Article pubs.acs.org/JPCA
High-Level Ab Initio Predictions of the Energetics of mCO2·(H2O)n (n = 1−3, m = 1−12) Clusters K. Sahan Thanthiriwatte,† Jessica R. Duke,† Virgil E. Jackson,† Andrew R. Felmy,‡ and David A. Dixon*,† †
Department of Chemistry, The University of Alabama, Shelby Hall, Box 870336, Tuscaloosa, Alabama 35487-0336, United States Fundamental and Computational Sciences Division, Pacific Northwest National Laboratory, Richland, Washington 99352, United States
‡
S Supporting Information *
ABSTRACT: Electronic structure calculations at the correlated molecular orbital theory and density functional theory levels have been used to generate a reliable set of clustering energies for up to three water molecules in carbon dioxide clusters up to n = 12. The structures and energetics are dominated by Lewis acid−base interactions with hydrogen-bonding interactions playing a lesser energetic role. The actual binding energies are somewhat larger than might be expected. The correlated molecular orbital MP2 method and density functional theory with the ωB97X exchange−correlation functional provide good results for the energetics of the clusters, but the B3LYP and ωB97X-D functionals do not. Seven CO2 molecules form the first solvent shell about a single H2O with four CO2 molecules interacting with the H2O via Lewis acid−base interactions, two CO2 interacting with the H2O by hydrogen bonds, and the seventh CO2 completing the shell. The Lewis acid−base and weak hydrogen bond interactions between the water molecules and the CO2 molecules are strong enough to disrupt the trimer ring configuration for as few as seven CO2 molecules. Calculated 13C NMR chemical shifts for mCO2·(H2O)n show little change with respect to the number of H2O or CO2 molecules in the cluster. The O−H stretching frequencies do exhibit shifts that can provide information about the interactions between water and CO2 molecules.
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INTRODUCTION Carbon dioxide emissions has been implicated as a prime component of global warming, and reducing the quantities of CO2 released into the atmosphere is of high importance.1−4 The capture and storage of CO2 and other greenhouse gases in deep geologic formations represents one of the most promising options for mitigating the impacts of greenhouse gases on global warming owing to the potentially large capacity of these formations and their broad regional availability.5−11 A critical issue is demonstrating that CO2 will remain stored over the long-term in the geological formation where it is injected. Mineral−fluid interactions are of prime importance since such reactions can result in the long-term sequestration of CO2 by trapping in mineral phases such as carbonates as well as influencing the subsurface migration of the disposed fluids via creation or plugging of pores or fractures in the host rock strata.12−14 The CO2 will most likely be injected as a supercritical fluid and will probably contain some water either in the initial injection or as it travels from the injection site.15−20 In order to develop new molecular models of how such chemistry may occur, we need to understand the properties of CO2·H2O clusters. With a zero dipole moment and a low dielectric constant, CO2 is normally considered a nonpolar solvent and thus should not be appropriate for the dissolution of polar molecules such as H2O, metal complexes, etc.21 However, due to a large charge separation between the C and O in a bond and the quadrupole © 2012 American Chemical Society
moment of CO2, it can act as a weak Lewis acid and participate in bonding with a polar Lewis base such as H2O via the Lewis acidic carbon.22−32 This moderate interaction, which we label as a Lewis acid−base interaction following other work to distinguish it from hydrogen-bond interactions, is dominated by electrostatic interactions rather than HOMO−LUMO overlaps as found in complexes such as BH3NH3 with a much stronger interaction.33 The dissolution of water in the CO2-rich phase has been shown to increase the molecular polarity and thus the solvent strength of the CO2-rich phase34−36 A number of studies have observed a weak OCO2···HW secondary interaction between CO2 and H2O, which can play a role in the structure of the complex.24−26,31,37 With Lewis bases like H2O, metal complexes, or other O/N-containing organic compounds (alcohols, ketones, amines, and amides), CO2 behaves as a Lewis acid and can form weak electron acceptor−donor complexes.24−27,30,38−41 Numerous experimental studies of small binary molecular systems of H2O/CO2 including matrix isolation IR experiments28,30−32,37−48 and gas-phase molecular beam experiments,49 as well as theoretical studies,22,50−60 are available for the description of their structures, energetics, spectroscopic properties, and reactions. The reaction of CO2 with water Received: July 3, 2012 Revised: August 27, 2012 Published: August 27, 2012 9718
