Directory UMM :wiley:Public:journals:jcc:suppmat:20:

Supplementary Material for:

MMFF VII. Characterization of MMFF94, MMFF94s, and Other

Widely Available Force Fields for Conformational Energies and for

Intermolecular-Interaction Energies and Geometries.

THOMAS A. HALGREN

Molecular Systems, Merck Research Laboratories, P.O. Box 2000, Rahway, NJ 07065

Appendix A: Experimental Conformational Energies for Set 1

Table A.I lists some, but by no means all, of the experimental conformational energies that are available for the comparisons in Set 1. It also lists experimental uncertainties (a few of which we estimated from data in the original report), indicates the type of quantity measured, and specifies the method used. When two or more experimental values are listed, the first is used in the comparisons of conformational energies made in this paper. As will be noted, in a few instances we have chosen a different experimental value than the one we employed in our earlier work.1 _{We also wish to point out that our earlier paper cited previous theoretical papers}

as the basis for the listed values, whereas we now give citations to the original literature. For

conformational Set 2, we adopted the experimental values cited by Gundertofte2 _{without further}

examination.

The table shows that the measured conformational energies form a disparate set. In particular, many different experimental techniques have been used. More significantly, the derived quantities sometimes refers to the gas phase and sometimes to the liquid phase or to solution, and some are free energies rather than enthalpies. Most pointedly, the table also lists

many incorrect experimental results. This fact is established simply by noting the many

instances in which alternative experimental values for the same conformational difference differ by many multiples of the stated uncertainty in either. In such cases, both experimental results cannot be correct (except possibly where strong medium effects are involved).

Given that some of the listed experimental values are wrong, it is fair to ask how a choice can be made. One approach is to consider the reliability of the experimental technique. Our own, somewhat untutored, prejudice is for determinations based on spectroscopic intensities measured as a function of temperature, either directly (indicated by "/T" in the table) or on samples cryogenically deposited from different initial temperatures (indicated by "/cdT"). In such cases, a plot of the logarithm of relative intensity vs. 1/T gives ∆Η directly. Even this technique, however, can give poor results, as the differences of more than 1 kcal/mol between alternative experimental values determined in this way for 1,difluoroethane and for 2-butanone attest. We also favor determinations in which vibrational band progressions are used to construct a complete torsional potential along a one-dimensional torsional coordinate. In

these cases, differences between local minima then give ∆E for that coordinate (though we call

this quantity ∆Η0 _{in recognition of the fact that the subsumed coordinates include zero-point and} thermal vibrational energy contributions), in close analogy to energy differences taken between local minima on a force field or quantum mechanical energy surface. Conversely,

determinations based on conformationally averaged nmr chemical shifts or coupling constants for which the isolated-conformer end-point values could not be measured directly seem to us particularly prone to error.

The date of the measurement is also a factor, as we presume that more recent values are more likely to be accurate, in part because of improved experimental technique but also because any substantial variation from previously published values is likely to have been closely examined by the authors. In some cases, however, our choice simply came down to which measurement

paper. Given their general success in predicting the observed conformational energies, we presume that these very high level quantum calculations are unlikely to be seriously in error in any individual case. To be sure, this choice minimizes the rms "error" reported for GVB-LMP2 (cf. Table IV), and its use might seem to compromise our claim that this method is the most accurate. In point of fact, however, even selection of the conformational energies from Table

A.I in worst agreement with the GVB-LMP2 results still finds that it best reproduces the

experimental data. Moreover, we can think of no better approach for dealing with cases in which discordant experimental values appear to have equal claims to validity. We had used much the same approach previously,1 _{but with "MP4SDQ(T)/TZP" calculations serving as the}

best reference values then available to us.

The reasons underlying most choices reflected in the table should be apparent from the foregoing. Thus, we shall comment here only on a few cases. One of these is 2-butanone, where all the higher-level calculations in Table III, as well as several others we had previously reported,1 _{clearly favor the lower, liquid-phase result. A second case is 1,3-butadiene, where}

we had cited a gauche - trans conformational energy difference of 2.5 kcal/mol, this being the average of values referenced by Wiberg et al.4 _{This value, as it happens, also corresponds to an}

often cited2,3b,5 _{but suspect early determination in which Carreira constructed a one-dimensional}

torsional potential but used an erroneous torsional coordinate that incorrectly identified the

second, higher-energy conformer as being cis rather than gauche.22 _{The higher, more recent}

values20,21 _{shown in Table A.I seem to us preferable. They are also consistent with the pattern}

in Table III in which the theoretical method finds a larger gauche - trans difference for 1,3-butadiene than for 2-methyl-1,3-1,3-butadiene, evidently because the more compact trans conformer in the methyl compound is somewhat destabilized by nonbonded repulsions involving the added 2-methyl group; Table I shows that MMFF94 and most of the other force-field methods show the same pattern.

