Application of a Semi-homodesmotic Approach in Estimating Ring

Article pubs.acs.org/JPCA

Application of a Semi-homodesmotic Approach in Estimating Ring Strain Energies (RSEs) of Highly Substituted Cyclobutanes: RSEs for c‑C4R8 That Make Sense Thomas M. Gilbert* Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115, United States S Supporting Information *

ABSTRACT: A semi-homodesmotic method for estimating of ring strain energies (RSEs) of substituted cyclopropanes is applied to substituted cyclobutanes c-C4HxR8−x (R = F, Cl, Me; x = 0, 2, 4). Whereas (hyper)homodesmotic reaction methods predict implausible results, particularly for c-C4R8, the semi-homodesmotic approach provides RSEs consistent with thermodynamic and independent computational data regardless of the degree of substitution. The method requires employing homodesmotic group equivalent reactions only for disubstituted cyclobutanes, relying solely on absolute energy calculations for more substituted rings. We find that, consistent with QTAIM data, RSEs increase with substitution regardless of the electronic nature of R, although the increase is more dramatic when R is electron-withdrawing. Overall, the semi-homodesmotic method is simpler than hyperhomodesmotic approaches and gives more trustworthy results.

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INTRODUCTION In the preceding paper,1 we showed that (hyper)homodesmotic reaction methods give implausible, sometimes negative, ring strain energies (RSEs) for highly substituted cyclopropanes. It appears that the source of the problem is that such methods do not properly cancel the intramolecular interaction energies associated with substituents in the acyclic reference molecules. Such energies can be significant; Corminbouef et al. suggested2 that the repulsion energy associated with the methyl groups in RMe2C···CMe2R interactions can reach ca. 18 kcal mol−1. It is obvious that if an energy contribution of this magnitude is not fully balanced in a homodesmotic reaction, the resulting RSE will be sizably inaccurate. It seems likely that this problem has engendered a modest controversy in the field of fluorosubstituted cyclobutanes. On the basis of thermodynamic3 and computational4 homodesmotic calculations, it has been suggested that substituting fluorine for hydrogen in cyclobutanes lowers the RSEs, such that RSE(c-C4F8) is approximately half to two-thirds as large as that of c-C4H8 (14−18 vs 26.5 kcal mol−1).5,6 It is possible that the observation that perfluoroethene dimerizes to form octafluorocyclobutane7 supports this, but such a view neglects the fact that thermodynamically fluorine prefers binding to an sp3 carbon over an sp2 carbon (an outcome of Bent’s Rule).8 A later thermodynamic calculation suggested RSE(c-C4F8) = 53 ± 11 kcal mol−1, twice that of cyclobutane.9 Liebman et al.5 showed that using (hyper)homodesmotic reactions to predict RSEs for such highly substituted cyclobutanes is the root of the disagreements, finding RSEs (c-C4F8) ranging from 13−70 kcal mol−1, and RSEs (c-C4Cl8) ranging from −42 to +70 kcal mol−1, depending upon the acyclic reference molecules employed. That such wide ranges are observed means that (hyper)homodesmotic reactions here are inherently incon© 2014 American Chemical Society

sistent, and thus unusable. Liebman et al. recognized that intramolecular interactions between halide substituents in the acyclic reference molecules were probably not being canceled properly, but they were unable to find a methodology that reliably did so. Their use of diagonal/ultradiagonal methods5 gave RSE(c-C4F8) = 18.2 kcal mol−1 and RSE(c-C4Cl8) = −5.5 kcal mol−1, the former of which is incompatible with the thermodynamic prediction, and the latter of which is implausible as a negative value. We overcame this problem in the preceding paper by developing and employing a semi-homodesmotic approach that relied on canceling intramolecular interactions and on limiting the use of acyclic reference molecules to reactions involving disubstituted rings. The RSEs derived were consistent with limited thermodynamic data and with trend predictions from quantum theory of atoms in molecules (QTAIM) calculations. It was of interest to determine whether an analogous semihomodesmotic approach could be used to predict RSEs for highly substituted cyclobutanes. We report here RSEs for 1,1,2,2-tetra-, 1,1,2,2,3,3-hexa-, and octasubstituted cyclobutanes containing methyl, fluoro, and chloro substituents, estimated by several different (hyper)homodesmotic reactions and by a semi-homodesmotic approach. We find that the former method provides implausible RSE values and trends, whereas the latter gives RSEs that appear sensible and consistent with thermodynamic and QTAIM computational data. Received: June 13, 2014 Revised: July 10, 2014 Published: July 21, 2014 6060

dx.doi.org/10.1021/jp5058995 | J. Phys. Chem. A 2014, 118, 6060−6067

The Journal of Physical Chemistry A

Article

Figure 1. Skeleton homodesmotic reactions used to estimate RSEs of cyclobutane (A = B = X = Y = H), and 1,1-disubstituted (A = substituent R, B = X = Y = H), 1,1,2,2-tetrasubstituted (A = B = R, X = Y = H), 1,1,2,2,3,3-hexasubstituted (A = B = X = R, Y = H), and octasubstituted (A = B = X = Y = R) cyclobutanes.

