Structures and Energetics of (MgCO3)n Clusters (n ≤ 16) - The

Article pubs.acs.org/JPCA

Structures and Energetics of (MgCO3)n Clusters (n ≤ 16) Mingyang Chen,† Virgil E. Jackson,‡ Andrew R. Felmy,§ and David A. Dixon*,‡ †

National Center for Computational Sciences, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, United States Department of Chemistry, The University of Alabama, Shelby Hall, Tuscaloosa, Alabama 35487-0336, United States § Fundamental Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington 99352, United States ‡

S Supporting Information *

ABSTRACT: There is significant interest in the role of carbonate minerals for the storage of CO2 and the role of prenucleation clusters in their formation. Global minima for (MgCO3)n (n ≤ 16) structures were optimized using a tree growth−hybrid genetic algorithm in conjunction with MNDO/MNDO/d semiempirical molecular orbital calculations followed by density functional theory geometry optimizations with the B3LYP functional. The most stable isomers for (MgCO3)n (n < 5) are approximately 2-dimensional. Mg can be bonded to one or two O atoms of a CO32−, and the 1-O bonding scheme is more favored as the cluster becomes larger. The average C−Mg coordination number increases as the cluster size increases, and at n = 16, the average C−Mg coordination number was calculated to be 5.2. The normalized dissociation energy to form monomers increases as n increases. At n = 16, the normalized dissociation energy is calculated to be 116.2 kcal/mol, as compared to the bulk value of 153.9 kcal/mol. The adiabatic reaction energies for the recombination reactions of (MgO)n clusters and CO2 to form (MgCO3)n were calculated. The exothermicity of the normalized recombination energy ⟨RE⟩CO2 decreases as n increases and converged to the experimental bulk limit rapidly. The normalized recombination energy ⟨RE⟩CO2 was calculated to be −52.2 kcal/mol for the monomer and −30.7 kcal/mol for n = 16, as compared to the experimental value of −27.9 kcal/mol for the solid phase reaction. Infrared spectra for the lowest energy isomers were calculated, and absorption bands in the previous experimental infrared studies were assigned with our density functional theory predictions. The 13C, 17O, and 25 Mg NMR chemical shifts for the clusters were predicted. The results provide insights into the structural and energetic transitions from nanoclusters of (MgCO3)n to the bulk and the spectroscopic properties of clusters for their experimental identification.

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INTRODUCTION Magnesium carbonate (MgCO3) is of broad interest in a number of scientific areas. Bulk MgCO3 can be utilized as precursors and catalysts for the preparation of bulk and nanomaterials.1−5 MgCO3 minerals may play an important role in the mitigation of global warming, as MgCO3 is the product of CO2 capture reactions from aqueous Mg2+ or from mineral reactions. In many of these applications, changing the particle size can impact the mechanical, physical, and chemical properties of MgCO3, such as surface adsorption rate and catalytic reactivity,6,7 as a result of topological changes such as surface−volume ratio and density of the defect sites that vary with the particle size. There is substantial interest in the process of biomineralization, for example, the formation of amorphous calcium carbonate,8 and it has been suggested that nanoclusters play a role in such processes.9−12 The structures of nanoclusters of magnesium carbonate clusters are of interest in terms of whether they can serve as precursors to the formation of amorphous magnesium carbonate. To understand the chemical processes of MgCO3 that are affected by the particle size and to utilize the material more efficiently in different applications, the investigation of different particle sizes, especially nanoclusters, © 2015 American Chemical Society

of MgCO3 is important. Additionally, the reaction of MgO with CO2 to form MgCO3 is of interest, as this reaction is important for CO2 capture and long-term sequestration.13−15 Minerals of MgCO3, especially its most common anhydrous form in the earth’s mantle, magnesite, have been extensively studied.16−20 The di-, tri-, and pentahydrates are barringtonite (MgCO3·2H2O), nesquehonite (MgCO3·3H2O), and lansfordite (MgCO3·5H2O). The crystal structure of MgCO3 magnesite has been determined by X-ray diffraction studies.21−23 The infrared spectra of MgCO3 were measured from ambient pressure to high pressure by Grzechnik et al.24 and also reported in a more recent study of octavite−magnesite solid solution by Bromiley et al.17 The valence orbital binding energies of Mg, C, and O in dypingite ((MgCO3)4·Mg(OH)2·5H2O) were measured using XPS.25 Catti et al. first calculated the structural and electron properties of magnesite using a periodic Hartree−Fock method, in which the calculated structural parameters agree well with the experimental data.26 They showed that the C−O interactions Received: November 26, 2014 Revised: March 12, 2015 Published: March 13, 2015 3419

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The Journal of Physical Chemistry A