In the case of 1-butene, we had previously cited a conformational energy difference of 0.53

kcal/mol.1 _{We now realize, however, that this value is derived from the free-energy difference}

of 0.94 kcal/mol measured by Van Hemelrijk et al.65 _{by simply applying an entropic correction}

of R ln2 = 1.18 e.u. to allow for the two-fold statistical factor favoring skew. However, the looser skew conformation is also expected to have a higher vibrational entropy. With this mind, we have applied the full entropic correction of 2.3 e.u. favoring skew found by Durig and Compton64 _{to arrived at the value of 0.24 ± 0.42 kcal/mol listed in Table A.I. This correction to}

the measured ∆G brings the derived value for ∆Η into line with Durig and Compton's value of

0.22 ± 0.02 kcal/mol and with the GVB-LMP2 result for ∆E.

The conformational energy difference for methyl vinyl ether is of particular interest. We ourselves had previously referenced the Sullivan, Dickson, and Durig value of 1.70 kcal/mol favoring cis over skew.49 _{Friesner and co-workers,}3b _{however, cited the earlier Durig and}

Compton difference of 1.15 kcal/mol,51 _{and worked intently to improve their theoretical}

methodology to reduce the large discrepancy with their higher LMP2/cc-pVTZ(-f) theoretical

estimate of 2.62 kcal/mol.6 _{They subsequently published a GVB-LMP2 result of 1.45 kcal/mol}

favoring skew.3b _{However, calculations using the current version of Jaguar now find the}

conformational energy difference to be 2.14 kcal/mol (Table III, manuscript) when a rigorously consistent protocol for lone-pair delocalization is employed in the localized MP2 calculation in connection with improved grid and dealiasing functions. Furthermore, we find that this value falls to 1.61 kcal/mol when zero-point energy differences3a _{are taken into account. This last}

estimate is fully consistent with the Sullivan, Dickson, and Durig result and with the enthalpy difference of 1.59 kcal/mol obtained Beech et al.,50 _{the experimental result that caused Durig to}

reinvestigate this system and led him to raise his lower early estimate.

For the "simple" but conformationally critical gauche - anti conformational difference in n

-butane, we list what now appears to be a definitive value of 0.67 ± 0.10 kcal/mol.55 _{Also shown}

0.75 kcal/mol value we had previously cited1 _{on the basis of Allinger, Yuh, and Li's}

recommendation.7 _{Much as in the case of methyl vinyl ether, both the new value and one of the}

earlier values it has superseded are by Durig and co-workers. Unfortunately, Durig et al. do not discuss the reasons for rejecting their higher earlier value. However, they do cite a number of other experimental determinations, made using a variety of methods, that agree with their lower value of 0.67 kcal/mol.55 _{Other recent high-level quantum calculations}8 _{also support this value,}

as does the GVB-LMP2/cc-pVTZ(-f) value of 0.72 kcal/mol cited in Table III of the manuscript.

As an indication of the limitations of experimental data, we point out that the cis - trans difference for methyl acetate is particularly tenuous: the listed ∆G of 8.5 ± 1 kcal/mol represents the relative intensity of a single weak band in the infra-red carbonyl region that was observed in a sample cryogenically deposited from a temperature of 879 K and was thought to probably arise from the cis conformer.14 _{Indeed, the original authors cite this conformational energy}

difference as being a ∆Η, though this interpretation apparently assumes no entropy difference

between cis and trans conformers. We think it remarkable that the theoretical values in Table

III of the manuscript agree with the experimental value as well as they do, but caution that a

even a disagreement of 1 – 2 kcal/mol should not be viewed as indicative of a problem with the theoretical calculation.

Finally, we discuss two entries for which we had previously based our comparisons on free-energy differences measured in solution. First, we now list a single value of ∆G = 1.15

kcal/mol for the axial - equatorial difference in cyclohexyl amine rather than the previously cited range of 1.1 - 1.8 kcal/mol.1 _{The reason for this change is that the larger values in the}

range are for determinations in polar media that are inappropriate for comparison to calculated isolated-molecule properties. Even this new reference value, however, is higher than the theoretical calculations cited in Table III can accommodate. Second, we previously cited a free

enthalpy difference of 0.58 kcal/mol found by Eliel and Gilbert in dilute nonpolar medium for the model 4-t-butylcyclohexanol system;46 _{these authors criticized the consensus value of 0.52}

kcal/mol that Hirsch recommended for nonpolar solvents47 as being too low because it

incorporates low values for early determinations that they believed to be unreliable.

