Carbon Dioxide Clathrate Hydrates: Selective Role of Intermolecular

Article pubs.acs.org/JPCA

Carbon Dioxide Clathrate Hydrates: Selective Role of Intermolecular Interactions and Action of the SDS Catalyst M. Albertí,*,† F. Pirani,‡ and A. Laganà‡ †

IQTCUB, Departament de Química Física, Universitat de Barcelona, Barcelona, Spain Dipartimento di Chimica, Università di Perugia, Perugia, Italy

‡

ABSTRACT: The ability of a single sodium dodecyl sulfate (SDS) molecule to promote the formation of CO2 clathrate hydrates in water (as it does for methane) has been investigated at the microscopic level. For this purpose, the components of the related force field were carefully formulated and assembled following the procedure previously adopted for methane. The properties of the whole system (as well as those of its components) were analyzed by carrying out extended molecular dynamics calculations. Contrary to what happens for methane, the calculations singled out the propensity of CO2 (pure) water clusters to form clathrate hydrate-like structures and the disappearance of such propensity when a single SDS molecule is added to the clusters. This feature was found to be due to the strong interaction of carbon dioxide with the additive that makes the SDS molecule lose its shape together with its ability to drive water molecules to form a suitable cage.

1. INTRODUCTION

Macroscopic level theoretical investigations of such important phenomena provide estimates for their stability, spontaneity degree, and phase equilibrium features. However, basic details of the involved elementary processes, depending on molecular rearrangements, energy barriers, energetics, and shape of the first solvation shells, can be more directly obtained by investigating the microscopic behavior of the system. The two approaches, however, are not alternative. They are instead complementary in the sense that the first one, by considering the average at thermal equilibrium conditions on several molecules (of the order of magnitude of the Avogadro number), provides the thermodynamical properties of the systems. Whereas, the second one, being applied to a limited number of molecules, is suited to isolate relevant details of the microscopic structures and mechanisms involved. In this article, we adopt the latter approach in order to compare, under the same conditions,11 the microscopic behavior of different guest molecules. In particular we compare here at molecular level how SDS distorts to drive the H2O molecules to form a cage suitable to host CH4 with its behavior when CH4 is substituted by CO2. For this reason, similarities and differences of the properties of the CO2 and CH4 molecules are investigated. For instance, the fact that the average values of the polarizability of CO2 and CH4 are, indeed, almost identical (2.65 and 2.56 Å3, respectively)12 makes the average size repulsion and dispersion attraction of the two molecules similar when interacting with

At low temperature (T) and moderate pressure (p), fairly large clusters of water molecules can lead to the formation of clathrate hydrates (which are ice-like solid inclusion compounds) as a result of the encapsulation of gaseous species into appropriate cages. Clathrate hydrates and pure water, under identical p and T conditions, solidify in different crystallographic systems (isometric and hexagonal, respectively1) with the difference being ascribable to the noncovalent intermolecular component of the interaction of the trapped species (guest) with the cage (host) made of water molecules. Such noncovalent guest−host intermolecular interaction2,3 is, in fact, strong enough to affect the structure and stability of the water cage. Because of this, some methodologies aimed at mitigating the greenhouse effect,4 based on the use of clathrate hydrates as CO2 capturing agents, have been recently proposed.5 Along the same line it has been also proposed to use CO2 to replace methane in related clathrate hydrates so as to achieve at the same time the goal of both sequestering carbon dioxide3,6 and releasing CH4 trapped in deep seawater. The fact that, under the same p and T conditions, clathrate hydrates of different guest molecules show different stability (as is the case of the already mentioned CH4 and CO2 ones) prompted in the recent past studies mainly focused on the related macroscopic phase equilibrium properties7,8 together with attempts to rationalize the long induction time and the low assemblage rate of the solvent cage.9 Both bottlenecks could be, in fact, reduced when use is made of proper additives (like the sodium dodecyl sulfate (SDS) tensioactive considered in this article, whose formula is Na-SO4-(CH2)11-CH3) to catalyze the process.10 © XXXX American Chemical Society

Special Issue: Joel M. Bowman Festschrift Received: December 21, 2012 Revised: April 24, 2013

A

dx.doi.org/10.1021/jp3126158 | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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contributions, however, were further decomposed into an electrostatic (Velec) and a nonelectrostatic (Vnelec) component by assuming again separability. Therefore, one can also write, in general,

the same partner. However, this is not true for the charge distributions determining the permanent multipole moments. CH4 is, in fact, a highly symmetric (nearly spherical) molecule, without permanent electric dipole and quadrupole moment (with only moments from octupole up being nonnull). On the contrary, CO2 is linear and has a pronounced polarizability anisotropy and quadrupole moment due to a highly asymmetric charge distribution over the molecular frame. This fact makes the size repulsion and dispersion attraction (as well as all the stereospecific electrostatic contributions to the CO2 interaction with partners involved in the clathrate formation like H2O, SDS, and CO2) highly anisotropic. At the same time, the ratio of the CO2 and CH4 masses is ∼2.75, making the mobility and the diffusion of the two species in solution quite different. All this can help in understanding the characteristics of the CO2 microscopic solvation (with and without SDS) and in singling out its differences. For this reason, we performed extended molecular dynamics (MD) calculations of the title system (water, carbon dioxide, and SDS) using the same roadmap followed for the water, methane, and SDS one.11 The charge transfer (perturbative) stabilization effect, affecting the interactions of CH4 and CO2 with H2O, has been indirectly included by properly correcting the value of the parameters used in the formulation of the intermolecular potential.13,14 To perform the MD calculations, the workflow of GEMS15 (the Grid Empowered Molecular Simulator developed in our laboratories) was adopted, and its first module was modified to enable it to generate a suitable analytical representation of the potential energy surface (PES) of a complex system. Moreover, we articulated the second module of GEMS in a way that allowed the run of the related trajectory calculations. Accordingly, section 2 of this article addresses the presentation of the assemblage of an accurate force field (and of its various components) for the title system; section 3 is devoted to a MD study of the static and dynamical properties of the pure water−carbon dioxide system. Finally, section 4 is focused on the discussion of the actual outcomes of the MD calculations for the dynamics of the water, carbon dioxide, and SDS systems to the end of understanding the possible effects of the additive on the clathrate hydrate formation mechanism. Concluding remarks are given in section 5.

