How Strained are Carbomeric-Cycloalkanes? - American Chemical

May 20, 2010 - The ring strain energies of carbomeric-cycloalkanes (molecules with one or more acetylene spacer units placed into carbon single bonds)...
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J. Phys. Chem. A 2010, 114, 6705–6712

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How Strained are Carbomeric-Cycloalkanes? Matthew D. Wodrich, Je´roˆme F. Gonthier, Stephan N. Steinmann, and Cle´mence Corminboeuf* Laboratory for Computational Molecular Design, Institut des Sciences et Inge´nierie Chimiques, Ecole Polytechnique Fe´de´rale de Lausanne, CH-1015 Lausanne, Switzerland ReceiVed: April 1, 2010; ReVised Manuscript ReceiVed: May 7, 2010

The ring strain energies of carbomeric-cycloalkanes (molecules with one or more acetylene spacer units placed into carbon single bonds) are assessed using a series of isodesmic, homodesmotic, and hyperhomodesmotic chemical equations. Isodesmic bond separation reactions and other equations derived from the explicitly defined hierarchy of homodesmotic equations are insufficient for accurately determining these values, since not all perturbing effects (i.e., conjugation and hyperconjugation) are fully balanced. A set of homodesmotic reactions is proposed, which succeeds in balancing all stereoelectronic effects present within the carbomeric rings, allowing for a direct assessment of the strain energies. Values calculated from chemical equations are validated using an increment/additivity approach. The ring strain energy decreases as acetylene units are added, manifesting from the net stabilization gained by opening the C-CH2-C angle around the methylene groups and the destabilization arising from bending the C-CtC angles of the spacer groups. This destabilization vanishes with increasing parent ring size (i.e., the angle distortion is less in the carbomeric-cyclobutanes than in the carbomeric-cyclopropanes), leading to strain energies near zero for carbon-cyclopentanes and carboncyclohexanes. Introduction Ring strain1 represents an important and useful paradigm in chemistry, the release of which provides the driving force for many proposed reaction mechanisms. Despite being predominately associated with organic systems, considerable attention has been devoted to determining the strain energies of both organic2–5 and inorganic6–9 compounds. While not an experimental observable, numerous attempts to quantify these energetic values remains a hotly debated topic, none so more than for the deceptively simple hydrocarbon cyclopropane.10–12 Evaluations frequently employ chemical equations, which attempt to balance all structural and stereoelectronic features present within a ring, except the strain itself. These equations can be grouped into various reaction classes, based on the degree to which bonding and hybridization environments are matched,13 including isodesmic,14–16 homodesmotic,17–19 hyperhomodesmotic,20,21 as well as numerous others.22–30 Since hyperhomodesmotic and, to a lesser degree, homodesmotic reactions were designed to match hybridization and bonding environments in products and reactants, they are generally used to derive “conventional” estimates of strain energies for small cycloalkane rings (Figure 1).18,31 Similar values are also obtained using additivity schemes based on the assumption that cyclohexane is a strain-free molecule.31 By dividing the heat of formation of cyclohexane by six, one derives an idealized “strain-free” heat of formation for each methylene group. The ring strain of a molecule of interest is then assessed by subtracting this idealized heat of formation (based on the additivity scheme) from the actual molecule heat of formation (based on experiment or computation). Carbomers,34 expanded organic molecules with one or more CtC moieties inserted into the bonds of a parent compound were first synthesized by Scott and co-workers,35,36 and have since seen continued interest by chemists, particularly in regards to the possible (homo)aromatic character of carbo1-cycloal* To whom correspondence [email protected].

should

be

addressed.

