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An Ab Initio Study of Annulation Effects on the Valence Isomerism of Benzene

Alan B. Brown a,*, Scott E. McKay a, and Paul Kiprof b,*

a Department of Chemistry, Florida Institute of Technology, Melbourne, FL 32901, U.S.A.

bDepartment of Chemistry, University of Minnesota-Duluth, 10 University Drive, Duluth, MN 55812, U.S.A.

Benzene valence isomerism is known to depend on substitution [1]; for example, the first synthesis of a Dewar benzene depended on destabilization of a benzene by juxtaposition of bulky substituents [2]. Annulated benzenes are the subject of current interest, in connection with attempts to induce bond-length alternation [3]. For the past several years, as part of an effort to produce an isolable [5]paracyclophane [4], we have been studying annulation effects on the equilibrium between benzene and Dewar benzene. By ab initio calculations, we have now compared the energies and geometries of the [n]annulated Dewar benzenes 1.n to those of the corresponding annulated benzenes 2.n (Scheme).

Methods. Calculations employed the SPARTAN package, versions 3.0 [5a] and 3.1 [5b], on a Silicon Graphics Indy platform; default computational parameters were used throughout. Symmetry constraints were not used at any level. Structures were fully optimized using the AM1 [6] and MNDO [7] semiempirical methods, and by restricted Hartree-Fock ab initio calculations with the STO-3G, 6-31G, and 6-31G* basis sets; single-point MP2(fc)/6-31G*//RHF/6-31G* energies (hereafter termed "MP2") were calculated (Supplement: Table S1) [8]. Hexamethyl Dewar benzene (3) and hexamethylbenzene (4) were also studied, because theirs is the most closely related isomerization whose experimental H has been measured [9]; the "MP2" energy difference (isomerization energy) is within the range of the experimental values [9], and the RHF/6-31G* value is almost as good (Table 1). The isomerization energy of the simple system 1. -> 2. was calculated by the RHF/6-311G** and MP2(fc)/6-3111G**//RHF/6-311G** methods; these values were within 1.4 kcal/mol of the RHF/6-31G* and "MP2" values respectively. This suggests that the agreement between the "MP2" and experimental values for 3 -> 4 represents a real convergence of theory with experiment, not happenstance.

Table 1: Isomerization Energies (kcal/mol)
Reaction E6-31G E6-31G* E"MP2"
3 -> 4 -70.0 - 56.8 - 58.4a
1. -> 2. - 93.0 - 79.0 b - 75.6 c
1.8 -> 2.8 - 94.8 - 80.9 - 78.8
1.7 -> 2.7 - 94.0 - 79.9 - 77.1
1.6 -> 2.6 - 97.5 - 83.3 - 79.5
1.5 -> 2.5 -111.3 - 96.3 - 91.4
1.4 -> 2.4 -128.8 -112.5 -105.9
(a)exp. -59.4 ± 2.1 (ref 9);
(b) RHF/6-311G**: -78.5;
(c) MP2/6-311G**//RHF/6-311G**: -74.2

Results and Discussion. The calculated isomerization energies for l.n - 2.n (Table 2) are similar for n = and n = 7; the "no-ring" models are 2,3-dimethyl Dewar benzene (1.) and o-xylene (2.),because the Dewar and benzene fragments of l.n and 2.n (n ) bear carbon substituents in the same places as the methyls of 1. and 2.. Isomerization becomes more exothermic for n < 6 than for no ring; the "threshold" ring (the largest with any significant effect) is six-membered. Progressively larger jumps in exothermicity are predicted from n = 6 to n = 5 and from n = 5 to n = 4. The trend reflects an annulation effect, not merely ring strain: the strain of simple cycloalkenes decreases from seven to six members [10].