Zero point energy (ZPE) corrections were included in ⟨DE⟩. ZPE’s are obtained from the vibrational frequency calculations using the optimized geometry at the B3LYP/DZVP level. The gas phase heats of formation of the (MgCO3)n clusters at 298 K, ΔHf(n), were calculated using eq 2:

are covalent bonds and that the Mg−O interactions are mainly ionic. Hossain et al. calculated the indirect band gap of magnesite to be 5.0 eV using first-principles density functional theory and predicted the fundamental absorption edge to be ∼6 eV using the scissors approximation.27 Brik calculated the structural, electronic, optical, and elastic properties of magnesite using a first-principles method with the Perdew− Burke−Ernzerhof GGA function or the Ceperly−Alder− Perdew−Zunger LDA parametrization and predicted a significant band gap of 5.08 eV for magnesite.28 Zhuravlev and Poplavnoi ̆ calculated the electron density of the MgCO3 crystal using local density functional theory (DFT) and the sublattice technique29 and obtained an electron density that is in good agreement with Malsen et al.’s X-ray experiment.23 Although there are a number of studies on small CaCO3 nanoclusters,10−12 there have only been a few theoretical studies of small MgCO3 clusters. The structures of Mg(CO3)nm− (n = 1−3, m = 0, −2, −4) were studied as part of an effort to develop isotope fractionation factors for carbonates using density functional theory and correlated molecular orbital theory.30,31 Solvated MgCO3 has also been studied by Car−Parrinello density functional theory simulations.32 MgCO3 nanoclusters are bridges between molecule and crystal structures and thus can exhibit interesting properties. They can also serve as prenucleation clusters leading to mineral formation. The task of predicting the structures of (MgCO3)n clusters is difficult because it has three atom types, which can lead to many local energy minima on the potential energy surfaces of (MgCO3)n, even for the small clusters. Fortunately, the CO32− in (MgCO3)n is a covalently bonded moiety and can be treated as a rigid planar group for the generation of initial structures. Our tree growth−hybrid genetic algorithm (TG-HGA)33 is a global geometry optimization approach that can search for the global minima of clusters progressively. The tree growth algorithm (TG) is used to generate initial structures from scratch that are taken as input by the hybrid genetic algorithm (HGA). HGA is a variation of the genetic algorithm (GA), in which relaxation is performed between the crossover and evaluation operations. The TG-HGA has been successfully applied in the study of metal and metal oxide clusters33−35 and can be extended to more complex mineral clusters by treating chemical groups (such as CO32−) as fragments. To the best of our knowledge, there has not been a systematic theoretical study of (MgCO3)n clusters. In this work, we use a modified version of the TG-HGA where biases were imposed on the geometries to enforce the rigid planar CO3 groups to reduce the search space for the global minima for the (MgCO3)n clusters.

ΔHf (n) = n(ΔHf (1) − ⟨DE⟩(n))

where ΔHf(1) is the heats of formation for the MgCO3 monomer calculated using the Feller−Peterson−Dixon (FPD) method46−49 at the CCSD(T)/CBS (coupled cluster with single and double excitations and an approximate triples correction50 extrapolated to the complete basis set limit using the correlation-consistent basis sets51,52) level with additional corrections. This follows the approach used previously for the MgO monomer.53 The CCSD(T) energies included the outer 2s and 2p core electrons on the group IIB elements and the 1s electrons on the C and O and were extrapolated to the complete basis set limit using the aug-cc-pWCTZ basis sets for N = D, T, and Q using a mixed exponential/Gaussian function of the form54 E(n) = ECBS + A exp[− (n − 1)] + B exp[− (n − 1)2 ] (3)

Zero point energies were taken from the DFT calculations. Scalar relativistic effects were obtained from the expectation values for the two dominant terms in the Breit−Pauli Hamiltonian (the mass-velocity and one-electron Darwin (MVD) corrections)55 from configuration interaction singles and doubles (CISD) calculations with the aug-cc-pWCTZ basis set. The atomic spin−orbit corrections for the atoms were calculated from the experimental values of their respective ground states and are ΔESO(C) = 0.07 kcal/mol and ΔESO(O) = 0.223 kcal/mol.56 The normalized reaction energies for the CO2 dissociation reactions (MgCO3)n → (MgO)n + nCO2

(4)

were calculated using eq 5 ⟨DE⟩(n)CO2 = E(CO2 ) + (E((MgO)n ) − E((MgCO3)n ))/n (5)

and the normalized CO2 recombination energy ⟨RE⟩(n)CO2 for (MgO)n is the negative of ⟨DE⟩(n)CO2 ⟨RE⟩(n)CO2 = −⟨DE⟩(n)CO2

(6)

The geometries and DFT energies for the (MgO)n clusters are taken from our previous work.34 The DFT calculations were done with the Gaussian09 program system57 and the CCSD(T) calculations with the Molpro program system.58 Modified TG-HGA. A detailed description for the TG-HGA can be found in our previous work.33 In the TG algorithm, the clusters grow from a small seed to the size of interest stepwise. New atoms are added to the smaller clusters from the previous step, by analogy to new leaves grown by a tree. The addition of the new atoms is controlled by predefined rigid geometry parameters to reduce the size of the search space and to provide physically meaningful structures. In each step, the energies for the various generated structures are evaluated with low-cost pairwise potentials (see Supporting Information for parameters),59−61 and those with the lowest energies for each molecular formula are carried into the next step. The structures that

