A Semi-homodesmotic Approach for Estimating Ring Strain Energies

Jul 21, 2014 - Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115, United States. J. Phys. Chem. A , 2014,...
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A Semi-homodesmotic 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 Ashley M. De Lio, Bridget L. Durfey, Austin L. Gille, and Thomas M. Gilbert* Department of Chemistry and Biochemistry, Northern Illinois University, DeKalb, Illinois 60115, United States S Supporting Information *

ABSTRACT: Estimation of ring strain energies (RSEs) of substituted cyclopropanes c-C3HxR6−x (R = F, Cl, Me; x = 0, 2, 4) using homodesmotic reaction methods has been plagued by implausible results. Prior work suggests that this stems from poorly canceled interactions between substituents on the acyclic reference molecules. We report a semi-homodesmotic approach that minimizes use of acyclic references, focusing instead on canceling substituent interactions. The method requires employing homodesmotic group equivalent reactions only for disubstituted cyclopropanes and relies solely on absolute energy calculations for more substituted rings. This provides RSEs consistent with chemical intuition regardless of the degree of substitution. We find that RSEs increase with substitution regardless of the electronic nature of R, although the increase is more dramatic when R is electronwithdrawing. The RSEs determined are consistent with QTAIM data, which show that progressive substitution always increases critical path angles. Overall, the semihomodesmotic approach is simpler than hyperhomodesmotic reaction methods, and gives more trustworthy results.

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INTRODUCTION Though not a physical measure, the ring strain energy (RSE) represents a useful construct for explaining reactivities and thermodynamics of cyclic compounds.1 Generally speaking, the RSE combines angle (Baeyer) strain, torsional (Pitzer) interaction strain, and transannular interaction strain.2,3 For cycloalkanes, the first of these reflects deviations from the ideal 109.5° for angles around carbon atoms in the ring, the second reflects eclipsing of substituents enforced by ring geometry, and the third reflects interactions between moieties on opposite sides of the ring. The tendency of cyclopropanes to undergo ring-opening processes is an example of ring strain-related phenomena.4 For cyclopropanes, it is felt that angle strain dominates the RSE, because the deviation of ring angles from ideality is severe, whereas the three-membered ring geometry minimizes torsional and transannular interactions.5 RSEs can be estimated by comparing experimental heats of combustion or computationally determined energies. Either way, typically the method involves creating hypothetical reactions wherein characteristics of moieties in the cyclic molecule balance those in acyclic reference molecules. Such balancing can involve varieties of acyclic references, meaning that different degrees of accounting for intramolecular interactions in the cycle are possible. Wheeler et al. developed a terminological hierarchy for the hypothetical reactions based on how completely component reference molecules incorporated the various atoms, hybridization types, bond types, and © 2014 American Chemical Society

other structural parameters contained in the strained molecule, characterizing the range from isogyric through homodesmotic to hyperhomodesmotic.6 They showed that homodesmotic and hyperhomodesmotic reaction classes performed well against a test set of hydrocarbon bond separation enthalpies7,8 but noted (with little detail) that the (hyper)homodesmotic reactions9 performed less well in predicting ring strain energies (RSEs) for cyclic hydrocarbons. They suggested that modifying the component molecules to account for torsional strain (Pitzer strain) would be necessary, and called for a general study for modifying homodesmotic reactions to account for ring and cage strain. The need to properly account for intramolecular interactions such as angle strain and torsional strain when estimating RSEs of substituted cyclopropanes has become apparent over the past decade. Using different homodesmotic reactions, one where geminal difluoride substitution was balanced between reactant ring and acyclic products and one where it was not, Bach and Dmitrenko10,11 found RSE values for c-1,1-C3H4F2 that differed by 20 kcal mol−1. Liebman et al. described more extreme examples in a series of papers.12−14 They found that, depending upon the type of homodesmotic reaction employed (and in turn upon which intramolecular interactions were properly Received: June 13, 2014 Revised: July 10, 2014 Published: July 21, 2014 6050

