13C Chemical Shift of Adsorbed Acetone for Measuring the Acid

Jul 2, 2010 - Yueying Chu , Zhiwu Yu , Anmin Zheng , Hanjun Fang , Hailu Zhang ... Zhang , Ningya Yu , Chih-Yi Yang , Shang-Bin Liu , and Feng Deng...
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J. Phys. Chem. C 2010, 114, 12711–12718

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C Chemical Shift of Adsorbed Acetone for Measuring the Acid Strength of Solid Acids: A Theoretical Calculation Study Hanjun Fang,†,‡ Anmin Zheng,*,† Yueying Chu,†,‡ and Feng Deng*,† State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics, Wuhan Center for Magnetic Resonance, Wuhan Institute of Physics and Mathematics, The Chinese Academy of Sciences, Wuhan 430071, China, and Graduate School, The Chinese Academy of Sciences, Beijing 100049, China ReceiVed: May 17, 2010; ReVised Manuscript ReceiVed: June 18, 2010

Adsorption of basic probe molecules is one of the widely used methods to characterize the acid strength of solid acids. In this contribution, the adsorptions of acetone on various Brønsted and Lewis acid sites (from weak acid to superacid) are theoretically studied, in order to elucidate the quantitative relationships between 13 C chemical shifts of acetone and intrinsic acid strength of solid acids. The Brønsted acid sites are represented by a series of 8T zeolite models with varying terminal Si-H bond lengths, and the different extents of acidic proton transfer from these acid sites to acetone are revealed explicitly. We found that three adsorption conformations (hydrogen-bonded, proton-shared, and ion-pair) exist for acetone, and concurrently, a correlation of three-broken lines is obtained for the 13C chemical shift of acetone versus the deprotonation energy (DPE). The correlation can be used as a scale for quantitatively measuring the Brønsted acid strength of solid acids. A threshold of 245 ppm is determined for superacidity, in good agreement with the experimental value (244 ppm). The Lewis acid sites are modeled by tricoordinate framework aluminum species and various extraframework aluminum cations or neutral species such as Al3+, AlO+, AlOH2+, Al(OH)2+, Al(OH)3, and AlOOH. We found that acetone is coordinately adsorbed on the aluminum atoms of Lewis acid sites and that the 13C chemical shift of acetone is almost linear to the lowest unoccupied molecular orbital (LUMO) energy of the acid sites. 1. Introduction Environmentally friendly solid acid catalysts (including zeolites, complex oxides, sulfated metal oxides, heteropoly acids, etc.) have been extensively applied in the chemical and petroleum industries.1-3 Activity of solid acid-catalyzed reactions is usually correlated with the acid properties of solid acids, such as acid type (Brønsted acid or Lewis acid), strength, concentration, and distribution. It is well recognized that Brønsted acid-catalyzed reactions involve proton transfer from acid sites to reactant molecules, while Lewis acid-catalyzed reactions involve electron transfer from reactant molecules to acid sites.4,5 Acid strength is related to the capability of donating a proton for Brønsted acid sites and accepting an electron pair for Lewis acid sites, and the characterization of acid strength is fundamental and important for revealing the relationship between acid strength and catalytic activity. Many techniques were used to evaluate the strength of solid acids, such as Hammett indicator titration,6 temperatureprogrammed desorption (TPD),7 microcalorimetry,8 Infrared (IR),9 solid-state NMR,10-13 etc. All of these methods involve the adsorption of various basic probe molecules and then evaluate the variation of Hammett acidity function, adsorption energy, shift of stretching frequency, isotropic chemical shift, etc. Among them, solid-state NMR spectroscopy of 2-13Cacetone is a useful method for measuring the acid strength of solid acids.11 It was first found that the 13C isotropic chemical * To whom correspondence should be addressed. Fax: +86-27-87199291. E-mail: [email protected] (A.Z.); [email protected] (F.D.). † State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics. ‡ Graduate School.

