Correlated Molecular-Orbital Theory Study of the Al + CO2 Reaction

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Correlated Molecular-Orbital Theory Study of the Al + CO Reaction Rezvan Chitsazi, Jeffrey D. Veals, Yi Shi, and Tommy Sewell J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.7b11443 • Publication Date (Web): 14 Dec 2017 Downloaded from http://pubs.acs.org on December 25, 2017

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The Journal of Physical Chemistry

Correlated Molecular-Orbital Theory Study of the Al + CO2 Reaction

Rezvan Chitsazi, Jeffrey D. Veals,*† Yi Shi, and Tommy Sewell* Department of Chemistry, University of Missouri-Columbia, Columbia, Missouri 65211-7600 †

U.S. Army Research Laboratory, Aberdeen Proving Ground, Maryland 21005

ABSTRACT Density functional theory (DFT) and correlated molecular orbital electronic structure calculations were used to study the Al + CO2 → AlO + CO reaction on the electronic groundstate potential-energy surface (PES). Geometries were optimized using DFT (M11/jun-ccpV(Q+d)Z) and more accurate energies were obtained using the composite Weizmann-1 theory with Brueckner doubles (W1BD). The results comprise the most complete, most systematic characterization of the Al + CO2 reaction surface to date and are based on consistent application of high-level methods for all stationary points identified. The pathways from Al + CO2 to AlO + CO on the electronic ground-state PES all involve formation of one or more stable AlCO2 complexes denoted η-AlCO2, trans-AlCO2, and C2v-AlCO2, among which η-AlCO2

and

C2v-AlCO2 are the least and most stable, respectively. We report a new minimum-energy pathway for the overall reaction, namely formation of η-AlCO2 from reactants and dissociation of that same complex to products via a bond-insertion reaction that passes through a fourth (weakly metastable) AlCO2 complex denoted cis-OAlCO. Natural Bond Orbital analysis was applied to study trends in charge distribution and the degree of charge transfer in key structures

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along the minimum-energy pathway. The process of aluminum insertion into CO2 is discussed in the context of analogous processes for boron and first-row transition metals. *E-mail addresses: [email protected] and [email protected]


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1. Introduction The chemistry of aluminum is less fully understood than one might expect. At standard ambient conditions aluminum is a crystalline solid. When exposed to the terrestrial atmosphere the pure metal oxidizes rapidly to form an Al2O3 passivation layer that renders it essentially inert below the normal melting point. The electronic structure of Al makes it reactive with both oxidizers and reducers, and the reactions occur extremely fast. These facts perhaps account for the limited knowledge we have of Al elementary reactions despite their importance in many technological applications. As an example, even though in propellant formulations Al typically exists as particles with a relatively thick passivation layer, much of Al atom combustion chemistry involves gas-phase species. Although as discussed below there has long been an interest in the elementary reactions of Al atoms, most experimental studies have focused on the combustion of particles with the goal of engineering better practical uses. Reactions with O2, CO2, and H2O are among the more important ones in Al combustion. There have been some significant experimental and theoretical studies of these, but they are not as well understood as modern techniques in both domains would permit. Our interest here is to apply state-of-the-art electronic structure theory to accurately determine the critical points on the electronic ground-state potential-energy surface (PES) for the overall gas-phase reaction Al + CO2 → AlO + CO.

(1)

It is useful to briefly review the literature for reaction (1), with a focus on the fundamental gas-phase reaction as opposed to applied engineering and modeling approaches to the chemistry. This task is complicated due to the wide variety of experimental and theoretical methods used, the wide intervals of pressure and temperature studied, the rather large number of species and



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processes identified, and the different conventions used by various authors to label and characterize the species. Fontijn and Felder1 used fast-flow reactor experiments to study reaction (1). They measured the rate coefficient at five temperatures between 300 and 1900 K and determined that it is independent of pressure, average gas velocity, and initial Al concentration but exhibits distinct non-Arrhenius behavior at temperatures above 750 K. They suggested that either the participation of another reaction channel or "preferential reaction of Al with CO2 in bending modes" is the cause of the non-Arrhenius behavior. The activation energy for the reaction in the Arrhenius range (310-750 K) was determined to be 2.6 ± 1.3 kcal mol-1. Parnis et al.2 studied the pressure dependence of the rate coefficient for reaction (1) in the gas phase at 296 K and reported that the rate coefficient increases with increasing total pressure, in disagreement with the results of Fontijn and Felder.1 Parnis et al. proposed the following mechanism based on their results: Al + CO2 ↔ AlCO2*

→

AlCO2

(2a)

→

AlO + CO.

(2b)

They suggested that Al and CO2 react according to reaction (2a) to form an energized complex, AlCO2*, and determined that the rate coefficient for that reaction is (2.4 ± 0.3)×10-12 cm3 molecule-1 s-1. They suggested that the energized complex can be stabilized by collisions or can dissociate either back into reactants or into products (i.e., reaction (2b)). Their primary support for this mechanism is that the yield of AlO product, monitored by laser-induced fluorescence (LIF), decreases with increasing pressure. Costes et al.3 reported results for reaction (1) based on molecular beam experiments using pulsed crossed supersonic molecular beams of Al atoms and CO2 molecules. They probed the