E-mail:

Figure 1. “Conventional” estimates for the ring strain of small cycloalkanes derived using homodesmotic equations. Values calculated from experimental heats of formation.32,33

kanes37 (cycloalkanes with one CtC inserted into each CH2-CH2 bond).38–45 The effect on the ring strain energy caused by incorporation of a single or multiple acetylene moieties into a cycloalkane is of key interest, as it may lead to enhanced understanding of the physical properties underlying carbomers in general. In this article, we employ computational methodologies coupled with the use of isodesmic, homodesmotic, and hyperhomodesmotic equations to assess the ring strain of carboncycloalkanes (n ) 1,2) (Figure 2). These results are compared with ring strain energies derived using an additivity/increment approach. Computational Details Since experimental heats of formation are not available for most compounds tested, the B3LYP46,47 and M06-2X48,49 energies along with unscaled ZPE/298K thermal corrections with the cc-pVTZ basis set have been utilized.50 B3LYP represents the most used functional for chemical applications, despite welldocumented inadequacies dealing with energetic descriptions of some organic systems.51–68 In contrast, the M06-2X functional

10.1021/jp1029322  2010 American Chemical Society Published on Web 05/20/2010

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Figure 2. Schematic representation of cycloalkanes (a), carbo1cycloalkanes (b), and carbo2-cycloalkanes (c) studied.

was developed and parametrized largely to overcome known shortcomings of earlier functionals, and has been shown to perform well for organic system energies.69–71 For the purposes of benchmarking the density functional theory (DFT) computations, the G4,72 G3,73 and G3MP274 298 K enthalpies are also given. The T1 and D1 diagnostics of carbon-cycloalkanes indicate negligible multireference character.75 All structures are minima on the potential energy surface as indicated by vibrational frequency analysis. The out-of-plane tensor component of the nucleus independent chemical shifts (NICSzz)76–79 were computed using the GIAO approach with PW9180 and the IGLO-III basis set. All computations were performed using Gaussian09.81 Results and Discussion The total (de)stabilization of a molecule may be evaluated using the isodesmic bond separation reaction of Pople.14–16 In this type of reaction, the number of bonds of a given formal type is retained, but their relationship to one another is changed. The isodesmic bond separation reactions and their energies for n-cycloalkanes (n ) 3-6), along with their carbomeric counterparts, are provided in Figure 3 and Table 1. The different carbomeric structures are separated into classes (i.e., cycloalkanes with 0, 1, or 2 acetylene spacers) by their bond separation energies (BSEs) (Figure 4). Although these equations are not representative of ring strain energies for these compounds, the increased endothermicity illustrates the significant energetic stabilization from conjugation and hyperconjugation interactions introduced upon incorporation of the acetylene and diacetylene spacer units.82 For the carbomeric-cyclopropanes, the addition of one acetylene spacer adds roughly 40 kcal/mol of stabilization, while the addition of two acetylene spacers between each methyl group adds nearly 100 kcal/mol! As the parent ring size increases (i.e., the number of methylene groups), these differences grow even larger, caused by the ever increasing stabilization arising from the conjugation and hyperconjugation present in carbomers, but absent in the parent cycloalkane species. Thus, carbo2-cyclohexane (4c) has a BSE over 160 kcal/mol greater than cyclohexane (4a), indicating greatly enhanced stabilization. While the energies associated with isodesmic bond separation reactions allow for an assessment of net (de)stabilization within a molecule of interest, equations providing a more complete balance of hybridization and bonding effects allow for the accurate assessment of only the ring strain in carbon-cycloal-

Figure 3. Bond separation equations and energies (computed at the G3 level) for compounds 1a-4c. Equations 9 and 12 computed at the G3MP2 level.

kanes. Within the hierarchy of homodesmotic equations,13 those which satisfy the rigid rules of hyperhomodesmotic provide a quite accurate matching of such elements. For hydrocarbons, a chemical equation is hyperhomodesmotic if 16 different bond types are conserved (H2CdCH, HCdCH, H2CdC, HC)C, CdC, HC-CH, HC-C, C-C, H3C-CH2, H3C-CH, H2C-CH2, H3C-C, H2C-CH, H2C-C, HCtC, CtC).83 To a large extent, hyperhomodesmotic equations remove energetic perturbations from the assessment of ring strain by balancing stereoelectronic interactions present within the ring with large reference molecules containing the same or similar types of interactions. However, for some systems, as is the case for carbon-cycloalkanes, these effects are not fully balanced. Figure 5 provides hyperhomodesmotic descriptions of the cyclopropane through the cyclohexane family of carbomers (1a-4c). Hyperhomodesmotic equations 14, 17, 20, and 23 do balance all hyperconjugation interactions, but the energetic attenuation present when one methylene group is situated between two CC bonds (cross-hyperconjugation10) is not considered. The same problems plague the hyperhomodesmotic evaluations of the ring strain energy of carbo2-cycloalkanes (1c-4c) (eqs 15, 18, 21, and 24). For instance, in eq 15 the number of conjugation interactions is balanced, but the matching of hyperconjugation, again, does not take into account attenuation from cross-hyperconjugation10. The results of such imbalances

How Strained are Carbomeric-Cycloalkanes?