Scheme 1

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COMPUTATIONAL METHODS Most of the computational methodology employed was described in the preceding paper1 and so will not be repeated here. One difference involved polymethyl cyclobutanes and associated acyclic reference molecules, for which initial optimizations and frequency analyses were performed at the M06-2X10/6-31+G(d) level. This was done because the starting structures were routinely taken directly from conformation space scans that used this model chemistry. The structures were then reoptimized at the Model/6-311+G(d, p) levels (Model = M06-2X, MP211); the wB97Xd model was not used because our previous data showed that RSEs determined from it differed little from those from the M06-2X model. As before, quantum theory of atoms in molecules (QTAIM)12−14 critical point, bond path, and bond path angle calculations were performed using M06-2X/6-311+G(d,p) (6d, 10f) wave functions and the AIMAll program.15 Skeleton homodesmotic reactions used to estimate RSEs for gem-substituted rings are shown in Figure 1. As before,1 reaction 1 is a hypohomodesmotic group equivalent reaction,16 reaction 2 is homodesmotic, and reaction 3 is hyperhomodesmotic.17 Reactions 4−6 were used to estimate RSEs for the cis/trans correction term in the semi-homodesmotic

approach. The designator shorthand involves using c or t to imply cis or trans orientations, and a or b to designate different products.

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RESULTS AND DISCUSSION Semi-homodesmotic Approach. As previously described,1 the semi-homodesmotic approach to estimating RSEs for highly substituted cycloalkanes involves designing reactions involving highly substituted rings in terms of disubstituted rings, where the key feature is that geminal RCR and cofacial RCCR/RCCH/HCCH interactions cancel rather than ensuring that bond energies/atom environments cancel. The error associated with the latter is treated as a parameter Δ, calculated by comparing electronic energies of rings alone. This is why we characterize the method as semihomodesmotic. RSEs of disubstituted rings are employed because they are expected to exhibit the smallest errors resulting from incorrect accounting of intramolecular interactions in acyclic reference molecules. Semi-homodesmotic reactions pertinent to estimating RSEs for highly substituted cyclobutanes appear in Scheme 1. The energetic components of the species in the top reaction in the 6061



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Figure 2. Skeleton homodesmotic reactions used to estimate RSEs of cis- and trans-1,2-disubstituted cyclobutanes.

scheme can be rearranged18 to express the RSE of a 1,1,2,2tetrasubstituted cyclobutane as

three terms: one characterizing the extent to which 1,1disubstitution affects the RSE vs that of cyclobutane, one a cis/ trans ring correction term associated with the difference in RSEs between cis- and trans-1,2 disubstituted cyclobutane isomers, and one the Δ correction term that accounts for uncanceled interactions. The last two terms are expected to be small, because the RSEs for the 1,2-disubstituted rings are unlikely to differ significantly, and because the bond energy differences incorporated into Δ tend to cancel.18 The Δ term is

RSE(c ‐1,1,2,2‐C4H4R 4) = [2RSE(c ‐1,1‐C4H6R 2) − RSE(c ‐C4 H8)] + 2[RSE(c ‐cis‐1,2‐C4H6R 2) − RSE(c ‐trans‐1,2‐C4H6R 2)] + Δ

(1)

Equation 1 mimics that for 1,1,2,2-tetrasubstituted cyclopropanes in that RSE(c-1,1,2,2-C4H4R4) is determined by 6062



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Table 1. Predicted RSEs (kcal mol−1) for 1,1Difluorocyclobutane, 1,1,2,2-Tetrafluorocyclobutane, 1,1,2,2,3,3-Hexafluorocyclobutane, and Octafluorocyclobutane Using Different Models (6311+G(d,p) Basis Set) and the Homodesmotic Reactions in Figure 1

estimated as the overall electronic reaction energy of the reaction, so its determination requires no RSE calculations. The energetic components of the species in the middle reaction in Scheme 1 can be rearranged to express the RSE of a 1,1,2,2,3,3-hexasubstituted cyclobutane as RSE(c ‐1,1,2,2,3,3‐C4H 2R 6) = 2RSE(c ‐1,1,2,2‐C4H4R 4) − RSE(c ‐1,1‐C4H6R 2)

This is more appropriately represented in terms of the semihomodesmotic method by substituting for RSE(c-1,1,2,2C4H4R4) from eq 1: RSE(c ‐1,1,2,2,3,3‐C4H 2R 6) = 3RSE(c ‐1,1‐C4H6R 2)

(2)

Similarly, the energetic components of the species in the bottom reaction in Scheme 1 can be rearranged to express the RSE of an octasubstituted cyclobutane as RSE(c ‐C4 R 8) = 4RSE(c ‐1,1,2,2‐C4H4R 4) − 4RSE(c ‐1,1‐C4H6R 2) + RSE(c ‐C4H8)

RSE(c ‐C4R 8) = 4RSE(c ‐1,1‐C4H6R 2) − 3RSE(c ‐C4H8) + 8[RSE(c ‐cis‐1,2‐C4H6R 2) − RSE(c ‐trans‐1,2‐C4H6R 2)] (3) 1

1 2 3

28.9 28.7 28.4

MP2

M062X

27.8 27.8 27.9

15.2 15.0 33.0

MP2

M062X

14.2 14.5 32.1

27.5 27.2 27.8

c-C4F8

MP2

M062X

MP2

26.4 26.4 27.2

24.0 24.2 25.7

23.4 22.9 24.6

Table 2. Difference between the QTAIM Bond Path Angle and the Geometric Bond Angle (deg) for Ring Carbon Atoms in Cyclobutane, 1,1-Disubstituted Cyclobutanes, 1,1,2,2-Tetrasubstituted Cyclobutanes, 1,1,2,2,3,3Hexasubstituted Cyclobutanes, and Octasubstituted Cyclobutanes (M06-2X/6-311+G(d,p) Wavefunctions) (Average Values in Brackets)