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AlO product using LIF and determined the product ro-vibrational energy distribution and the reactive cross section as functions of relative translational energy. A simple analytical model reproduced the cross sections for translational energies between 0.20 eV and 0.39 eV but not at the highest energy studied experimentally (0.53 eV). Costes et al. associated this discrepancy at high translational energy with the non-Arrhenius high-temperature behavior reported by Fontijn and Felder.1 The reaction endoergicity calculated by Costes et al. for ground-state reactants Al(2P1/2) + CO2(X 1Σg+) is 4.38 ± 0.69 kcal mol-1. Honma and Hirata 4 recently studied the dynamics of the gas-phase reaction of Al + CO2 using a crossed-beam technique. They obtained the angular and speed distributions of product (AlO) at collision energies 6.7 kcal mol-1 and 12.6 kcal mol-1 (27.9 kJ mol-1 and 52.8 kJ mol-1, respectively). From their results, Honma and Hirata suggested that the reaction mechanism involved a stable but short-lived intermediate. They used the kinetic energy distributions to estimate the rotational energy of CO and argued that the low rotational energy of CO observed might be an indication that the O-C-O linkage in the intermediate has a linear geometry. Le Quéré et al.5 studied infrared (IR) vibrational spectra of the AlCO2 complex in argon matrices using matrix-isolation spectroscopy. Their measured IR spectra provide evidence for two stable geometric isomers of the AlCO2 complex. They concluded that the higher-temperature (≈17 K) isomer is likely to be planar and ring-like with C2v symmetry (C2v-AlCO2), whereas at low temperature (≈9 K) a structure with non-equivalent CO bonds and Cs symmetry is more stable. They estimated the enthalpy difference between the two isomers to be 0.37 ± 0.1 kcal mol-1 but found no reversible conversion between them at temperatures above ≈25 K. Howard et al.6 studied the reaction of Al and Ga atoms with CO2 and CS2 in a rotating cryostat at 77 K. Among five AlCO2 complexes identified in their study, the two main ones had



C2v structures. Under the experimental conditions in their study, Howard et al. did not find evidence for the Cs species, trans-AlCO2, proposed by Le Quéré et al.5 Garland et al.7 studied the reaction of Al + CO2 using laser pump-probe techniques. They reported rate coefficients for total pressures between 10 and 600 Torr and temperatures between 298 and 1215 K. They reported that below 700 K the rate coefficient exhibits a strong pressure dependence, which suggests a complex-formation mechanism, with activation energy 0.48 ± 0.16 kcal mol-1. At temperatures above 700 K, the dominant reaction mechanism is a direct O-atom abstraction to produce AlO + CO. The activation energy for this process is 6.4 ± 0.4 kcal mol-1. Garland et al. reported that the reaction endothermicity is 1.5-2.0 kcal mol-1 lower than the activation energy. Several theoretical studies have addressed the pathways and energetics of reaction (1).8,9,11-14 Marshall et al.8 and Sakai9 relied largely on geometries optimized at the UHF level with various basis sets (3-21G, 6-31G, 6-31G*, 6-31+G*, and 6-31G(d,p)). Panek and Latajka11 and Politzer et al.13 used higher levels of theory but did not study the complete reaction mechanism of Al + CO2, as these works were part of more broad-based studies of Al atom reactions with a wide variety of molecules. Marshall et al.8 studied the mechanism of Al + CO2 using ab initio theory and gave a thorough discussion of the thermochemistry and kinetics. The geometries of various minima (denoted cis-, trans-, and box-AlCO2 (C2v symmetry)), "transition states" (first-order saddle points), and product species were optimized at the UHF/6-31G* level. Single-point energies at these geometries were obtained using PMP4/6-31G* theory. The UHF/6-31G* minima were further optimized using UMP2/6-31G*. Starting from cis-AlCO2, this resulted in a structure close to box-AlCO2. Starting from trans-AlCO2, a significant change in Al-O-C angle occurred


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that resulted in a "new-trans" structure. Using UHF/6-31G* stationary-point geometries, Marshall et al. obtained a PMP4//UHF barrier of 1.6 kcal mol-1 for Al + CO2 → trans-AlCO2. The isomerization of trans-AlCO2 to box-AlCO2 was found to be "barrierless", meaning that the PMP4//UHF energy for the UHF saddle-point geometry was lower in energy than the corresponding energy for trans-AlCO2. Their calculations predicted that AlCO2 dissociates into products, AlO + CO, via barriers of ≈104 kcal mol-1 (relative to C2v-AlCO2) and 21 kcal mol-1 (relative to trans-AlCO2). Marshall et al. used the quantum Rice-Ramsperger-Kassel (RRK) model 10 to perform kinetic analysis and obtain "total rate constants" based on the Al + CO2 PMP4//UHF PES. They empirically reduced the 21 kcal mol-1 barrier relative to trans-AlCO2 noted above to 14 kcal mol-1, to improve agreement between their model and experiment. Sakai9 studied the Al + CO2 reaction using UHF, MP2, MP4(SDTQ), and multiconfigurational

self-consistent

field

(MCSCF)

theory.

He

found

that

at

the

MP4(SDTQ)/6-31G(d)//HF/6-31G(d) level the initial step involved the formation of a trans-AlCO2 complex with a barrier of 2.3 kcal mol-1 relative to Al + CO2. This barrier is slightly larger than the value 1.6 kcal mol-1 calculated by Marshall et al.8 Sakai described two additional AlCO2 structures, denoted cis and C2v. The trans-AlCO2 complex was found to isomerize to cis-AlCO2 via a 0.4 kcal mol-1 barrier. The conversion of cis-AlCO2 to the most stable AlCO2 complex, C2v-AlCO2, was reported to be barrierless. Sakai studied the possibility of intersecting electronic states along the AlCO2 → AlO + CO reaction channels, using geometries and energies calculated at the MCSCF/3-21G level. At that level of theory the dissociation "transition states" (first-order saddle points) from trans-AlCO2 and C2v-AlCO2 to AlO + CO had barriers of 19.0 kcal mol-1 and 23.6 kcal mol-1, respectively, relative to Al + CO2.



