at 3360 (the peak with largest wavenumber above 3000, assigned to the experimental bands at 342343 and 343444). The other Raman lines occur at 3131 (Ag), 3211 (Ag), 3225 (Ag), 3248 (Bg), 3263 (Ag), and 3299 (Bg). Figures 14 and 15 depict the normal modes assigned to the infrared (Raman) absorption maxima for anhydrous calcite (top), monohydrated calcite (middle), and ikaite (bottom), except for the ikaite normal mode at 837, which is responsible for a vibrational signature of this crystal in comparison with monohydrocalcite. In particular, one can see how the anhydrous calcite νs CO32− normal mode at 1061 is J


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Figure 16. Phonon dispersion curves for anhydrous (A), monohydrated (M) and hexahydrated (H) calcite. (left) Full wavenumber range. (right) Close-up showing the 0−200 cm−1 wavenumber range.

2800−3500 cm−1 in comparison with the monohydrated form. At the wavevector q = 0, the longitudinal optical−transverse optical (LO-TO) phonon splitting (labeled here ΔLO‑TO) calculated for calcite was 30.6 cm−1, with four TO bands belonging to the G irreducible representation (point group D3d) crossing at 90.1 cm−1 and two Eu LO bands at 120.7 cm−1. In the case of monohydrocalcite, we have ΔLO‑TO(q = 0) = 11.2 cm−1 between a single TO band at 81.7 cm−1 and a single LO band at 92.8 cm−1. For hexahydrocalcite, last, ΔLO‑TO(q = 0) = 4.4 cm−1 with a single TO band crossing the q = 0 axis at 68.6 cm−1 and a single LO band at 73.0 cm−1. It is worth remarking that the inclusion of van der Waals forces can induce phononic band gaps distinct from other effects such as Bragg scattering and local resonances.47 Some thermodynamic potentials evaluated for calcite and its hydrated crystalsnamely, the enthalpy (H), entropy times temperature (ST), and free energy (G = H − TS)are shown, in this order, at the top, middle, and bottom parts of Figure 17. Recently Demichelis et al.24 showed that DFT calculations are unable to describe in a consistent way the thermodynamic stability of monohydrocalcite and hexahydrocalcite due to their different structures. Even if one takes into account empirical corrections, this picture does not change, leaving a direct comparison between these structures unattainable. However, it is reasonable to use DFT calculations to reproduce well thermodynamical trends, and a rigid energy shift is likely to improve the agreement with experiment. Monohydrocalcite exhibits a larger rate of increase with temperature of H and ST in comparison to hexahydrocalcite, while the latter follows a curve just a bit above the curve of the anhydrous form. Looking at the enthalpy curves we have, at T = 300 K, the following energies: 0.886 eV (20.4 kcal/mol, for anhydrous calcite), 1.82 eV (41.9 kcal/mol, for monohydrocalcite), and 0.949 eV (21.8 kcal/mol, for hexahydrocalcite). Calculated values of ST at the temperature T = 300 K are 1.63 eV (37.5 kcal/mol), 3.27 eV (75.2 kcal/mol), and 1.73 eV (39.8 kcal/mol) for calcite, monohydrocalcite, and hexahydrocalcite,

respectively. The free energies for these materials are negative, as the enthalpy is smaller than the entropy contributions. In Figure 18 one can see the calculated constant volume heat capacity of each crystal (CV, top) and the Debye temperature (TD, bottom) as a function of temperature (T) obtained from the phonon density of states. Between 0 and 200 K, CV displays a rapid rise for the three forms of calcite, with the curve for the monohydrated one following closely the curve of the anhydrous crystal. The behavior of CV(T) in the case of the ikaite crystal is distinct from the others one, with a larger rate of increase. At 300 K, we have CV,Anhy = 115 cal/cell·K, CV,Mono = 242 cal/cell· K, and CV,Hexa = 130 cal/cell·K. The Debye temperature, by the way, shows a boost from T = 0 to 10 K and then a sharp decrease with minima at T = 40, 30, and 30 K for the anhydrous, monohydrated, and hexahydrated forms of calcite, respectively. Afterward, it builds smoothly, reaching 945 K (for anhydrous calcite), 1093 K (for monohydrated calcite), and 1274 K (for hexahydrated calcite) at T = 300 K.