Vtotal = Vinter + Vinter = Vnelec + Velec

(1)

Owing to the fact that, as mentioned above, the molecular polarizability, α, is the key property for the characterization of Vnelec, in our work, it was partitioned into separate contributions distributed over the different interaction centers attributed to each molecule. Because of that, Vnelec was expressed as a sum of all possible pairs of interactions (whose nature and number depend on how the molecular polarizability is partitioned) associated with the centers located both on different molecules (contributions to Vinter) and on the same molecule (contributions to Vintra), provided that the latter are separated by, at least, four bonds. As usual, Velec was described as a sum of Coulombic potentials calculated for all pairs of charges located on the molecular frame of the involved partners. The charge distribution on CO2 and H2O were taken to be consistent with related permanent quadrupole and dipole moments, respectively, while that on SDS was the one adopted in MD simulations of micelles formation,17 which was also used to investigate the formation of methane clathrates.11 In the following, the analysis will be concentrated on Vinter because Vintra was used only to define the conformation energy of the flexible SDS molecule.11 2.2. Nonelectrostatic Host−Guest and Guest−Guest Intermolecular Interactions. For the title system, the formation and stability of the host solvent cages around the guest gas molecule are governed by the host−guest (H2O− CO2) and host−host (H2O−H2O) interactions (and to a minor extent by the guest−guest CO2−CO2 ones) when no third species, as is, for instance, the SDS (tensioactive) additive considered in our case, is introduced. The procedure followed by us is already documented:11,18−26 the H2O−CO2 contribution was formulated without any partitioning of the H2O polarizability because of its small value (1.47 Å3) when compared with that of CO2 (2.65 Å3). Accordingly, a single interaction center placed on O, having a polarizability value equal to that of the water molecule and labeled as OW, was used. On the contrary, for the carbon dioxide molecule three interaction centers were placed on the CO2 molecular axis and the related polarizability values were chosen so as to be compatible with the molecular one. More in detail, the three centers were placed one on C (labeled as CD) and two on the O atoms (labeled, respectively, as (OD1) and (OD2). This means that the nonelectrostatic energy associated with the H2O−CO2 heterodimer was formulated as

2. FORMULATION OF THE INTERACTION As already mentioned in the introduction, in order to properly account for the more complex nature of the interaction of large systems, we adapted the scheme of GEMS.15 To this end, the first computational module of the present version of GEMS, designed first to generate the PES of fairly small molecular systems was modified. The modification consists in adopting empirical (or semiempirical) force field representations of the interaction16 and calibrating it to properly describe the investigated system. As the systems grow larger, in fact, as is the case of the present ones, the iterative search of convergence via calculation of an increased set of ab initio values and a further adjustment of the fitting becomes rapidly unmanageable. 2.1. Separation of Electrostatic and Nonelectrostatic Components. In the adopted representation, the total interaction energy, Vtotal, was decomposed into inter- and intramolecular contributions (Vtotal = Vinter + Vintra). Vinter and Vintra were taken to be mutually independent (Vinter embodies the interaction between the involved molecules, while Vintra embodies the interaction internal to the molecules). Both

2

Vnelec(H 2O−CO2 ) = VOW−CD +

∑ VOW−(OD)

i

i=1

(2)

The detailed representation of the Vnelec component is necessary to the end of performing a proper comparison of the information related to the most stable geometry and to the related binding energy of the isolated H2O−CO2 gas phase heterodimer (see below) with ab initio data. However, when considering the isolated CO2−CO2 homodimer, as it was done for H2O−H2O,19−21 the CO2 molecular polarizability was not partitioned due to the limited relevance of the specific features of such dimer for the present investigation. Accordingly, a B



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single interaction center (labeled as C1) was considered, and the nonelectrostatic energy, associated with the CO2−CO2 homodimer, was represented as Vnelec(CO2 −CO2 ) = VC1−C1

VILJ

(3)

n

j

(4)

2.3. Nonelectrostatic Interaction with the SDS Tensioactive. When a tensioactive (the SDS molecule in our case) is added to a system containing carbon dioxide in an environment of water molecules, the SDS−H2O and SDS− CO2 intermolecular interactions must also be accounted for (as in the work performed on methane clathrates,11 only one SDS molecule was added to the corresponding system). Bearing in mind that the polarizability of both, H2O and CO2 (see above), is small in comparison with that of SDS (∼32 Å3), water and carbon dioxide were considered as single centers when interacting with SDS. Such procedure was found to be appropriate (and was actually adopted) in our previous study of methane clathrates.11 On the contrary, multiple interaction centers were considered for the SDS molecule whose molecular polarizability was decomposed into effective values associated with the CH3−, CH2−, S, O, and Na+ groups or atoms (related interaction centers were labeled as C3, C2, S, O, and Na, respectively) and were placed on the C, S, O, and Na atoms, respectively.11 This decomposition was adopted to formulate the nonelectrostatic components for SDS−H2O and SDS−CO2 energy contributions as follows:

∑ VOW−(C2) + VOW−S i

i=1 4

+

∑ VOW−(O) + VOW−Na i

i=1

(5)

11

Vnelec(SDS−CO2 ) = VC1−C3 +

∑ VC1 − (C2) + VC1−S i

i=1 4

+

∑ VC1 − (O) + VC1−Na i

i=1

m

⎜

0⎟

(7)

3. MD FOR THE PURE CARBON DIOXIDE−WATER SYSTEM In order to learn how the various molecular components of a CO2, water, and SDS system behave, in our study, we run first MD simulations for the pure carbon dioxide−water system. For this purpose, we constructed pair interaction components of the involved species: H2O−CO2, CO2−CO2, and H2O−H2O (for the latter other details are given in refs 19−21). Basic features and the role played by the interaction components, relevant to the present MD study, were analyzed for a constant number of particles, N, volume, V, and total energy, Etotal (NVE). For larger systems, equilibrations to reach a chosen limit temperature value were performed also using an NVE ensemble. Moreover, at higher temperatures, the carbon dioxide, carbon dioxide−water and carbon dioxide−water− sodium dodecyl sulfate systems were investigated by running trajectories for an isothermal−isobaric (NpT) ensemble so as to allow the simulation shell to freely expand or contract. A time step of 0.001 ps was used in all simulations and, after being equilibrated for 0.5 ns, all trajectories were run for 10 ns (a simulation time of 2 ns was large enough to observe the formation of a clathrate methane structure11). The Ewald sum method was used to calculate the electrostatic energy for large systems, while for dimers a direct application of the Coulomb sum was adopted. MD calculations were performed using the DL−POLY program31 after implementing in it the abovedescribed interaction potentials and assuming H2O and CO2 to be rigid. 3.1. H2O−CO2 Dimer Interaction. In order to directly compare the predictions of the semiempirical H2O−CO2 interaction adopted by us, with results of ab initio approaches available in the literature, as indicated in section 2.2, the simple H2O−CO2 system was considered isolated in gas phase.