Panek and Latajka 11 and Selmani and Ouhlal 12 addressed the stability of various minima associated with the AlCO2 complex. Panek and Latajka11 studied the complexes of metal atoms (M = Al and Ga) with CO2, CS2, and COS using B3LYP and MP2 methods with the 6-311G(d) and 6-311+G(3df) basis sets and at the QCISD(T)/6-311+G(3df)//MP2/6-311G(d) level of theory. Basis set superposition error was taken into account. Panek and Latajka optimized the initial structures with the B3LYP method and both the 6-311G(d) and 6-311+G(3df) basis sets. In another set of calculations, the B3LYP geometries were re-optimized at the MP2 level with the smaller basis set, 6-311G(d). The results showed good agreement between the DFT and ab initio optimized structures, indicating that MP2/6-311G(d) was sufficient for geometry predictions. More reliable energies were calculated at the MP2/6-311+G(3df)//MP2/6-311G(d) level. The QCISD(T)/6-311+G(3df)//MP2/6-311G(d) approach (the highest level used) was used only for MCO2 structures. For the AlCO2 complex, Panek and Latajka found three stable minima: C2v-AlO2C, trans-AlOCO, and Al-(C,O-η)-CO2. However, the stabilities of these complexes depend on the level of theory: Both MP2 and B3LYP predict trans-AlOCO to be the lowest-energy complex whereas QCISD(T) predicts that C2v-AlO2C is the most stable. Although their computational methods are quite robust, Panek and Latajka only studied stable minima (i.e., no saddle points) of the AlCO2 complex. Selmani and Ouhlal12 studied the structures of AlCO2 complexes and the related vibrational spectra using a local-spin DFT method. They found four structures for the AlCO2 complex, denoted AlCO2(a), AlCO2(b), AlCO2(c), and AlCO2(d). They reported the most stable structure to be AlCO2(a), with an energy of -19.5 kcal mol-1 relative to Al + CO2. This structure corresponds to η-AlCO2 in the present study. Selmani and Ouhlal suggested that the AlCO2(b) and AlCO2(d) complexes are C2v structures and that AlCO2(c) is trans-like. The AlCO2(b) and


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AlCO2(c) structures are consistent with those assigned in the experimental study by Le Quéré et al.5 discussed above. Politzer et al.13 used the CBS-QB3 extrapolation method based on B3LYP geometries to study the mechanisms of some reactions involving aluminum atoms, including reaction (1), and calculated the free energies and enthalpies of Al-containing molecules. They found a saddle point that connects Al + CO2 directly to AlO + CO with a 14.4 kcal mol-1 activation barrier relative to Al + CO2. The overall reaction enthalpy was calculated to be 8.6 kcal mol-1. Sharipov et al.14 studied the Al + CO2 reaction using B3LYP and CBS-QB3. They optimized the structures using B3LYP/6-311+G(3df,2pd) and then refined the energies using CBS-QB3. They identified a single AlCO2 complex in their study. The CBS-QB3 barrier to form the AlCO2 complex was calculated to be 9.94 kcal mol-1, which is much larger than the corresponding barriers calculated by Marshall et al.8 (1.6 kcal mol-1) and Sakai9 (2.3 kcal mol-1). The barrier reported by Sharipov et al. for the indirect ''abstraction channel" leading from AlCO2 to AlO + CO is 14.84 kcal mol-1 relative to Al + CO2. In the present study, we characterize theoretically the electronic ground-state PES for reactions involving one Al atom and one CO2 molecule. We do so in a consistent, systematic manner and using higher levels of theory than previously employed; DFT and correlated molecular orbital methods with appropriately sized basis sets that should yield reliable structures and energies. This was done with the goal of unifying the zero kelvin energetics of the entire electronic ground state of the AlCO2 PES at a consistent high level of theory.



2. Computational Methods After preliminary testing (see Supporting Information) the M11 density functional of Peverati and Truhlar15 was used in conjunction with the jun-cc-pV(Q+d)Z basis set16 to perform geometry optimizations and frequency calculations. The cc-pV(N+d)Z-style basis sets include an extra set of tight d functions on the Al atom to provide a better description of the electronic structure.17 Single-point energies at the M11 geometries were calculated using the Weizmann-1 theory with Brueckner doubles18 (W1BD) composite approach. This yields high quality coupled cluster (CC) complete basis set (CBS)-level energies. W1BD energies are known to be accurate to within 0.62 ± 0.48 kcal mol-1 of experiment in cases for which spin contamination is small.18 Note that the W1BD method normally uses B3LYP/cc-pVTZ+d geometries and frequencies, but during testing we concluded that the M11 functional is more reliable than B3LYP for the Al + CO2 system (refer to the Supporting Information for details). Harmonic vibrational analysis was performed to confirm that all stationary points corresponded to either minima or first-order saddle points and to obtain frequencies for harmonic zero-point energy (ZPE) corrections. Intrinsic reaction coordinate (IRC) calculations were performed to determine which minima were connected by a given saddle point. All geometry optimizations were carried out using GAUSSIAN09, Revision B.0119 (for B3LYP and W1BD) or GAMESS20 (for M11). A limited number of CCSD(T) single-point energy calculations (using M11/jun-cc-pV(Q+d)Z geometries and ZPE corrections) were performed using the PSI421 code. (See the Supporting Information for more details on the methods tested and used.) The ChemCraft software 22 was used to visualize the optimized geometries and extract geometric parameters.