SCHEME 1: Adsorption Complexes of Acetone on Brønsted and Lewis Acid Sites

shift of the carbonyl carbon of acetone is quite sensitive to an environment of protic solvents, and the shift reflects the degree of proton transfer from the solvent molecule to acetone.14,15 Then, it was introduced to the solid acid field and utilized to characterize the acid strength of both Brønsted and Lewis acid sites.16-31 As shown in Scheme 1, when an acetone molecule adsorbs on a Brønsted acid site of zeolites, the formation of a hydrogen bond between the acidic hydroxyl group and the carbonyl oxygen of adsorbed acetone will cause a downfield 13 C isotropic chemical shift of the carbonyl carbon, and the change of the 13C chemical shift reflects the extent of the proton transfer from the acid site to the carbonyl oxygen. As for Lewis acid sites, the virtual orbital of the metal atom (M) can interact with the unshared electron pair on the carbonyl oxygen of acetone, which will make the 13C chemical shift of the carbonyl carbon move downfield as well. Generally, the experimentally observed 13C chemical shift increases roughly with the increasing

10.1021/jp1044749  2010 American Chemical Society Published on Web 07/02/2010

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acid strength for both Brønsted and Lewis acid sites.32 According to the experimental 13C chemical shifts, the Brønsted acid strength of zeolite H-ZSM-5 (223 ppm)16,17 is stronger than that of HY (220 ppm)16,17 and HSAPO-34 (217 ppm)22 but weaker than that of SO42-/ZrO2 (230 ppm)21,31 and H3PW12O40 (235 and 246 ppm);25 meanwhile, the Lewis acid strength of AlCl3 (245 ppm) is stronger than that of AlBr3 (243 ppm) and AlI3 (238 ppm) but weaker than that of SbF5 (250 ppm).18,20 Although the 13C chemical shift of adsorbed acetone has been extensively utilized in qualitatively characterizing the acid strength of various solid acids, the quantitative relationship between the 13 C chemical shift of acetone and intrinsic acid strength is still lacking. For a Brønsted acid site, deprotonation energy (DPE) is a criterion to measure the intrinsic acid strength of zeolites and other solid acids.33-35 It is defined as the energy required to remove the acidic proton from the acid site to form an anionic conjugate base (AHf H+ + A-), and a smaller DPE value indicates a stronger acidity.33-35 For a Lewis acid site, it has been reported that the Lewis acidity or ability to gain electron pairs could be related to the lowest unoccupied molecular orbital (LUMO) energy of the acid site. Generally, the lower the LUMO energy of the acid site, the easier the electron pair transfer and thus the stronger the Lewis acid strength.36-39 For instance, Corma and co-workers employed LUMO energy to estimate the Lewis acidity of different T-sites for Ti-Beta and Ti silicalite (TS-1) zeolites, and found that Ti-Beta in general has a higher Lewis acidity than TS-1.36 Thus, the DPE and LUMO energy can be utilized to represent the intrinsic acid strengths of Brønsted and Lewis acid sites, respectively, and they can be readily obtained by theoretical calculations. As a valuable complement to experimental study, theoretical methods can also offer an atomic-scale description of the interaction between acid sites and guest molecules40,41 and can give rise to the chemical shifts of adsorbed probe molecules.20,26,27 For instance, Haw and co-workers calculated the 13C chemical shifts for the complexes of acetone with a variety of different molecules, such as CH3OH, HCl, HF, H2F2, BF3, AlF3, AlCl3, and Al2Cl6, as well as the ZSM-5 cluster model and found that the theoretical method could reproduce the experimental results.20 In this work, the acid strengths of a series of solid Brønsted and Lewis acid site models have been systematically studied by using the density functional theory (DFT) calculation method, aiming for revealing the explicit relationships between the 13C chemical shift of adsorbed acetone and the intrinsic acid strength (as DPE and LUMO values) for Brønsted and Lewis acid sites, respectively. 2. Computational Methods It has been demonstrated that Brønsted acid strength can be theoretically simulated by changing terminal Si-H distances of zeolite models, and the influence of Brønsted acid strength on many acid-catalyzed reactions has been studied by using a 3T zeolite model.42-44 The variation of peripheral Si-H bond lengths would lead to the change of charge distributions of the cluster model, which would further influence the bond length and strength of the bridging hydroxyl group (SiOHAl) and thus its acid strength. In the present study, 8T H-ZSM-5 zeolite models with different terminal Si-H bond lengths were used to represent a series of Brønsted solid acids with varying acid strengths. First, H-ZSM-5 was modeled as a cluster of stoichiometry [(H3SiO)3-Si-OH-Al-(OSiH3)3] which was extracted from the crystalline structure of the H-ZSM-5 zeolite.45 The Si12O24(H)-Al12 site was used to represent the Brønsted acid site

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Figure 1. 8T Brønsted acid site model based on H-ZSM-5 zeolite.