The level of theory needed in these systems depends on the purpose of the calculations. Bonding in Dewar benzenes is difficult to describe using hybrids of s and p gaussian functions only [11]; for quantum chemistry, therefore, it seems evident that carbon d polarization functions and correlation corrections are needed. However, the qualitative finding of a six-membered threshold ring also holds at the 6-31G level (Figure 1), and 6-31G bond lengths and angles are within 0.02 Å and 0.6&deg; of experimental data where available (Figure 2 and Supplement Tables S2-S6). Like others, we find that bond alternation is small in benzene rings fused to a single, saturated ring of four or more members [12]. We conclude that for molecular design, in the ring-size range n = 4 to n = 7, the 6-31G basis set suffices. For n = 8, the isomerization energy is close to that for n = 6 at the "MP2" level only.

Figure 1. Isomerization Energies (kcal/mol) versus annulating ring size (N).

SEtot = TEstrained - TEunstrained (1)
SEtot = SE"bnz" + SEann (2)
SE"bnz" = TE"bnz",def. - TEbenzene (3)
SEann = TEann,def. - TEann (4)

The structural basis of the annulation effect was studied by dissection of strain energies (eqs 1-4) [13]. The strain energy SEtot is defined as the difference between the total energies of the strained molecule and a fictitious unstrained molecule (eq 1 and Table 8). one can partition SEtot into two theoretically accessible parts (eq 2) [13]: SE"bnz" is the difference between the total energy of the deformed "benzene" ("benzene" in quotes denotes "either benzene or Dewar benzene as appropriate") and that of benzene itself (eq 3 and Table 9). Similarly, SEann is the difference between the total energy of the deformed annulating ring and that of the fully optimized alkane with the same number of sp3 carbons as the annulating ring [13], e.g., ethane for 2.4 (eq 4 and Table 2).

Table 2. Partial Strain Energies [MP2(fc)/6-31G*//RHF/6-31G*; kcal/mol]
Cpd. SE"bnz" SEann Cpd SE"bnz" SEann
1. 80.91 2.55 2. 0.09 5.54
1.8 81.09 8.78 2.8 0.30 10.76
1.7 80.92 5.11 2.7 0.16 6.72
1.6 83010 4.28 2.6 0.14 3.69
1.5 96011 13.77 2.5 4.06 10.56
1.4 142.20 38.86 2.4 36.05 33.84

The increase in isomerization exothermicity between n.7 and n.6 is reflected in the strain-energy change, and is split about evenly between SE"bnz" and SEann (Table 3). The change in SE"bnz" is an increase in SE"bnz" from Dewar benzene 1.7 to 1.6, but not observed going from benzene 2.7 to 2.6. This effect appears to depend primarily on the "exocyclic" angles Q' and Q (Figure 1; mean: Qav), which drop by 8&deg; between 1.7 and 1.6, but are unchanged between 2.7 and 2.6 (Table 3). Plots of DE versus Qav in the Dewar benzenes are linear (Figure 2) with r > 0.983. Thus, annulation affects benzene valence isomerism in large part by manipulating Qav. Changes in strain energy evaluated in this way (DStot) are close both to strain energy changes evaluated using homodesmotic reactions (DShomo) [13] and to "MP2" energy changes (DE"MP2", Table 3).


Figure 2. Isomerization energies (kcal/mol) versus Qdew (&deg;), with least-squares lines. 6-31G*, filled circles, r=0.990: "MP2", empty diamonds, r=0.983.

Table 3. Strain Energy Changes and "Exocyclic" Angles
[MP2(fc)/6-31G*//RHF/6-31G*; kcal/mol, &deg;]
Reaction DSE"bnz"a DSEanna DSEtotb DSEhomo DE"MP2"c Qdewd Qbene
1.> 2. -80.8 +3.0 -77.8 -75.6 135.2 120.9
1.8 > 2.8 - 80.8 +2.0 - 78.8 -84.8 - 78.8 136.5 122.4
1.7 > 2.7 - 80.8 +1.6 -79.2 -77.1 -77.1 134.7 121.6
1.6 > 2.6 - 83.0 -0.6 -83.6 -79.5 -79.5 126.4 121.6
1.5 > .5 - 92.1 -3.2 -95.3 -91.4 -91.4 114.1 110.6
1.4 > 2.4 -106.1 -5.0 -111.2 -105.9 -105.9 95.4 93.6
(a) SE is the change in SE from l.n to 2.n;
(b) sum of previous two columns;
(c) from Table 1;
(d) Qav for l.n;
(e) Qav for 2.n.