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3. Results and Discussion 3.1. Overview We used DFT and correlated molecular orbital methods to study the reactions leading from Al + CO2 to AlO + CO on the electronic ground-state PES. Minima, first-order saddle points, and IRCs were obtained. The results of our study in the main article are summarized in Tables 1 and 2 and Figures 1-4. Tables 1 and 2 contain energies of minima and saddle points, respectively, relative to Al + CO2 obtained in the present study at various levels of theory. Results from the literature are provided in Tables 3 and 4. Figures 1(a) and 1(b) contain the optimized geometries of minima and saddle points, respectively, at the M11/jun-cc-pV(Q+d)Z level. Figure 2 contains a schematic diagram of the Al + CO2 PES at the W1BD//M11 level with M11 harmonic ZPE corrections. Figure 3 contains the results of Natural Bond Orbital (NBO) analysis of atomic natural charges along the minimum-energy pathway from reactants to products at the M11/jun-cc-pV(Q+d)Z level. Figure 4 contains an analysis of bond lengths along the M11/jun-cc-pV(Q+d)Z IRC that spans the highest-energy saddle point along the minimumenergy path. In the Supporting Information, Tables S1-S5 contain optimized structures, energies, and vibrational frequencies obtained with M11/jun-cc-pV(Q+d)Z and B3LYP/cc-pVTZ+d. Tables S6 and S7 contain Brueckner doubles "T1" values for minima and saddle-point structures optimized with M11/jun-cc-pV(Q+d)Z. Table S8 contains NBO charges and natural electron configurations calculated with M11/jun-cc-pV(Q+d)Z. Figures S1-S3 show energy-level diagrams analogous to Figure 2 but for M11/jun-cc-pV(Q+d)Z without ZPE correction, M11/jun-cc-pV(Q+d)Z with ZPE correction, and W1BD//M11 without ZPE correction, respectively. Figures S4-S6 contain IRCs for all seven M11/jun-cc-pV(Q+d)Z saddle points.



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The present results are based mainly on the W1BD//M11 approach. Based on what is known for W1BD//B3LYP and in light of the close agreement between B3LYP- and M11-based W1BD results

in

Tables

1

and

2,

we

regard

this

as

more

reliable

than

UCCSD(T)/CBS//M11/jun-cc-pV(Q+d)Z in cases for which spin contamination could be a factor. As discussed by Marshall et al.,8 it can be difficult to describe the AlO molecule correctly using a single-reference method. Therefore, extra care was taken for all saddle-point structures leading to this product. In particular, the wave functions of all optimized structures were checked for instabilities and none was found. Also, the level of spin contamination was checked and found to be less than 5% of the expectation value of total spin, which we regard as evidence that the single-reference description is acceptable. 3.2. Complex formation Both Parnis et al.2 and Garland et al.7 suggested the possibility of AlCO2 complex formation. Le Quéré et al.5 and Howard et al.6 reported geometric isomers of the AlCO2 complex. The M11/jun-cc-pV(Q+d)Z optimized geometries and relevant structural parameters of the minima and saddle points are shown in Figures 1(a) and 1(b), respectively. All structures are precisely planar. In the C2v-AlCO2 conformation, which has the highest symmetry point group among the complexes we identified, the Al atom interacts equivalently with both O atoms of the CO2 moiety. The other complexes have Cs or lower symmetry. The stability ordering of these complexes, C2v-AlCO2 > trans-AlCO2 > η-AlCO2, is consistent with that predicted by Panek and Latajka11 using the QCISD(T) 23 - 25 method with the 6-311+G(3df) basis set. The primary difference is that the QCISD(T)/6-311+G(3df) approach under-binds the complexes compared to W1BD//M11 (see Tables 1 and 3). This systematic effect is likely due, at least in part, to the


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QCISD(T)/6-311+G(3df) relative energies not being fully converged to the QCISD(T) CBS limit. Our results suggest that the cis-AlCO2 structure is either completely unstable or else exists in a shallow minimum that we failed to identify.

Thus, while others reported a cis-AlCO2

minimum (see Table 3), we conclude that it is not a major factor in the overall reaction mechanism. A fourth minimum, cis-OAlCO (see Figure 1a), which is a distinct structure from cis-AlCO2, was found that connects η-AlCO2 to the AlO + CO products. The structure of this minimum differs from the other three complexes in that it resembles more closely the product of reaction (2b) than the reactant species and is higher in energy than Al + CO2 by 4.5 kcal mol-1. Politzer et al.13 reported a closely related OAlCO structure at the CBS-QB3 level of theory. While most of the geometric parameters are close to those found here for cis-OAlCO, the structure reported by Politzer et al. exhibits a trans-like geometry. We sought but did not find a corresponding structure. The energy-level diagram for the Al + CO2 electronic ground-state PES, based on W1BD//M11 with M11 harmonic ZPE corrections, is shown in Figure 2. There are two saddle points (SP1 and SP1ʹ) that connect the reactants to the structures of the AlCO2 complex basin. The most favorable saddle point is designated SP1, which connects Al + CO2 to η-AlCO2 via a barrier of 0.8 kcal mol-1. Based on their experimental results, Parnis et al.2 and Garland et al.7 reported barriers to complex formation of > 1.0 kcal mol-1 and 0.48 ± 0.16 kcal mol-1, respectively. Our calculated value for SP1 falls between those two experimental values. The η-AlCO2 complex is 15.0 kcal mol-1 more stable than Al + CO2 and is connected to the slightly more stable complex trans-AlCO2 via SP2 through a small barrier of 1.4 kcal mol-1 at the