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TABLE 1: Evaluations of Ring Strain Energies (in kcal/mol) for Compounds 1a-4c Using Various Equationsa compound (number)

reaction type (number)

B3LYP/cc-pVTZ

M06-2X/cc-pVTZ

G3MP2

G3

cyclopropane (1a) carbo1-cyclopropane (1b) carbo2-cyclopropane (1c) cyclopropane (1a) carbo1-cyclopropane (1b) carbo2-cyclopropane (1c) carbo1-cyclopropane (1b) carbo2-cyclopropane (1c) cyclobutane (2a) carbo1-cyclobutane (2b) carbo2-cyclobutane (2c) cyclobutane (2a) carbo1-cyclobutane (2b) carbo2-cyclobutane (2c) carbo1-cyclobutane (2b) carbo2-cyclobutane (2c) cyclopentane (3a) carbo1-cyclopentane (3b) carbo2-cyclopentane (3c) cyclopentane (3a) carbo1-cyclopentane (3b) carbo2-cyclopentane (3c) carbo1-cyclopentane (3b) carbo2-cyclopentane (3c) cyclohexane (4a) carbo1-cyclohexane (4b) carbo2-cyclohexane (4c) cyclohexane (4a) carbo1-cyclohexane (4b) carbo2-cyclohexane (4c) carbo1-cyclohexane (4b) carbo2-cyclohexane (4c)

isodesmic (1) isodesmic (2) isodesmic (3) hyperhomodesmotic (13) hyperhomodesmotic (14) hyperhomodesmotic (15) homodesmotic (25) homodesmotic (26) isodesmic (4) isodesmic (5) isodesmic (6) hyperhomodesmotic (16) hyperhomodesmotic (17) hyperhomodesmotic (18) homodesmotic (27) homodesmotic (28) isodesmic (7) isodesmic (8) isodesmic (9) hyperhomodesmotic (19) hyperhomodesmotic (20) hyperhomodesmotic (21) homodesmotic (29) homodesmotic (30) isodesmic (10) isodesmic (11) isodesmic (12) hyperhomodesmotic (22) hyperhomodesmotic (23) hyperhomodesmotic (24) homodesmotic (31) homodesmotic (32)

-18.70 18.55 89.58 -23.46 -36.17 -20.76 -27.04 -16.63 -16.82 50.83 136.57 -23.17 -22.13 -10.54 -9.95 -5.04 2.80 72.20 175.40 -5.14 -19.00 -8.50 -3.79 -1.62 9.47 87.15 210.81 -0.06 -22.29 -9.86 -4.03 -1.60

-17.88 17.11 77.12 -25.94 -35.88 -20.85 -26.01 -16.10 -17.41 49.23 119.86 -28.16 -21.43 -10.77 -8.26 -4.43 3.64 69.25 154.99 -9.81 -19.07 -8.31 -2.61 -0.38 12.57 83.35 185.41 -3.56 -22.64 -10.54 -2.89 -1.02

-20.27 19.29 76.06 -28.71 -30.58 -14.06 -22.92 -13.15 -15.89 50.01 116.14 -27.13 -16.49 -4.02 -6.28 -2.81 6.42 69.42 148.49 -7.64 -13.70 -1.71 -0.93 -0.20 15.68 83.56 177.17 -1.19 -16.49 -3.07 -0.87 -1.26

-20.11 19.61 78.50 -28.60 -33.22 -18.12 -23.73 -13.65 -15.74 51.17 119.84 -27.05 -19.27 -8.97 -6.61 -3.02 6.62 71.21

a

-7.52 -16.84 -1.02 15.93 85.81 -1.05 -19.85 -0.86

Recommended equations and their corresponding quantitative values are given in bold.