4. CONCLUSIONS In summary, we have performed DFT calculations to elucidate the role of water in the electronic, optical, vibrational, and thermodynamic properties of two hydrated forms of calcite: monohydrocalcite and hexahydrocalcite. Structural optimizations performed using the GGA-PBE exchange-correlation functional taking into account a dispersion correction scheme have produced unit cell lattice parameters in excellent agreement with experimental data, even improving previous calculations using more sophisticated methods. With respect to the electronic structure, we have shown that water molecules increase the band gap of the monohydrated calcite crystals by 0.4 eV relative to the anhydrous form, while hexahydrocalcite (ikaite) has practically the same gap value. Uppermost valence bands for the hydrated calcite systems are very flat, as well as the lowermost conduction bands except in the region near the Γ point. Relevant electronic contributions from orbitals of the water molecules to the frontier bands are significant only in the K


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Figure 18. Calculated constant volume specific heat (top) and Debye temperature for calcite and its hydrated forms.

4.4 cm−1 (hexahydrated). Thermodynamic potentials such as entropy, enthalpy, and free energy, as functions of temperature, behave in a very distinct way for monohydrocalcite and hexahydrocalcite, with the hexahydrated form following closely the curves for anhydrous calcite, while the monohydrated system curves increase more rapidly as the temperature increases. The same trend is also observed in the constant volume heat capacity, with CV,Anhy = 115 cal/cell·K, CV,Mono = 242 cal/cell·K, and CV,Hexa = 130 cal/cell·K at T = 300 K. The Debye temperature of monohydrocalcite, however, stays below (above) the value found for hexahydrocalcite (anhydrous calcite) at a given temperature.

Figure 17. Calculated thermodynamic properties for calcite and its hydrated variants.

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case of ikaite. The type of the main gap for monohydrocalcite (hexahydrocalcite) is indirect (direct), involving the transition A → Γ (Γ → Γ), in contrast with the indirect gap of anhydrous calcite (M → Γ). Curiously, the calculated optical absorption of hexahydrate calcite has an onset much smoother than those obtained for the anhydrous and monohydrated crystals, probably due to the very low density of electron states at the bottom of the conduction band. Vibrational spectra calculations have allowed us to obtain the infrared absorption and Raman intensities of monohydrocalcite and hexahydrocalcite for the first time by theoretical means. The location of the normal modes is in good agreement with the experimental data for wavenumbers smaller than 2000 cm−1, with largest errors (of the order of tens of cm−1) occurring beyond this limit, corresponding to stretching bond vibrations of water molecules. In comparison with experiment, our calculated spectra for monohydrocalcite are red-shifted by 54 cm−1, on average, while for ikaite the redshift is smaller, of ∼16 cm−1. We also have found an infrared absorption peak at 837 cm−1, which is a vibrational signature specific of hexahydrocalcite relative to the monohydrated crystal. The phonon spectra, however, reveal that the hydration decreases the LO-TO phonon-splitting, from 30.6 cm−1 (anhydrous) to 11.2 cm−1 (monohydrated) and to

ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.6b05436. A more detailed description of the electronic band structure of each crystal and tables with all the vibrational assignments corresponding to the calculated infrared and Raman spectra of anhydrous, monohydrated, and hexahydrated calcite (PDF) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) Animation file displaying selected normal modes (AVI) L


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(AVI) (AVI) (AVI) (AVI) (AVI) (AVI) (AVI) (AVI) (AVI)

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Phone: +55 85 3366 99 06. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS V.N.F. and E.L.A. would like to acknowledge the financial support received during the development of this work from the Brazilian Research Agency CAPES (PNPD) and CNPq (INCT-Nano(Bio)Simes). E.W.S.C. and U.L.F. received financial support from CNPq through Project Nos. 307843/ 2013-0 and 454328/2014-1, respectively.

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