The change in DSEann arises because SEann does drop significantly from benzene 2.7 to 2.6, but not from Dewar benzene 1.7 to 1.6. The effect appears to come from elongation and narrowing of the six-membered ring of 1.6, and will be discussed in detail elsewhere.

In sum, benzene valence isomerism can be manipulated by annulation; isomerization of 2,3-annulated Dewar benzenes to annulated benzenes is calculated to become more exothermic with decreasing size of the annulating ring. The largest effective annulating rings are six-membered; the exocyclic C=C-C angles of the Dewar benzene are forced down, and the six-membered ring is deformed. To reproduce experimental isomerization energies, MP2(fc)/6-31G*//RHF/6-31G* methods are needed; for molecular design, 6-31G calculations suffice to produce the same trends seen at higher theoretical levels.

Acknowledgements. We are indebted to Professor J. Clayton Baum for many helpful discussions; we thank I. Beros and J.P.M. Fessenden for preliminary calculations, and a referee for useful suggestions. This study was supported in part by the donors of the Petroleum Research Fund, administered by the American Chemical Society; purchase of computers was assisted by the National Science Foundation.

References

[1] Review: A.T. Balaban, M. Banciu, and V. Ciorba, Annulenes, Benzo-, Hetero-, Homo-Derivatives, and their Valence Isomers, CRC, Boca Raton, FL, 1987, Vol II, pp 5-21.

[2] E.E. van Tamelen and S.P. Pappas, J. Am. Chem. Soc., 84 (1962) 3789.

[3] A review of the Mills-Nixon effect: N.L. Frank and J.S. Siegel, Adv. Theor. Interesting Mol., 3 (1995) 209.

A very recent overview: A.M. Rouhi, Chem. & Eng. News, 74(14) (1996) 27.

See also F. Cardullo, D. Giuffrida, F.H. Kohnke, F.M. Raymo, J.F. Stoddart, and D.H. Williams, Angew. Chem., Int. Ed. Engl., 35 (1996) 339.

[4] A recent review: F. Bickelhaupt and F.H. de Wolf, Adv. Strain Org. Chem., 3 (1993) 185.

The most recent approach: D.S. van Es, F.J.J. de Kanter, W.H. de Wolf, and F. Bickelhaupt, Angew. Chem., Int. Ed. Engl., 34 (1995) 2553.

[5] Spartan Userts Guide, Versions (a) 3.0 and (b) 3.1, Wavefunction, Inc., Irvine, CA, (a) 1993 and (b) 1994.

[6] M.J.S. Dewar, E.G. Zoebisch, E.F. Healy, and J.J.P. Stewart, J. Am. Chem. Soc., 107 (1985) 3902, 115 (1993) 5348.

[7] M.J.S. Dewar and W. Thiel, J. Am. Chem. Soc., 99 (1977) 4899.

[8] For methods, see W.J. Hehre, L. Radom, P.v.R. Schleyer, and J.A. Pople, Ab Initio Molecular Orbital Theory, Wiley-Interscience, New York, 1986, pp 10-42, 63-100.

[9] W. Schäfer, Angew. Chem., Int. Ed. Engl., 5 (1966) 669. J.F.M. Oth, Recl. Trav. Chim. Pays-Bas, 87 (1968) 1185. W. Adam and J.C. Chang, Int. J. Chem. Kinet., 1 (1969) 487.

[10] S.W. Benson, F.R. Cruickshank, D.M. Golden, G.R. Haugen, H.E. O'Neal, A.S. Rodgers, R. Shaw, and R. Walsh, Chem. Rev., 69 (1969) 279, and references therein.

[11] An early discussion: M. Randic and Z. Majerski, J. Chem. Soc. B, (1968) 1289.