Most other minor differences between the present data and that cited previously1 _{either reflect}

the substitution of representative specific determinations for previously referenced average values or merely a more accurate conversion to kcal/mol of the originally published data.

TABLE A.I.

___________________________________________________

References for Experimental Conformational Energies (Set 1), in kcal/mol.

Conf. Comparisona _{Expt.b Deltac Typed Methode Ref.}

N-methylformamide, c - t 1.4 ? ∆Η_sol ir/cdT,

nmr/T

9

N-methylacetamide, c - t 2.3

2.8 ? ? ∆Ηsol ∆Ηsol ir/cdT nmr/T 10 11

formic acid, trans - cis 3.90 ± 0.09 ∆Ggp mw 12

glyoxylic acid,

( O = C - C = O t , O = C - O - H c ) - ( O = C - C = O t , O = C - O - H t )

1.2 ± 0.5 ∆Ggp mw 13

methyl formate, t - c 4.75

3.85 ± 0.19 ± 0.20 ∆Ηgp ∆Ηgp ir/cdT ir/td 14 15

methyl acetate, t - c 8.5 ± 1 ∆Ggp ir 14

ethyl formate,

( O = C - O - C c , C - O - C - C g ) - ( O = C - O - C c , C - O - C - C a )

0.19 ± 0.06 ∆Ggp mw 16

propionaldehyde, sk - cis 0.67

1.03 ± 0.03 ± 0.13 ∆Η0 gp ∆Ηsol ir,r/tp ir/T 17 18

2-butanone, skew - cis 1.07

2.02 ± 0.10 ± 0.10 ∆Ηsol ∆Ηgp ir/T ir/T 19 19

1,3-butadiene, g - s-trans 2.89

2.75 2.5 ? ± 0.07 ? ∆Η0 gp ∆Ηgp ∆Η0 gp ir,r/tp ir/tp 20 21 22 2-methyl-1,3-butadiene,

gauche - s-trans

2.65 ? ∆Η0

gp ir,r/tp 23

acrolein, cis - trans 1.70

1.89 ± 0.04 ± 0.11 ∆Ηgp ∆Ηgp ir/cdT uv/T 24 25

1,2-difluoroethane, a - g 0.56

0.80 1.98 ± 0.1 ? ± 0.08 ∆Ηgp

∆Ggp

∆Ηsol ir/cdT nmr/cc r/T 26 27 28

1,2-dichloroethane, g - a 1.08

1.09 ± 0.10 ± 0.10 ∆Ηgp ∆Ηgp ed/T ir 29 30

1-fluoropropane, a - g 0.35

0.47 ± 0.03 ± 0.31 ∆Η0 gp ∆Ηgp ir,r/tp mw/T 31 32

1-chloropropane, g - a 0.09 0.37 0.04 ± 0.02 ± 0.03 ± 0.07 ∆Ηgp ∆Η0 gp ∆Ηgp ir/T ir,r/tp mw 33 31 34 2-methoxytetrahydropyran,

(OCOMe g, OMe eq) - (OCOMe g, OMe ax)

1.05 ? ∆Η_sol nmr/T 35

2,5-dimethyl-1,3-dioxane, (2 eq, 5 ax) - (2 eq, 5 eq)

0.92 ± 0.01 ∆Η_sol mCal 36

isopropylamine,

lp-N-C-H gauche - anti

0.45 0.12 ? ± 0.02 ∆Ηgp ∆Ηsol ir,r/tp ir/T 37 38

cyclohexylamine, ax - eq 1.15 ? ∆Gsol nmr 39

piperidine, ax - eq 0.53 ± 0.13 ∆Η_gp ir/T 40

N-methylpiperidine, ax - eq 3.15 ± 0.1 ∆Ggp nmr 41

ethanol, gauche - anti 0.12

0.3, 0.5 0.7

± 0.01 ? ± 0.1

∆Ggp

∆Ggp

∆Ηgp mw ir ir/T 42 43 44

isopropanol, H-C-O-H a - g 0.28 ? ∆Ggp mw 45

cyclohexanol, ax C1 - eq C1 0.58

0.52

± 0.02 ?