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COMPUTATIONAL METHODS The initial structures for the search of the global minima of (MgCO3)n clusters were generated using a modified version of our TG-HGA.33 The energy evaluation and geometry optimization during the hybrid genetic algorithm steps were done using the MNDO/MNDO/D36−38 semiempirical method in the AMPAC39 program suite. The lowest energy structures generated by TG-HGA were further optimized using density functional theory40−42 with the B3LYP43,44 functional with the DZVP basis set.45 The normalized dissociation energy (⟨DE⟩) were calculated for the (MgCO3)n → nMgCO3 reaction, given by eq 1: ⟨DE⟩(n) = E(MgCO3) − E((MgCO3)n )/n

(2)

(1) 3420

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C2v symmetry and is calculated to be only 3.0 kcal/mol higher in energy than 5a. Thus, there are a number of structures that are very close in energy for n = 5, and all might be present at equilibrium given the accuracy of the computational method. Starting from n = 5, the puckered rings are no longer the lowest energy isomers for (MgCO3)n. The lowest energy C3 symmetry structure for (MgCO3)6 (6a) has a center Mg incorporating six −O−CO2 moieties. The five outer Mg’s occupy the trigonalbipyramidal coordination sites around the central Mg. A C2 isomer and a C1 isomer (6b and 6c) are 2.1 and 5.5 kcal/mol higher in energy than 6a. The lowest energy isomer for (MgCO3)7 has C1 symmetry (7a). A Cs structure (7b) and a C2 isomer (7e) are found to be 5.1 and 10.4 kcal/mol higher in energy than 7a. Structures 7c and 7d are 6.0 and 7.3 kcal/mol higher in energy than 7a and are distorted isomers of a higher energy structure 7e. The lowest energy isomer 8a for (MgCO3)8 is predicted to have Cs symmetry. Structures 8b, 8c, and 8d with C1 symmetry are only 2.8, 4.1, and 4.2 kcal/mol higher in energy than 8a, respectively, again continuing with the theme of a number of low energy structures. The lowest energy (MgCO3)9 nanocluster 9a has C1 symmetry with no terminal O’s. A C1 structure 9b with one terminal O is calculated to be only 0.1 kcal/mol higher in energy than 9a. A Cs isomer 9c with one terminal O is found to be 1.4 kcal/mol less stable than structure 9a. Again, there are a number of different structures with comparable energies. Structure 10a with C1 symmetry is calculated to be the lowest energy isomer for (MgCO3)10. A C1 isomer (10b) and a Cs isomer (10c) are found to be 2.2 and 4.3 kcal/mol higher in energy than structure 10a. A more compact isomer with C2 symmetry (10d) is 11.1 kcal/mol less stable than structure 10a. All of the low energy (MgCO3)11 isomers have C1 symmetry. Structure 11a is the lowest energy isomer, 0.9 kcal/mol more stable than structure 11b. The lowest energy structure for (MgCO3)12 12a has C1 symmetry. The other two low energy structures 12b and 12c are 4.4 and 5.0 kcal/mol higher in energy than 12a.The prism-like D4h structure 12d and the antiprism-like D2d structure 12e are significantly less stable. The lowest energy isomer for (MgCO3)16 16a contains an approximate C4 axis. A similar structure, 16b, is predicted to be 5.1 kcal/mol higher in energy. The compact prolate isomer 16c is 14.8 kcal/mol higher in energy than 16a. No terminal oxygen atoms are found in the low energy (MgCO3)10, (MgCO3)11, (MgCO3)12, and (MgCO3)16 isomers. Cluster Structural Evolution. The average coordination numbers (CN) and bond distances for the C−Mg and Mg−O bonds are shown in Table 1. Both the CN and the Mg−O bond distances increase as n increases. The Mg−O bond distances converged quickly to the bulk magnesite value. At n = 6, r(Mg−O) is calculated to be 2.11 Å as compared to the Mg−O distance of 2.10 Å in bulk magnesite. The Mg−O CN’s are converging to the bulk value of 6.62,63 At n = 16, the Mg−O CN has increased to be 5.19, with most of the Mg atoms coordinated by 5 O’s. The number of six-O-coordinated Mg atoms is still small because of the surface-to-volume ratio of the nanoclusters. Mg can be bonded to either 1 or 2 O’s of CO3, forming corresponding Mg⟨O2⟩CO or Mg−O−CO2 local structures (Figure 1). The Mg−C distances in the Mg⟨O2⟩CO sites are ∼0.5 Å shorter than the Mg−C distances in the Mg−O−CO2 sites. In the lowest energy isomers for (MgCO3)n, n = 1−4, all of the Mg’s are bonded to the Mg⟨O2⟩CO sites exclusively. Both Mg⟨O2⟩CO and Mg−O−CO2 sites were found in the lowest energy isomers for (MgCO3)n, n = 5−12 and 16. Besides