Figure 4. Isodesmic BSEs (from Figure 3 equations) of 1a-4c, in kcal/mol. Negative values indicate net molecular strain, while positive values indicate net molecular stabilization.

are easily visualized in the ring strain energies provided in Figure 6, which show two unexpected results: (i) carbon-cyclohexanes having appreciably higher strain energies than the carboncyclopentanes and (ii) carbo1-cyclopropane (1b) having a larger strain energy than cyclopropane (1a). These shortcomings arising from the various hyperconjugation imbalances make hyperhomodesmotic assessments of strain for the carboncycloalkanes less than ideal.

Since equations derived from the homodesmotic hierarchy13 are unsuitable for assessing the ring strain of carbon-cycloalkanes, we propose a set of homodesmotic reactions that match conjugation and hyperconjugation interactions as closely as possible (Figure 7). Equation 25 balances the six crosshyperconjugations10 (two for each methylene group) in carbo1cyclopropane (1b) with three 1,4-pentadiyne molecules. The use of 1,4-pentadiyne as a reference molecule allows for the accurate matching of the energetic attenuation when multiple triple bonds are hyperconjugated to a single methylene group (crosshyperconjugation). Similarly, eq 26 matches all conjugation and hyperconjugation in carbo2-cyclopropane (1c) with three 1,3,6,8nonatetrayne molecules. Corresponding equations (27-32) provide assessments of the strain energies of larger carbomers (2b-4c). Alternatively, a different strategy based on the additivity/ increment method can be employed to determine ring strain energies. This option is beneficial since it allows determination of energetic perturbations arising from homoaromaticity, which may not be compensated for in the recommended chemical equations. As the experimental heats of formation are unavailable for carbon-cycloalkanes values must first be derived from computation. The quantities may be obtained from any chemical reaction for which well-established experimental ∆Hf of reactants and products (other than the ∆Hf of the unknown compound) are available. It has been shown that equations matching hybridization and bonding elements benefit greatly from error cancellation and provide more accurate values of the unknown heat of formation. Therefore, we have used the hyperhomodesmotic reactions shown in Figure 5 to determine these quantities (Table 2).84 Since the carbon-cyclohexanes show

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Figure 5. Hyperhomodesmotic reactions for 1a-4c. Values computed at the G3 level of theory.

no appreciable angle deformations from ideal values, they are taken as a “strain-free” reference compounds from which an increment value can be derived and a corresponding “ideal ∆Hf” determined. The strain energies of other carbomers are calculated by multiplying the “strain-free” increment value by the number of units in the molecule of reference (i.e., three for carbomcyclopropane, four for carbom-cyclobutane, etc.) and subtracting the actual molecular heat of formation (third column of Table 3) from that of the ideal value (second column of Table 3) calculated from the increment scheme. The process is demonstrated by the following equation: SE(n - carbom - cycloalkane) ) ∆Hf(carbom - cyclohexane) - ∆Hf(n - carbom - cycloalkane) n 6

(

)

where m is the number of acetylene spacer units and n is the parent ring size. The corresponding ring strain energies determined by this additivity/increment method are provided in Table 3. These newly derived ring strain values closely parallel those from the chemical equations (Figure 8). This serves as an independent validation of our choice of homodesmotic equations and, further, rules out any significant stabilization arising from

Figure 6. Hyperhomodesmotic assessments of the strain energy of compound 1a-4c, in kcal/mol.

How Strained are Carbomeric-Cycloalkanes?

J. Phys. Chem. A, Vol. 114, No. 24, 2010 6709 TABLE 3: Strain Energies Calculated Using the Additivity Methoda compound 1

carbo -cyclopropane carbo1-cyclobutane carbo1-cyclopentane carbo1-cyclohexane carbo2-cyclopropane carbo2-cyclobutane carbo2-cyclopentane carbo2-cyclohexane

ideal ∆Hf298K

actual ∆Hf298K

strain energy

159.84 213.12 266.40 319.68 316.71 422.29 527.86 633.43

182.27 218.71 266.48 319.69 329.24 424.26 527.01 633.43

-22.43 -5.59 +0.08 0.00 -12.53 -1.97 +0.85 0.00

a Carbo1-cycloalkane values are derived from G4 heats of formation, and carbo2-cycloalkanes are derived from G3MP2 heats of formation. All values in kcal/mol.