(see Figure 1). The terminal Si atoms were saturated with H atoms, and the H atoms were positioned on the vector from the Si atom to the O atom that the H atom was replacing. The terminal Si-H bond lengths r(Si-H) were varied at 1.30, 1.47, 1.60, 1.75, 1.90, 1.95, 2.00, 2.05, 2.10, 2.25, 2.35, 2.50, and 2.75 Å. A similar method was employed in our previous studies on 1H and 31P chemical shift calculations of pyridinium-d5 ions and trialkylphosphine oxides adsorbed on zeolites, and the acid site models can represent Brønsted acidity from weak acid, strong acid, to superacid.46-48 On the other hand, several extra-framework aluminum or oxoaluminum cations such as Al3+, AlO+, AlOH2+, and Al(OH)2+, and neutral species such as Al(OH)3 and AlOOH were allowed to coordinate with the deprotonated 8T H-ZSM-5 model, to represent a series of solid Lewis acid models, designated as L-Al3+, L-AlO+, L-AlOH2+, L-Al(OH)2+, LAl(OH)3, and L-AlOOH, respectively. Three tricoordinate framework aluminum species in which the central Al atom was connected with framework O atoms or OH groups were also proposed to represent the Lewis acid models and designated as L-AlSi3, L-AlSi2, and L-AlSi1. Similar Lewis acid models were used in previous works.27,49-51 To keep the cluster model electrically neutral, as many framework aluminum atoms as necessary were used to compensate the positive charges of the models. Likewise, for the L-Al(OH)3 and L-AlOOH acid sites, an additional proton was included and linked to the oxygen atom near the framework Al atom. The terminal Si-H and Al-H bond lengths were set to 1.47 and 1.55 Å, respectively. It is noteworthy that only the isolated acid site and not its synergetic interaction27,52 with the neighboring Brønsted acid site was taken into account in the calculation to establish the correlation between the 13C chemical shift of acetone and Lewis acid strength (LUMO energy). During the structure optimization of bare acid sites and adsorption complexes, all of the atoms except the terminal -SiH3 and -AlH3 groups were allowed to relax. The B3LYP hybrid density functional53,54 combined with DZVP255 basis sets were employed for all of the optimizations and single point energies. The B3LYP/DZVP2 scheme has been demonstrated to successfully predict the structures of probe molecules adsorbed on zeolites.20,46 Atomic charges were obtained using a natural population analysis (NPA). On the basis of optimized structures, the 13C NMR chemical shifts were calculated using the gauge independent atomic orbital (GIAO)56 method at the B3LYP/ TZVP55 level of theory. Because it has been approved that the 8T Brønsted acid site model with r(Si-H) being 1.47 Å can represent the acid site of H-ZSM-5 zeolite, the experimental 13 C chemical shift of adsorbed acetone (ca. 223 ppm) was adopted as an internal standard for the conversion from the calculated isotropic absolute shielding constant to the final calculated chemical shift.17,20 All of the calculations were performed using the Gaussian 03 software package.57

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TABLE 1: O1-H1 Bond Length and Deprotonation Energy (DPE) of Isolated Brønsted Acid Site Models with Terminal Si-H Bond Lengths Increasing from 1.30 to 2.75 Å; O1-H1 and H1-Oa Distance, CdOa Bond Length, Natural Charge on the Carbonyl Carbon and Acetone, and 13C Chemical Shift (δ(13C)) of Carbonyl Carbon for Acetone Adsorption Complexes on these Brønsted Acid Sites; Several True Solid Brønsted Acid Sites with Experimental 13C Chemical Shift Values of Acetonea isolated acid site r(SiH)

r(O1H1)

DPE

1.30 1.47 1.60 1.75 1.90 1.95 2.00 2.05 2.10 2.25 2.35 2.50 2.75

0.9704 0.9707 0.9711 0.9716 0.9721 0.9723 0.9724 0.9726 0.9727 0.9730 0.9732 0.9735 0.9739

310.8 301.6 294.9 286.5 278.7 276.2 273.8 271.4 269.2 263.0 259.2 254.2 246.7

acetone adsorption complex r(O1H1) r(H1Oa) r(CdOa)b charge (C) charge (acetone) δ(13C) 1.032 1.043 1.054 1.073 1.100 1.118 1.190 1.306 1.333 1.383 1.407 1.441 1.500