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conformational space were optimized at the M06-2X21/631+G(d) level to determine that of lowest energy or a pseudohelical structure based on that of the analogous polyfluoroalkane was used. The latter choice was based on our observations that the lowest energy structures for polymethylalkanes determined by Corminbouef et al.22 using molecular dynamics calculations, and those extracted from our conformation space scans, tended to be pseudohelical. Examination of the optimized structures by analytical frequency analyses at the HF level demonstrated that they were minima (no imaginary frequencies). The analyses also provided zero point energies (ZPEs), which were appropriately scaled23,24 when used to calculate ring strain energies (RSEs). All structures were then reoptimized at the Model/6-311+G(d, p) level (Model = M06-2X, wB97XD,25 MP226); frequencies were redetermined for the density functional theory cases to ensure that the stationary point structures were still minima. The models were selected to cover a range of modeling issues: M06-2X is a post-GGA model that includes a high degree of HF exchange and incorporates the kinetic energy density; wB97Xd includes dispersion terms and a smaller degree of HF exchange; MP2 as a perturbation theory model inherently captures a reasonable amount of electronic correlation and dispersion energy self-consistently. A sizable integration grid (Gaussian keyword INT(UltraFineGrid)) was used in all cases; the M06-2X model in particular is known to be sensitive to grid size.27 Skeleton homodesmotic reactions used to estimate RSEs for gem-substituted cyclopropane rings are shown in Figure 1.

balanced), RSE values for c-C3F6 spanned the range 41−85 kcal mol−1,15 whereas those for c-C3Cl6 spanned the range −12 to +64 kcal mol−1. Tellingly, the predicted RSEs for these decreased as the reactions employed became more hyperhomodesmotic, implying that accounting for more intramolecular interactions present in reactant ring and acyclic products actually worsened the balance. Of course, the negative RSEs observed for c-C3Cl6 are implausible, but also implausible is the prediction that RSE(c-C3F6) = 41 kcal mol−1. This is the value predicted for RSE(c-1,1-C3H4F2), and it seems likely that if substituting two fluorines for hydrogen in changing c-C3H6 to c-1,1-C3H4F2 increases the RSE from 27 to 41 kcal mol−1, then substituting the remaining four hydrogens with fluorines should increase the RSE substantially, to perhaps 70 kcal mol−1 if the increase is nearly linear with fluorines. In this regard, a calculation based on experimental thermochemical data suggested RSE(c-C3F6) = 83 ± 6 kcal mol−1.16 As will be seen below, (hyper)homodesmotic reactions predict similarly unlikely RSEs for tetra- and hexamethylsubstituted cyclopropanes. We were drawn to this area by our studies of RSEs of hexasubstituted di- and trisiliranes.17 We noted that RSE estimates for tetra- and hexasubstituted cyclopropanes were rare; in particular, to our knowledge no studies exist for 1,1,2,2tetramethyl- and hexamethylcyclopropane, even though they would bear directly on the issue of branching10 and associated intramolecular interactions as a source of error in RSE determination. That homodesmotic methods predicted negative RSEs for highly chloro-substituted cyclopropanes was intriguing. We wished to determine whether different approaches, particularly those that explicitly balance intramolecular interactions, would provide more reliable RSEs. We report here RSE predictions for tetra- and hexasubstituted cyclopropanes containing methyl, fluoro, and chloro substituents. We find support for the view that (hyper)homodesmotic methods fail for such rings because intramolecular interactions in the acyclic reference molecules represent a source of error that the (hyper)homodesmotic reactions do not fully cancel, and because the errors increase with the number of substituents (and in turn the number of interactions). This is particularly problematic for hexamethyland hexachlorocyclopropanes. Consequently, we describe a semi-homodesmotic approach that restricts the use of homodesmotic reactions to disubstituted cyclopropanes, the systems where uncanceled errors are likely to be smallest. The approach is semi-homodesmotic because it does not fully cancel bond energies but instead fully cancels intramolecular interactions while treating uncanceled bond energies as an error parameter accounted for by a rings-only homodesmotic reaction. This gives RSEs of highly substituted cyclopropanes that are consistent with QTAIM predictions of trends and with chemical intuition in the sense that the RSEs are not implausibly small or negative. We therefore believe the semihomodesmotic approach gives the most reliable RSEs available for highly substituted cyclopropanes.

Figure 1. Skeleton reactions for estimating RSEs of cyclopropane (A = B = H), and 1,1-disubstituted (A = substituent R, B = H), 1,1,2,2tetrasubstituted (A = H, B = R), and hexasubstituted (A = B = R) cyclopropanes.