M11/jun-cc-pV(Q+d)Z level. However, the SP2 saddle-point geometry, which was verified by IRC to connect η-AlCO2 and trans-AlCO2 for M11/jun-cc-pV(Q+d)Z (see Figure S5 in the Supporting Information), is predicted to be lower in energy than η-AlCO2 at the W1BD//M11 level and thus η-AlCO2 → trans-AlCO2 is regarded by us to be "barrierless". While we also observed a reduction of the barrier heights for several other saddle points when using the highlevel wave function methods (see Table 2), the SP2 case is the only one for which the W1BD//M11 barrier "disappears" completely. The trans-AlCO2 complex, which is 15.9 kcal mol-1 more stable than Al + CO2, can isomerize via SP2ʹ to yield C2v-AlCO2. The energy of SP2ʹ relative to trans-AlCO2 is 1.9 kcal mol-1 and 0.8 kcal mol-1 at the M11/jun-cc-pV(Q+d)Z and W1BD//M11 level, respectively. The C2v-AlCO2 structure is 18.2 kcal mol-1 lower in energy than Al + CO2 and is the global minimum-energy structure found in our study for all method and basis set combinations considered (see Tables 1 and 2). Le Quéré et al.5 reported an enthalpy difference of 0.37 ± 0.1 kcal mol-1 between the two AlCO2 isomers C2v and Cs, the latter of which corresponds to either a trans-like or cis-like structure that was not resolvable from their experimental data. In our study, we find that the energies of trans- and C2v-AlCO2 differ by 2.3 kcal mol-1 at the W1BD//M11 level. The reactants and trans-AlCO2 are connected directly via saddle point SP1ʹ. However, this saddle point is 9.0 kcal mol-1 higher in energy than the reactants, and is not likely to be a factor at lower temperatures. We did not find a saddle point that connects the reactants directly to the C2v-AlCO2 complex, nor did we find a direct O-abstraction saddle point that connects the reactants directly to final products AlO + CO. Politzer et al.13 reported a saddle point (TS2 in their paper) that apparently directly connects Al + CO2 to AlO + CO. We note that their reported


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structure is geometrically quite similar to the saddle point (SP3ʹ) that connects trans-AlCO2 to AlO + CO in our study. Sakai9 reported a saddle point geometrically similar to SP1 but that connects Al + CO2 to trans-AlCO2, as opposed to η-AlCO2 in our study. We were able to reproduce Sakai’s result by using the UHF/6-31G(d) method. However, we were unable to identify η-AlCO2 as a stable complex using that same level of theory. Using W1BD//M11 we found a cis-OAlCO structure located 4.5 kcal mol-1 higher in energy than Al + CO2. The saddle point connecting cis-OAlCO to η-AlCO2 is 0.1 kcal mol-1 above the cis-OAlCO minimum as shown in Figure 2. Politzer et al. did not report a saddle point connecting η-AlCO2 and the OAlCO structure, but they did calculate equilibrium properties of the two isomers based on free energy differences for the reaction AlCO2 ↔ trans-OAlCO at 298 K (∆G = 19.8 kcal mol-1) and 2000 K (∆G = -0.4 kcal mol-1). They found that the equilibrium constant, Keq, shifts from 3.1 × 10-15 at 298 K to 1.1 at 2000 K. All method and basis set combinations used in our calculations located the C2v-AlCO2 and trans-AlCO2 minima and the saddle points associated with those structures, but cis-AlCO2, η-AlCO2, cis-OAlCO, and the saddle point from η-AlCO2 to the products are method- and basis set-dependent (see Supporting Information for more details). 3.3. Dissociation of the AlCO2 complex into AlO + CO The AlCO2 complex can dissociate into products (AlO + CO). Three M11 saddle-point structures were located that lead to AlO + CO (see Figure 2). The global minimum, C2v-AlCO2, connects to AlO + CO via SP3″ with a 34.4 kcal mol-1 barrier. A barrier of ≈104 kcal mol-1 relative to C2v-AlCO2 was reported by Marshall et al.8 The large disagreement between our value and that predicted by Marshall et al. could be due to the basis-set size used for the PMP4 energies or errors associated with using PMP4 for this open-shell species.



The trans-AlCO2 complex is connected to AlO + CO via SP3ʹ, with a barrier of 28.6 kcal mol-1 relative to trans-AlCO2. Within 0.1 kcal mol-1 precision, this is in exact agreement with the value 28.6 kcal mol-1 obtained using energies from Table IV of Sakai.9 As shown in Figure 2, the η-AlCO2 complex is connected to AlO + CO by way of the cis-OAlCO structure mentioned in Sec. 3.2. The SP3 saddle point connects the η-AlCO2 and cis-OAlCO structures. We sought but could not locate a saddle point that directly connects η-AlCO2 to AlO + CO. The barrier for SP3 is 19.6 kcal mol-1 relative to η-AlCO2, and the cis-OAlCO structure lies in a very flat region of the PES. This indirect pathway that passes through cis-OAlCO yields the smallest overall predicted barrier between Al + CO2 and AlO + CO that we identified in our study. Although Politzer et al.13 reported structures closely related to η-AlCO2 and cis-OAlCO, the mechanistic details of this pathway do not appear to have been reported. 3.4. NBO charge analysis on the minimum-energy pathway and IRC calculations for

η-AlCO2 → cis-OAlCO The NBO charges of each atom in the key structures along the minimum-energy pathway are shown in Figure 3. The Al atom charge increases from zero in the free atom to +0.77 in the η-AlCO2 structure, mostly between the SP1 saddle point and η-AlCO2. The charge is primarily donated to the O and C atoms involved in the η2-C,O ligand interaction (see Scheme 1). Those atoms become more negative relative to their charges in free CO2, while the non-interacting O of CO2 is practically unaffected. In the cis-OAlCO structure, Al becomes more positive, the O involved in the AlO bonding interaction becomes more negative, and the charges of the C and non-interacting O atoms change very little. Overall, the large charge shifts occur in two stages; between Al + CO2 and η-AlCO2 , and between η-AlCO2 and cis-OAlCO. Charge shifts between


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cis-OAlCO and AlO + CO are minimal in comparison. This supports the view that cis-OAlCO is essentially an AlO radical interacting with a CO molecule, with a binding energy of 1.6 kcal mol-1 at the W1BD//M11 level.