1.514 1.478 1.444 1.398 1.342 1.313 1.219 1.125 1.108 1.083 1.073 1.059 1.041

1.238 1.239 1.240 1.242 1.244 1.246 1.251 1.259 1.260 1.263 1.264 1.267 1.272

0.705 0.709 0.713 0.704 0.712 0.717 0.728 0.745 0.746 0.750 0.756 0.759 0.763

0.100 0.113 0.126 0.146 0.169 0.183 0.229 0.284 0.295 0.313 0.320 0.327 0.332

221.8 223.0 224.5 226.4 227.9 229.1 233.1 238.0 239.2 241.4 242.6 244.0 245.3

experimental δ(13C) of acetone on solid Brønsted acid sites HY (220),c,d,e Mordenite (222)d H-ZSM-5 (223)c,d,f VOx/Al2O3 (225)g SO42-/TiO2 (227)h WOx/ZrO2 (228)i BF3/γ-Al2O3 (230)j dealuminated HY (234),e AlPW12O40 (235)k AlCl3/MCM-41 (241)l AlCl3/MCM-41 (245),l (SG)nAlCl2 (245)m H3PW12O40 (246)n

a Distances are in Å, charges in |e|, energies in kcal/mol, and chemical shifts in ppm; atom labeling is shown in Figures 1 and 2. b CdO bond lengths are 1.224 and 1.288 Å for free gas acetone and protonated acetone, respectively, calculated at the same level. c Ref 16. d Ref 17. e Ref 27. f Ref 20. g Ref 28. h Ref 29. i Ref 26. j Ref 24. k Ref 30. l Ref 23. m Ref 19. n Ref 25.

Figure 2. Three types of acetone adsorption complexes: (a) hydrogen-bonded adsorption, (b) proton-shared adsorption, and (c) ion-pair adsorption on the Brønsted acid sites with the terminal Si-H bond length being 1.47, 2.00, and 2.50 Å, respectively. Selected interatomic distances (in Å) are indicated.

3. Results and Discussion 3.1. Acid Strength of Brønsted Acid Sites. As shown in Table 1, the bridging O1-H1 bond length in isolated Brønsted acid sites increases slightly from 0.9704 to 0.9739 Å with the terminal Si-H bond lengths, r(SiH), increasing from 1.30 to 2.75 Å. Accordingly, the DPE value of these isolated Brønsted acid sites decreases gradually from 310.8 to 246.7 kcal/mol, revealing the increasing order of acid strength. When r(SiH) is 1.47 Å, the DPE of the acid site (301.6 kcal/mol) is almost in the range of the experimental value for H-ZSM-5 zeolite (291-300 kcal/mol).33 Meanwhile, the acid site with r(SiH)

being 2.50 Å (DPE)254.2 kcal/mol) can represent the acidity of solid superacid.46,47 Therefore, the intrinsic acid strength of the Brønsted acid sites herein covers that of weak, strong, and superacid. Table 1 also gives the results of acetone adsorption complexes. First, it is remarkable that the bridging O1-H1 bond lengths (or distances) in adsorption complexes are all elongated in comparison with those in isolated Brønsted acid sites. More importantly, with r(SiH) increasing from 1.30 to 2.75 Å (i.e., acid strength increasing), the O1-H1 distance in the adsorption complex increases from 1.032 to 1.500 Å, while the H1-Oa

