Studies on Unusually Long Carbon–Carbon Bond Distances in

Article pubs.acs.org/JCTC

Molecular Mechanics (MM4) Studies on Unusually Long Carbon− Carbon Bond Distances in Hydrocarbons Norman L. Allinger,† Jenn-Huei Lii,‡ and Henry F. Schaefer, III*,† †

Center for Computational Chemistry, University of Georgia, Athens, Georgia 30602, United States CNC Gelcaps Corporation, No. 1205 Zhongzheng Road, Caotun Township, Nantou County 54254, Taiwan

‡

ABSTRACT: The carbon−carbon single bond is of central importance in organic chemistry. When the molecular mechanics MM4 force field was developed beginning in the early 1990s, C−C bond lengths were not known very reliably for many important molecules, and bond lengths greater than 1.6 Å were quite poorly known experimentally. Quantum-mechanically computed values could not yet be obtained with useful accuracy in a general way. This paper examines structures now available from experiment and quantummechanical computations and extends the fit of the MM4 methodology to include new bond distances as long as 1.71 Å.

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INTRODUCTION MM4 is a generally useful computer algorithm and program1,2 developed for the computation of the structures, energetics, and many other properties of organic molecules. The training set used in originally constructing the program was mainly experimental because when the development was begun, relatively little information was available from quantummechanical calculations. Most of the structural features that can be computed by MM4 remain useful and accurate today, but there is an important exception: bond lengths for unusually long carbon−carbon single bonds. “Ordinary” C−C bond lengths range from about 1.52 to 1.56 Å. The equations used to compute C−C bond lengths with MM4 were well-checked over this range and give reliable results. Longer bond distances can be predicted with the program, but these are derived from extrapolations from what was known at the time and are now of uncertain reliability.

match available experimental data well. Such a modification is conveniently made by changing only higher-power terms in the above expression (eq 1). As long as the lower-power terms up through the quartic term are unchanged, the bond lengths of the more ordinary bonds remain unchanged. The actual numerical changes made were as follows: old MM4(2008): Es = 71.94K s[ΔS2 − 3.0ΔS3 + +

Es = 71.94K s[ΔS2 − 3.0ΔS3 +

METHODOLOGY We now have available bond lengths up to 1.706(4) Å from experiment (X-ray crystallography) confirmed by corresponding values from quantum-mechanical [M06-2X/6-31G(d,p)] computations3 [1.703 Å]. We find that the bond lengths obtained by the original MM4 method for long C−C bonds are much too long. The original MM4 stretching function is given in the form of a polynomial:

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The bond length stretching function in MM4 has been modified to fit the newer structural information. Bonds with distances as long as 1.571 Å have revised MM4 values that are unchanged. Bonds with longer distances have been shortened to fit the newer experiments. Bond lengths can sometimes be measured with an accuracy approaching 0.001 Å by a number of methods. The length of a particular bond in most compounds is usually close to some “standard value”. This means that when a particular bond is

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In this research we changed only the portion of the function that affects “long” bonds, as ordinary MM4 bond distances still © XXXX American Chemical Society

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7 ( −3.0)2 ΔS 4 12

+ 0.03( −3.0)3 ΔS5 + 0.17(− 3.0)4 ΔS 6]

1 K s(ΔS2 + CsΔS3 + Q f Cs 2ΔS 4 + Pf Cs 3ΔS5 2 + Hf Cs 4ΔS 6 + ...)

1 31 ( −3.0)3 ΔS5 + ( −3.0)4 ΔS 6] 4 360

new MM4(2015):

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Es =

7 ( −3.0)2 ΔS 4 12

Received: September 28, 2015

A

DOI: 10.1021/acs.jctc.5b00926 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation Table 1. Long C−C Bond Lengths (rg)a in Angstroms expt hexafluoroethane hexamethylethane tri-tert-butylmethane 1,2-diarylindane[a]indane isododecahedrane 2,3-di-1-adamantyl-2,3-dimethylbutane 5,6-dibutyl-5,6-diphenyldecane diamantane−diamantane adamantane−triamantane tetra-tert-butylmethane hexakis(3,5-di-tert-butyl-1-phenyl)ethane bromoisododecahedrane hexaphenylethane diamantane−triamantane mean error AADe