match the formulas of interest are collected as HGA candidates during the various steps. Low-energy candidates are fed to the HGA component to search for the global minimum for each formula of interest, where the structures generated from the crossover operations were optimized using semiempirical methods. The lowest energy structures from the HGA are then optimized by using density functional theory. Symmetry was not imposed during either the TG-HGA or DFT optimization steps. In the current work, we treated CO3 as a fragment in the tree-growth step. The expansion (or growth) of Mg (to form Mg-(CO3)x) is similar to the regular growth pattern in our previous work. For the growth of the CO3 fragments (to form CO3−Mgx), we use z-matrix-like parameters to define “anchoring” positions that Mg can be anchored to, instead of the umbrella expansion parameters33 used for the growth of MgO. Mg atoms are positioned either to form a C−O2−Mg bond with two O’s on C or to form a linear C−O−Mg bond with one O. The crossover operation in the hybrid genetic algorithm can potentially break the CO3 fragments apart, and the global minima search becomes much less efficient as unstable structures with pieces of the CO3 fragment will be generated. To avoid such cases, we applied a distance check after a crossover operation. If a CO pair with its distance comparable to the CO distance in CO32− was separated by the cutting plane after a crossover operation, the O was assigned to the opposite of the cutting plane to retain the CO pair.

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RESULTS AND DISCUSSION Optimized Geometries. The optimized (MgCO 3 ) n structures at the B3LYP/DZVP level are shown in Figure 1 for those isomers within 10 kcal/mol of the lowest energy isomer. Alternative views of the lowest energy structures and additional optimized structures are given in the Supporting Information together with the Cartesian coordinates (in Å) to enable viewing of the structures (Figure S1 and Table S5). The lowest energy MgCO3 monomer has C2v symmetry (1a), with the Mg bonded to two O’s from the CO3. The lowest energy structure for (MgCO3)2 (2a) has C2h symmetry with four corner O atoms, each of which is bonded to one Mg atom. Structure 2d, the boat conformation of 2a, is calculated to be ∼15 kcal/mol higher in energy than structure 2a. The presence of corner O atoms that commonly exist in all of the lowest energy (MgCO3)n nanoclusters is one of the reasons why (MgCO3)n clusters are so different from the bulk crystal (see Figure 1 and discussion below). Isomer 2b with 3 corner O and 1 dangling terminal O is predicted to be 9 kcal/mol higher in energy than structure 2a. The ladderlike isomer with C2h symmetry (2c) with 2 terminal O’s is predicted to be ∼13 kcal/mol higher in energy than 2a. Similar to the dimers, the lowest energy isomer for the trimer is 3a, with structure 3b 12.2 kcal/mol higher in energy. Both are puckered rings with 2 corner O’s on the each edge of the puckered ring. The lowest energy isomer for (MgCO3)4 is also a puckered ring with S4 symmetry. The puckered ring with C2h symmetry (4b) is 7.7 kcal/mol higher in energy. A cubelike isomer with Td symmetry, with all of the 12 O’s bonded to 1 Mg, is 40 kcal/mol higher in energy than 4a. Structure 5a with C1 symmetry is predicted to be the lowest energy isomer for (MgCO3)5, with the C2 symmetry puckered ring (5b) only 1.4 kcal/mol higher in energy. A Cs isomer with one terminal O (5c) is only 3.0 kcal/mol higher in energy than 5a. Structure 5d has a geometry similar to that of 5a but with 3421

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Figure 1. Geometries and relative energies in kcal/mol at the B3LYP/DZVP level for the low energy (ΔHrel < 10.0 kcal/mol) (MgCO3)n nanoclusters.

the CN for the number of O atoms bonded to a Mg, we can also examine the number of carbonate groups about an Mg, which is represented by CN(Mg−C), which has the same value as CN(C−Mg). For most of the lowest energy (MgCO3)n clusters, n = 5−12 and 16, the CN(Mg−C) for the Mg−O− CO2 sites is greater than CN(Mg−C) for the Mg⟨O2⟩CO sites as more carbonates can be bonded to a Mg with Mg−O−CO2

coordination due to smaller steric effects. (MgCO3)6 is the only exception, where CN(Mg−C) for the Mg⟨O2⟩CO sites is twice the CN(Mg−C) for the Mg−O−CO2 sites. In general, the number of Mg⟨O2⟩CO sites decreases as the size of the (MgCO3)n nanocluster increases and the number of the Mg−O−CO2 sites increases, which is consistent with the fact that in the bulk magnesite there are only Mg−O−CO2 sites. 3422

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Table 1. Average Coordination Numbers (CN) and Bond Distances (Å) for C−Mg and Mg−O Bonds in (MgCO3)n Clusters and Magnesite r(C−Mg) < 2.7 Ǻ

a

2.7 ≤ r(C−Mg) ≤ 3.6 Ǻ

n

CN(C−Mg)

bond(C−Mg)

CN(C−Mg)

1 2 3 4 5 6 7 8 9 10 11 12 16 ∞

1 2 2 2 1.2 2 1.43 1.38 1 1.1 1.09 1.25 1.19 0

2.249 2.306 2.360 2.372 2.406 2.473 2.447 2.482 2.471 2.452 2.507 2.509 2.532 2.952

0 0 0 0 1.8 1 1.71 1.87 2.44 2.3 2.64 2.5 2.69 6

r(C−Mg) < 3.6 Ǻ

r(Mg−O) < 3.0 Ǻ

bond(C−Mg)