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distance decreases from 1.514 to 1.041 Å (see Table 1 and Figure 2), which implies a gradual transfer of the acidic proton H1 from the O1 atom of acid sites to the carbonyl oxygen (Oa) of acetone. When acetone adsorbs on Brønsted acid sites with r(SiH) being below 2.00 Å (DPE > 273.8 kcal/mol), all of the O1-H1 distances are less than 1.12 Å, while H1-Oa distances are more than 1.30 Å. Obviously, the acidic proton H1 is always bonded to O1 and is involved in a strong hydrogen bond with acetone. Therefore, in such cases, acetone adsorbs on Brønsted acid sites in the form of hydrogen-bonded adsorption (Figure 2a). In contrast, all of the H1-Oa distances are much shorter than the O1-H1 distances when acetone adsorbs on Brønsted acid sites with r(SiH) being larger than 2.00 Å (DPE < 273.8 kcal/mol, strong or superacidity). This implies that the acidic proton H1 has been transferred to acetone, forming ion-pair adsorption (Figure 2c). When r(SiH) is 2.00 Å (DPE ) 273.8 kcal/mol, medium acidity), O1-H1 and H1-Oa distances are similar (1.190 and 1.219 Å, respectively). The acidic proton H1 is almost located midway between the acid site and acetone, which can be referred to as proton-shared adsorption (Figure 2b). We found that proton-shared adsorption exists in a rather narrow acidity range. Increasing r(SiH) from 2.00 to 2.05 Å or decreasing to 1.95 Å (DPE from 273.8 to 271.4 or to 276.2 kcal/mol), both lead to pronounced transfer of the acidic proton H1, either to acetone or to the zeolite oxygen atom. Similar proton-shared complexes were also found in a previous theoretical study of the processes of hydrogen bonding and proton transfer.58 When H3O+ interacted with the oxygen atom (O1) of furan, a complex with nearly symmetric O1...H...O structure was formed, in which O1-H and H-O distances are 1.176 and 1.213 Å, respectively.58 Along with the proton transfer from the acid site to acetone, the CdOa bond length in adsorption complexes increases in the range of 1.238-1.272 Å, which subsequently affects the 13C chemical shift of the carbonyl carbon of adsorbed acetone. It was found that the 13C chemical shift increases gradually from 221.8 to 245.3 ppm, almost in line with the variation of natural charge on the carbonyl carbon atom, which increases from 0.705 to 0.763 |e| (see Table 1). The more complete the proton transfer, the more positive the 13C chemical shift, thus indicating a stronger acidity. The 13C chemical shift on the weakest Brønsted acid site model (r(SiH) ) 1.30 Å) herein is 221.8 ppm, close to the experimental values of some weaker acidic zeolites, such as HY (220 ppm) and mordenite (222 ppm).17 With r(SiH) increasing to 1.75, 1.90, and 1.95 Å, the 13C chemical shifts are 226.4, 227.9, and 229.1 ppm, respectively, and the corresponding acid sites reach the acid strength of true solid acids of SO42-/TiO2 (227 ppm),29 WOx/ZrO2 (228 ppm),26 and BF3/ γ-Al2O3 (230 ppm),24 respectively. When r(SiH) is 2.00 Å, the 13 C chemical shift of the acid site is 233.1 ppm, similar to that of the Brønsted acid site in dealuminated HY zeolite (234 ppm).27 It has been accepted that the experimental value of acetone adsorbed in 100% H2SO4 (244 ppm) is used as the threshold of superacidity.32,59 Thus, the acid strength of the acid site with r(SiH) being 2.50 and 2.75 Å (244.0 and 245.3 ppm) can be considered as solid superacids, almost identical to some true solid superacids, such as AlCl3/MCM-41 (245 ppm),23 (SG)nAlCl2 (245 ppm),19 and H3PW12O40 (246 ppm).25 On the basis of the 13C chemical shifts, the Brønsted acid site models used here can represent acid strengths of the true solid acids that lie in the range from weak acid to superacid (see Table 1). We can now obtain the explicit relationship between the 13C chemical shift of acetone and the DPE (intrinsic acid strength) for Brønsted acid sites. As shown in Figure 3, a correlation of

Fang et al.

Figure 3. Plot of 13C chemical shift of acetone on Brønsted acid sites (in ppm) versus deprotonation energy (DPE, in kcal/mol).