5

1.545(6) 1.582(10)6 1.611(5)7 1.621(2)8,c − 1.642(4)9,c 1.645(6)10,c,d 1.649(4)11,c 1.661(2)11,c − 1.677(30)12,c,d 1.693(11)13,c − 1.706(4)11,c

MM3

MM4(2008)

Δb

MM4(2015)

Δb

1.554 1.577 1.615 1.618 1.620 1.645 1.656 1.667 1.678 1.700 1.726 1.636 1.720 1.724

1.548 1.571 1.611 1.618 1.643 1.644 1.648 1.674 1.692 1.725 1.788 1.653 1.799 1.808

+3 −11 0 −3 − +2 +3 +25 +31 − +111 −40 − +102 +20 30

1.548 1.571 1.609 1.616 1.637 1.638 1.640 1.657 1.666 1.686 1.693 1.689 1.696 1.702

+3 −11 −2 −5 − −4 −5 +8 +5 − +16 −4 − −4 +0 6

M06-2X/6-31G(d,p) 1.540 1.585 1.612 1.620 1.659 1.635 1.655 1.660 1.669 1.682 1.678 1.700 1.719 1.703

(1.533) (1.576) (1.602) (1.610) (1.647) (1.622) (1.643) (1.648) (1.654) (1.662) (1.669) (1.685) (1.702) (1.687)

Δb −5 +3 +1 −1 − −7 +10 +11 +8 − +1 +7 − −3 +2 5

a

All of the bond lengths in this paper are rg values unless they are given in parentheses, in which case they are re values. The re values are as given directly by M06-2X/6-31G(d,p) computations. The rg values are either as given by the literature or corrected to rg by MM4 using the Kuchitsu method.18−20 bError in units of 0.001 Å. cA correction of 0.002 Å was added to transform rα to rg. dThermal motion of 0.005 Å was added (this structure refers to room temperature). eAAD = average absolute deviation.

found or predicted to have a significantly different value, there is likely an unusual steric or electronic effect responsible, and the above approach offers us a way to study such effects. The C−C bond is of special interest because of its wide occurrence.4 The standard value for an ordinary C−C bond length is usually taken as 1.54 Å, and bonds with lengths in the range of 1.52− 1.56 Å are usually regarded as “ordinary” and as such are not normally of particular interest in the present sense. For bond distances outside of this range, one can and should ask why this is the case.

However, for a molecular mechanics model we do not need more than four figures, a much more modest computing task.17 Importantly, we also know that basis set/correlation truncations lead to errors that are mainly systematic and susceptible to reasonably accurate empirical corrections. Moreover, experimental C−C bond lengths may vary by up to about 0.01 Å depending on how they are measured, since the different kinds of experiments actually measure different physical quantities, which thus have different definitions and correspondingly different numerical values.18 Again, ordinarily it is possible to correct for this with acceptable accuracy.19,20 Long C−C bonds are sometimes accompanied by short C− H bonds in the same molecule, and these distortions may often be viewed as mainly the result of steric effects. It is instructive to think of a typical hydrocarbon as having an “inside” (carbon atoms) and an “outside” (hydrogen atoms). Severe steric interactions are usually found to occur between hydrogen atoms, as they are on the “outside” of the molecule, whereas the carbons are on the “inside” and largely physically shielded from one another by the hydrogens. In the following discussion, numerical examples other than those from experiment or quantum mechanics are from MM4 (or other specifically identified force fields). The fundamental ideas, however, are applicable to force fields in general. The basic force field unit is the atom. The electron and nucleus are explicitly utilized in only a few special cases. The atoms are identified by the usual symbols for the elements. They are neutral, and each has its own van der Waals properties. Each has a mass, which may be the (nuclear plus electron) mass of a particular isotope or the natural-abundance mass depending on the type of calculation being carried out.21 Each atom is taken to be spherical, with its mass (and net charge if any) centered at the nuclear position (i.e., the center of the sphere), with the exception of hydrogen (and its isotopes, deuterium and tritium).1,2 With hydrogen, its one electron is used for bonding, and we know how to treat that distortion accurately with quantum mechanics. For molecular mechanics we need a simpler model. The most often previously used model puts the mass and net