CN(C−Mg)

bond(C−Mg)

CN(Mg−O)

bond(Mg−O)

rC−Oa

3.001 3.277 3.092 3.094 3.028 3.000 3.061 3.028 3.014 2.952

1 2 2 2 3 3 3.14 3.25 3.44 3.4 3.73 3.75 3.88 6

2.249 2.306 2.360 2.372 2.763 2.741 2.798 2.834 2.866 2.823 2.899 2.855 2.866 2.952

2 4 4 4 4.4 5 4.29 4.88 4.67 4.8 5.18 5.25 5.19 6

1.866 2.059 2.031 2.016 2.067 2.112 2.031 2.120 2.085 2.116 2.144 2.136 2.119 2.101

1.214, 1.380(2) 1.286(4), 1.348(2) 1.281(6), 1.351(3) 1.277(8), 1.358(4) 1.273(10), 1.363(5) 1.273(12), 1.362(6) 1.275(14), 1.348(7) 1.268(16), 1.365(8) 1.267(18), 1.352(9) 1.266(20), 1.364(10) 1.275(22), 1.350(11) 1.269(24), 1.362(12) 1.264(20), 1.321(28) 1.283

The values in parentheses for each bond distance are the number of times this distance occurs in the structure.

As a result, the average Mg−C distance of the smaller clusters is significantly smaller than the average Mg−C distance of the bulk material. The existence of the bidentate bonded Mg⟨O2⟩CO sites also lowers the average Mg−C CNs of the small (MgCO3)n nanoclusters. For the largest cluster that we have investigated, (MgCO3)16, the average Mg−C distance in Mg−O−CO2 sites is calculated to be 3.014 Å, as compared to the average Mg−C distance of 2.95 Å in magnesite. In the Mg⟨O2⟩CO sites, the Mg’s are essentially anchored in the CO32− planes, which leads to rigidity in the local structures. For smaller cluster sizes, the Mg⟨O2⟩CO clusters are more stable because the bonding between Mg and CO32− are stronger than in the Mg−O−CO2 sites. As the size of the cluster increases, such local rigidity leads to higher strain. The resulting structures will either have dangling CO’s or are higher in energy. In contrast, the Mg−O−CO2 sites show high local flexibility, and local geometry relaxation can easily occur which stabilizes the structures. The Mg−C and Mg−O pair distribution functions (PDFs) for the lowest energy (MgCO)n clusters are given in the Supporting Information for comparison with experiment when such data may become available. In the PDF plots, the strong peaks in the 1.5−3.5 Å region represent the Mg−C and Mg−O bond distance distributions of the first coordination shell. The PDF diagrams for (MgCO3)n, n = 1−4, show only single Mg−C and Mg−O peaks in the first shell region, and in the PDF diagrams for n > 4, two Mg−C and two Mg−O peaks are found, indicating two different bonding schemes between Mg and CO3. This is consistent with our discussion of the average coordination numbers and bond distances of the (MgCO3)n clusters. As the size of the cluster increases, weaker peaks begin to appear for the second and third coordination shells, indicating that the cluster does not grow evenly in all three dimensions up to n = 16. The crystal structure of magnesite is layered with alternating layers of cations and anions, and the Mg is an octahedral site with 6 oxygen atoms from 6 different CO32− groups. The optimized nanoclusters do not exhibit this type of structure up to n = 16. Thus, one cannot readily cut a nanocluster out of the crystal, which is possible in some simpler metal oxides, such as MgO. As shown in Figure 2, structures for n = 4, 6, and 8 were cut from the crystal and then optimized. The results show that the clusters derived from the crystal structure are much higher in energy than those derived from the TG-HGA. An issue with

Figure 2. Optimized cluster structures for n = 4, 6, and 8 starting from initial clusters cut from the crystal. Energies in kcal/mol relative to the most stable structure in Figure 1.

some of these structures is the presence of dangling CO bonds, which cannot be eliminated without significant manual manipulation of the starting structure to overcome additional energy barriers. Thus, the use of the TG-HGA or other approaches is important in generating optimal structures. For many of the clusters, multiple isomeric structures that are very close in energy were found. This suggests that there may be complex equilibria for nanoclusters of the same number of MgCO3 units and that detection of such nanoclusters could be complicated by the presence of more than one isomer with differing structures and spectroscopic signatures. We also examined the process for loss of a CO2 from (MgCO3)10 as shown in Figure 3. Loss of CO2 generates an O2− defect site, and the loss of the CO2 to generate this site requires only 12 kcal/mol (ΔH(0 K)). This initial observation will be pursued in future work to study the mechanism of decarboxylation of MgCO3 clusters and subsequently minerals such as magnesite and nesquihonite. Mg(CO3)n Dissociation Energies and Heats of Formation. The ⟨DE⟩ and ΔHf(g,298) for (MgCO3)n are shown in Table 2, and the calculated ⟨DE⟩ (at the B3LYP/DZVP) vs n plot and 3423

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Figure 3. Formation of an O2− defect site in (MgCO3)10. The O2− site is circled in blue.