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Reactions 1−3 were used to confirm literature data indicating that (hyper)homodesmotic reactions give implausible RSEs for highly substituted systems, and to show that methyl-substituted cyclopropanes exhibit the same problem (see below). The reactions are designated using Nx format, where N is an index, and x differentiates between isomers in the acyclic reference molecules where the central unit is CA2 (a) and where it is CB2 (b). The reactions can be characterized on the basis of what

COMPUTATIONAL METHODS Optimizations and frequency analyses were performed using the Gaussian (G09)18 suite. All molecules examined were fully optimized without constraints at the HF/6-31+G(d,p) level. Starting structures for many of the acyclic reference molecules were taken from the literature.22,19,20 In cases where literature data were not available, either multiple conformers spanning 6051

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ring moiety is “capped” to form the acyclic reference product. Reaction 1, a group equivalent reaction,28 isolates each ring CA2/CB2 unit and attaches an appropriate methyl-based CA3/ CB3 “cap” to each “side” (unpaired electron) to form the acyclic reference product molecules. This is the least homodesmotic case (in Wheeler’s terminology, this is hypohomodesmotic),6 as the caps differ substantially in structure/substitution pattern from the ring CA2/CB2 units. Reactions 2a/2b involve placing CA3/CB3 caps on the “opened ring” CA2CB2CB2 unit. This makes the reaction homodesmotic. Reactions 3a/3b are similar to 2a/2b but involve substituted ethyl-like caps; this makes these reactions hyperhomodesmotic. Other homodesmotic reactions were occasionally used for comparison of results with those from the reactions in Figure 1 and to probe ranges of values. Data for some of these appear in the Supporting Information. As shown below, applying the semi-homodesmotic approach involves a correction term derived from the RSEs of the cis- and trans-1,2-substituted rings. Reactions 4−6 (Figure 2) provide data for the correction. They mimic reactions 1−3 but were simplified by having the cap be CH3 rather than one appropriate to the substitution pattern of the cyclopropane ring. This simplification minimized use of computer resources and allowed us to avoid concerns with conformational issues of the terminating group. The reactions are designated using Nxr format as above, with the r referring to cis (c) or trans (t) substitution. The HF-predicted RSEs (Supporting Information) typically differed sizably from those for the more higher-level models, supporting the view that strain can only be modeled well using models that include correlation.29 The three advanced models generally gave similar results, although it appeared that the M06-2X model gave consistently smaller RSEs for methylsubstituted rings, whereas the wB97Xd model tended to underestimate RSEs for halide-containing rings. On the basis of prior work, and the fact that the ZPE corrections ranged from 0−5 kcal mol−1, we take differences in RSE values smaller than ±3 kcal mol−1 to be negligible. In the discussion below, the only exception to this will involve the methyl-substituted cyclopropanes, for which the QTAIM trend and the application of the semi-homodesmotic approach suggest slight increases in RSE with substitution, despite the small range the RSEs span. 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,30 which implements the quantum theory of atoms in molecules (QTAIM) theory developed by Bader and co-workers.31−33 Molecules were reoptimized using the Cartesian basis set functions34 before running the QTAIM jobs; this had no impact on structural parameters. Distinction will be made between bond paths and geometric paths, and between bond path angles and geometric angles. The geometric paths and angles are the conventional ones used to define molecular geometries. The bond path can be thought of as the path of maximum electron density between atomic nuclei, with a bond critical point as the position where an entity traveling the path away from one nucleus finds equilibrium between that nucleus and another. Metaphorically, a bond critical point is a transition point between two nuclear attractors, just as a conventional transition state is a stationary point between reactants and products. Bond path angles are angles formed by intersection of two bond paths.

Figure 2. Skeleton reactions for estimating RSEs of cis-(designated Nxc) and trans-(designated Nxt) 1,2-disubstituted cyclopropanes..

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RESULTS AND DISCUSSION Semi-homodesmotic Approach. As mentioned above, Wheeler et al. suggested that the accuracy of (hyper)homodesmotic reactions in predicting RSEs might be improved by accounting more exactly for torsional strain.6 The results of Liebman et al.12 imply that simply making the acyclic reference molecules larger cannot accomplish this, and in fact, doing this injects more intramolecular interactions that are not canceled in the (hyper)homodesmotic reaction. We therefore sought means of calculating RSEs that minimized the use of (hyper)homodesmotic reactions and their associated acyclic molecules, and that involved explicitly canceling as many intramolecular angle and torsional interactions as possible. Bach and Dmitrenko10 employed the approach shown at the top of Scheme 1, where the RSE of a substituted cyclopropane is determined relative to that of cyclopropane. This accounts to some degree for the eclipsed torsional interactions in the rings being different (presumably more repulsive) from the staggered 6052