In terms of the semi-homodesmotic method,

+ 4Δ

reaction

M062X

c-1,1,2,2,3,3C4H2F6

reactions, problems plausibly resulting from uncanceled intramolecular interactions in the acyclic reference molecules. As for the fluorocyclopropanes,1 we employed QTAIM data to suggest the proper trend for RSEs with fluorine substitution prior to applying the semi-homodesmotic approach. Previous reports indicate that ring strain is related to the degree to which the critical points are displaced from the geometric positions, which can be assessed by analyzing bond path angle differences.26−30 The data in the top two rows of Table 2

− 2RSE(c ‐C4H8) + 4[RSE(c ‐cis‐1,2‐C4H6R 2) − RSE(c ‐trans‐1,2‐C4H6R 2)] + 2Δ

c-1,1,2,2C4H4F4

c-1,1-C4H6F2

16

As before, we used Bachrach’s group equivalent method to provide RSE(c-1,1-disubstituted cyclobutane) values for the semi-homodesmotic approach. The cis/trans ring corrections were determined using the reactions in Figure 2, and Δ terms were determined as described in the Supporting Information. All terms were obtained as averages over the different model chemistries, and standard deviations were determined from the averages. The uncertainties described by the standard deviations were propagated through the semi-homodesmotic calculations using standard propagation of error techniques.19 RSE of c-C4H8. Our determinations of RSEs for cyclobutane employing the reactions in Figure 1 average 26.6(0.4) kcal mol−1 over the two models that include correlation (Supporting Information). This agrees well with the most recent computational predictions20−24 and with the “standard” thermodynamic value used in Benson’s calculations.25 We rounded this value to 27 kcal mol−1 and treated it as exact when propagating uncertainties within the semi-homodesmotic approach (see below). RSEs of Fluoro-Substituted c-C4HxF8−x. As stated in the Introduction, thermodynamic and computational estimations of RSEs based on (hyper)homodesmotic reactions are inconsistent. We confirmed this by estimating RSEs (Table 1) for gem-substituted fluorinated cyclobutanes using the reactions in Figure 1. Two features of the data are notable: one, the trend in RSEs with increased substitution is erratic, with RSE(c-1,1,2,2C4H4F4) < RSE(c-C4F8) < RSE(c-1,1,2,2,3,3-C4H2F6) = RSE(cC4H8) < RSE(c-1,1-C4H6F2); and two, though most predicted RSEs for a particular substituted cyclobutane are similar, reaction 3 gives a result for c-1,1,2,2-C4H4F4 pathologically disparate from the others. Both results suggest problems associated with determining RSEs from (hyper)homodesmotic

angle Δ

angle Δ

cC4H8

c-1,1-C4H6F2

6.3

15.2, 6.2, 6.2, 5.5 [8.3]

cC4H8

c-1,1-C4H6Me2

6.3 cC4H8

angle Δ

6.3

c-1,1,2,2C4H4F4

c-1,1,2,2,3,3C4H2F6

cC4F8

14.4, 14.4, 5.1, 5.1 [9.8] c-1,1,2,2C4H4Me4

13.9, 12.9,12.9, 5.2 [11.2] c-1,1,2,2,3,3C4H2Me6

12.2

c-1,1-C4H6Cl2

8.1, 8.1, 6.7, 6.7 [7.4] c-1,1,2,2C4H4Cl4

7.5, 7.6, 7.6, 6.9 [7.4] c-1,1,2,2,3,3C4H2Cl6

15.3, 5.6, 5.6, 5.5 [8.0]

13.7, 13.7, 4.7, 4.7 [9.1]

12.2, 12.2, 12.2, 3.9 [10.1]

7.2, 6.6, 6.6, 6.5 [6.7]

cC4Me8 7.5 cC4Cl8 10.7

show that these increase with increased substitution, predicting a forward [RSE(c-C4H8) < RSE(c-1,1-C4H6F2) < RSE(c-1,1,2,2C4H4F4) < RSE(c-1,1,2,2,3,3-C4H2F6) < RSE(c-C4F8)] trend for RSEs with substitution. This supports Inagaki et al.’s prediction of RSE(c-C4F8) = 53 kcal mol−1 and undermines the view that fluorine substitution decreases strain. To further explore the issue using the semi-homodesmotic approach, we determined the average RSE(c-1,1-C4H6F2) = 28.3(0.5) kcal mol−1 from group equivalent reaction 1. Data for the cis/trans ring correction term appear in Table 3. One sees that the different reactions predict quite variable RSEs, but the differences between RSEs for cis- and trans-isomers are nearly identical. This is a significant benefit of using the semihomodesmotic approach. The average correction amounts to 3.9(0.2) kcal mol−1. The value of Δ = 1.6(0.6) kcal mol−1 (Supporting Information). That both corrections are positive supports the prediction of a forward trend for the RSEs with substitution. As noted, the value of RSE(c-C4H8) was set to 27 kcal mol−1. 6063