11

Vnelec(SDS−H 2O) = VOW−C3 +

2

where the relevant parameters ε (the well depth) and r0 (the equilibrium distance) were determined from the effective values of the polarizability assigned to the pair of centers involved in the interaction.29 The transferability of the ε and r0 values30 (which can be used for the same pair in different environments) is ensured by the β parameter of eq 7 that adds flexibility to both the repulsive (positive) and attractive (negative) terms of the VILJ function. As a matter of fact, thanks to the β dependence of the repulsion exponent and of both fraction coefficients, the VILJ function is more realistic and flexible than the traditional Lennard-Jones potential model.28 In particular, by lowering the β value, it is possible to include the contribution of further stabilizing interaction components coming into play at intermediate and short distances, like the charge transfer effects evaluated in the perturbative limit.20,25 Again, this means that the same values of ε and r0 can be used, for a given pair of interaction centers, regardless of their location on the same or different molecule.

m i

2

2

2

⎛ r0 ⎞ β+ 4.0( r0 ) ⎜ ⎟ ⎝r⎠

( ) −m ⎤ β + 4.0( ) ⎛ r ⎞ ⎥ ⎥ − ⎝r⎠ ⎥ β + 4.0( ) − m ⎥⎦ r r0

∑ ∑ V(OW) − (C1) i=1 j=1

r

r r0

Such formulation was then taken as the ground to describe large ensembles (clusters) of CO2 molecules. Moreover, the use of a single interaction center on CO2 was also exploited in the investigation of more complex systems, as those involving several CO2 and H2O molecules. In this case, the nonelectrostatic interaction energy, due to all asymmetric pairs, of a system containing n molecules of H2O and m of CO2 was formulated as Vnelec((H 2O)n − (CO2 )m ) =

⎡ ⎢ m = ε⎢ ⎢ β + 4.0 r ⎢⎣ r0

(6)

In all cases (including also those of section 2.2), each pair interaction was represented by an improved Lennard-Jones function, ILJ,18,27,28 that was formulated as C



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Table 1. Values of ε (Well Depth), r0 (Equilibrium Distance), β. and m Parameters Used to Define the Nonelectrostatic Interaction Contribution for H2O−CO2 (OW-CD and OW-OD), CO2−CO2 (C1−C1), H2O−H2O (OW−OW), and for Carbon Dioxide Water Solutions (OW−C1)

For such system, the electrostatic contribution was calculated by considering the charge distributions compatible with the dipole moment of H2O in gas phase (1.85 D) and the quadrupole moment of CO2 (4.28 D·Å) as shown in Figure 1 for CO2 together with its geometry.

Figure 1. CO2 equilibrium geometry and charge distribution (× indicates the points where the negative charges are placed). The punctual charges, of the row given above the picture, are in atomic units.

3 i=1

3 cos2 γ + 1 αi 2(rOW−X i)6

(8)

which is applicable because of the small dimension of water with respect to the related intermolecular distances. In eq 8, the leftmost coefficient −2140 (that incorporates the square of the water dipole moment value) is given in meV·Å3, Xi refers either to the C or to the O atoms of CO2, αi is the polarizability (in Å3) associated with them and γ is the angle formed by the rOW−Xi vector and the dipole moment of H2O. Accordingly, the total interaction was expressed as 2

V(H2O − CO2) = VOW − CD +

ε (meV)

r0 (Å)

β

m

OW−CD OW−OD OW−C1 OW−OW C1−C1

6.61 10.93 14.46 9.06 18.53

3.400 3.510 3.876 3.730 4.053

7.0 7.0 8.0 6.6 8.5

6 6 6 6 6

atom of water and the C atom is equal to 2.962 Å and the potential energy of this configuration is equal to −112.2 meV. The estimated induction contribution (−12.7 meV) amounts to about 10% of the total energy. These results are in good agreement with the available ab initio data,34−38 which predicts for symmetrically T-shaped equilibrium structures stabilization energies of about −120 meV. Moreover, mostly due to the CO2 linear symmetry, the obtained PES is quite flat near the expected minimum36 implying the possibility of some mobility/ adaptation of the monomer orientation and bending within the aggregates. The proposed potential model, in agreement with data quoted by Sadlej et al.,39 also predicts, for the hydrogen bonded configuration, a lower binding energy of −51 meV. The higher stability of the T-shaped nonhydrogen bonded structure agrees with spectroscopic information40,41 and is confirmed by more recent experiments.42,43 Despite the fact that induction is an important contribution to the total interaction energy of the H2O−CO2 dimer, for CO2 surrounded by several H2O molecules, compensation effects associated with many body contributions may come into play. Some balancing effects on the dimer were singled out by systematic MD calculations, which estimated an identical relative stability for the two leading molecular geometries mentioned above even when excluding induction effects. Moreover, it was also found that, when increasing T, the H2O−CO2 system tends to evolve toward a T-shaped geometry, regardless of the initial configuration. In addition, the configuration energy Ecfg (the mean potential energy calculated along the trajectory at a fixed value of Etotal) varies negligibly because any increase of T and Etotal is almost entirely converted into kinetic energy, Ekin. As an example, an increase of Etotal of 100 meV leads to an increase of Ecfg of only about 5 meV (Ecfg takes the values of −100 and −95.4 meV at the mean temperatures of 10 and 300 K, respectively). This means that the already mentioned flatness of the PES near the minimum fosters the population of various configurations having similar energy. Moreover, the reliability of eq 4 has been probed by performing MD simulations of the H2O−CO2 dimer adopting the two center representation of the nonelectrostatic contribution and using the OW−C1 parameters given in Table 1. Such simulations suggested that eq 4 provides values of the configuration energy, for the two relevant geometries indicated above, similar to those given by the three center representation (with very small differences of ∼3%). 3.2. H2O−H2O and CO2−CO2 Interactions. The nonelectrostatic contribution of the H2O−H2O interaction was formulated by considering a single interaction center (placed on the O atom and represented by OW) and to that was

Bearing in mind that charge transfer and induction effects may be important in the interaction between H2O and CO2, a careful separate characterization of each contribution was performed. Charge transfer effects in the perturbative limit were taken into account indirectly by lowering the value of β as discussed, for instance, in refs 18−21 and 25. On the contrary, induction due to the permanent water dipole was estimated and incorporated explicitly using the following semiempirical asymptotic expression (in meV) Vind = −2140 ∑

interaction partners

∑ VOW− (OD) + Vind + Velec i

i=1

(9)

with Velec being calculated by summing the Coulombic potentials derived from the above-mentioned five point charge distribution of CO2 (see Figure 1) and a three point charge distribution of the water monomer (0.3292 au on the H atoms and −0.6584 au on O). This agrees with the mentioned value of 1.85 D for the dipole moment of gas phase water. The five point charge distribution was successfully used recently to describe the CO2 dimer interaction.32 VOW−CD and VOW−OD were formulated by means of the ILJ function (see eq 7) using the parameters of Table 1. An important aspect, singled out by the ab initio calculations and worth to be emphasized here, is the fact that the H2O− CO2 dimer exhibits a binding energy at least a factor 2.2 higher than that of H2O−CH4 that is due to the higher value of Velec. Moreover, while the H2O−CO2 preferred geometry is a relatively floppy T-shaped one, that of H2O−CH4 tends to form more rigid H-bonds.33 As a matter of fact, the potential energy function given in eq 9 predicts at equilibrium a symmetrically T-shaped geometry of the H2O−CO2 dimer mainly stabilized at long-range by the dipole−quadrupole interaction. The related equilibrium distance between the O D