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disubstituted cyclopropane isomers) plus the Δ correction. The cis/trans ring correction term in most cases should be quite small, because the RSEs for the 1,2-disubstituted rings are unlikely to differ significantly. That said, the correction will likely be positive if it is not negligible, because most homodesmotic methods penalize cis-substituted rings owing to steric repulsions between the eclipsed cis-substituents (see below for examples). The Δ term involves uncanceled ring carbon bond energies;36 it can be estimated as the overall electronic reaction energy of the top reaction in Scheme 1, so its determination requires no (hyper)homodesmotic calculations. The magnitude of Δ characterizes the similarity of bond types/energies; it is unlikely to equal zero, and will only do so fortuitously. Unlike the cis/trans ring correction term, it is impossible to predict the sign of Δ. It is for these reasons that we characterize eq 1 (and more broadly, the approach resulting from Scheme 2) as semi-homodesmotic. As will be seen below, in general, the bond types/energies are sufficiently similar that Δ contributes little to the RSE predictions. The energetic components of the species in the bottom reaction in Scheme 2 can be manipulated36 to express the RSE of a hexasubstituted cyclopropane as

Scheme 1

ones in the acyclic references, at the cost of requiring knowledge of the RSE of cyclopropane. Liebman et al.,12,35 and also Bach and Dmitrenko10 employed the “diagonal” approach shown at the bottom of Scheme 1, which avoids use of ever-larger acyclic reference molecules, at the cost of assuming that RSEs for the reference cyclohexanes are negligible, which is broadly false.10 We chose to modify the approach at the top of Scheme 1 to more completely account for as many substituent-based intramolecular interactions as possible. With this criterion in mind, we derived the reactions in Scheme 2.36 They solely involve substituted cyclopropanes, so the need for (hyper)homodesmotic reactions incorporating acyclic reference molecules is minimized (see below), and all geminal RCR and cofacial RCCR/RCCH/HCCH interactions cancel between reactants and products. As shown below, the reactions allow comparison of RSEs for the tetra- and hexasubstituted rings on the basis of RSEs of disubstituted rings only. The latter RSEs must be estimated using homodesmotic reactions and so represent a source of error. However, the acyclic reference molecules in these reactions have the fewest substituent-based intramolecular interactions possible for a polysubstituted chain and therefore would be expected to exhibit the smallest errors resulting from incorrect accounting of the interactions. We therefore believe the approach is sound and will demonstrate its self-consistency and agreement with computational and thermodynamic data in the subsections below. The energetic components of the species in the top reaction in Scheme 2 can be manipulated36 to express the RSE of a 1,1,2,2-tetrasubstituted cyclopropane as

RSE(c ‐C3R 6) = RSE(c ‐C3H6) + 3[RSE(c ‐1,1,2,2‐C3H 2R 4) − RSE(c ‐1,1‐C3H4R 2)] (2)

Here, the RSE of a hexasubstituted cyclopropane is the RSE of cyclopropane corrected by a term involving the difference in RSEs between the 1,1,2,2-tetra- and 1,1-disubstituted rings. If the correction is small, the RSE of the hexasubstituted cyclopropane will be nearly the same as that of cyclopropane. Substituting eq 1 into eq 2 gives RSE(c-C3R6) in terms of RSEs of disubstituted cyclopropanes only: RSE(c ‐C3R 6) = [3RSE(c ‐1,1‐C3H4R 2) − 2RSE(c ‐C3H6)] + 6[RSE(c ‐cis‐1,2‐C3H4R 2) − RSE(c ‐trans‐1,2‐C3H4R 2)] + 3Δ

One sees that eq 3 is analogous to eq 1, except for having different coefficients on the terms and components. Conceptually, the two are identical: the first term reflects the effect of substitution on RSEs, the second the effect of regiosubstitution on RSEs, and the third the effect of different substitution patterns on bond energies. It is apparent that determining trustworthy RSEs for 1,1disubstituted rings is crucial for application of eqs 1−3, as the difference between these and the RSE for cyclopropane determines the value of the first term. With this in mind, we evaluated literature data10,12,37 and that from our (hyper)homodesmotic calculations (see below) in determining which

RSE(c ‐1,1,2,2‐C3H 2R 4) = [2RSE(c ‐1,1‐C3H4R 2) − RSE(c ‐C3H6)] + 2[RSE(c ‐cis‐1,2‐C3H4R 2) − RSE(c ‐trans‐1,2‐C3H4R 2)] + Δ

(3)

(1)