Table 2. Calculated Normalized MgCO3 Dissociation Energies (⟨DE⟩) at the B3LYP/DZVP Level and Gas Phase Heats of Formation in kcal/mol at 298 K for (MgCO3)n n

⟨DE⟩

ΔHf(g,298)

n

⟨DE⟩

ΔHf(g,298)

1 2 3 4 5 6 7

0 62.4 86.5 95.9 98.2 102.6 105.7

−111.8a −348.4 −595.0 −830.7 −1050.1 −1286.4 −1522.5

8 9 10 11 12 16 ∞

107.3 108.9 110.1 111.4 112.3 116.2 153.9b

−1752.8 −1986.2 −2219.0 −2455.2 −2689.2 −3648.0

a ΔHf(g,298) for MgCO3 monomer calculated using the FPD method as described in the text. bCalculated from the experimental64 ΔHf(MgCO3(s),298) = −265.7 ± 2 kcal/mol and the calculated ΔHf(g,298) for the MgCO3 gas phase monomer using the FPD method.

⟨DE⟩ vs n−1/3 plot are shown in Figures 4A and 4B, respectively. The ΔHf(g,298) were calculated using the ⟨DE⟩ for (MgCO3)n at the B3LYP/DZVP level and ΔHf(g,298) of the monomer calculated using the FPD approach. We expect the calculated results for the ⟨DE⟩ to be reliable as our previous study34 of (MgO)n nanoclusters showed good agreement between the B3LYP/DZVP and CCSD(T)/CBS values for the normalized MgO dissociation energies to within 1 kcal/mol, and a similar type of ionic bonding is expected in the carbonate clusters. We found that the ⟨DE⟩ increases as size of the (MgCO3)n cluster increases, and the increment per n (slope) decreases in general. The increase in the slope at n = 5 is due in part to the introduction of a different Mg−CO3 bonding scheme for these clusters versus the smaller clusters. The increment per n becomes almost constant for n = 7−16, showing slow convergence to the estimated bulk limit (153.9 kcal/mol). The bulk limit of the ⟨DE⟩ was estimated from the experimental ΔHf(298,s)64 of the solid and the calculated ΔHf(298,g) for the gas phase monomer of −111.8 kcal/mol predicted using the FPD method and the experimental heats of formation of the atoms.64 The ⟨DE⟩ bulk limit can also be extrapolated from the ⟨DE⟩ vs n−1/3 plot. The y-intercept of the extrapolated ⟨DE⟩ vs n−1/3 linear fit is the estimated ⟨DE⟩ value at n−1/3 = 0 (i.e., n → ∞). The y-intercept using n = 4−16 is 152 kcal/mol, in excellent agreement with the estimated bulk value of 154 kcal/mol. Our extrapolation could be improved by increasing the number of data points. The good agreement shows that this approach could be used to provide estimates of the heat of formation of the solid mineral to check, for example, calculated heats of formation using ab initio thermodynamics.65 We can do this by using accurate values for the gas phase monomer from experiment or from FPD calculations which are good to ±1 kcal/mol for most compounds and the extrapolated ⟨DE⟩. The appropriate difference gives the heat of formation of the bulk.

Figure 4. Normalized MgCO3 dissociation energy ⟨DE⟩ for (MgCO3)n at the B3LYP/DZVP level (A) vs n and (B) vs n−1/3 in black. The linear fit for ⟨DE⟩ vs n−1/3, n = 5 − 16, is shown in red.

The smoothness of the ⟨DE⟩ vs n plot can be used as a semiquantitative measurement to determine whether the global energy minimum structure or an isomer close in energy to the global energy minimum has been found, especially for new predictions with available comparisons. A data point lower than the linear fit in the ⟨DE⟩ vs n plot may imply the existence of lower energy structures than those predicted. In our case, the plot is smooth before and after n = 5, where, as noted above, there is a “2-D” to “3-D”structural transition at n = 5. Thus, the lowest energy structures reported in the work are very likely to be global energy minima or structures close in energy to the global minima. The slope change in the ⟨DE⟩ vs n plot (at n = 5 in our cases) also indicates the presence of a structural phase transition as n increases. The reaction energies DECO2 and ⟨DE⟩CO2 of the CO2 dissociation reactions for (MgCO3)n are given in Table 3, and the ⟨DE⟩CO2 vs n plot is shown in Figure 5. The ⟨DE⟩CO2 were found to decrease as n increases although there are fluctuations. The fluctuations arise because both the reactant and the product of the reaction (i.e., (MgCO3)n and (MgO)n) can have significant local geometry changes as n increases. The ⟨DE⟩CO2 for n = 12 and 16 is calculated to be 30.0 and 30.7 kcal/mol, respectively, close to the experimental bulk value of 27.9 kcal/mol. The gas phase values for the larger clusters are similar to that for the bulk and as expected converge from above. This suggests that (MgCO3)n and (MgO)n clusters with n = 12 and 16 ((MgO)12 3424