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assigned the polarizability value of the whole molecule. In order to take into indirect account of induction and charge transfer effects,25 also in this case, the value of the β parameter was lowered19−21 (the corresponding OW−OW VILJ parameters are shown in Table 1). Because of the variation of the dipole moment with the number of monomers in the cluster that can be attributed to an increase of charge transfer, polarization, and many-body effects,21,44 different values of the effective dipole moment were considered to calculate 11,18 the effective electrostatic contribution of the different systems containing water. A dipole moment equal to 2.1 D44,45 was used for the gas phase water dimer. An extension of the dynamics simulations to systems containing a high number of nonrigid water molecules aimed at comparing theoretical predictions with experimental results,18 suggested an increase of that value to 2.4 D. Using the same value of the ε and r0 parameters, our potential model was able to reproduce the second virial coefficients of the dimer for a wide range of temperatures and to provide binding energies in agreement with ab initio calculations.20,21 Moreover, the potential model predicted density values and RDFs for liquid water in agreement with experimental data.18−21 Some features of the CO2−CO2 dimer interaction were investigated in detail in the recent past32 and here we refer to the extension of the investigation to the case of an ensemble of 512 carbon dioxide molecules (the corresponding C1−C1 VILJ parameters are shown in Table 1). At first, as indicated before, the system was simulated by considering a NVE ensemble of particles in order to reach the chosen temperature. The system was placed inside a cubic box of size 33.837 Å, and boundary conditions were imposed. NVE calculations were performed at increasing values of T, taking as initial configuration, at a given temperature, that of the last step of the previous run. Once the system was equilibrated at 200 K, NpT trajectories, allowing to investigate possible changes of volume and density, were run. The simulations were performed at a pressure of 9.5 atm (0.96 MPa) and by increasing the temperature from 200 to 300 K. The equilibration was in any case reached within a time interval of 0.5 ns, and the corresponding results were excluded from the final statistics. Trajectories were run for 10 ns using a time step of 0.001 ps. A pressure of 9.5 atm was chosen in order to include the formation of the carbon dioxide liquid phase (carbon dioxide cannot become liquid at pressures lower than 5.1 atm) and to ensure that the range of temperatures to investigate the possible phase changes (needed to describe the destabilization of clathrates) is not large. Results of isothermal−isobaric simulations are given in Table 2 in which the mean configuration potential energy (Ecfg), its nonelectrostatic (Enel) and electrostatic (Eel) contributions, the density of the system (ρ), and the mean diffusion coefficients (D) are shown. As apparent from the table, by increasing T from 200 to 285 K, Ecfg increases (by assuming less negative values) because of the expansion of the system, associated with a widening of the intermolecular distances probed. The behavior of both the density (top panel) and the mean diffusion coefficient (lower panel) as a function of T is shown in Figure 2. As can be seen in the figure, at T ≈ 285 K, a fast decrease of the density, ρ, and a sudden increase of the mean diffusion coefficient, D, is observed as typical of an evolution from liquid to gas phase. 3.3. Formation of CO2 Clathrate Microscopic HydrateLike Structures. The first significant step toward the rationalization of the formation of CO2 clathrate hydrates was

Table 2. Mean Configuration Energy (Ecfg) and Its Nonelectrostatic (Enel) and Electrostatic (Eel) Components As a Function of Temperature, T; CO2 Density (ρ) and Mean Diffusion Coeficients (D) Are Also Given T

Ecfg (eV)

Enel (eV)

Eel (eV)

ρ (g cm−3)

D (10−9 m2 s−1)

200 205 210 215 220 225 230 240 250 260 270 275 280 285 290 295

−87.17 −85.35 −83.73 −82.22 −80.58 −79.14 −77.52 −74.01 −70.78 −67.25 −63.71 −61.68 −59.64 −57.29 −54.39 −50.25

−48.42 −47.73 −47.14 −46.62 −45.99 −45.42 −44.76 −43.45 −42.01 −40.41 −38.77 −37.75 −36.76 −35.53 −33.95 −31.05

−38.75 −37.62 −36.59 −35.60 −34.59 −33.72 −32.76 −30.56 −28.77 −26.84 −24.94 −23.93 −22.88 −21.76 −20.44 −19.20

1.437 1.415 1.397 1.383 1.365 1.343 1.327 1.287 1.246 1.199 1.149 1.118 1.088 1.049 0.999 0.720

1.938 2.159 2.292 2.605 2.854 3.201 3.721 4.656 5.686 6.575 7.924 8.545 9.624 10.004 12.456 21.245

Figure 2. Density, ρ, and mean diffusion coefficients, D, of CO2 plotted as a function of T obtained from 10 ns of MD simulation.

given by the study of clathrate hydrate formation in pure water. Pure water solutions of CO2, in fact, typically form clathrate hydrates at T ≈ 273 K and moderate pressure. Neutron diffraction experiments,46 performed to follow the structural changes occurring when D2O ice is pressurized using CO2 (p = 6.2 MPa) suggest that the complete conversion of ice into clathrate hydrate occurs at 276.8 K by slowly warming the pressurized sample from 272.2 to 278 K. Incomplete conversions have been observed in the 230 K ≤ T ≤276 K temperature range, indicating that the conversion of ice to clathrate hydrate is, indeed, a temperature dependent process. To the end of carrying out a detailed comparison with the results of our previous methane clathrate hydrate study,11,26 we considered at first a system made of one CO2 molecule surrounded by an ensemble of 256 water ones (weight fraction equal to 0.0095). The system was thermalized to reach a temperature of 200 K using a microcanonical ensemble of E