∆Ηsol

∆Gsol

nmr/T nmr

46 47

methyl ethyl ether, g - a 1.5 ± 0.2 ∆Η_gp ir/T 48

methyl vinyl ether, C=C-O-C skew - cis

1.70 1.59 1.15 ± 0.09 ± 0.08 ± 0.05 ∆Ηgp ∆Ηgp ∆Η0 gp r/T ir/cdT ir,r/tp 49 50 51 diethyl ether,

(C-C-O-C a, C-O-C-C g) - (C-C-O-C a, C-O-C-C a)

1.14 ± 0.05 ∆Η_sol ir/T 52

methoxycyclohexane, ax C1 - eq C1

0.55 0.4

± 0.02 ± 0.05

∆Gsol,lT

∆Gsol

nmr nmr/cs

53 54

butane, gauche - anti 0.67

0.97 1.09 0.75 ± 0.10 ± 0.05 ± 0.05 ± 0.25 ∆Ηgp ∆Ηgp ∆Η0 gp

∆Ggp

ir/T r/T ir,r/tp ed 55 56 57 58 cyclohexane,

twist boat - chair

5.5 ? ∆Η_sol,lT nmr/T 59

2,3-dimethylbutane,

H-C2-C3-H g - a

0.05 0.17

± 0.03 ?

∆Ηgp

∆Ggp

r/T ed

57 61 cyclooctane,

D4d - Cs boat chair

1.9 ± 0.2 ∆Η_sol,lT nmr/T 62

cyclononane,

[255] C2 - [333] D3

1.0 ? ∆Η_sol,lT nmr 63

1-butene, cis - skew 0.22

0.07 0.24 ± 0.02 ? ± 0.42 ∆Ηsol ∆Ηgp ∆Ηgp r/T ir,r/tp ed/mw 64 64 65

2-butene, cis - trans 1.2

1.0 ± 0.1 ? ∆Ηgp ∆Ηgp mCal comb. 66 67

a _{In the conformational notation, idealized dihedral angles are: cis or c, 0°; trans, t, anti, or a,}

180°; gauche or g, 60°; and skew or sk, 120°.

b _{When more than one value for the conformational energy is cited, the first listed value is used}

in the comparisons in the body of this paper

c _{Error in measurement as cited by the authors or as explained in a note accompanying the}

literature citation.

d _{gp = gas phase; sol = solution or liquid-phase; superscript "0" in} ∆Η0 _{denotes a difference}

between the bottoms of potential wells constructed for a one-dimensional torsional coordinate, lT means determined at low temperature.

e _{"r", "ir", "mw", "uv", nmr, and "ed" denote raman, infrared, microwave, ultraviolet, nuclear}

magnetic resonance, and electron-diffraction spectroscopy; "/T" means as "a function of temperature"; "/cdT" indicates sample collection via cryogenic deposition from thermalized molecular beams as a function of temperature; "/tp" signifies construction of a one-dimensional torsional potential; "mCal" stands for microcalorimetry; "nmr/cc" and "nmr/cs" denote nmr determinations based on conformationally averaged chemical shifts and coupling constants, respectively; "ir/td" stands for temperature-drift ir spectroscopy; and "comb." indicates differences in measured heats of combustion.

1. T. A. Halgren and R. B. Nachbar, J. Comput. Chem., 17, 587-615 (1996).

2. K. Gundertofte, T. Liljefors, P.-O. Norrby, and I. Petterssen, J. Comput Chem., 17, 429-449 (1996).

3. (a) R. A. Friesner, R. B. Murphy, M. D. Beachy, M. N. Ringnalda, W. T. Pollard, B. D.

Duneitz, and Y. Cao, J. Chem. Phys., submitted (1998); (b) R. B. Murphy, W. T. Pollard, and R.

A. Friesner, J. Chem. Phys., 106, 5073-5084 (1997).

4. K. B. Wiberg, P. R. Rablen, and M. Marquez, J. Am. Chem. Soc., 114, 8654-8668 (1992).

5. (a) N. L. Allinger, F. Li, L. Yan, and J. C. Tai, J. Comput. Chem., 11, 868-895 (1990); (b) C.

J. Casewit, K. S. Colwell, and A. K. Rappé, J. Am. Chem. Soc., 114, 10035-100046 (1992).

6. R. B. Murphy, M. D. Beachy, R. A. Friesner, and M. N. Ringnalda, J. Chem. Phys., 103,

1481-1490 (1995).