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1300−1500 cm−1. There is a group of much less intense C−O symmetric stretches in the 1000−1100 cm−1 region. The CO3 inversions are in the 800−900 cm−1 region. The frequencies of the CO3 asymmetric modes differ with different coordination numbers of the O’s and appear in mainly two regions. The CO3 asymmetric bands in the 1600−1750 cm−1 region can be assigned to the stretching modes between C and the corner O’s (i.e., O bonded to 1 C and 1 Mg only) of an exterior CO3 in (MgCO3)n. The CO3 asymmetric bands in the 1300−1500 cm−1 region are assigned to the modes between C and interior O’s, in which O is bonded to multiple Mg’s and thus the C−O bond is weakened. Previous experimental IR spectroscopic studies of magnesite showed only one strong, broad band in the 1300− 1500 cm−1 region representing the CO3 asymmetric stretching modes.17,24 Our predicted values are in line with the experimental results, as the bulk crystal has essentially no corner O atoms that can give rise to the peaks in the 1600−1800 cm−1 region, due to the small surface/volume ratio. The experimental IR spectrum for magnesite also shows a moderate band near 900 cm−1 and a weak band near 750 cm−1, ∼100 cm−1 lower than the CO3 symmetric stretching modes and CO3 inversion modes predicted for the small clusters at the B3LYP/DZVP level. Such red-shifts are most likely due to the higher CN(C−Mg) in the bulk magnesite, where C−O bonds are weaker than in the small clusters. NMR Chemical Shifts. The calculated NMR chemical shifts at the B3LYP/Ahlrichs VTZP level66 (Gaussian09) and at the BLYP/TZ2P level67 with and without a ZORA correction68,69 (ADF)70,71 for the relativistic effects are given in the Supporting Information for 13C, 17O, and 25 Mg with respect to the standards tetramethylsilane for C, H2O for O, and Mg(H2O)62+ for Mg. The calculations are all done in the gauge-independent atomic orbital GIAO approximation.72,73 We focus on the BLYP/TZ2P results and note that the effects of the relativistic ZORA corrections are small. In general, there is reasonable agreement between the chemical shifts calculated at the B3LYP/Ahlrichs VTZP and BLYP/TZ2P levels. The 13C chemical shift in the monomer is 195 ppm and decreases to 189 ppm in the dimer and ∼182 ppm in the trimer. The values continue to decrease to ∼169−175 ppm for n = 10. The 13C shifts are in a similar range at the B3LYP/VTZP level. The 17O chemical shifts show a broader range of values. The only significant difference that occurs between the Gaussian09 and ADF results is for the unique CO in the monomer. The oxygen chemical shifts show different variations. The four oxygen atoms that are on the exterior are predicted to have chemical shifts near 250 ppm, and the two more interior oxygens are predicted to be at 274 ppm in the dimer. The six exterior oxygens in the trimer are predicted to be at 233 ppm and the three more interior ones at 243 ppm. The four interior oxygens have a predicted chemical shift of 223 ppm in the tetramer, and the eight exterior oxygens are predicted to be a 233 ppm. The larger clusters show a larger range of NMR chemical shifts for the oxygens. The 25 Mg chemical shifts are predicted to be substantially different from Mg(H2O)62+ for the monomer, but for the clusters with higher coordination for the Mg, the values are slightly positive by 0 to ∼10 ppm except for a Mg for n = 6 which has a negative shift. This Mg is in the center of the cluster with approximate CN of 6 and is unique in the hexamer.

Table 3. Calculated Stepwise Reaction Energy (DECO2) and Normalized Reaction Energies (⟨DE⟩CO2) in kcal/mol for Reaction 4 at the B3LYP/DZVP Level n

DECO2

⟨DE⟩CO2

n

DECO2

⟨DE⟩CO2

1 2 3 4 5 6 7

52.2 (50.1)a 98.3 141.1 174.3 216.2 214.3 270.6

52.2 49.1 47.0 43.6 43.2 35.7 38.7

8 9 10 11 12 16 ∞

281.0 286.8 340.5 363.1 363.0 490.5

35.1 31.9 34.1 33.0 30.0 30.7 27.9 ± 2.2b

a

Calculated from the experimental64 heat of formation of CO2 and the FPD calculated values for MgCO3 and MgO.53 bCalculated from the experimental values.64 ΔHf(MgO(s),298) = −143.7 ± 0.2 kcal/mol, ΔHf(MgCO3(s),298) = −265.7 ± 2 kcal/mol, ΔHf(CO2(g),298) = −94.1 kcal/mol.