Scheme 1. Typical CO2 ligand interactions with first-row transition metals. The superscript 1 or 2 denotes whether it is a monodentate or bidentate interaction, and the atomic symbols following the hyphen denote which ligand atoms are involved in the ligand interaction.

The preceding conclusion is corroborated by the IRC and bond-length results in Figure 4. The IRC depicted is for η-AlCO2 to cis-OAlCO. The initial energy rise is very gradual; it occurs with modest changes in the r(Al-C) and r(Al-O1) bond lengths and smaller changes in the r(C-O1) and r(C-O2) lengths. As the energy curve steepens, more significant changes in bond lengths occur, especially for r(C-O1). However, the lengths of bonds that exist in AlO + CO (r(Al-O1) and r(C-O2)) exhibit essentially final values well before the SP3 saddle point geometry is reached. 3.5. Additional factors in the dissociation of the AlCO2 complex Although the pathway from η-AlCO2 to products is the minimum-energy route leading to AlO + CO, the overall picture is somewhat more complicated. The barrier for the dissociation of the η-AlCO2 structure into reactants is 15.8 kcal mol-1 relative to η-AlCO2, which is 5.3 kcal 17 ACS Paragon Plus Environment


mol-1 lower in energy than the overall energy needed to pass from η-AlCO2 to AlO + CO at the W1BD//M11 level. Garland et al.7 reported a consistent result from their experimental study of Al + CO2, for temperatures below 700 K, insofar as they suggested Al + CO2 reacts to form the AlCO2 complex, which can be stabilized or can dissociate back to reactants or forward to products. A saddle point SP(η-O-η) that connects equivalent η-AlCO2 structures by way of an in-plane rocking motion of Al along the Al-C-O angle was also located (see Figure 1b). The energy of SP(η-O-η) relative to Al + CO2 at the W1BD//M11 level is 1.1 kcal mol-1, which is 16.1 kcal mol-1 relative to η-AlCO2. This result suggests that this isomerization reaction will be competitive with the dissociation of η-AlCO2 back to reactants, Al + CO2, which further complicates the picture. 3.6. The OAlCO bond-insertion pathway: Comparison to transition metals and Boron It is known that first-row transition metals M can readily insert into the CO bond of CO2. Early transition metals (Sc, Ti, V) insert either spontaneously or with very small barriers to form OMCO products.26-28 Later transition metals form one-to-one complexes with CO2; for instance ″C-coordinated″ for Fe and Co, ″side-on″ for Ni, and ″end-on″ for Cu.29, 30 (See Scheme 1.) For early transition metals the bond-inserted products tend to be more stable than the reactant (either M + CO2 or η-MCO2). For the later transition metals the behavior varies; for Cr,31 Cu,32 and Ni, 33 the bond-inserted products are endothermic relative to reactant, whereas the bondinserted products for Fe, Co, and Mn are predicted to be more stable than other isomers.34 The trend for the neutral transition metals has been attributed to the tendency of early transition metals to donate d-orbital electron density to the in-plane π*-orbital of CO2 through ligand backdonation.26,27,35


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Similar behavior is observed for transition-metal cation complexes, for which early transition-metal cation (Sc+, Ti+, and V+) bond-inserted species, OM+-CO, are more stable than the M+ + CO2 reactants; whereas for the later transition-metal cations (Cr+ through Cu+) the bond-inserted products are less stable than the reactants.35 It is expected that the Al interaction would differ from those for transition metals since for Al no d orbitals would be involved. However, in studies of boron + CO2 using G2M(MP2)//B3LYP/6-311+G(d) it was found that OBCO is the most stable minimum on the B + CO2 electronic ground-state PES.36 One interesting difference between the present results and those of the boron study is that the BCO2 complexes are much more stable relative to B + CO2 than are the corresponding Al complexes. The BO + CO product is also much more stable than B + CO2, due to the high stability of the BO bond. This drives the B + CO2 reaction forward. Another important difference is that, in bonding and ligand interactions of B- and Al-CO2 complexes, the 2p versus 3p orbitals are primarily involved. It is likely that the orbitals of B have better overlap with the orbitals of O and C, which allows boron to approach those atoms more closely and to form stronger bonding interactions compared to the Al case. An important finding from the present study is that the CO bond-insertion route is the most favorable route to products. This is in line with the transition-metal studies discussed above. However, the bond-insertion product, cis-OAlCO, is only very slightly stable. The reaction to form cis-OAlCO from η-AlCO2 is significantly endothermic whereas the back barrier is very small. This stands in contrast to many of the results for the early transition metals reacting with CO2. In most of those cases (Sc, Ti, and V) the bond-insertion product is more stable than the reactant (either M + CO2 or η-MCO2). Moreover, the bond-insertion barrier is small for Sc and V and barrierless for Ti. Together, these facts suggest spontaneous bond insertion, which is



opposite from the present case of Al. The stability of the OM-CO bond-inserted species is linked to the strength of the M-O bond. If the energy of the M-O bond is similar or larger than the energy required to break the CO bond of CO2, then the OMCO insertion product tends to be more stable than η-MCO2. The stability shifts to a greater or lesser degree depending on the bond strength of the metal oxide that is eventually formed. Aluminum forms a much weaker bond with oxygen than does boron; D0(AlO) = 121.2 kcal mol-1 and D0(BO) = 192.3 kcal mol-1. The M-O bond strengths for the early transition metals Sc, Ti, and V are D0(ScO) = 161.7 kcal mol-1, D0(TiO) = 159.6 kcal mol-1, and D0(VO) = 148.4 kcal mol-1, respectively.37 Thus, it is expected that Al would not form products as stable as boron or the mentioned transition metals.