Equation 1 indicates that the RSE of the tetrasubstituted cyclopropane equals the first bracketed term (the value of which will depend on the degree to which even a slight amount of substitution affects the RSE vs that of cyclopropane) plus the second bracketed term (a cis/trans ring correction associated with the difference in RSEs between cis- and trans-1,2 Scheme 2

6053

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Table 1. Predicted RSEs (kcal mol−1) for 1,1-Difluorocyclopropane, 1,1,2,2-Tetrafluorocyclopropane, and Hexafluorocyclopropane Using Different Models (6-311+G(d,p) Basis Set) and the Reactions from Figure 1 c-1,1-C3H4F2

c-1,1,2,2-C3H2F4

c-C3F6

reaction

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

1 2a 2b 3a 3b

39.7 39.3 38.7 39.8 39.4

40.3 39.9 39.5 40.6 40.3

41.1 41.1 40.6 41.9 41.5

47.7 47.0 47.5 48.0 47.9

45.9 45.2 45.8 46.3 46.2

49.0 48.9 49.2 50.2 50.1

51.0 51.4

46.5 46.2

52.5 52.5

51.9

46.4

53.4

difluoro- and hexafluorocyclopropane.12,15,40 However, as noted above, thermochemical data suggest RSE(c-C3F6) = 83 kcal mol−1,16 significantly above the computationally predicted average. This suggests that some aspect of the (hyper)homodesmotic reaction method biases the calculations to underestimate RSEs. The most likely candidate for this is uncanceled intramolecular interactions. Specifically, in the homodesmotic reactions in Figure 1, a number of eclipsed 1,3-interactions are not accounted for. Scheme 3 shows this simplistically for

homodesmotic method appeared to provide the most reliable RSEs for c-1,1-C3H4R2 compounds. We decided upon Bachrach’s group equivalent method,28 which uses the smallest possible acyclic reference molecules, even though such an approach inherently removed proper nearest-neighbor corrections. Some justifications for this choice are discussed in the subsections below. A benefit of using the semi-homodesmotic approach, however, is that it is unnecessary to determine accurate RSEs for the cis/trans-1,2-disubstituted rings, because only the difference between the two matters. The RSEs predicted for each can be inaccurate compared to putative experimental values so long as they are similarly inaccurate, thereby making their difference “correct”. We employed a series of (hyper)homodesmotic reactions to estimate these RSEs in the hope that the differences between averaged RSEs would prove adequately accurate. It would be useful if eqs 1−3 predicted trends in RSEs with degrees of substitution without requiring specific values. Unfortunately, this is not possible given their forms. That said, one can infer the most probable outcome. If the cis/trans ring correction term is positive as expected, then its coefficient of 2 in eq 1 and 6 in eq 3 will yield large positive terms in the overall calculation. The makeup of the Δ term36 suggests that it too will usually be positive if it is not negligible, particularly for halogen-substituted systems. For example, an approximate calculation for c-1,1-C3H4F2 using experimental thermodynamic data gives Δ = +10 kcal mol−1. Under these conditions, if RSE(c-1,1-C3H4R2) ≥ RSE(c-C3H6), then the overall trend will be RSE(c-C3R6) > RSE(c-1,1,2,2-C3H2R4) > RSE(c-1,1C3H4R2) > RSE(c-C3H6) (hereafter called a forward trend). Only if RSE(c-1,1-C3H4R2) ≪ RSE(c-C3H6) will this not hold, in which case an irregular trend or a reverse trend of RSE(cC3R6) < RSE(c-1,1,2,2-C3H2R4) < RSE(c-1,1-C3H4R2) < RSE(c-C3H6) is possible. RSE of c-C3H6. The RSE of cyclopropane is established from experimental and computational data to be 27−29 kcal mol−1;5 Benson’s additivity rules set it to 27.6 kcal mol−1.38,39 Over the three model chemistries and the three independent (hyper)homodesmotic reactions in Figure 1, the average of the nine RSEs we determined is 27(1) kcal mol−1 (Supporting Information). The M06-2X model predicted RSEs slightly lower than those from the other models; this is the major contributor to the size of the standard deviation. RSEs of Fluorosubstituted c-C3HxF6−x. Applying the (hyper)homodesmotic reactions in Figure 1 to fluorosubstituted rings gives the RSE estimations in Table 1. One sees that the predictions agree within 7 kcal mol−1 regardless of model chemistry and typically are within 3 kcal mol−1. The average RSEs are 40(1), 48(2), and 50(3) kcal mol−1 for the 1,1-di-, 1,1,2,2-tetra-, and hexafluorocyclopropanes, respectively. These values are consistent with those published previously for 1,1-