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coefficient of water is higher than that of CO2. Then, when slowly warming the sample in the 230−260 K temperature range, the difference in the diffusion coefficient of CO2 and water tends to vanish as a result of the trapping of the carbon dioxide molecule within a water molecule cage. When further increasing T, the CO2 diffusion increases so rapidly that, at T = 297.5 K, it becomes equal to 15.9 × 10−9 m2 s−1 (about ten times larger than the one of H2O that is equal to 2.1 × 10−9 m2 s−1). This is due to the destabilization of the trapping cage and to the consequent release of the CO2 molecule. Similar results were obtained when systems containing more than one molecule of CO2 were considered. Related diffusion coefficients show a temperature dependence comparable to that of the single CO2 molecule with the main difference being a change in the extent of the temperature range of stability. In particular, at a pressure of 8 MPa, systems containing 1, 5, and 50 CO2 molecules become clearly unstable at temperatures of 290, 300, and 315 K. Moreover, when D reaches a value close to 20 × 10−9 m2 s−1, a release of the gas occurs.

particles. Then, isothermal−isobaric MD simulations were carried out at a pressure of 8 MPa in the 200−300 K temperature range.11,26 Trajectories were run for 10 ns using a time step of 0.001 ps. The same calculations were later repeated using 5 and 50 molecules of CO2 placed initially at the center of a box containing an ensemble of 256 surrounding H2O molecules (weight fractions of 0.048 and 0.48, respectively). The OW−OW and the OW−C1 parameters (used before to test the reliability of the two center representation) of Table 1 were adopted to represent the nonelectrostatic contributions, and in this study, the value of β for the OW−OW interaction was increased from 6.6 (gas phase) to 7.5 (condensed phase).11,18 The dependence of the radial distribution functions (RDFs) on T indicates a propensity of water molecules to naturally cluster around CO2 (a feature distinctive of clathrate hydrate formation) as shown by the OW−C1 and OW−OW RDFs plotted in Figure 3 and calculated for a system containing one

4. SDS ROLE IN CARBON DIOXIDE CLATHRATE HYDRATE FORMATION The MD simulations were finally run also for SDS−CO2 and SDS−CO2−H2O systems (the characteristics of the SDS−H2O system were already discussed in our study of methane hydrates11) in order to understand the role played by SDS at microscopic level. The basic features of the interaction of SDS added to environments containing carbon dioxide and water molecules and the role played by its components were also analyzed by considering a NVE ensemble of particles. The focus of the investigation was the search of whether and how the catalytic effect of SDS applies also to carbon dioxide−water systems (which, as already commented, have a natural propensity to form clathrate hydrates in pure water). 4.1. SDS−CO2 System. In the case of methane water systems,11 the catalytic effect of SDS was found to be associated with the property of the SDS molecule to weakly interact with CH4 and to fold in a way that drives the solvent molecules to form a cage suitable to host the solute gas molecule. Our goal when investigating the carbon dioxide−water case was therefore to find out if and how SDS folds in such environment. For this purpose, as in the methane case, a first step of the study was the analysis of the behavior of the simple SDS−guest molecule system by allowing the tensioactive molecule to get deformed. Accordingly, the intramolecular energy V intra determining the stability of the SDS conformation was evaluated from bond, angle (see ref 48), and dihedral contributions17 with the interaction between groups separated by more than three bonds being calculated using the parameters of Table 3 for Vnelec and the charge distribution of refs 11 and 17 for Velec. For the SDS−H2O interaction component, we took the same as that of our previous methane hydrate investigation,11,26 in which, at low temperature, the equilibrium geometry of the isolated SDS does not get modified by the presence of H2O. In particular, water interacts with the polar head of the SDS molecule without altering its geometry. Finally, for SDS−CO2 the parameters used to determine the Velec component of Vinter were specifically worked out as described above, while those used to evaluate the Vnelec one were taken from Table 3. The key result of our study is the singling out of evidence for the fact that, contrary to what occurs for the SDS−CH4 system, a significant distortion of the SDS molecule from its

Figure 3. Radial distribution functions for OW−C1 (top panel) and OW−OW (lower panel) derived from MD simulations at several values of T and p = 8 MPa.

molecule of CO2 surrounded by 256 water molecules at a pressure of 8 MPa. The top panel of the figure clearly shows that the OW−C1 RDF has its main peak at 3.9 Å immediately following a shoulder located at about 3.3 Å. Such structure is the fingerprint of the particular nearest-neighbor organization of the molecules of the system. As a matter of fact, this and the OW−OW RDF (shown in the lower panel of Figure 3 and having both a well resolved short distance peak at rOW−OW ≈ 2.8 Å and a larger distance one peaking at rOW−OW ≈ 4.3 Å) are structures similar to those obtained by Cygan et al.47 in a MD simulation of the CO2 capture by montmorillonite (these structures survive only for a limited interval of temperature). Some clues on the formation of CO2 clathrate hydrate-like structures can be obtained by analyzing the value of the mean molecular diffusion coefficients as a function of temperature. MD simulations show that, at low temperature, the diffusion F



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Table 3. Values of ε (Well Depth), r0 (Equilibrium Distance), β, and m Parameters Used to Define the Nonelectrostatic SDS−H2O and SDS−CO2 Interaction Components

significantly in the 35−100 K temperature range (an increase of 10 meV per K in the 5−35 K temperature range is observed). This behavior is well illustrated in Figure 5 where Ecfg is plotted against T.

interaction partners

ε (meV)

r0 (Å)

β

m

C2−C2 C2−C3 C2−SO C3−SO C3−OW C2−OW S−OW O−OW C3−Na+ C2−Na+ S−Na+ O−Na+ OW−Na+ C1−Na+ C1−C3 C1−C2 C1−S C1−O

10.86 11.70 20.69 22.91 10.56 9.85 6.96 6.96 2.86 2.76 1.75 1.75 151.89 3.374 16.160 14.859 11.017 11.017

3.886 3.919 4.422 4.440 3.850 3.814 3.946 3.946 3.595 3.538 3.742 3.742 2.732 3.760 4.049 4.020 4.127 4.127

8 8 8 8 8 8 8 8 8 8 8 8 6.5 8 8 8 8 8

6 6 6 6 6 6 6 6 6 6 6 6 4 6 6 6 6 6

Figure 5. SDS−CO2 configuration energy plotted as a function of T.

In order to illustrate in more detail the SDS−CO2 structure, the distribution of some distances during the trajectory evolution is shown in Figure 6 as a histogram. The histogram

equilibrium geometry occurs when the additive interacts with CO2. For illustrative purposes, a typical configuration obtained from MD simulations at 10 K is shown as a pseudo tridimensional picture in Figure 4 (similar structures are obtained also at higher temperature).