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clusters (mCO2·nH2O, n > 1), the hydration of CO2 including the formation of carbonic acid, has been the subject of extensive studies.22,29,61−67 Several experimental studies have confirmed that the water is almost “free” (monomeric) in supercritical CO2 (sc-CO2). In the presence of ions in sc-CO2, the water aggregates about the ion leading to a more bulklike (hydrogenbonded) water.47,48 The dissolution of water in sc-CO2 has been shown to increase the molecular polarity of the CO2 and thus the solvent strength of the CO2-rich phase68 The intermolecular interactions of H2O molecules with CO2 clusters, mCO2·nH2O (where m > 1), provides a first step in understanding “wet-sc-CO2”, but only a few studies are available. A combined infrared and classical molecular dynamics study using density functional theory (DFT) of D2O rotational relaxation in supercritical CO2 showed that the rotation of water in CO2 was hindered due to dipole−quadrupole interactions between H2O and CO2.69 Ortega et al.70 studied small clusters of mCO2·nH2O as a model for co-condensation/ nucleation processes in the Martian atmosphere using DFT at the B3LYP/DZP level and the RI-CC2/aug-cc-pVTZ method. Glezakou studied the formation of water clusters in sc-CO2 using density functional theory-based molecular dynamics.71 They found that the basic sc-CO2 structure is preserved and that water clusters were formed at higher water concentrations. To our knowledge, CO2 clusters with more than a single water molecule have not been studied by employing ab initio molecular orbital theory at the CCSD(T)/CBS level and at the DFT level. In the present study, the structures of mCO2·(H2O)n clusters for n = 1−3 as a function of the number of CO2 molecules in the cluster have been studied to gain an understanding and better insight into the properties of such clusters.
frequencies. The most stable conformer was chosen if two or more stable cluster conformations were available. The geometry optimizations of some of these clusters can take hundreds of steps and geometry convergence can be difficult due to the weak interactions and thus the flexible structure of the cluster. Single point energy evaluations were also performed with the ωB97X-D86 functional with the aug-cc-pVTZ basis set at the MP2/aug-cc-pVTZ- and B3LYP/aug-cc-pVTZ-optimized geometries. All of the DFT computations were performed with the standard grid in Gaussian 09 for numerically integrating the exchange−correlation contributions. All DFT and MP2 geometry optimizations and frequency calculations were done with the Gaussian 0987 program We calculated electronic energies extrapolated to the CBS limit using the MP2, RI-MP2,88 and CCSD(T) methods using aug-cc-pVnZ (n = D, T, Q) basis sets for the smaller mCO2·(H2O)n clusters using the MP2 geometries. The CCSD(T)/aug-cc-pVnZ energies were extrapolated using a mixed exponential/Gaussian function of the form: E(n) = ECBS + A exp[− (n − 1)] + B exp[− (n − 1)2 ] (1)
as first proposed by Peterson et al.89 with n = 2(D), 3(T), and 4(Q). We estimated the CCSD(T)/CBS energies for selected larger clusters by extrapolating to the CBS MP2 limit using eq 1 and adding in a “coupled-cluster correction”, ΔE(CCSD(T)), estimated as the difference between E(CCSD(T)) and E(MP2) with the aug-cc-pVTZ basis set ECBS(CCSD(T)) ≈ ECBS(MP2) + ΔE(CCSD(T))
(2)
where
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ΔE(CCSD(T)) = E(CCSD(T)/aug‐cc‐pVTZ)
COMPUTATIONAL PROCEDURE Density functional theory (DFT)72 is currently one of the most widely used electronic structure methods due to its computational efficiency. However, the application of DFT to the calculation of structures dominated by noncovalent interactions, is hampered by the failure of most common density functionals to properly describe the long-range electron correlation involved in weak interactions.73−77 Reliable computations of such interactions typically require a correlated molecular orbital approach at least at the second-order perturbation theory (MP2) level78,79 or higher levels such as coupled-cluster singles and doubles substitutions with perturbatively connected triples, CCSD(T).80 However, the computational scaling of