[12] A recent example with leading references: A. Stanger, N. Ashkenazi, A. Schachter, D. Blaser, P. Stellberg, and R. Boese, J. Org. Chem., 61 (1996) 2549.

[13] Cf.: F. Bockisch, J.C. Rayez, D. Liotard, and B. Duguay, J. Comput. Chem., 13 (1992) 1047.

Supplementary Material

Table S1: Energies (SCF Etot, a.u.)
Cpd. STO-3G 6-31G 6-31G* a "MP2"b
4 -459.37090 -464.72755 -464.90081 -466.46654
2. -305.05911 -308.66606 -308.77622 c -309.79798 d
2.8 -458.22325 -463.56752 -463.74384 -465.28998
2.7 -419.65036 -424.55656 -424.71672 -426.12859
2.6 -381.07499 -385.54259 -385.68637 -386.96442
2.5 -342.49032 -346.51995 -346.64727 -347.79287
2.4 -303.85334 -307.44953 -307.56543 -308.57922
3 -459.29613 -464.62596 -464.81023 -466.37341
l. -304.94909 -308.51781 -308.65039 e -309.67746 f
1.8 -458.11066 -463.41640 -463.61494 -465.16437
1.7 -419.53834 -424.40684 -424.58941 -426.00567
1.6 -380.95674 -385.38722 -385.55356 -386.83780
1.5 -342.34904 -346.34263 -346.49388 -347.64717
1.4 -303.67988 -307.24433 -307.38607 -308.41042
(a) RHF/6-31G*//RHF/6-31G*; (b) MP2(fc)/6-31G*//RHF/6-31G*;
(c) RHF/6-311G**//RHF/6-311G**: -308.84474;
(d) MP2(fc)/6-311G**//RHF/6-311G**: -309.97552;
(e) RHF/6-311G**//RHF/6-311G**: -308.71965;
(f) MP2(fc)/6-311G**//RHF/6-311G**: -309.85727.

Table S2. Bond Lengths (Å) and Symmetries for Benzenes (literature values parenthesized)
ab bc cd de ef fa Sym.
4 (expt.: 1.417 1.417 1.417 1.417 1.417 1.417)a
STO-3G: 1.393 1.414 1.390 1.415 1.396 1.410 C1(~D3)
6-31G: 1.399 1.399 1.399 1.399 1.399 1.399 C,
6-31G*: 1.397 1.397 1.397 1.397 1.397 1.397
2. STO-3G: 1.402 1.389 1.387 1.383 1.387 1.389 Cl (~Cs)
(STO-3G: 1.381 1.390 1.381 1.395 1.381 1.390)b
6-31G: 1.402 1.390 1.388 1.384 1.388 1.390 C1
6-31G*: 1.401 1.387 1.387 1.381 1.387 1.387 C1
6-311G** 1.401 1.387 1.386 1.380 1.386 1.386 C1
2.8 STO-3G: 1.399 1.393 1.384 1.385 1.384 1.392 C1
6-31G: 1.401 1.394 1.385 1.386 1.385 1.393 C1
6-31G*: 1.399 1.392 1.384 1.384 1.383 1.391
2.7 STO-3G: 1.400 1.389 1.386 1.383 1.386 1.389 Cl (~Cs)
6-31G: 1.402 1.391 1.388 1.384 1.388 1.391 C1
6-31G*: 1.400 1.388 1.386 1.381 1.386 1.388 C1
2.6 (expt.: 1.399 1.393 1.384 1.383 1.384 1.393)c
STO-3G: 1.393 1.394 1.381 1.388 1.381 1.394 C1
6-31G: 1.396 1.395 1.382 1.389 1.382 1.395 C1
6-31G*: 1.393 1.394 1.380 1.388 1.380 1.394 C1
2.5 (expt.: 1.393 1.382 1.391 1.381 1.391 1.382)c
STO-3G: 1.390 1.384 1.390 1.397 1.390 1.384 C1 (~Cs)
6-31G: 1.391 1.385 1.390 1.389 1.390 1.385 C1
6-31G*: 1.388 1.384 1.388 1.388 1.388 1.384
2.4 (expt.: 1.391 1.385 1.400 1.399 1.400 1.385)d
STO-3G: 1.388 1.374 1.399 1.387 1.399 1.374 C2v
(STO-3G: 1.388 1.374 1.399 1.387 1.399 1.374)b,e
6-31G: 1.387 1.376 1.398 1.392 1.398 1.376 C2v
(6-31G: 1.387 1.376 1.399 1.392 1.399 1.376)b,l
6-31G*: 1.380 1.378 1.394 1.392 1.394 1.378
(6-31G*: 1.380 1.378 1.394 1.392 1.394 1.378)g
(a) Ref 14; (b) ref 15; (c) ref 16 (averages from a collection of crystal structures containing this part structure); (d) ref 17; (e) ref 18; (f) ref 19; (g) ref 20.