Figure 8. Strain energies of carbon-cycloalkanes calculated via chemical equations (y-axis) and increment scheme (x-axis). The R2 value of 0.9998 shows excellent agreement between the two methods.

Figure 7. Recommended equations for the evaluation of strain energies of 1b-4c. Values computed at the G3 or G3MP2 (for eqs 30 and 32) level of theory.

TABLE 2: Deviations from Calculated Heats of Formation at Various Theoretical Levels Computed from Hyperhomodesmotic Equationsa compounds 1

carbo -cyclopropane carbo1-cyclobutane carbo1-cyclopentane carbo1-cyclohexane carbo2-cyclopropane carbo2-cyclobutane carbo2-cyclopentane carbo2-cyclohexane carbo1- increment carbo2- increment

B3LYP/ M06-2X/ cc-pVTZ cc-pVTZ G3MP2 3.95 3.50 2.62 2.72 2.65 1.59 6.79 6.79 0.46 1.13

3.67 2.80 2.69 3.07 2.75 1.59 6.60 7.47 0.51 1.25

G3

-1.63 1.01 -2.14 0.64 -2.68 0.46 -3.38 0.27 -4.05 333.28 -4.93 429.20 527.01 633.43 -0.56 0.05 105.57

G4 182.27 218.71 266.48 319.69

53.28

a

Heats of formation (at the highest computed level) in italics. Increment values used for computing the strain energy via the additivity method are given in bold. Values given in kcal/mol.

homoaromaticity within the carbon-cycloalkane system. The presence of any perturbing effects would cause noted deviations between those evaluations provided by the two methods, which is not seen in Figure 8. Figure 9 shows the ring strains (derived from the recommended chemical equations) of carbo1-, carbo2-, and their parent cycloalkanes as a function of the number of methylene groups. Readily apparent is the decrease in strain energy as the parent ring size increases, resulting from the expansion of the

Figure 9. Strain energies, in kcal/mol, of carbon-cycloalkanes (n ) 0-2) as a function of ring size.

C-CH2-C angles that are closer to the idealized 109° (Figure 10). The addition of acetylene and, to an even greater extent, diacetylene groups plays a key role in reducing strain. The small difference in strain energy between cyclopropane and cyclobutane of only 1 kcal/mol likely arises from the presence of σ-delocalization3,85,86 within cyclopropane (1a), which is reduced in carbo1-cyclopropane (1b) and carbo2-cyclopropane (1c) as indicated by the out-of-plane tensor component of NICS (NICSzz, Table 4), a more accurate reporter (as compared to isotropic NICS) of magnetic aromaticity.87–91 The single largest factor introducing strain into carbo1- and carbo2-cycloalkanes

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Figure 10. B3LYP/cc-pVTZ geometries and point groups of 1a-4c.92 Structures correspond to global minima on the potential energy surface.93

TABLE 4: NICS Out-of-Plane Tensor Component Values at the Geometric Center of 1a-1c compound

NICS(0)zz

cyclopropane (1a) carbo1-cyclopropane (1b) carbo2-cyclopropane (1c)

-30.6 -7.2 +9.1

is the deviation of the acetylene and diacetylene groups from their idealized linear (180°) geometry. For carbo1-cyclopropane (1b), the angle deviation is greater than 20° for the CtC-C angle (Figure 10). The resulting increase in the C-CH2-C bond angle coupled with the decrease in the CtC-C has an overall net effect of reducing the ring strain energy. For carbo2cyclopropane (1c), which has greater flexibility owing to its

larger size, the angles around the acetylene groups are opened compared to carbo1-cyclopropane, to 166.5° and 170.0°, resulting in further strain reduction. As the number of methylene groups increases, these angles deviate from the ideal 180° even less. For the carbo1-cycloalkane (1b-4b), the angles are 159.1°, 170.8°, 177.9°, and 179.5°, respectively, thus strain is reduced from 24 kcal/mol in carbo1-cyclopropane to ∼0 kcal/mol in carbo1-cyclopentane and carbo1-cyclohexane (3b, 4b). These angle values rationalize the nearly nonexistent ring strain in 3b and 4b, since neither the C-CH2-C nor the CtC-C angles deviate significantly from their ideal values as derived from their hybridization state. The carbo2-cycloalkanes benefit from this same effect, although their larger structures permit angle deviations that are smaller from idealized values. This is