CCSD(T) O(N7), where N is the number of basis functions, is high so that larger clusters cannot be studied, especially with the size of basis sets needed for convergence to the complete basis set limit. Thus, we explored which DFT functionals can provide a reasonable description of the structures, clustering energetics, and vibrational spectra of such clusters. The geometries of the mCO2·(H2O)n (n = 1−3 and m = 1− 12) clusters were optimized with the B3LYP,81 PW91,82 PBE,83 and ωB97X84 functionals with the augmented correlationconsistent aug-cc-pVTZ (aTZ) basis set.85 The aug-cc-pVTZ basis set was chosen for the DFT calculations because of the presence of weak interactions. The structures of many of the smaller clusters were also optimized at the MP2 level with the aug-cc-pVDZ (aDZ) and aug-cc-pVTZ basis sets. Second derivative calculations were used to show that the optimized geometries were minima and to provide harmonic vibrational
− E(MP2/aug‐cc‐pVTZ)
(3)
The electronic interaction energy (Eint(elec)) is given by eq 4 with each structure at an optimized geometry. E int(elec) = Eelec(nCO2 ·mH 2O) − nEelec(CO2 ) − mEelec(H 2O)
(4)
The CCSD(T) and RI-MP2 computations were carried out with the MOLPRO201090 package of ab initio programs. 13 C NMR chemical shifts were calculated with the ADF program system91 with the BLYP functional92 and the TZ2P basis set93 in ADF. The NMR calculations were done in the gauge invariant atomic orbital (GIAO) approach94 at the DFT level based on the developments in the Ziegler group.95,96
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RESULTS AND DISCUSSION Total energies; MP2-, B3LYP-, and ωB97X-optimized geometry parameters with the aTZ basis set; and harmonic frequencies are in the Supporting Information. Geometries. Structures for sequential addition of CO2 molecules to the water monomer, dimer, and trimer are presented in Figures 1, 2, and 3, respectively. From experiment, the structure of H2O·CO2 is planar and T-shaped with C2v symmetry31,37,46,29,65 with a OW···CCO2 distance of 2.836 Å.46 The OW···CCO2 distance 2.773 Å, obtained at the MP2/aug-ccpVTZ level, is in reasonable agreement with experiment and with the other theoretical values.31,37 This structure is best described as a Lewis acid (CO2)/Lewis base (H2O) adduct. 9719
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Another local minimum has been reported at the MP2/TZ2P level corresponding to a complex having a hydrogen-bonded arrangement of the moieties with an intermolecular distance OCO2···OW of ∼4.25 Å.29,65 This structure is 1.1 kcal/mol above the T-shaped Lewis adduct at this level and calculations of the energy up to MP4(SDTQ)/TZ2P do not change the relative energies by more than a few cm−1. This structure is difficult to find, as there is essentially no barrier between it and the Lewis adduct structure. The various energy values are shown in Table 1 and show that the Lewis acid−base adduct structure is 0.8 Table 1. Relative Energetics of Lewis Acid/Base Adduct (LAB) and H-Bonded (HB) Structures of CO2·H2O in kcal/ mol
Figure 1. Sequential addition of CO2 molecules to H2O. Optimized structures of mCO2·H2O (m = 1−12) clusters.
energya
LAB → HB
ΔEelec(MP2/aTZ) ΔEelec(MP2/CBS) ΔEelec(CCSD(T)/CBS) ΔHrx(0K) ΔHrx(298K) ΔGrx(298K)
0.82 1.12 1.21 0.90 0.89 0.35
a
The CBS extrapolations and harmonic vibrational calculations were performed using the MP2/aVTZ-optimized geometries.
kcal/mol lower at the MP2/aug-cc-pVTZ for the electronic energy, and this difference reduces to 0.35 kcal/mol for ΔG298 due to the presence of one additional small frequency in the hydrogen-bonded structure. The electronic energy difference between the H-bonded structure and the Lewis adduct is 1.2 kcal/mol at the CCSD(T)/CBS level. The results show that the surface for binding H2O to CO2 is very flat all around the CO2 molecule within about 1 kcal/mol, so the H2O is bound by 7) clusters leads to the formation of a second solvation shell. The eighth CO2 molecule is clearly outside the first shell with a CCO2···OW distance of 5.25 Å. The dominant interaction of the second shell CO2 molecules is formation of a pseudo-T-shaped CCO2···OCO2 Lewis acid−base complex with an intermolecular distance of ∼3.0 to ∼3.2 Å in the outer shell. These outer shell CO2 molecules can also interact with the inner shell CO2 molecules through the T-shaped CCO2···OCO2 Lewis acid−base bonds. These types of interactions in the outer solvation shell resemble the pseudo-T-shape CCO2···OCO2 found in (CO2)n clusters as noted above. Lewis acid−base interactions CCO2···OW and CCO2···OCO2 (