Figure S1. Structures of 1.n and 2.n, showing geometric descriptors. Dihedrals: D1 h-b-a-f; D2, a-f-c-d; D3, c-d-e-g. Qav is the mean of Q and Q'.

Table S3. Angles for Benzenes (&deg;; literature values parenthesized)
abc bcd cde def efa fab Q' Q
4 STO-3G: 120.1 120.0 120.0 119.9 120.0 120.0 122.7 122.7
6-31G: 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0
6-31G*: 120.0 120.0 120.0 120.0 120.0 120.0 120.0 120.0
2. STO-3G: 119.2 121.2 119.7 119.7 121.2 119.2 120.8 120.8
6-31G: 119.0 121.4 119.5 119.5 121.4 119.0 120.9 120.9
6-31G*: 119.0 121.5 119.5 119.5 121.5 119.0 120.9 120.9
6-311G** 119.0 121.5 119.5 119.5 121.5 119.0 121.0 121.0
2.8 STO-3G: 118.8 121.5 119.6 119.5 121.4 119.2 122.7 121.9
6-31G: 118.7 121.7 119.5 119.4 121.6 119.1 122.8 121.9
6-31G*: 118.6 121.8 119.5 119.4 121.7 119.1 122.9 121.9
2.7 STO-3G: 119.1 121.3 119.6 119.6 121.3 119.1 121.4 121.4
6-31G: 119.0 121.6 119.5 119.5 121.6 119.0 121.5 121.5
6-31G*: 118.9 121.6 119.4 119.4 121.6 118.9 121.6 121.6
2.6 (expt.: 119.6 120.1 120.2 120.2 120.1 119.6 117.2 117.2)a
STO-3G: 119.2 121.2 119.6 119.6 121.2 119.2 121.8 121.8
6-31G: 119.1 121.4 119.5 119.5 121.4 119.1 121.7 121.7
6-31G*: 119.0 121.5 119.5 119.5 121.5 119.0 121.6 121.6
2.5 (expt.: 120.8 118.2 120.9 120.9 118.2 120.8 108.0 108.0)a
STO-3G: 120.5 119.0 120.5 120.5 119.0 120.5 111.0 111.0
6-31G: 120.4 119.2 120.3 120.3 119.2 120.4 110.8 110.8
6-31G*: 120.4 119.2 120.4 120.4 119.2 120.4 110.6 110.6
2.4 (expt.: 122.3 116.0 121.7 121.7 116.0 122.3)b
(expt.: 93.8 93.8)a
STO-3G: 122.4 115.8 121.8 121.8 115.8 122.4 93.4 93.4
(STO-3G: 122.4 115.9 121.8 121.8 115.9 122.4)c
6-31G: 122.3 116.1 121.6 121.6 116.1 122.3 93.7 93.7
6-31G*: 122.4 116.0 121.7 121.7 116.0 122.4 93.6 93.6
(a) ref 16 (averages from a collection of crystal structures containing this part structure); (b) ref 17; (c) ref 18.