4. Conclusions Reactions of Al + CO2 leading to AlO + CO on the electronic ground-state potential-energy surface (PES) were studied using M11/jun-cc-pV(Q+d)Z optimized geometries in conjunction with W1BD//M11 single-point energies with M11 harmonic ZPE corrections. This work is an effort to unify the zero kelvin energetics of the entire electronic ground state of the AlCO2 PES in a systematic fashion by treating all reactions in a consistent manner and using higher levels of theory than previously employed. The key conclusions from our study are: •

All pathways leading from reactants to products pass through AlCO2 complex structures. We sought but could not find evidence of a direct abstraction channel Al + CO2 → AlO + CO.

•

Three of the four AlCO2 complexes identified are more stable than either Al + CO2 or AlO + CO. The relative stability of those complexes is η-AlCO2 < trans-AlCO2 < C2v-AlCO2. The fourth complex, cis-OAlCO, is endothermic relative to Al + CO2 and is intermediate in energy between Al + CO2 and AlO + CO.


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•

The stable complexes η-AlCO2 and trans-AlCO2 connect directly to Al + CO2. All three stable complexes connect to AlO + CO (by way of cis-OAlCO in the case of η-AlCO2). While C2v-AlCO2 is energetically most stable, it cannot be reached directly from reactants and it has the highest saddle-point energy among any of the three complexes for dissociation to products.

•

A newly reported, indirect bond-insertion pathway Al + CO2 → η-AlCO2 → cis-OAlCO → AlO + CO is the lowest-energy mechanism by which AlO + CO can be formed from Al + CO2. This agrees well with previous works on transition metals reacting with CO2. The saddle point associated with this pathway is lower in energy than any of the other saddle points we identified for AlCO2 complex dissociation to products.

•

The AlO + CO product is predicted to be higher in energy than Al + CO2 by 6.1 kcal mol-1, which is in excellent agreement with experiment. Thus, it is likely that the overall forward reaction is driven by subsequent steps that remove AlO from the system, for instance oxidation to Al2O3.

Supporting Information More details about the various DFT and wave function methods tested, Cartesian structures and energies of stationary points, vibrational frequencies, Brueckner Doubles T1 values for all stationary points, NBO atomic charges and natural electron configurations, reaction energy-level diagrams, and IRC results.



Acknowledgments The U.S. Air Force Office of Scientific Research (AFOSR) supported this research under grant numbers FA9550-14-1-0091 and FA9550-17-1-0223. The authors wish to acknowledge Prof. Donald L. Thompson for originally recognizing the need for a consistent, comprehensive study of Al + CO2 reactions and for useful discussions over the course of work.

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35

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Page 26 of 42

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Table 1. Energies of minima relative to Al + CO2. Units are kcal mol-1. C2v

trans

cisa

ߟ

cis-OAlCO

AlO + CO

M11/jun-cc-pV(Q+d)Zb

-17.7

-17.2

-

-16.7

6.3 (6.29)c

9.7

W1BD//M11d

-18.2

-15.9

-

-15.0

4.5 (4.51)

6.1

CCSD(T)/CBSd

-17.6

-15.9

-

-15.0

6.0 (6.04)

7.1

W1BDe

-17.6

-16.0

-

-15.1

-

6.1

a

Reported by others (see Table 3), but not identified in the present study.

b

M11 values, including M11 harmonic ZPE corrections.

c

Numbers in parentheses show one additional digit of precision, due to the small energy

difference between cis-OAlCO in this table and saddle point SP3 in Table 2. d

Based on M11/jun-cc-pV(Q+d)Z optimized geometries and M11 harmonic ZPE corrections.

e

"True" W1BD calculations based on B3LYP/cc-pVTZ+d optimized geometries and B3LYP

harmonic ZPE corrections.



Page 28 of 42

Table 2. Energies of saddle points relative to Al + CO2. Units are kcal mol-1. SP1

SP1ʹ

SP2a

SP2ʹ

SP3

SP3ʹ

SP3ʹʹ

1.3

8.4

-15.3

-15.3

6.4 (6.42)c

16.3

16.8

W1BD//M11d

0.8

9.0

-15.2

-15.1

4.6 (4.59)

12.7

16.2

CCSD(T)/CBSd

0.9

9.7

-15.2

-15.1

5.8 (5.83)

13.3

16.7

W1BDe

0.9

8.0

-15.2

-15.1

-

11.9

-

M11/ b

jun-cc-pV(Q+d)Z

a

SP2 is an identified saddle point at the M11/jun-cc-pV(Q+d)Z level.

b

M11 values, including M11 harmonic ZPE corrections.

c

Numbers in parentheses show one additional digit of precision, due to the small energy

difference between saddle point SP3 in this table and cis-OAlCO in Table 1. d

Based on M11/jun-cc-pV(Q+d)Z optimized geometries and M11 harmonic ZPE corrections.

e

"True" W1BD calculations based on B3LYP/cc-pVTZ+d optimized geometries and B3LYP

harmonic ZPE corrections.