Figure 5. Normalized CO2 dissociation energy ⟨DE⟩ vs n for (MgCO3)n at the B3LYP/DZVP level.

is a hexagonal prism and ((MgO)12 is cuboid)34 can serve as models for the study of CO2 adsorption and desorption reactions on the defect sites of the bulk MgO and MgCO3. Vibrational Frequencies. The calculated infrared spectrum of (MgCO3)n using the analytical harmonic frequency calculation method at the B3LYP/DZVP level is shown in Figure S3 of the Supporting Information and tabulated in Table S1. The MgCO3 monomer has three CO stretching modes, and all three are infrared-active. The vibrational frequency for the CO stretching mode between C and the terminal O was calculated to be 1787 cm−1 with a large intensity, and the vibrational frequencies for the antisymmetric and symmetric C−O stretches were calculated to be 1003 and 908 cm−1, with strong and weak intensities, respectively. The CO32− inversion frequency was predicted to be near 800 cm−1 and to be weak. The vibrational frequency for the stretching mode between Mg and CO3 in the monomer was calculated to be 521 cm−1, with weak infrared intensity. The (MgCO3)2 dimer has six CO stretching modes with four asymmetric stretching modes and two symmetric stretching modes. Because of the C2h symmetry of the dimer, three of the stretching modes are infrared-active and three are inactive. Two of the antisymmetric modes were calculated to be intense bands at 1581 and 1353 cm−1, and a weak symmetric stretch is predicted at 1034 cm−1. The dimer also has two moderately intense Mg−CO3 stretching modes at 409 and 504 cm−1. As the size of the cluster increases, the pattern continues. There is a group of intense asymmetric C−O stretches in the region of 1550−1750 cm−1 and a second group in the region of

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CONCLUSIONS We used a modified version of our original TG-HGA in conjunction with semiempirical molecular orbital calculations 3425

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The Journal of Physical Chemistry A followed by DFT geometry optimizations to predict the global minima for (MgCO3)n clusters. Mg can be bonded to 1 or 2 O’s of a CO3 unit, forming Mg⟨O2⟩CO or Mg−O−CO2. The Mg−C distances in the Mg⟨O2⟩CO bonding scheme are ∼0.5 Å shorter than the Mg−C distances in the Mg−O−CO2 sites. The (MgCO3)n, n = 1−4, clusters have Mg⟨O2⟩CO sites exclusively. The Mg−O−CO2 bonding scheme becomes favored as the cluster size increases. The average CN(C−Mg) increases as the cluster size n increases. The average CN(C−Mg) was calculated to be 5.2 for (MgCO3)16, slightly lower than the CN(C−Mg) of 6 in magnesite. For many of the nanoclusters, there are a number of energetically low-lying isomers, which may be present at equilibrium. Thus, continued nucleation could occur via different nanoclusters of the same size depending on the kinetics of the nucleation process. The ⟨DE⟩ increases as n increases for the cluster dissociation reaction to form the MgCO3 monomers. At n = 16, ⟨DE⟩ is calculated to be 116.2 kcal/mol as compared to the estimated bulk value of 153.9 kcal/mol. The adiabatic reaction energies ⟨RE⟩CO2 for the recombination reactions of (MgO)n clusters and CO2 to form (MgCO3)n were calculated using the lowest energy isomers for both (MgO)n and (MgCO3)n. The exothermicity of ⟨RE⟩CO2 decreases as n increases and converges to the experimental bulk limit rapidly. ⟨RE⟩CO2 was calculated to be −52.2 kcal/mol for the monomer and calculated to be −30.7 kcal/mol for n = 16, as compared to the −27.9 kcal/mol for the solid phase reaction. The extrapolated ⟨DE⟩ vs n−1/3 linear fit can be used to estimate the heat of formation of the bulk mineral as described above and could help to provide bounds on these values and to check the consistency of other types of calculations of the bulk thermodynamics.65 The results suggest that the calculated clusters can serve as nucleation sites for the formation of amorphous magnesium carbonate analogous to the formation of amorphous calcium carbonate and its role in biomineralization.9 A long-term goal of our effort is to understand the speciation of solutions containing MgCO3. Our results show that the stable structures for the solid phases are not good guides to the structures of nanoclusters that may be present in solution. We thus calculated the vibrational frequencies for (MgCO3)n and used our analysis of the results to interpret the major absorption bands in previous experimental IR studies for bulk magnesite. The calculated 13C, 17O, and 25Mg chemical shifts together with the calculated vibrational spectra should be useful in identifying these clusters in solution.

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ACKNOWLEDGMENTS

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REFERENCES

Part of this work was work was supported by the Geosciences Research Program in the U.S. Department of Energy, Office of Basic Energy Sciences, Division of Chemical Sciences, Geosciences & Biosciences. This research used resources of the Oak Ridge Leadership Computing Facility at the Oak Ridge National Laboratory, which is supported by the Office of Science of the U.S. Department of Energy under Contract DE-AC0500OR22725. D.A.D. also thanks the Robert Ramsay Chair Fund of The University of Alabama for support.

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ASSOCIATED CONTENT

S Supporting Information *

Complete references for refs 57 and 58; pair distribution function vs distance plot for the lowest energy isomers of (MgCO3)n at the B3LYP/DZVP level; calculated infrared spectra for (MgCO3)n at the B3LYP/DZVP level and tabulated frequencies and IR intensities; calculated 13C, 17O, and 25Mg chemical shifts for (MgCO3)n; optimized Cartesian coordinates and total energies for the lowest energy (MgCO3)n at the B3LYP/DZVP level. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail [email protected]; phone 205-348-8441 (D.A.D.). Notes

The authors declare no competing financial interest. 3426

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DOI: 10.1021/jp511823k J. Phys. Chem. A 2015, 119, 3419−3428