Figure 6. S−C1, S−Na, and C1−Na distance distributions obtained at 60 K along 10 ns.

confirms that Na+ interacts with both the CO2 molecule and the polar head of the SDS molecule. However, the larger S− CO2 distances (though slightly smaller than those obtained for SDS−CH4)11 suggest that for the S−CO2 pair, the interaction is weaker than for the Na+−CO2 one. 4.2. SDS−CO2 Hydrated System. The above-mentioned (completely different) calculated SDS−CO2 and SDS−CH4 microscopic behaviors clearly indicate that one cannot invoke for carbon dioxide the same clathrate hydrate formation mechanism found for methane. In fact, the strong distortion of the SDS molecular geometry induced by its interaction with CO2 (as shown in Figure 4, the SDS molecule folds to form a kind of helix) persists when adding water molecules. This completely differs from the behavior of SDS with CH4 (that does not lead to such radical molecular geometry deformation) and allows the additive to freely exert its full action in driving water molecules to form a basket trapping methane into a clathrate hydrate structure.11 The observed microscopic behavior prevents a single SDS molecule from acting as catalyst of the CO2 clathrate hydrate formation. Such effect was further investigated by carrying out MD calculations in which one carbon dioxide molecule was set close to a SDS one and the two species were surrounded, as previously done for methane,11 by a quite large ensemble of 2043 flexible water molecules. To carry out related calculations, the intramolecular interactions of flexible water49 were again described, as in our

Figure 4. SDS−CO2 structure obtained from NVE MD simulations at 10 K.

Bearing in mind that, as already mentioned, the values of αCH4 and αCO2 are similar, the different behavior of SDS−CH4 and SDS−CO2 has to be attributed to the different strength of the electrostatic component of the interaction. As a matter of fact, this is a direct consequence of the highly anisotropic distribution of the charges on the carbon dioxide molecule (that is responsible for its quadrupole moment) whose distortion effect on SDS is large even when MD simulations are performed at high temperature. Because of this, the SDS molecule loses its shape (in order to face CO2 with both its polar and apolar ends) and becomes unable to exert any significant driving activity with respect to the water molecules. The mean configuration energy, Ecfg, increases appreciably with T at temperatures below 35 K, while it does not vary G



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study of methane clathrate hydrates, by means of harmonic bonds and angles. The outcomes of the MD calculations indicate that, over the whole range of temperature values of the investigation, the SDS molecule of the SDS−CO2 hydrated system remains largely distorted (as already seen for pure SDS−CO2) even if the SDS−CO2 interaction is to a certain extent weaker (i.e., less negative) making the average intermolecular distance between the two molecules larger. As already anticipated, this prevents the formation of any specific ordered structure when water molecules surround SDS and CO2. As a matter of fact, when SDS is added to the CO2−H2O system, contrary to what is observed when no SDS is added, the OW−C1 RDF shows a single peak at 4.0 Å. This indicates the existence of only one structure, in agreement with MD trajectory data, from which not ordered structures are observed. An illustration of this is given in some detail in Figure 7 where in panels a−c the Figure 8. Radial distribution functions for OW−C1 (top panel) and OW−OW (lower panel) derived from MD simulations at 275 K temperature and at p = 8 MPa. The electrostatic charges of CO2 have been taken equal to zero.

shown in the lower panel of Figure 8 is also similar to the one obtained for methane clathrate hydrate. This indicates that the modulation of the electrostatic interaction is a key factor in determining the different behavior of CO2 and CH4 in forming clathrate hydrates and that this approach is well suited to support the search for designing a new catalyzer for the clathrate hydrates production.

Figure 7. CO2 and the closer 39 (a), 88 (b), and 199 (c) water molecules. SDS is also represented. The arrow indicates the position of the carbon atom of CO2.

5. CONCLUDING REMARKS The microscopic dynamics of the water−carbon dioxide systems, investigated using MD calculations performed with and without the presence of a SDS molecule, has offered significant clues on the microscopic mechanisms governing the formation of CO2 clathrate hydrates, pointing out their different nature from that of the CH4 ones, previously investigated.11 The first clue is the fact that MD simulations performed at proper p and T conditions confirm the ability of pure water solutions of CO2 to form clathrate hydrate structures. The second (and most important) clue is the fact that the individual pair intermolecular interactions, characterizing the SDS−guest molecule systems, are such that the SDS− CO2 and SDS−CH4 behaviors are completely different. This is due to the very strong distortion of SDS in the interaction with carbon dioxide. Such an effect persists when further CO2 molecules are added, as pointed out by further MD calculations performed at a pressure of 8 MPa, there are several temperature values, and an increasing number (from 1 to 50) of carbon dioxide molecules are surrounded by 256 molecules of H2O. Another indication obtained from the MD calculations is the fact that the mean diffusion coefficient of CO2 in water remains unchanged when increasing T in the range of temperature values relevant to the formation of clathrate hydrates structures. This occurs because at low temperature the CO2 mobility increases with T and at high temperature the water cages surrounding the trapped carbon dioxide molecules break down and leave CO2 a higher freedom to diffuse. Additional clues offered by the microscopic study are some information on the characteristics of the water−carbon dioxide structures, on the radial distribution functions (see Figure 3) of both the carbon atom of CO2 and the oxygen atom of H2O, which were found to be similar to those obtained when CO2 is

systems made of the 39, 88, and 199 H2O molecules closer to the CO2 one are graphically represented in a pseudo tridimensional picture, respectively. This agrees with recent experimental findings,50 which indicate that an addition of SDS (0.3 wt %) does not lead to the observation of CO2 clathrate hydrate formation even if the dissolution of carbon dioxide in water becomes more rapid. To investigate whether the different masses of CO2 and CH4 play a role in differentiating the ability of SDS in promoting the formation of the related clathrate hydrates, we carried out additional MD calculations by artificially assigning to CO2 the same molecular mass of CH4 (i.e., by giving to the O atoms of CO2 a mass of 2 au). The outcomes of such calculations show that also in this case (as for the true O mass) the SDS molecule gets distorted and the RDFs is single peaked. To probe the role played by the electrostatic interaction, additional MD calculations were also performed by setting equal to zero the charges placed on CO2, while all the other initial conditions were set equal to those of the runs performed with the electrostatically charged CO2 molecule. In this case, as shown in the top panel of Figure 8, the shoulder of the OW−C1 RDF also vanishes, showing a single peak (which appears at a shorter distance than before), indicating again the persistence of only one structure that, in this case, is an ordered one. As a matter of fact, the OW−C1 RDF obtained at 275 K peaks at 3.725 Å (like the one observed between the O atoms of H2O and the C atom of CH4 in our previous study on the formation of methane clathrate hydrates).11 This similarity is well in line with the fact that the molecular polarizability of CO2 and CH4 is similar, and the electrostatic contributions (because of the suppression of electrostatic charges on the CO2 molecule) become now comparable. Moreover, the OW−OW RDF H