Table S4. Bond Lengths (Å) and Symmetries for Dewar Benzenes (literature values parenthesized)
ab bc cd de ef fa cf Sym.
3 (expt.: 1.352 1.523 1.523 1.352 1.523 1.523 1.629)'
STO-3G: 1.321 1.542 1.542 1.321 1.542 1.542 1.567 C2v
6-31G: 1.334 1.541 1.541 1.334 1.541 1.541 1.579 C2v
6-31G*: 1.326 1.532 1.532 1.326 1.532 1.532 1.558
1. STO-3G: 1.322 1.538 1.534 1.316 1.534 1.538 1.558 C1 (~Cs)
6-31G: 1.336 1.535 1.536 1.332 1.536 1.535 1.574 C1
6-31G*: 1.328 1.526 1.526 1.323 1.526 1.526 1.551
6-311G** 1.327 1.526 1.527 1.323 1.527 1.526 1.553 C1
1.8 STO-3G: 1.323 1.539 1.534 1.316 1.534 1.538 1.556 C1
6-31G: 1.337 1.536 1.536 1.332 1.536 1.534 1.571 C1
6-31G*: 1.330 1.527 1.526 1.324 1.526 1.525 1.548 C1
1.7 STO-3G: 1.321 1.537 1.535 1.316 1.535 1.535 1.558 C1
6-31G: 1.336 1.534 1.536 1.332 1.536 1.534 1.573 C1
6-31G*: 1.328 1.525 1.526 1.323 1.526 1.525 1.551 C1
1.6 STO-3G: 1.315 1.536 1.536 1.316 1.536 1.536 1.566 C1
6-31G: 1.328 1.534 1.537 1.331 1.537 1.534 1.584 C1
6-31G*: 1.321 1.525 1.527 1.323 1.526 1.525 1.560 C1
1.5 STO-3G: 1.307 1.536 1.537 1.315 1.537 1.536 1.574 C1 (~Cs)
6-31G: 1.320 1.536 1.538 1.330 1.538 1.536 1.594 C1
6-31G*: 1.312 1.526 1.528 1.322 1.528 1.526 1.570
1.4 STO-3G: 1.299 1.539 1.538 1.315 1.537 1.539 1.592 C1 (~Cs)
6-31G: 1.310 1.543 1.536 1.330 1.536 1.543 1.619 C1
6-31G*: 1.303 1.533 1.526 1.321 1.526 1.533 1.589 C1
(a) Ref 21.

Table S5. Dihedrals for Dewar Benzenes (degrees; literature values parenthesized)
Dl D2 D3 Dl D2 D3
3 (-163.9 124.5 -163.9: expt.)a
-177.7 114.8 -177.7: STO-3G 1.6 -177.2 116.2 -177.6: STO-3G
-177.3 115.5 -177.3: 6-31G -177.0 117.0 -177.6: 6-31G
-177.2 116.0 -177.2: 6-31G* -176.6 117.6 -177.3: 6-31G*
l. -177.5 116.2 -177.4: STO-3G 1.5 -175.2 116.3 -178.0: STO-3G
-176.5 117.0 -177.5: 6-31G -173.7 117.0 -177.8: 6-31G
-176.3 117.6 -177.0: 6-31G* -171.5 117.6 -177.7: 6-31G*
-176.2 117.4 -177.0 6-311G**
1.8 -178.3 116.3 -177.4: STO-3G 1.4 -172.2 116.4 -178.5: STO-3G
-178.1 117.0 -177.4: 6-31G -172.1 117.2 -178.4: 6-31G
-177.9 117.7 -177.0: 6-31G* -167.1 117.6 -178.3: 6-31G*
1.7 -175.5 116.2 -177.4: STO-3G
-173.5 117.0 -177.4: 6-31G
-173.1 117.7 -177.0: 6-31G*
(a) Ref 21.