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Table 3. Predicted RSEs (kcal mol−1) for cis- and trans-1,2Difluorocyclobutane and Differences Using Different Models (6-311+G(d,p) Basis Set) and the Homodesmotic Reactions in Figure 2 c-cis-1,2-C4H6F2

appear in Table 5. The corrections for reaction 6 are larger than those for the other reactions, but all are sufficiently small Table 5. Predicted RSEs (kcal mol−1) for cis- and trans-1,2Dimethylcyclobutane and Differences Using Different Models (6-311+G(d,p) Basis Set) and the Reactions in Figure 2

Δ

c-trans-1,2-C4H6F2

reaction

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

4a 4b 5a 5b 6

19.3 32.1 18.8 32.5 30.1

17.5 32.0 17.8 32.1 29.4

15.4 28.2 15.0 28.7 26.5

13.3 27.9 13.7 28.0 25.6

3.9 3.9 3.8 3.8 3.6

4.2 4.1 4.1 4.1 3.8

Substituting these values into eq 1 and propagating the uncertainties gave RSE(c-1,1,2,2-C4H4F4) = 39(1) kcal mol−1. This is markedly larger than the values predicted by homodesmotic reactions 1 and 2, and noticeably larger than that predicted by reaction 3. Using eqs 2 and 3, we found RSE(c-1,1,2,2,3,3-C4H2F6) = 50(2) kcal mol−1 and RSE(cC4F8) = 70(4) kcal mol−1. These are obviously significantly larger than those predicted by homodesmotic methods. However, they are consistent with the QTAIM-predicted trend. Moreover, the predicted RSE(c-C4F8), though overestimated compared to Inagaki et al.’s thermodynamic value,9 is far closer to it than most values predicted (hyper)homodesmotically. We therefore view the semi-homodesmotic approach as more successful here in predicting RSEs for highly fluoro-substituted cyclobutanes than (hyper)homodesmotic methods. RSEs of Methyl-Substituted c-C3HxMe6−x. RSEs for methyl-substituted cyclobutanes determined from homodesmotic reactions show behavior similar to that of methylsubstituted cyclopropanes: a reverse RSE trend with methyl substitution, and implausible, inconsistent negative RSEs for octamethylcyclobutane (Table 4). Even the RSEs for tetrasubstituted c-1,1,2,2-C4H4Me4 vary over an uncomfortably large 6 kcal mol−1 range. As for the cyclopropanes, the most likely cause is uncanceled intramolecular methyl−methyl interactions in the acyclic reference molecules, leading to sizable energetic consequences.2,31 QTAIM bond path angle data predict a modest forward RSE trend (Table 2, middle rows). As for the fluorocyclobutanes, the displacement of the critical points increases with substitution, implying that the RSEs should increase as well. However, the changes are extremely small, with the bond path angle increasing only 1.2° between c-C4H8 and c-C4Me8. Consequently, we anticipate RSEs that increase only slightly with substitution, in contrast to predictions from the (hyper)homodesmotic reaction results. The presence of a forward trend is further supported by the values for both the cis/trans ring correction and Δ terms in the semi-homodesmotic approach. Data regarding the former

Δ

c-cis-1,2-C4H6Me2

c-trans-1,2-C4H6Me2

reaction

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

4a 4b 5a 5b 6

26.1 17.9 25.4 18.1 23.4

25.7 17.5 24.9 18.4 23.6

26.0 17.9 25.4 18.0 22.3

25.5 17.3 24.8 18.2 22.6

0.1 0.0 0.0 0.1 1.1

0.2 0.2 0.1 0.2 1.0

as to have little impact on the semi-homodesmotic result. We chose to use the average value of 0.3(0.4) kcal mol−1. The value of Δ is also small, 1.3(0.1) kcal mol −1 (Supporting Information). That both corrections are positive points to a forward RSE trend. Because the QTAIM data and the small cis/trans ring correction and Δ terms in the semi-homodesmotic approach suggest only modest increases in RSEs with methyl substitution, it was especially critical to select a reliable value for RSE(c-1,1-C4H6Me2) before applying eqs 1−3. The QTAIM data suggested that this should be slightly larger than RSE(c-C4H8) = 26.6 kcal mol−1. The values for RSE(c-1,1C4H6Me2) in Table 5 oppose this, being similar and ca. 3 kcal mol−1 smaller than RSE(c-C4H8). This observation has been noted before,20,22 leading to its characterization as an example of the gem-dimethyl effect.23,24 Most recently, Bachrach examined a larger array of homodesmotic reactions and model chemistries,24 concluding that RSE(c-1,1-C4H6Me2) was at most about 2 kcal mol−1 smaller than RSE(c-C4H8). In this work, we estimated RSE(c-1,1-C4H6Me2) using a group equivalent reaction (Supporting Information),32 finding an average value of 25.2(0.3) kcal mol−1. Although this is still smaller than RSE(c-C4H8), and so will give rise to an erratic trend, in view of the prior results as well as ours, we cannot justify choosing another value. Moreover, as will be seen, this RSE when used with eqs 1−3 gives values acceptably consistent with the QTAIM data. Inserting the values above into eqs 1−3, we find RSE(c1,1,2,2-C4H4Me4) = 25(1) kcal mol−1, RSE(c-1,1,2,2,3,3C4H2Me6) = 26(2) kcal mol−1, and RSE(c-C4Me8) = 28(3) kcal mol−1. To the degree one can describe these as constituting a trend with increased substitution, it is forward (albeit irregular) and consistent with the very small changes in the QTAIM values. To give perspective regarding the trend, we assumed RSE(c-1,1-C4H6Me2) = RSE(c-C4H8) = 26.6 kcal mol−1 (i. e., setting the first term in eqs 1−3 to this value) and