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(11) Albertí, M.; Costantini, A.; Laganà, A.; Pirani, F. Are Micelles Needed to Form Methane Hydrates in Sodium Dodecyl Sulfate Solutions? J. Phys. Chem. B 2012, 116, 4220−4227. (12) Olney, T. N.; Cann, N. M.; Cooper, G.; Brion, C. E. Absolute Scale Determination for Photoabsorption Spectra and the Calculation of Molecular Properties Using Dipole Sum Rules. Chem. Phys. 1997, 223, 59−98. (13) Cappelletti, D.; Ronca, E.; Belpassi, L.; Tarantelli, F.; Pirani, F. Revealing Charge-Transfer Effects in Gas-Phase Water Chemistry. Acc. Chem. Res. 2012, 45, 1571−1580. (14) Cappelletti, D.; Candori, P.; Falcinelli, S.; Albertí, M.; Pirani, F. A Molecular Beam Scattering Investigation of Methanol-Noble Gas Complexes: Characterization of the Isotropic Potential and Insights into the Nature of the Interaction. Chem. Phys. Lett. 2012, 545, 14−20. (15) Costantini, A.; Gervasi, O.; Manuali, C.; Faginas Lago, N.; Rampino, S.; Laganà, A. COMPCHEM: Progress Towards GEMS a Grid Empowered Molecular Simulator and Beyond. J. Grid Comput. 2010, 8, 571−586. (16) Frenkel, D.; Smit, B. Understanding Molecular Simulations; Academic Press: New York, 2002. (17) Bruce, C. D.; Berkowitz, M. L.; Perera, L.; Forbes, M. D. E. Molecular Dynamics Simulation of Sodium Dodecyl Sulfate Micelle in Water: Micellar Structural Characteristics and Counterion Distribution. J. Phys. Chem. B 2002, 106, 3788−3793. (18) Faginas Lago, N.; Huarte-Larragaña, F.; Albertí, M. On the Ssuitability of the ILJ Function To Match Different Formulations of the Electrostatic Potential for Water−Water Interactions. Eur. Phys. J. D 2009, 55, 75−85. (19) Albertí, M.; Aguilar, A.; Bartolomei, M.; Cappelletti, D.; Laganà, A.; Lucas, J. M.; Pirani, F. Small Water Clusters: The Cases of Rare Gas-Water, Alkali Ion-Water and Water Dimer. Lect. Notes Comput. Sci. Eng. 2008, 5072, 1026−1035. (20) Albertí, M.; Aguilar, A.; Cappelletti, D.; Laganà, A.; Pirani, F. On the Development of an Effective Model Potential To Describe Water Interaction in Neutral and Ionic Clusters. Int. J. Mass Spectrom. 2009, 280, 50−56. (21) Albertí, M.; Aguilar, A.; Bartolomei, M.; Cappelletti, D.; Laganà, A.; Lucas, J. M.; Pirani, F. A Study To Improve the van der Waals Component of the Interaction in Water Clusters. Phys. Scr. 2008, 78, 058108(1)−058108(7). (22) Paolantoni, M.; Faginas Lago, N.; Albertí, M.; Laganà, A. Tetrahedral Ordering in Water: Raman Profiles and Their Temperature Dependence. J. Phys. Chem. A 2009, 113, 15100−15105. (23) Albertí, M.; Faginas Lago, N.; Laganà, A.; Pirani, F. A Portable Intermolecular Potential for Molecular Dynamics Sstudies of NMANMA and NMA-H2O aggregates. Phys. Chem. Chem. Phys. 2011, 13, 8422−8432. (24) Albertí, M.; Faginas Lago, N.; Pirani, F. Benzene Water Interaction: From Gaseous Dimers To Solvated Aggregates. Chem. Phys. 2012, 399, 232−239. (25) Albertí, M.; Aguilar, A.; Lucas, J. M.; Pirani, F. Competitive Role of CH4−CH4 and CH−π Interactions in C6H6−(CH4)n Aggregates: The Transition from Dimer to Cluster Features. J. Phys. Chem. A 2012, 116, 5480−5490. (26) Costantini, A.; Albertí, M.; Pirani, F.; Laganà, A. A Molecular Dynamics Study of Sodium Dodecyl Sulfate-Methane System in Water Using the Improved Lennard Jones Formulation. Int. J. Quantum Chem. 2012, 112, 1810−1817. (27) Pirani, F.; Albertí, M.; Castro, A.; Moix Teixidor, M.; Cappelletti, D. Atom-Bond Pairwise Additive Representation for Intermolecular Potential Energy Surfaces. Chem. Phys. Lett. 2004, 394, 37−44. (28) Pirani, F.; Brizi, S.; Roncaratti, L. F.; Casavecchia, P.; Cappelletti, D.; Vecchiocattivi, F. Beyond the Lennard-Jones Model: A Simple and Accurate Potential Function Probed by High Resolution Scattering Data Useful for Molecular Dynamics Simulations. Phys. Chem. Chem. Phys. 2008, 10, 5489−5503. (29) Pirani, F.; Cappelletti, D.; Liuti, G. Range, Strength and Anisotropy of Intermolecular Forces in Atom−Molecule Systems: An

captured inside some minerals. These properties, however, not only persist just for a limited interval of T but also vanish when adding a SDS molecule (contrary to what is observed in the formation of the methane clathrate). The study showed that the responsibility for such microscopic behavior has to be attributed to the large distortion of the SDS molecule caused by its interaction with CO2. This marks a radical difference between the behavior of CO2 water systems from that of the CH4 ones. Such effect was found, in fact, to be entirely ascribable to the different nature of the electrostatic component of the SDS−CO2 and SDS−CH4 interactions, whereas no appreciable effect could be attributed to the heavier mass of CO2.

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AUTHOR INFORMATION

Corresponding Author

*(M.A.) E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.A. acknowledges financial support from the Ministerio de Educación y Ciencia (Spain, Projects CTQ2010-16709) and the Comissionat per a Universitats i Recerca del DIUE (Generalitat de Catalunya, Project 2009-SGR 17). Also, thanks are due to the SUR and the Departament d’Economia i Coneixement de la Generalitat de Catalunya (Project 2011 ́ i Acadèmics de BE1-00063). The Centre de Serveis Cientifics Catalunya CESCA and Fundació Catalana per a la Recerca are also acknowledged for the allocated supercomputing time. A.L. and F.P. acknowledge financial support from the COST Action CM1002 (CODECS), INSTM, and the Italian Ministry of University and Research (MIUR) for a PRIN Grant.