Scheme 3

reaction 3a. One sees that the acyclic reference product contains 10 such interactions of two different types, whereas the acyclic reference reactant accounts for only 4 of one type. These interactions are (nearly) negligible when the A and/or B substituents are sterically small41 but become more significant as substituent sizes increase. So when RSE(c-1,1-C3H4F2) is estimated, where A = H and B = F, the A−C−C−C−B ( H− C−C−C−F) interactions are probably energetically negligible. The B−C−C−C−B (=F−C−C−C−F) interactions are probably energetically non-negligible, but as only two are present, their impact may be moderated by other energetic approximations within the homodesmotic method, so errors associated with them are not easily detected. However, for RSE(c-1,1,2,2-C3H2F4) and RSE(c-C3F6), the number of uncanceled F−C−C−C−F interactions increases to 4 and 6, respectively, so they affect the magnitude of the RSE. There are of course other uncanceled interactions we have not mentioned. The point is that most will occur with greater frequency as the sizes of acyclic reference molecules increase and will be more energetically significant as the substituent size increases. Consequently, (hyper)homodesmotic methods cannot be expected to give accurate RSE predictions either for highly substituted rings or for rings with large substituents. We therefore employed the semi-homodesmotic approach of eqs 1 and 3 described above to test the reliability of the homodesmotic reaction-based results. For the fluorinated rings, reaction 1 corresponds to a group equivalent reaction, so its prediction of RSE(c-1,1-C3H4F2) = 40(1) kcal mol−1 (average of the three model chemistry values, rounded to ±1 kcal mol−1) was used. The value of Δ = 3(1) kcal mol−1 (Supporting Information), somewhat smaller than that estimated above 6054

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Table 2. Predicted RSEs (kcal mol−1) for cis- and trans-1,2-Difluorocyclopropane and Differences Using Different Models (6311+G(d,p) Basis Set) and the Reactions from Figure 2 c-cis-1,2-C3H4F2

Δ

c-trans-1,2-C3H4F2

reaction

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

4 5a 5b 6a 6b

41.6 38.7 39.4 36.0 36.4

43.1 40.1 40.4 37.1 37.5

44.5 41.4 41.6 38.6 38.9

38.9 39.2 37.0 36.4 36.7

40.1 40.3 37.8 37.3 37.6

41.6 41.6 39.0 38.7 38.9

2.7 −0.5 2.4 −0.4 −0.3

3.0 −0.2 2.6 −0.2 −0.1

2.9 −0.2 2.6 −0.1 0.0

Table 3. Predicted RSEs (kcal mol−1) for 1,1-Dimethylcyclopropane, 1,1,2,2-Tetramethylcyclopropane, and Hexamethylcyclopropane Using Different Models (6-311+G(d,p) Basis Set) and the Reactions from Figure 1 c-1,1-C3H4Me2

c-1,1,2,2-C3H2Me4

c-C3Me6

reaction

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

M06-2X

wB97Xd

MP2

1 2a 2b 3a 3b

23.1 22.8 22.9 22.5 22.7

25.3 25.0 25.7 25.5 25.4

25.3 25.1 26.0 26.0 26.0

15.1 11.1 13.5 11.1 10.0

16.6 13.5 15.3 13.5 12.6

17.9 15.3 16.9 15.3 14.4

−11.6 −24.4

−11.4 −23.4

−7.7 −19.7

−37.7

−35.5

−32.8

predictions being within one standard deviation of this regardless of which cis/trans correction is used. This argues that the semi-homodesmotic approach represents a true improvement over (hyper)homodesmotic methods in estimating RSEs of highly substituted cyclopropanes. RSEs of Methyl-Substituted c-C3HxMe6−x. In contrast to the homodesmotically determined RSEs for fluorosubstituted cyclopropanes, those for methyl-substituted cyclopropanes, though reasonably consistent across reactions and model chemistries for the 1,1-di- and 1,1,2,2-tetrasubstituted rings, exhibit a reverse RSE trend with methyl substitution. Moreover, (hyper)homodesmotic reactions give inconsistent results in predicting extremely implausible negative RSEs for hexamethylcyclopropane (Table 3). We examined this latter observation through a number of tests of computational and homodesmotic methodologies. It is not an artifact of computational methodology; increasing and decreasing the size of the basis set had little effect on the RSEs, whereas test counterpoise calculations showed that basis set superposition error is also negligible (