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RESULTS In Table 1 we have listed the long C−C bonds for which we have reasonably accurate experimental results.5−13 These distances were almost all determined by crystallographic methods, as most of them occur in fairly large molecules, where microwave and electron diffraction methods are challenging. High-level quantum-mechanical methods may be applicable now but have not been much applied as of yet to molecules of the size that we would like to study. Most quantum and molecular mechanics calculations are carried out for isolated molecules. In crystallographic studies the molecules mutually distort one another. These distortions are ordinarily small, on the order of the experimental error, but sometimes they are quite a bit larger. However, if the structure of the lattice is known, one can pack the MM4 molecules into the lattice and optimize the structures of the molecule and the lattice simultaneously. We have done this in several cases for large hydrocarbons (among others).2 The structure of the isolated molecule can then be compared with the structure of the molecule in the lattice. The bond length distortions are typically only 0.001−0.002 Å. Not unexpectedly, the angular distortions are larger (in linear distortion), typically 1−2° or less but occasionally up to about 5°. Experimental errors are typically about 0.003 Å and 0.3° in modern work. The quantum-mechanical computations are limited largely by computing power at present. We know that we can sometimes obtain C−C bond lengths to five-figure accuracy for very small molecules with highly sophisticated theoretical methods.14−16 B

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Journal of Chemical Theory and Computation charge (if any) at the actual nuclear position but puts the “electrons” (represented as a van der Waals sphere) closer in toward the bonded carbon by a small amount, about 0.1 Å. The approximate amount of the above-described inward shift was estimated from quantum mechanics and subsequently modified somewhat to best fit experimental information. This scheme works well enough for the purposes for which it has been used to date. Additional and more accurate experimental information and quantum-mechanical computations on molecular structures are constantly becoming available. It may be that some of the approximations described above will prove to be too crude in the future, and an understanding of where we are now, and how we got there, may then be helpful. We wish to set the background for this paper into the above context. We have gathered together the available information on “long” carbon−carbon bonds with lengths that are known with reasonable accuracy, plus a representative few bonds that are not very long for comparison purposes. These molecules have all been examined using MM4 (except for those previously studied by MM4, for which the published data are simply restated and referenced here). In the old force fields (1965 and earlier), the steric properties of each atom were represented by van der Waals spheres centered on the nuclear positions. Later force fields often tried to improve this “soft-sphere” model in two ways. One was to recognize that an atom really has two different centers: one (which is normally called “the center”) is the actual nuclear position, and the other is the center of electron density, which here we will call the van der Waals center. These two centers were originally taken to be coincident. For most atoms in most molecules this is a good approximation, but in one case it appears not to be. This special case is the hydrogen atom. The hydrogen atom has only one electron, and in an ordinary molecule that electron is used for bonding. If the electron density is still to be represented as spherically symmetrical, this van der Waals center needs to be moved in somewhat along the bond axis by an amount that can be estimated by quantum mechanics. The nuclear position and the mass are retained at the atom position, as might be known from microwave spectra or otherwise. A better model might be to substitute an ellipsoid for the current sphere in the case of hydrogen. Whether the ellipsoid should be oblate or prolate might be determined empirically. The second attempted improvement along these lines was to alter the van der Waals properties of the amino-type nitrogen (ammonia) so as to better reproduce the van der Waals surface around the lone pair. This was done by taking explicit account of the lone pair in the calculation, using the amino group as the most important example of an electronically nonspherical atom. It was soon found that this method had the disadvantage in the general case of greatly complicating the calculation. However, there was no significant improvement over what could be obtained without the use of an explicit lone pair but with the aid of a better parametrization than that previously used. Therefore, this “lone pair” was abandoned. Figure 1 can be used to correlate the bond length data given in Table 1. Experimental bond lengths are plotted as black triangles at the same value on both axes. The 2015-modified MM4 values are indicated by blue × symbols, one for each bond listed in Table 1, in order of increasing bond length, which also corresponds to ascending order in the figure. A straight line is drawn through the experimental points. The

Figure 1. Graphical tabulation of C−C single-bond distances from MM4 and experiment. The red error bars showing the experimental uncertainties represent one standard deviation.