Table 4. Predicted RSEs (kcal mol−1) for 1,1-Dimethylcyclobutane, 1,1,2,2-Tetramethylcyclobutane, 1,1,2,2,3,3Hexamethylcyclobutane, and Octamethylcyclobutane Using Different Models (6-311+G(d,p) Basis Set) and the Reactions in Figure 1 c-1,1-C4H6Me2

c-1,1,2,2-C4H4Me4

c-1,1,2,2,3,3-C4H2Me6

c-C4Me8

reaction

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

1 2 3

23.7 23.7 23.2

23.1 23.1 23.3

12.5 10.6 16.2

12.0 10.4 16.7

1.7 0.1 −3.8

2.0 1.0 −2.4

−25.2 −35.4 −47.1

−23.7 −33.3 −44.8

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Table 6. Predicted RSEs (kcal mol−1) for 1,1-Dichlorocyclobutane, 1,1,2,2-Tetrachlorocyclobutane, 1,1,2,2,3,3Hexachlorocyclobutane, and Octachlorocyclobutane Using Different Models (6-311+G(d,p) Basis Set) and the Reactions in Figure 1 c-1,1-C4H6Cl2

c-1,1,2,2-C4H4Cl4

c-1,1,2,2,3,3-C4H2Cl6

c-C4Cl8

reaction

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

1 2 3

28.2 27.8 27.1

28.0 28.0 27.6

13.8 12.1 26.1

17.6 16.6 27.5

7.5 7.4 5.9

10.1 12.0 10.4

−21.6 −22.8 −24.6

−19.5 −19.2 −20.4

predict an approximate Δ = 0.3 kcal mol−1. The former result is clearly more in line with the overall Δ. Using it, and assuming that the cis/trans bond energy difference is ca. 1 kcal mol−1, the overall Δ is estimated to be 6.4 kcal mol−1, in agreement with the homodesmotically predicted value. The cis/trans ring correction data appear in Table 7; the average is 0.3(0.2) kcal mol−1.

recalculated the RSEs, finding RSE(c-1,1,2,2-C4H4Me4) = 29 kcal mol−1, RSE(c-1,1,2,2,3,3-C4H2Me6) = 30 kcal mol−1, and RSE(c-C4Me8) = 34 kcal mol−1. These values show a more obvious forward trend but are essentially statistically identical to the original ones. Thus, we assert that methyl substitution has little effect on the RSEs for highly methyl-substituted cyclobutanes; the RSE for the fully substituted ring is within 3−8 kcal mol−1 of that of cyclobutane, with RSEs for less substituted rings in between. The values and trends predicted by hyper(homodesmotic) reaction methods are incorrect. RSEs of Chloro-Substituted c-C3HxCl6−x. As mentioned above, the range of RSEs estimated for c-C4Cl8 using (hyper)homodesmotic reactions is so large5 as to be unusable for predictive purposes. Table 6 shows that the (hyper)homodesmotic reactions we employed for RSE predictions for c-1,1,2,2-C4H4Cl4 struggle with this as well. As Liebman et al.5 found, such reactions also predict unlikely negative RSEs for cC4Cl8. That (hyper)homodesmotic reaction methods give more implausible RSE predictions for highly substituted chlorocyclobutanes than for highly substituted fluorocyclobutanes suggests that uncanceled intramolecular interactions in the acyclic reference molecules are to blame rather than the electron-withdrawing characteristics of the halogen substituents.33 In contrast to the reverse trend with chlorine substitution predicted by the (hyper)homodesmotic reactions, the QTAIM bond path angle data (Table 2, bottom rows) indicate a forward RSE trend for the chlorocyclobutanes. The angle values suggest that RSEs for a particular chloro-substituted ring will likely fall between those for the identically methyl- and fluoro-substituted cyclobutanes but be closer to those for the latter. The Δ value for the chlorocyclobutanes was predicted to be 6.5(1.0) kcal mol−1 (Supporting Information). This is the largest Δ we have obtained for substituted cyclopropanes/ cyclobutanes, a possible indication that the semi-homodesmotic approach may not be trustworthy here. We attempted to determine the source of the issue by considering the relevant energies that determine Δ;18 these include −Cl2C−CCl2−, −Cl2C−CH2−, −H2C−CH2−, and the cis- and trans-ClHC− CHCl− bond energies. Of course, no data exist for the cis/trans pair because only acyclic alkanes have been studied, and for these (assuming free rotation around the C−C bond) no cis/ trans distinction exists. Regarding the other three moieties, published bond energies exist for H−Cl2C−CH2−H, H− Cl2C−CCl2−H, and H−H2C−CH2−H (87.3, 80.3, and 90.2 kcal mol−1, respectively);34,35 using these gave an approximate Δ = 4.1 kcal mol−1. However, given the angle distortions associated with the ring carbon environments in the chlorocyclobutanes, it is unclear that these bond energies are appropriate. That said, the only similar calculation for which data exist involves the C−C bond energies for Cl−Cl2C− CH2−Cl, Cl−Cl2C−CCl2−Cl, and Cl−H2C−CH2−Cl (77.4, 68.3, and 86.2 kcal mol−1, respectively),34 which combine to