three-broken lines (corresponding to three regions) is observed. In each region, the 13C chemical shift of acetone is linearly correlated to the intrinsic acid strength (DPE) of Brønsted acid sites. It is further found that region I corresponds to the ion-pair adsorption of acetone (strong acidity range), region II which is in a narrow and steep acidity range corresponds to the proton-shared adsorption (medium acidity range), and region III belongs to the hydrogenbonded adsorption (weak acidity range). It is noteworthy that a DPE value of ca. 250 kcal/mol is generally considered as the threshold of Brønsted superacidity.47,48 According to the correlation in Figure 3, the corresponding 13C chemical shift of acetone is predicted to be ca. 245 ppm, which is well consistent with the experimental value (244 ppm) for the threshold of Brønsted superacidity. This also demonstrates that our theoretical models and the derived relationship between 13C chemical shift of acetone and acid strength (DPE) are reliable. Therefore, the correlation shown in Figure 3 can be applied to quantitatively determine the acid strength of Brønsted acid sites. 3.2. Acid Strength of Lewis Acid Sites. The optimized geometries of isolated Lewis acid sites are shown in Figure 4. In tricoordinate framework aluminum models, the AlL atom and three neighboring oxygen atoms are nearly on a plane; meanwhile, the extra-framework Al3+, AlO+, AlOH2+, Al(OH)2+, Al(OH)3, and AlOOH species are coordinated tightly with the basic oxygen atoms of the zeolite framework. For all of these models, the coordinatively unsaturated AlL atoms potentially act as Lewis acid centers. According to the LUMO energies in Table 2, the L-Al3+ model (-6.48 eV) is the strongest Lewis acid site followed by L-AlOH2+ (-3.35 eV). The LUMO energies of other Lewis acid sites are within -1.99 ∼ -0.91 eV, and the differences in LUMO energy are so small that the order of acidity is confused. It can be seen from Figure 5, for most of the Lewis acid site models, that the LUMO orbital is attributed to a combination of σ* orbitals of Al-O bonds and is mainly localized on the AlL atom that accepts electron pairs from the nucleophilic molecule (e.g., acetone). However, for the L-Al(OH)3 and L-AlOOH acid sites, the LUMO orbital is not related to the AlL atom but mainly localized on the acidic proton of the bridging hydroxyl group in close proximity to the AlL atom. In this case, the LUMO energy mainly reflects electron-accepting ability of the bridging hydroxyl group rather than that of the AlL atom. When acetone adsorbs on Lewis acid sites, the carbonyl oxygen of acetone interacts with the AlL atom of the acid site to form a coordination adsorption complex. Figure 6 selectively shows the geometries of adsorption complexes

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Figure 4. Optimized geometries of the Lewis acid site models: L-AlSi3, L-AlSi2, and L-AlSi1 are tricoordinate framework aluminum species; L-Al3+, L-AlO+, L-AlOH2+, L-Al(OH)2+, L-Al(OH)3, and L-AlOOH are extra-framework aluminum species. Selected interatomic distances (in Å) are indicated.

TABLE 2: LUMO Energy of Isolated Lewis Acid Site Models; AlL-Oa Distance, CdO Bond Length, Natural Charge on the Carbonyl Carbon and Acetone, and 13C Chemical Shift (δ(13C)) for Acetone Adsorption Complexes on these Lewis Acid Sites; Several True Solid Lewis Acid Sites with Experimental 13C Chemical Shift Values of Acetonea Lewis acid site

acetone adsorption complex

species

lumo Energy

r(AlLOa)

r(CdOa)

charge (C)

charge (acetone)

δ(13C)

L-Al(OH)3 L-Al(OH)2+ L-AlSi1 L-AlSi2 L-AlOOH L-AlSi3 L-AlO+ L-AlOH2+ L-Al3+

-1.37 -0.97 -0.91 -1.08 -1.99 -1.46 -1.85 -3.35 -6.48

2.114 1.989 1.934 1.924 1.907 1.904 1.911 1.843 1.785

1.241 1.242 1.247 1.248 1.251 1.251 1.255 1.258 1.289

0.728 0.744 0.740 0.744 0.752 0.738 0.742 0.770 0.793

0.088 0.114 0.126 0.134 0.124 0.147 0.119 0.164 0.164

225.0 227.6 232.2 233.8 236.6 236.8 238.8 246.3 266.1

true Lewis acids with δ(13C)b ZnI2 (227) ZnCl2 (230), ZnY (231) TaCl5 (237) AlI3 (238), ScTf3 (239) AlCl3 (245), TaF5 (248) SbF5 (250)

a Lewis acid sites are arranged from top to bottom on the basis of the 13C chemical shift of adsorbed acetone. Distances are in Å, charges in |e|, LUMO energies in eV, and chemical shifts in ppm; atom labeling is shown in Figures 4 and 6. b All of the Lewis acids are solid or frozen at the experimental conditions, see refs 11, 18 and 20.

on L-AlSi3, L-AlOH2+, and L-Al(OH)3 acid sites. The AlL-Oa distances are 1.904, 1.843, and 2.114 Å, while CdOa bond lengths are 1.251, 1.258, and 1.241 Å, respectively (see Figure 6). The shorter AlL-Oa distance and concurrently the longer CdOa bond length may imply the stronger interactions between acetone and the acid site and thus the stronger Lewis acid strength. Acetone adsorption parameters such as struc-

tures, charges, and 13C chemical shifts on all of the Lewis acid sites are listed in Table 2. The natural charge of the adsorbed acetone is in the range from 0.088 to 0.164 |e|, which indicates that the acid-base interaction is accompanied with electron transfer from acetone to the acid sites, which would further influence the 13C chemical shift of the carbonyl carbon of acetone.