experimental values for the bonds are corrected to rg values, and the reported errors are represented by error bars that are one standard deviation in length. Table 1 includes all of the experimental information known to the authors for C−C bonds longer than 1.64 Å. The agreement between the new MM4 method and experiment is certainly satisfactory. It is worth noting that this agreement indicates more than simply the fact that it is possible to fit unusual bond lengths with molecular mechanics. To fit these bond lengths accurately with a relatively simple, straightforward, and physically reasonable model (MM4) requires that the forces that determine these bond lengths (i.e., stretching, bending, torsional, van der Waals, and electrostatic) have to be dissected out of the total force applicable from the model over a rather long range of distances. There is no guarantee that the classical-mechanical model used will be accurate enough for this to be done, so this example provides a stringent test of the validity of the model. It is worth noting that the usefulness (chemical accuracy) of classical mechanics for the calculation of the structures (and subsequently the physical properties of those structures) of organic molecules seems to hold up very well for all cases that we have carefully studied. There are many cases in the literature where it is claimed that a molecular mechanics calculation has given a wrong result, and most of these claims are correct. However, in the many such cases that we have reexamined, the wrong result has always been traced to a failure of something other than classical mechanics.22 Often the problem has been a result of inadequate parametrization, but unrecognized experimental error is a frequent and misleading problem too. The only major exception known to the authors involves conjugated systems.23 These require a quantum-mechanical treatment for that portion of the molecule. That is not to say that other exceptions do not exist but only that they are much less common than what one might conclude from the literature concerning molecular mechanics.

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DISCUSSION One inevitable problem with the development of a force field1 such as MM4 is that additional experimental and computational results continue to become available after the development is “finished”, continually highlighting the fact that some of the C

DOI: 10.1021/acs.jctc.5b00926 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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Journal of Chemical Theory and Computation earlier data that were reproduced by the force field were inaccurate. Thus, the force field can always be improved. However, a continuously changing force field would be of very limited use from the viewpoint of science, as one would not be able to reproduce the results of earlier computations in a reliable way. Instead, it seems that it would be better if the parts of the force field known to be accurate were continued in use and the known inaccuracies would be separately addressed. This practice was followed with our force fields MM2, MM3, and MM4. Infrequently, when sufficient corrections had been accumulated to make it worth the effort, a new force field would be developed that included corrections for all of the then-known errors. Newer versions of the same force field normally kept the earlier version intact, only adding to it without changing anything that would alter the calculated results for quantities that could have been determined earlier. In the present research, we have made modifications that would cause changes in quantities that could have been calculated earlier, and we want to explain here what has been done and why. The original MM4 force field for alkanes was finalized in about 1992 and was published in 1996.1 At the time, few experimental distances for “long” C−C bonds were available. “Ordinary” C−C bonds (with lengths of 1.52−1.56 Å) were accurately reproduced with MM4, and longer bonds were fit using our best guesses as to what the extrapolation would look like, consistent with what was known in 1992. We know that the relationship of the energy to the bond length (the stretching energy) generally follows a Morse curve, which in practical computations is ordinarily represented by a series expansion, Es = k1ΔS2 + k 2ΔS3 + ...

distances up to 1.706 Å, the longest bond for which we have a reliable experimental distance. Since the same stretching function is (with different parameters) also used for C−X bonds and X−Y bonds (where X and Y are atoms other than carbon), the longer values for such bond types are also expected to be more accurate. However, such bonds have not been studied to date, so they will provide a stringent test for this aspect of the MM4(2015) program.