Table 7. Predicted RSEs (kcal mol−1) for cis- and trans-1,2Dichlorocyclobutane and Differences Using Different Models (6-311+G(d,p) Basis Set) and the Reactions in Figure 2 c-cis-1,2-C4H6Cl2

Δ

c-trans-1,2-C4H6Cl2

reaction

M06-2X

MP2

M06-2X

MP2

M06-2X

MP2

4a 4b 5a 5b 6

21.5 29.7 19.8 30.8 28.6

25.5 27.5 24.4 28.7 29.3

21.1 29.3 19.3 30.3 28.1

25.4 27.3 24.2 28.6 28.8

0.4 0.4 0.5 0.5 0.5

0.1 0.2 0.2 0.1 0.5

Reaction 1 is the simplest group equivalent reaction providing RSE(c-1,1-C4H6Cl2), giving an average value of 27.8(0.4) kcal mol−1. Substituting the three values into eqs 1−3 gives RSE(c-1,1,2,2-C4H4Cl4) = 36(1) kcal mol−1, RSE(c1,1,2,2,3,3-C3H2Cl6) = 44(2) kcal mol−1, and RSE(c-C4Cl8) = 59(5) kcal mol−1. These are consistent with the comments above: the trend is forward, and the values are smaller than those for the fluoro congeners, but sizably larger than those for the methyl congeners.

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CONCLUSIONS For broad comments regarding the semi-homodesmotic approach, its utility, and interpretations of some of its results, the reader is directed to the Conclusions section in the preceding paper.1 RSEs for substituted cyclobutanes predicted by the approach are collected in Table 8. The differences Table 8. RSEs (kcal mol−1) for Highly Substituted Cyclobutanes Predicted by the Semi-homodesmotic Method c-1,1,2,2-C4H4R4 c-1,1,2,2,3,3-C4H2R6 c-C4R8

R = Me

R=F

R = Cl

25(1) 26(2) 28(3)

39(1) 50(2) 70(4)

36(1) 44(2) 59(5)

between electron-withdrawing halogen substituents and the slightly donating methyl substituent are stark: the latter has little impact on the RSEs even when the ring is fully substituted, whereas the former increase the RSEs sizably and regularly. These trends concur with QTAIM data regarding the positions of critical points with respect to the bond vectors. The trends oppose those expected from (hyper)homodesmotic reaction 6065



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Notes

approaches employing acyclic reference molecules, indicating that, for highly substituted cycloalkanes at least, canceling intramolecular interactions is more important than canceling bond energies and maintaining hybridization type. It would be of considerable interest to have confirmation of the predictions of Table 8. Most of the cyclobutanes therein have been synthesized,36−47 but to our knowledge thermodynamic determinations and uses of the data therefrom have been limited to RSE estimation only for c-C4F8.9 Extending this to other highly substituted cyclobutanes will require obtaining currently unavailable enthalpies of formation, such as that for cC4Me8. Moreover, it will likely prove problematic to determine thermodynamic RSEs, because the problem of employing acyclic reference molecules remains. Nonetheless, it should be possible to distinguish whether the enthalpic RSE trends are forward or reverse, thereby confirming whether the semihomodesmotic approach or (hyper)homodesmotic methods work best. It would also be useful if computational methods independent of homodesmotic reaction methods were applied. We employed QTAIM bond path angle data to predict trends in RSEs with substitution, but this is at best a crude, semiquantitative application of the technique. It has been observed that the Lagrange kinetic energy density G(r) at the ring critical point appears to correlate with the RSEs in parent and slightly substituted carbocycles;48 however, the RSEs employed in the study were taken from (hyper)homodesmotic reaction calculations and so are not reliable. A statistical concern is that the regression lines have y-intercept values that are inconsistent with the concept of a strain-free ring, although this could be explained as linearity holding only over a restricted range of G(r) values. More worrying, the correlation appears erratic; for example, the values of G(r) for cyclobutane, 1-methylcyclobutane, and 1,1-dimethylcyclobutane are 0.1017, 0.1055, and 0.1014. It is difficult to rationalize this trend, or even to decide if the values statistically/realistically differ. It should be emphasized here that the G(r) parameter reflects the kinetic energy density at the ring critical point (that is, a point within the confines of the ring atoms), and so is largely unrelated to the position of the bond path critical points, which lie outside the ring. That G(r) has at best a tenuous relationship with RSE has no bearing on our belief that the positions of the bond paths and values of the bond path angles are related to the magnitudes of the RSEs. It may be that some parameter within QTAIM correlates mathematically with RSEs, but as yet it has not been conclusively identified. We hope that computational/theoretical chemists with interest in electron localization techniques will find a methodology that directly and quantitatively links RSEs with computational observables.

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The authors declare no competing financial interest.

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ACKNOWLEDGMENTS The NIU Computational Chemistry Laboratory was created using funds from U.S. Department of Education Grant P116Z020095 and is supported in part by the taxpayers of the State of Illinois.

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ASSOCIATED CONTENT

S Supporting Information *

Graphic/tables showing details of the derivation of eqs 1−3; optimized Cartesian coordinates (MP2/6-311+G(d,p) level) of all molecules examined; tables containing absolute energies from all models and molecules surveyed using homodesmotic approaches, and the RSEs determined from them. This material is available free of charge via the Internet at http://pubs.acs.org.