How Strained are Carbomeric-Cycloalkanes? illustrated by the decreased strain energy of carbo2-cyclopropane (1c, 14 kcal/mol) as compared to carbo1-cyclopropane (1b, 24 kcal/mol) and cyclopropane (1a, 28 kcal/mol). Conclusion The ring strains of the carbomeric structures of cyclopropane, cyclobutane, cyclopentane, and cyclohexane have been computed using a series of isodesmic, homodesmotic, and hyperhomodesmotic equations. Both isodesmic and hyperhomodesmotic equations falling within the rigid definitions of the hierarchy of homodesmotic equations13 do not balance all conjugation and hyperconjugation effects present within the carbomeric ring systems and, thus, are ill-suited for assessing their ring strain energies. In contrast, our recommended homodesmotic reactions closely balance all stereoelectronic effects present other than the ring strain itself: they provide accurate and unbiased values from the ring strain of these systems. These chemical equation values are further supported by assessments based on an increment/additivity scheme. Approaches based on a combination of these two methodologies may also be used to probe the physical properties of other carbomeric systems, including those with a larger number of spacer units, cage compounds, or molecules doped with heteroatoms. A clear decrease in strain energy is seen as the parent number of methylene groups is increased. This trend holds for the acetylene- and diacetylene-carbomers: the strain energy of carbo1-cyclopropane (24 kcal/mol) > carbo1-cyclobutane (7 kcal/ mol) > carbo1-cyclopentane (1 kcal/mol) ≈ carbo1-cyclohexane (1 kcal/mol) and carbo2-cyclopropane (14 kcal/mol) > carbo2cyclobutane (3 kcal/mol) > carbo2-cyclopentane (0 kcal/mol) ≈ carbo2-cyclohexane (1 kcal/mol). The strain energy of the carbo2-species is also reduced in comparison to both the carbo1and parent cycloalkanes, owing to the closer matching of idealized bond angles, which result from having a more flexible ring. Acknowledgment. The Sandoz family foundation, the Swiss NSF Grant 200021_121577/1, and EPFL are acknowledged for financial support. Supporting Information Available: Electronic energies at various computational levels, experimental and computed heats of formation of relevant compounds, and computed molecular geometries at the B3LYP/cc-pVTZ level. This information is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) Baeyer, A. Ber. Dtsch. Chem. Ges. 1885, 18, 2269. (2) Brown, H. C.; Fletcher, R. S.; Johannesen, R. B. J. Am. Chem. Soc. 1951, 73, 212. (3) Cremer, D.; Kraka, E. J. Am. Chem. Soc. 1985, 107, 3800. (4) Wiberg, K. B.; Bonneville, G.; Dempsey, R. Isr. J. Chem. 1983, 23, 85. (5) Wiberg, K. B. Angew. Chem., Int. Ed. Engl. 1986, 25, 312. (6) Schoeller, W. W.; Staemmler, V.; Rademacher, P.; Niecke, E. Inorg. Chem. 1986, 25, 4382. (7) Gimarc, B. M.; Zhao, M. Inorg. Chem. 1996, 35, 3289. (8) Li, Z. H.; Moran, D.; Fan, K. N.; Schleyer, P. v. R. J. Phys. Chem. A 2005, 109, 3711. (9) Peverati, R.; Siegel, J. S.; Baldridge, K. K. Phys. Chem. Chem. Phys. 2009, 11, 2387. (10) Wodrich, M. D.; Wannere, C. S.; Mo, Y.; Jarowski, P. D.; Houk, K. N.; Schleyer, P. v. R. Chem.sEur. J. 2007, 13, 7731. (11) Fishtik, I. J. Phys. Chem. A 2010, 114, 3731. (12) Schleyer, P. v. R.; McKee, W. C. J. Phys. Chem. A 2010, 114, 3737. (13) Wheeler, S. E.; Houk, K. N.; Schleyer, P. v. R.; Allen, W. D. J. Am. Chem. Soc. 2009, 131, 2547.

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