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Figure 5. Lowest unoccupied molecular orbital (LUMO) of the Lewis acid sites.

Figure 6. Acetone adsorption complexes on (a) L-AlSi3, (b) L-AlOH2+, and (c) L-Al(OH)3 Lewis acid sites. Selected interatomic distances (in Å) are indicated.

Indeed, the calculated 13C chemical shift increases from 225.0 to 266.1 ppm, indicating an increasing Lewis acid strength. According to the 13C chemical shift, the L-Al3+ model (266.1 ppm) is the strongest Lewis acid site among these models followed by the L-AlOH2+ (246.3 ppm), and this is in line with

the results from LUMO energy. For other weaker acid sites, however, the 13C chemical shift is not rigorously correlated to LUMO energy. Figure 7 shows the explicit relationship between 13 C chemical shift of acetone and LUMO energy for these Lewis acid sites. A moderately linear correlation is observed (the dash

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J. Phys. Chem. C, Vol. 114, No. 29, 2010 12717 DFT calculation methods. On Brønsted acid sites, a correlation of three-broken lines was revealed for the 13C chemical shift of acetone versus the DPE, while on Lewis acid sites, the 13C chemical shift of acetone is moderately linear to the LUMO energy. The different adsorption conformations for acetone could account for the correlations of these acidity scales. The results obtained here can help to elucidate the acidic properties of solid acids more explicitly and could be applied to quantitatively determine the acid strength of various solid acids. Acknowledgment. We are very grateful for the support of the National Natural Science Foundation of China (20933009, 20773159, and 20703058). We also thank Shanghai Supercomputer Center (SSC, China) for the support in providing computing facilities.

Figure 7. Plot of 13C chemical shift of acetone on Lewis acid sites (in ppm) versus the lowest unoccupied molecular orbital (LUMO) energy (in eV). The dashed line corresponds to the case where all nine Lewis acid models are considered and the solid line to that where all of the Lewis acid models except the L-Al(OH)3 and L-AlOOH sites (2) are considered.

line, R2 ) 0.91), and deviations exist in the region of weak acidity. As mentioned above, the LUMO orbital of the LAl(OH)3 and L-AlOOH acid sites is mainly related to the acidic proton of the bridging hydroxyl group rather than the AlL atom, whereas the 13C chemical shift of acetone is related to electronaccepting ability of the AlL atom. Therefore, it is not appropriate to correlate the 13C chemical shift of acetone with LUMO energy for the L-Al(OH)3 and L-AlOOH acid sites. When these two sites are not involved, a fairly linear correlation is found (the solid line, R2 ) 0.97). Table 2 also gives the experimental values of the 13C chemical shift of acetone for several true solid Lewis acids, whose acid strengths are almost close to those of the Lewis acid site models here. It should be kept in mind that different center metal atoms (such as Al and Zn) may lead to different catalytic activities, though their acid strengths are similar. The oxidation-reduction properties of the metal atoms would also play an important role in catalysis reactions.60,61 Now, the quantitative relationships between the 13C chemical shift of acetone and intrinsic acid strength (as DPE and LUMO energy) have been established for Brønsted and Lewis acid sites, respectively. Thus, the acidic properties of solid acids would be understood more accurately and thoroughly. Recently, Iglesia and co-workers have developed rigorous relationships between rate constants for alkanol dehydration and alkane isomerization reactions and DPE values of Keggin-type heteropoly acids and H-BEA zeolite, and these relationships can be used to estimate the intrinsic acid strength (DPE) of solid acids with uncertain structures (such as sulfated zirconia, tunstated zirconia, and perfluorosulfonic acid resins, etc.) from their dehydration and isomerization rate constants.62 Herein, the correlations between the 13C chemical shift of acetone and DPE or LUMO energy may also be applied to quantitatively determine the intrinsic acid strength of Brønsted and Lewis acid sites with uncertain structures as long as the 13C chemical shift of acetone is determined experimentally. 4. Conclusions In this work, adsorptions of acetone on Brønsted and Lewis acid site models with varied acid strengths were studied by using

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