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REFERENCES

(1) De Lio, A. M.; Durfey, B. L.; Gille, A. L.; Gilbert, T. M. A Semihomodesmotic Approach For Estimating Ring Strain Energies (RSEs) Of Highly Substituted Cyclopropanes That Minimizes Use of Acyclic References And Cancels Steric Interactions: RSEs For c-C3R6 That Make Sense. J. Phys. Chem. A 2014, DOI: 10.1021/jp5058989. (2) Gonthier, J. F.; Wodrich, M. D.; Steinmann, S. N.; Corminbouef, C. Branched Alkanes Have Contrasting Stabilities. Org. Lett. 2010, 12, 3070−3073. (3) Liebman, J. L.; Dolbier, W. R., Jr.; Greenberg, A. Hexafluorocyclopropane And Octafluorocyclobutane: A Study Of The Strain Energies. J. Phys. Chem. 1986, 90, 394−397. (4) Baker, J. M.; Dolbier, W. R., Jr. Density Functional Theory Calculations Of The Effect Of Fluorine Substitution On The Cyclobutylcarbinyl To 4-Pentenyl Radical Rearrangement. J. Org. Chem. 2001, 66, 2662−2666. (5) Mahavadi, M.; Zeiger, D. N.; Naqib, D.; Roux, M. V.; Notario, R.; Liebman, J. F. The Strain Energy Of Perchlorocyclopropane Is Small: It Might Even Be Negative. A Density Functional Theory Study Of Perhaocycloalkanes. Int. J. Quantum Chem. 2003, 95, 784−790. (6) Vila, A.; Mosquera, R. A. On The Electronic Origin Of Strain Energy: QTAIM Study Of Perfluorocycloalkanes. J. Phys. Chem. A 2006, 110, 11752−11759. (7) Smith, M. B.; March, J. March’s Advanced Organic Chemistry, 5th ed.; Wiley Interscience: New York, 2001; Section 15−61. (8) Lemal, D. M.; Chen, X. Fluorinated Cyclobutanes And Their Derivatives. The Chemistry of Cyclobutanes, Rappoport, Z., Liebman, J. F., Eds.; Wiley: New York, 2005; Chapter 21. (9) Inagaki, S.; Ishitani, Y.; Kakefu, T. Geminal Delocalization Of σElectrons And Ring Strains. J. Am. Chem. Soc. 1994, 116, 5954−5958. (10) Zhao, Y.; Truhlar, D. G. The M06 Suite Of Density Functionals For Main Group Thermochemistry, Thermochemical Kinetics, Noncovalent Interactions, Excited States, And Transition Elements: Two New Functionals And Systematic Testing Of Four M06-Class Functionals And 12 Other Functionals. Theor. Chem. Acc. 2008, 120, 215−241. (11) Möller, C.; Plesset, M. S. Note On An Approximation Treatment For Many-Electron Systems. Phys. Rev. 1934, 46, 618−622. (12) Bader, R. F. W. Atoms in Molecules: A Quantum Theory; Oxford University Press: Oxford, U.K., 1990. (13) Bader, R. F. W. A Quantum Theory Of Molecular Structure And Its Applications. Chem. Rev. 1991, 91, 893−928. (14) Bader, R. F. W. Atoms In Molecules. Acc. Chem. Res. 1985, 18, 9−15. (15) Keith, T. A. AIMAll, Version 12.06.03; TK Gristmill Software: Overland Park KS, USA, 2012. (16) Bachrach, S. M. The Group Equivalent Reaction: An Improved Method For Determining Ring Strain Energy. J. Chem. Educ. 1990, 67, 907−908. (17) Wheeler, S. E.; Houk, K. N.; Schleyer, P. v. R.; Allen, W. D. A Hierarchy Of Homodesmotic Reactions For Thermochemistry. J. Am. Chem. Soc. 2009, 131, 2547−2560. (18) See Supporting Information for details on the derivations of the equations involved in employing the semi-homodesmotic method. (19) Harris, D. C. Quantitative chemical analysis, 8th ed.; Macmillan: New York, 2010; Chapter 3. (20) Bach, R. D.; Dmitrenko, O. Strain Energy Of Small Ring Hydrocarbons. Influence Of C−H Bond Dissociation Energies. J. Am. Chem. Soc. 2004, 126, 4444−4452.

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Corresponding Author

*E-mail: [email protected]. 6066



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(44) c-C4F8: Lewis, E. E.; Naylor, M. A. Pyrolysis Of Polytetrafluoroethylene. J. Am. Chem. Soc. 1947, 69, 1968−1970. (45) c-1,1-C4H6Cl2: Kirmse, W.; Kapps, M.; Hager, R. B. Reaction Of Allyl Halides With Diazomethane Using Copper Salt Catalysis. Chem. Ber. 1966, 99, 2855−2868. (46) c-1,1,2,2-C4H4Cl4: Chukovskaya, E. Ts.; Kamyshova, A. A.; Freidlina, Rh. Kh. Reactions Of Carbon Tetrachloride With Unsaturated Compounds In The Presence Of Dicyclohexyl Peroxydicarbonate Or Oxidation-Reduction Systems. Izv. Akad. Nauk SSSR, Ser. Khim. 1965, 461−465. (47) c-C4Cl8: Raasch, M. S. Syntheses With Halogen Derivatives Of Thiophene And Benzothiophene. J. Org. Chem. 1980, 45, 2151−2155. (48) Bauzá, A.; Quiñonero, D.; Deyà, P. M.; Frontera, A. Chem. Phys. Lett. 2012, 536, 165−169.