Page 29 of 42 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


Table 3. Literature values for minima energies relative to Al + CO2. Units are kcal mol-1.a C2v

trans

cis

η

AlO + CO

AlCO2b

Sakaic

-12.3

-9.6

-9.4

-

5.8

-

Marshall et al.d

-13.

-10.

-10.

-

-

-

-12.96

-12.08

-

-11.64

-

-

Sharipov et al.f

-

-

-

-

11.72

-14.90

Sharipov et al.g

-

-

-

-

8.942

-16.89

-18.0

-15.2

-

-19.5

-

-

Panek and Latajkae

Selmani and Ouhlalh Costes et al.i a

4.38±0.69

The numbers of significant figures in the table entries are the same as in the respective original

publications. b

Detailed structure not specified.

c

ZPE-corrected MP4(SDTQ)/6-31G(d)//HF/6-31G(d) energy from Table I of Ref. 9. The energy

for AlO (2Σ) + CO relative to Al + CO2 was extracted from Figure 6 of Ref. 9. d

ZPE-corrected PMP4/6-31G*//UHF/6-31G* energy extracted using Table 10 of Ref. 8.

e

QCISD(T)/6-311+G(3df) //MP2/6-311G(d) energy from Table 2 of Ref. 11.

f

ZPE-corrected B3LYP/6-311+G(3df,2pd) energy extracted from Figure 4 of Ref. 14.

g

ZPE-corrected CBS-QB3//B3LYP/6-311+G(3df,2pd) energy extracted from Figure 4 of Ref.

14. h

AlCO2(a), AlCO2(b), and AlCO2(c) complexes from Ref. 12 correspond to η-AlCO2,

C2v-AlCO2, and trans-AlCO2, respectively, in the present study. i

Reference 3, experimental study.



Page 30 of 42

Table 4. Literature values for saddle-point energies relative to Al + CO2. Units are kcal mol-1.a SP-Cb

a

SP1ʹ

SP-CPc

SP3ʹ

SP3″

Sakaid

-

2.3

-

19.0

23.6

Marshall et al.e

-

1.6

-

11.

91.

Sharipov et al.f

≈4.30

-

13.16

-

-

Sharipov et al.g

9.936

-

14.84

-

-

Parnis et al.h

> 1.0

-

-

-

-

Garland et al.i

0.48 ± 0.16

-

-

-

-

The numbers of significant figures in the table entries are the same as in the respective original

publications. b

SP-C denotes a saddle point for AlCO2 formation, but for which the detailed complex structure

was not specified. c

d

SP-CP denotes a saddle point that connects AlCO2 complex to products. ZPE-corrected MP4(SDTQ)/6-31G(d)//HF/6-31G(d) energy for SP1ʹ (“TS” in Ref. 9) from

Table I of Ref. 9. The relative energies for SP3ʹ and SP3″ (TS(2Π) and TS(2Σ), respectively) were extracted from Figure 6 of Ref. 9. e

ZPE-corrected PMP4/6-31G*//UHF/6-31G* energy extracted from Table 10 of Ref. 8.

f

ZPE-corrected B3LYP/6-311+G(3df,2pd) energy extracted from Figure 4 of Ref. 14.

g

ZPE-corrected CBS-QB3//B3LYP/6-311+G(3df,2pd) energy extracted from Figure 4 of Ref.

14. h


i



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(a)

AlO

η-AlCO2

CO

CO2

trans-AlCO2

C2v-AlCO2

cis-OAlCO

(b)

SP1

SP(η-O-η) SP1ʹ

SP2ʹ

SP3

SP2

SP3ʹ SP3″

Figure 1. (a) Optimized M11/jun-cc-pV(Q+d)Z geometries of all minimum-energy structures. (b) Optimized M11/jun-cc-pV(Q+d)Z geometries of all saddle-point structures. Bond lengths are in Å and bond angles are in degrees. All structures are precisely planar.



Figure 2. Schematic diagram of the Al + CO2 electronic ground-state potential-energy surface based on W1BD//M11 single-point energies calculated using M11/jun-cc-pV(Q+d)Z optimized geometries with the M11 harmonic ZPE correction. Energies are in kcal mol-1. The η-AlCO2 structure connects to trans-AlCO2 via the saddle point SP2 at M11/jun-cc-pV(Q+d)Z (see Figure S5 in the Supporting Information) but this saddle point is predicted to be lower in energy than η-AlCO2 at the W1BD//M11 level and therefore the isomerization between η-AlCO2 and trans-AlCO2 is regarded as barrierless in the present study. 32 ACS Paragon Plus Environment

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Figure 3. NBO natural charges of each atom in the reactant (non-interacting Al and CO2), SP1, η-AlCO2, SP3, cis-OAlCO, and products (non-interacting AlO and CO).



Figure 4. The relative energy (black curve, left ordinate) and bond lengths (red curves, right ordinate) along the intrinsic reaction coordinate from η-AlCO2 to cis-OAlCO.


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TOC Graphic



Scheme 1 62x69mm (96 x 96 DPI)

ACS Paragon Plus Environment

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Figure 1(a). 119x83mm (96 x 96 DPI)



Figure 1(b) 100x108mm (96 x 96 DPI)


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Figure 2 202x289mm (300 x 300 DPI)



Figure 3 150x86mm (150 x 150 DPI)


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Figure 4 130x70mm (150 x 150 DPI)



TOC Graphic 82x47mm (96 x 96 DPI)


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Correlated Molecular-Orbital Theory Study of the Al + CO2 Reaction

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