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ADDITIONAL COMMENTS The reviewers posed some general questions about the usefulness of molecular mechanics calculations in the year 2016. Some comments here seem appropriate. Quantummechanical and density functional theory (DFT) calculations can certainly solve many problems that only molecular mechanics could try to address, say, 20 or 30 years ago. But why go that route now? It depends on just what it is that one wants to learn. QM/DFT is most useful for small systems, where atoms and molecules are treated mostly as waves, whereas MM treats them mostly as particles. Also, of course, traditionally the final solutions to most problems came from experiment. All of these things have been widely discussed in the literature. No detailed discussion of them will be given here, but rather some published examples will be cited, which an interested reader may pursue. First is an example where MM competed with experiment, and experiment lost. Calorimetry is traditionally an exact science. Compounds under study are painstakingly purified. The work is carried out very carefully by skilled workers, and repeated on multiple samples. Nonetheless, errors can creep in. Such a case is described in “The Tim Clark Story”.22 Sometimes one gets wrong answers, and in general it can be worthwhile to have a confirming procedure.22 Three examples of problems that were solved using MM, where that method gave very helpful insights, will be given here. The first example25 outlines the “external anomeric torsional effect”. This is something only recently observed that may account for until-now unknown conformational energy differences of up to 4 kcal/mol in molecules that show the anomeric effect. It could be understood from QM/DFT, but we think that it is more easily understood by chemists from MM and qualitative valence bond theory, as published. Second, a series of catenanes, which are cycloalkanes that are interlocked like the links of a chain, have been studied in some detail by QM methods.26 What can MM add to such a study? Insighta different overview that makes a difference.27 Finally, the two rings in biphenyl are found to be rotated relative to one another along the long axis in the isolated molecule. However, in the crystal the molecule has the rings coplanar. Therefore, intuition quickly suggests that the molecules will pack in sheets with the molecules face to face, as in graphite, since that will maximize the intermolecular van der Waals attractions. However, this does not happeninstead, they pack with each molecule perpendicular to its neighbors. Why? And how does one prove that his or her conclusion is correct?28 In each of these cases, MM calculations have been used in a study that has led to what is believed to be a correct understanding of the problem. In each case, the problem was solved by MM. Certainly MM was not the only possible way to go, but often it provided different and additional viewpoints and information to supplement what was available from other methods.

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For C−C bonds with lengths in the range of 1.52−1.58 Å, the series is usually truncated after the third- or fourth-power term. In practice, the fourth-power term is almost always used now.24 In the original version of MM4, we added fifth- and sixth-power terms to better fit bonds longer than 1.58 Å. With the structures now available (Table 1), it is clear that the terms through the fourth-power term give good and unchanged bond lengths. This is true to the nearest 0.001 Å for values as long as 1.571 Å, with slightly larger differences above that (e.g., 1.609 instead of 1.611 Å). However, above 1.61 Å the new MM4 values become progressively shorter, and markedly so, e.g., 1.666 (new) vs 1.692 Å (old). The newer MM4 values are now in agreement with experiment and quantum mechanics up to 1.70 Å. It is disappointing that the original MM4 values for these very long bonds are deficient, but they did fit well to the very limited information available in 1992. We aspire to fit longer bonds better than was possible in 1992. We can do that now, as we have available several pieces of data in which we have confidence. The new corrections used involve only the fifthand sixth-power terms in the Morse curve, so they do not change significantly (less than 0.002 Å) bond lengths less than 1.60 Å. Hence, we are making a very slight exception to our usual rule of not making changes in the force field that would impact earlier computations. These long-bond structures are quite scarce in the real world (and to the authors’ knowledge unknown in nature). Thus, for C−C bond lengths up to 1.571 Å, the new version of MM4, now called MM4(2015), gives the same results as the old version, now called MM4(2008). For longer C−C bonds, the new version gives much improved D

DOI: 10.1021/acs.jctc.5b00926 J. Chem. Theory Comput. XXXX, XXX, XXX−XXX

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(21) The default option of the MM4 program is to carry out molecular property calculations (e.g., vibrational frequencies) using the most abundant isotopic mass for an atom. However, for bulk properties (e.g., heats of formation), the natural-abundance mass is used. Any other option for these masses may be chosen in MM4 as desired. (22) Mostly the problems resulted from one of two sources: either the use of literature data that contained experimental errors or poor parametrization. A reviewer suggested that we discuss this in more detail and perhaps discuss an example. One typical example previously published will be referenced: Allinger, N. L. The Tim Clark Story. In Molecular Structure: Understanding Steric and Electronic Effects from Molecular Mechanics; John Wiley & Sons: Hoboken, NJ, 2010; pp 269−272 and refs on p 298. (23) There is also one minor exception, which is tunneling. Here a hydrogen nucleus physically goes “through” an energy barrier rather than over it. This phenomenon has recently been found to occur in another case with a more massive particle.11 It depends on the width of the energy barrier compared with the wavelength of the particle. It is definitely a quantum effect and something that is not included in classical mechanics. (24) If the geometry is to be optimized, as is frequently the case, one may somehow start with or obtain a bond that is too long. If the series ends with an odd power, the bond may stretch out to infinity. If the series ends with an even power, the bond length will adjust to the correct value. (25) Allinger, N. L. Understanding Molecular Structure from Molecular Mechanics. J. Comput.-Aided Mol. Des. 2011, 25, 295. (26) Feng, X.; Gu, J.; Chen, Q.; Lii, J.-H.; Allinger, N. L.; Xie, Y.; Schaefer, H. F. J. Chem. Theory Comput. 2014, 10, 1511. (27) Lii, J.-H.; Allinger, N. L.; Hu, C.-H.; Schaefer, H. F. J. Comput. Chem. 2016, 37, 124. (28) Lii, J.-H.; Allinger, N. L. J. Am. Chem. Soc. 1989, 111, 8576.

AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

N.L.A. and H.F.S. were supported by the U.S. Department of Energy, Chemical Sciences Division, Fundamental Interactions Team (Grant DEFG02-97-ER14748). Notes

The authors declare no competing financial interest.

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REFERENCES

(1) Allinger, N. L.; Chen, K.; Lii, J.-H. J. Comput. Chem. 1996, 17, 642 and following papers. (2) For a recent review, see: Allinger, N. L. In Molecular Structure: Understanding Steric and Electronic Effects from Molecular Mechanics; John Wiley & Sons: Hoboken, NJ, 2010. (3) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision B.05.; Gaussian, Inc.: Wallingford, CT, 2004. (4) In this research, the term “C−C bond lengths” refers to carbon− carbon single bonds that are contained in saturated hydrocarbons, unless otherwise indicated. We exclude three- and four-membered cyclic compounds herein. (5) Zoellner, R. W.; Latham, C. D.; Goss, J. P.; Golden, W. G.; Jones, R.; Briddon, P. R. J. Fluorine Chem. 2003, 121, 193. (6) Bartell, L. S.; Boates, T. L. J. Mol. Struct. 1976, 32, 379. (7) Bartell, L. S.; Burgi, H. B. J. Am. Chem. Soc. 1972, 94, 5239. (8) Allinger, N. L.; Chen, K.; Katzenellenbogen, J. A.; Wilson, S. R.; Anstead, G. M. J. Comput. Chem. 1996, 17, 747. (9) Flamm-ter Meer, M. A.; Beckhaus, H. D.; Peters, K.; von Schnering, H. G.; Rüchardt, C. Chem. Ber. 1985, 118, 4665. (10) Littke, W.; Drück, U. Angew. Chem., Int. Ed. Engl. 1979, 18, 406. (11) Schreiner, P. R.; Chernish, L. V.; Gunchenko, P. A.; Tikhonchuk, E. Y.; Hausmann, H.; Serafin, M.; Schlecht, S.; Dahl, J. E. P.; Carlson, R. M. K.; Fokin, A. A. Nature 2011, 477, 308. (12) Kahr, B.; Van Engen, D.; Mislow, K. J. Am. Chem. Soc. 1986, 108, 8305. (13) Irngartinger, H.; Reifenstahl, U.; Prinzbach, H.; Pinkos, R.; Weber, K. Tetrahedron Lett. 1990, 31, 5459. (14) Gauss, J.; Cremer, D.; Stanton, J. F. J. Phys. Chem. A 2000, 104, 1319. (15) Bak, K. L.; Gauss, J.; Jørgensen, P.; Olsen, J.; Helgaker, T.; Stanton, J. F. J. Chem. Phys. 2001, 114, 6548. (16) Pawłowski, F.; Jørgensen, P.; Olsen, J.; Hegelund, F.; Helgaker, T.; Gauss, J.; Bak, K. L.; Stanton, J. F. J. Chem. Phys. 2002, 116, 6482. (17) Allinger, N. L.; Fermann, J. T.; Allen, W. D.; Schaefer, H. F., III J. Chem. Phys. 1997, 106, 5143. (18) Kuchitsu, K. In Molecular Structures and Vibrations; Cyvin, S. J., Ed.; Elsevier: New York, 1972. (19) Hedberg, L.; Mills, I. M. J. Mol. Spectrosc. 1993, 160, 117. (20) Ma, B.; Lii, J.-H.; Chen, K.; Allinger, N. L. J. Am. Chem. Soc. 1997, 119, 2570. E

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