(21) Bach, R. D.; Dmitrenko, O. The Effect Of Substituents On The Strain Energies Of Small Ring Compounds. J. Org. Chem. 2002, 67, 2588−2599. (22) Khoury, P. R.; Goddard, J. D.; Tam, W. Ring Strain Energies: Substituted Rings, Norbornanes, Norbornenes And Norbornadienes. Tetrahedron 2004, 60, 8103−8112. (23) Ringer, A. L.; Magers, D. H. Conventional Strain Energy In Dimethyl-Substituted Cyclobutane And The Gem-Dimethyl Effect. J. Org. Chem. 2007, 72, 2533−2537. (24) Bachrach, S. M. The gem-Dimethyl Effect Revisited. J. Org. Chem. 2008, 73, 2466−2468. (25) Lowry, T. H.; Richardson, K. S. Mechanism and Theory in Organic Chemistry, 3rd ed.; Harper & Row: New York, NY, 1987; Chapter 2.3. (26) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. Theoretical Analysis Of Hydrocarbon Properties. 1. Bonds, Structures, Charge Concentrations, And Charge Relaxations. J. Am. Chem. Soc. 1987, 109, 985−1001. (27) Wiberg, K. B.; Bader, R. F. W.; Lau, C. D. H. Theoretical Analysis Of Hydrocarbon Properties. 2. Additivity Of Group Properties And The Origin Of Strain Energy. J. Am. Chem. Soc. 1987, 109, 1001−1012. (28) Wiberg, K. B. Bent Bonds In Organic Compounds. Acc. Chem. Res. 1996, 29, 229−234. (29) Cremer, D.; Gauss, J.; Cremer, E. Strain In Three-Membered Rings Containing Silicon: The Inability Of Silicon To Form Flexible Hybrid Orbitals. J. Mol. Struct. (THEOCHEM) 1988, 169, 531−561. (30) Allard, C. L.; Gauthier, P.; Gille, A. L.; Thomas, G. E.; Gilbert, T. M. Optimized Structures And Ring Strain Energies Of Isoelectronic Homo- And Heterosiliranes c-AX2SiR2SiR2q (A/q = Al/−1, Si/0, P/ +1): Unexpected Effects Of Charge And Size. Organometallics 2013, 32, 2558−2566. (31) Navin de Silva, K. M.; Goodman, J. M. What Is The Smallest Saturated Acyclic Alkane That Cannot Be Made? J. Chem. Inf. Model. 2005, 45, 81−87. (32) It should be noted that, uniquely for rings in this paper, Reaction 1 is not the simplest group equivalent reaction when A = Me, B = H. (33) As noted in the previous paper (ref 41 of ref 1), the factor most likely to determine differences in the energies of intramolecular interactions is the relative van der Waals radii of the substituents. (34) Luo, Y.-R. Handbook of Bond Dissociation Energies in Organic Compounds; CRC Press: Boca Raton, FL, 2003; Chapter 4. (35) Franklin, J. A.; Huybrechts, G. H. Bond Energies In Chloroethanes And Chloroethyl Radicals. Int. J. Chem. Kinet. 1969, 1, 3−9. (36) Kostikov, R.; Baird, M. S. Synthesis Of Cyclobutanes. Sci. Synth. 2009, 48, 615−646. (37) c-1,1-C4H6Me2: Zotova, S. V.; Yatsenko, M. S.; Finkel’shtein, E. Sh.; Kazanskii, B. A. Preparation Of 1,1-Dimethylcyclobutane. Izv. Akad. Nauk SSSR, Ser. Khim. 1972, 734−735. (38) c-1,1-C4H6Me2: Torok, B.; Molnar, A. General Synthesis Of Methyl- And Dimethylcyclobutanes From Simple 1,3-Diols By Phase Transfer Catalysis. J. Chem. Soc., Perkin Trans. 1 1993, 801−804. (39) c-1,1,2,2-C4H4Me4: Schultz, P. G.; Dervan, P. B. Photochemistry Of A 1,1-Diazene, N-(2,2,5,5-Tetramethylpyrrolidinyl) Nitrene. J. Am. Chem. Soc. 1981, 103, 1563−1564. (40) c-C4Me8: Arnold, R. R.; Abraitys, V. Y. Photodimerization Of Tetramethylene. Reaction Of The Olefin π, π* Singlet. Chem. Commun. 1967, 1053−1054. (41) c-1,1-C4H6F2: Luntz, A. C. Microwave Spectrum And RingPuckering Vibration In 1,1-Difluorocyclobutane. J. Chem. Phys. 1969, 50, 1109−1118. (42) c-1,1,2,2-C4H4F4: Coffman, D. D.; Barrick, P. L.; Cramer, R. D.; Raasch, M. S. Synthesis Of Tetrafluorocyclobutanes By Cycloalkylation. J. Am. Chem. Soc. 1949, 71, 490−496. (43) c-1,1,2,2,3,3-C4H2F6: Mizukado, J.; Matsukawa, Y.; Quan, H.-d.; Tamura, M.; Sekiya, A. Fluorination Of Fluorocyclobutene With HighValency Metal Fluoride. J. Fluorine Chem. 2006, 127, 79−84. 6067


Application of a Semi-homodesmotic Approach in Estimating Ring

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