Table S6. "Endocyclic" and "Exocyclic" Angles for Dewar Benzenes (degrees; literature values parenthesized)
abc bcf fcd cde def efc cfa fab Q' Q
3 (expt.: 84.8 84.8 84.8 84.8)a
STO-3G: 94.6 85.4 85.4 94.6 94.6 85.4 85.4 94.6 135.0 135.0
6-31G: 94.6 85.4 85.4 94.6 94.6 85.4 85.4 94.6 134.9 134.9
6-31G*: 94.3 85.7 85.7 94.3 94.3 85.7 85.7 94.3 135.0 135.0
l. STO-3G: 94.4 85.6 85.5 94.5 94.5 85.5 85.6 94.4 135.2 135.2
6-31G: 94.4 85.6 85.5 94.5 94.5 85.5 85.6 94.4 135.2 135.2
6-31G*: 94.2 86.0 85.7 94.3 94.3 85.7 85.8 94.2 135.2 135.2
6-311G** 94.3 85.7 85.7 94.3 94.3 85.7 85.7 94.3 135.3 135.5
1.8 STO-3G: 94.2 85.7 85.5 94.5 94.5 85.5 85.6 94.5 136.6 136.2
6-31G: 94.2 85.7 85.6 94.4 94.5 85.5 85.6 94.5 136.8 136.2
6-31G*: 93.9 86.0 85.8 94.2 94.2 85.8 85.8 94.3 136.8 136.2
1.7 STO-3G: 94.4 85.6 85.5 94.5 94.5 85.5 85.6 94.4 134.4 134.4
6-31G: 94.4 85.6 85.5 94.5 94.5 85.5 85.6 94.4 134.8 134.8
6-31G*: 94.2 85.8 85.7 94.3 94.3 85.7 85.8 94.2 134.7 134.7
1.6 STO-3G: 94.7 85.3 85.3 94.7 94.7 85.3 85.3 94.7 126.5 126.5
6-31G: 94.8 85.2 85.3 94.7 94.7 85.3 85.2 94.8 126.3 126.4
6-31G*: 94.5 85.5 85.5 94.5 94.4 85.6 85.5 94.5 126.3 126.4
1.5 STO-3G: 95.0 85.0 85.2 94.8 94.8 85.2 85.0 95.0 114.5 114.5
6-31G: 95.1 84.9 85.0 94.9 94.9 85.1 84.9 95.1 114.3 114.3
6-31G*: 94.8 85.2 85.3 94.7 94.7 85.3 85.2 94.8 114.1 114.1
1.4 STO-3G: 95.5 84.5 84.8 95.2 95.2 84.8 84.5 95.5 95.5 95.5
6-31G: 95.7 84.3 84.6 95.4 95.4 84.6 84.3 95.7 95.5 95.5
6-31G*: 95.4 84.6 85.0 95.0 95.0 85.0 84.6 95.4 95.4 95.4
(a) Ref 21 (reported there as 84.78).

Table S7. Partial Energies [MP2(fc)/6-31G*//RHF/6-31G*; a.u.]
Cpd. TE"bnz",def. TEann,def. Cpd. TE"bnz",def. TEann,def.
1. -231.032756 -80.66082b 2. -231.45635 -80.65604a
1.8 -231.032728 -235.35104 2.8 -231.45602 -236.13935
1.7 -231.32755 -196.98296 2.7 -231.45625 -196.98040
1.6 -231.32406 -157.81871 2.6 -231.45627 -157.81965
1.5 -231.30333 -118.63803 2.5 -231.45004 -118.64315
1.4 -231.22989 -79.43258 2.4 -231.39905 -79.44058
(a)Two methyls.

Table S8. Unstrained Reference Compounds, and Their Energies [MP2(fc)/6-31G*//RHF/6-31G*; a.u.]
Cpd. Quantity Reference Energy
All TE"bnz" benzene -231.45650
n. TEann 2 x methane - 80.66488
n.8 TEann hexane -236.15668
n.7 TEann pentane -196.99110
n.6 TEann butane -157.82553
n.5 TEann propane -118065997
n.4 TEann ethane - 79.49451

Additional References for Supplementary Material

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