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REFERENCES

(1) Kvenvolden, K. A. Gas Hydrates-Geological Perspective and Global Change. Rev. Geophys. 1993, 31, 173−187. (2) Okano, Y.; Yasuoka, K. Free-Energy Calculation of Structure-H Hydrates. J. Chem. Phys. 2006, 124, 024510. (3) Koh, C. A.; Sloan, E. D. Natural Gas Hydrates: Recent Advances and Challenges in Energy and Environmental Applications. AIChE J. 2007, 53, 1636−1643. (4) Linga, P.; Adeyemo, A.; Englezos, P. Medium-Pressure Clathrate Hydrate/Membrane Hybrid Process for Postcombustion Capture of Carbon Dioxide. Environ. Sci. Technol. 2007, 42, 315−320. (5) Kumar Srivastava, H.; Narahari Sastry, G. Viability of Clathrate Hydrates As CO2 Capturing Agents: A Theoretical Study. J. Phys. Chem. A 2011, 115, 7633−7637. (6) Alavi, S.; Woo, T. K. How Much Carbon Dioxide Can Be Stored in the Structure H Clathrate Hydrates?: A Molecular Dynamics Study. J. Chem. Phys. 2007, 126, 044703. (7) Sloan, E. D., Jr.; Koh, C. A. Clathrate Hydrates of Natural Gases, 3rd ed.; CRC Press Taylor and Francis: Boca Raton, FL, 2008. (8) Sun, R.; Duan, Z. Prediction of CH4 and CO2 Hydrate Phase Equilibrium and Cage Occupancy from Ab Initio Intermolecular Potentials. Geochim. Cosmochim. Acta 2005, 69, 4411−4424. (9) Zhang, J. S.; Lo, C.; Somasundaran, P.; Lu, A.; Couzis, A.; Lee, J. W. Adsorption of Sodium Dodecyl Sulfate at THF Hydrate/Liquid Interface. J. Phys. Chem. C 2008, 112, 12381−12385. (10) Ning, F.; Jiang, G.; Zhang, L.; Dou, B.; Wu, X. Analysis on Characteristics of Drilling Fluids Invading into Gas Hydrates-Bearing Formation. In Proceedings of the 6th International Conference on Gas Hydrates (ICGH 2008), Vancouver, Canada, July 2008. I



Article

Atom−Bond Pairwise Additivity Approach. Chem. Phys. Lett. 2001, 350, 286−296. (30) Albertí, M.; Aguilar, A.; Lucas, J. M.; Pirani, F. A Generalized Formulation of Ion−π Electron Interactions: Role of the Nonelectrostatic Component and Probe of the Potential Parameter Transferability. J. Phys. Chem. A 2010, 114, 11964−11970. (31) http://www.ccp5.ac.uk/DL_POLY_CLASSIC/. (32) Bartolomei, M.; Pirani, F.; Laganà, A.; Lombardi, A. A Full Dimensional Grid Empowered Simulation of the CO 2 + CO2 Processes. J. Comput. Chem. 2012, 33, 1806−1819. (33) Raghavendra, B.; Arunan, E. Hydrogen Bonding with a Hydrogen Bond: The Methane−Water Complex and the PentaCoordinate Carbon. Chem. Phys. Lett. 2008, 467, 37−40. (34) Sadlej, J.; Mazurek, P. Ab Initio Calculations on the Water− Carbon Dioxide System. J. Mol. Struct. 1995, 337, 129−138. (35) Garden, A. L.; Lane, J. R.; Kjaergaard, G. Counterpoise Corrected Geometries of Hydrated Complexes. J. Chem. Phys. 2006, 125, 144317. (36) Makarewicz, J. Intermolecular Potential Energy Surface of the Water−Carbon Dioxide Complex. J. Chem. Phys. 2010, 132, 234305. (37) Wheatley, R. J.; Harvey, A. H. Intermolecular Potential Energy Surface and Second Virial Coefficients for the Water−CO2 Dimer. J. Chem. Phys. 2011, 134, 134309. (38) Lange de, K. M.; Lane, J. R. Explicit Correlation and Intermolecular Interactions: Investigating Carbon Dioxide Complexes with the CCSD(T)-F12 Method. J. Chem. Phys. 2011, 134, 034301. (39) Sadlej, J.; Makarewicz, J.; Chalasiński, G. Ab Initio Study of Energy, Structure and Dynamics of the Water−Carbon Dioxide Complex. J. Chem. Phys. 1998, 109, 3919−3927. (40) Peterson, K. J.; Klemperer, W. Structure and Internal Rotation of H2O−CO2, HDO−CO2, and D2O−CO2 van der Waals Complexes. J. Chem. Phys. 1984, 80, 2439−2445. (41) Tso, T. L.; Lee, E. K. C. FTIR Spectra of and the Hydrogen Bonding in Matrix-Isolated Molecular Complexes of Hydrogen Oxides, Carbon Monoxide, and Carbon Dioxide Formed in the Photooxidation of Isotopic Formaldehydes and Glyoxal in Sond O2 at 12−15 K. J. Phys. Chem. 1985, 89, 1612−1618. (42) Block, P. A.; Marshall, M. D.; Pedersen, L. G.; Miller, R. E. Wide Amplitude Motion in the Water−Carbon Dioxide and Water− Acetylene Complexes. J. Chem. Phys. 1992, 96, 7321−7332. (43) Columberg, G.; Bauder, A.; Heineking, N.; Stahl, W.; Makarewicz, J. Internal-Rotation Effects and Hyperfine-Structure in the Rotational Spectrum of Water−Carbon Dioxide Complex. Mol. Phys. 1998, 93, 215−228. (44) Liu, K.; Brown, M. G.; Saykally, R. Terahertz Laser VibrationRotation Tunneling Spectroscopy and Dipole Moment of a Cage Form of the Water Hexamer. J. Phys. Chem. A 1997, 101, 8995−9010. (45) Gregory, J. K.; Clary, D. C.; Liu, K.; Brown, M. G.; Saykally, R. J. The Water Dipole Moment in Water Clusters. Science 1997, 275, 814−817. (46) Henning, R. W.; Shultz, A. J.; Thieu, V.; Halpern, Y. Neutron Diffraction Studies of CO2 Clathrate Hydrate: Formation from Deuterated Ice. J. Phys. Chem. A 2000, 104, 5066−5071. (47) Cygan, R. T.; Romanov, V. N.; Myshakin, E. M. Molecular Simulation of Carbon Dioxide Capture by Montmorillonite Using an Accurate and Flexible Force Field. J. Phys. Chem. C 2012, 116, 13079− 13091. (48) Amber Force Field Parameters. http://ambermd.org/dbase. html. (49) Wallqvist, A.; Teleman, O. Properties of Flexible Water Molecules. Mol. Phys. 1991, 74, 515−533. (50) Torré, J. P.; Ricaurte, M.; Dicharry, C.; Broseta, D. CO2 Enclathration in the Presence of Water-Soluble Hydrate Promoters: Hydrate Phase Equilibria and Kinetic Studies in Quiescent Conditions. Chem. Eng. Sci. 2012, 82, 1−13.

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Carbon Dioxide Clathrate Hydrates: Selective Role of Intermolecular

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