7. N. L. Allinger, Y. H. Yuh, and J.-H. Lii, J. Am Chem. Soc., 111, 8551-8566 (1989). See also

N. L. Allinger and L. Yan, J. Am. Chem. Soc., 115, 11918-11925 (1993), and references therein.

8. G. D. Smith and R. L. Jaffe. J. Phys. Chem., 100, 18718-18724 (1996).

9. Average of values in: S. Ataka, H. Takeuchi, and M. Tasumi, J. Mol. Struct., 113, 147-160 (1984), and F. A. L. Anet and M. Squillacote, J. Am. Chem. Soc., 97, 3243-3244 (1974). 10. S. Ataka, H. Takeuchi, and M. Tasumi, J. Mol. Struct., 113, 147-160 (1984).

11

.

T. Drakenberg and S. Forsén, Chem. Commun., 1404-1405 (1971). This result is from a

difference in enthalpies of activation for isomerization in C2H4Cl2 as determined by nmr

line-shape analysis.

12. W. H. Hocking, Naturforsch., 31a, 1113-1121 (1976).

13. B. P. van Eijck and F. B. van Duijneveldt, J. Mol. Struct., 39, 157-163 (1977).

15. S. Ruschin and S. H. Bauer, J. Phys. Chem., 84, 3061-3064 (1980).

16. J. M. Riveros and E. B. Wilson Jr., J. Chem. Phys., 46, 4605-4612 (1967). This quantity is reported to be the "energy difference" between the lowest vibrational levels, but its calculation from measured microwave intensities at a single temperature suggests that it may be a free-energy difference, presumably corrected for the two-fold statistical factor favoring the C-O-C-C gauche conformer; no later report on this measurement appears to have been made.

17. J. R. Durig, D. A. C. Compton, and A. Q. McArver, J. Chem. Phys., 73, 719-724 (1980).

18. G. Sbrana and V. Schettino, J. Molec. Spectrosc., 33, 100-108 (1970). This value contributes

to the composite value of 0.95 kcal/mol cited in ref. 1. For other references, see: P. van Nuffel, L. van den Enden, C. van Alsenoy, and H. J. Geise, J. Mol. Struct., 116, 99-118 (1984).

19. T. Shimanouchi, Y. Abe, and M. Makami, Spectrochim. Acta A, 24A, 1037-1053 (1968).

20. Y. N. Panchenko, A. V. Abramenkov and C. W. Bock, J. Mol. Struct., 140, 87-92 (1985).

21. J. R. Durig, W. E. Bucy, and A. R. H. Cole, Can. J. Phys., 53, 1832-1837 (1975). 22. L. Carreira, J. Chem. Phys.,62, 3851-3854 (1975).

23. Y. N. Panchenko, V. I. Pupyshev, A. V. Abramenkov, M. Traetteberg, and S. J. Cyvin, J.

Mol. Struct., 130, 355-359 (1985).

24. C. E. Blom and A. Bauder, Chem. Phys. Lett., 88, 55-58 (1982). Note that this value

supersedes the earlier result of 1.6 kcal/mol obtained by C. E. Blom, R. P. Müller and Hs. H. Günthard, Chem. Phys. Lett., 73, 483-486 (1980).

25. E. J. Bair, W. Goetz, and D. A. Ramsay, Can. J. Phys., 49, 2710-2717 (1971). A note added

in proof to this paper reports a correction, agreed to by the original authors, to the value of 2.00 ±

0.11 kcal/mol published by: A. C. P. Alves, J. Christoffersen, and J. M. Hollas, Mol. Phys., 20,

26. P. Huber-Wälchi and Hs. H. Günthard, Chem. Phys. Lett., 30, 347-351. This result and the

cited uncertainty were obtained from the relative intensity vs. 1/T plots in Fig. 3. The authors appear to incorrectly label their determinations as ∆G.

27. K. T. Hirano, S. Nonoyama, T. Miyajima, Y. Kurita, T. Kawamura, and H. Sato, J. Chem.

Soc., Chem. Commun., 1986, 606-607.

28. W. C. Harris, J. R. Holtzclaw, and V. F. Kalasinsky, J. Chem. Phys., 67, 3330-3338 (1977).

29. Average of values in Table 5 of: K. Kveseth, Acta Chem. Scand. A, 29, 307-311 (1975).

30. K. Tanabe, Spectrochim. Acta, 28A, 407-424 (1972). An entropy difference calculated from

symmetry numbers, moments of inertia, and vibrational frequencies was used to correct the measured free-energy difference.

31. J. R. Durig, S. E. Godbey, and J. F. Sullivan, J. Chem. Phys., 80, 5983-5993 (1984). 32. E. Hirota, J. Chem. Phys., 37, 283-291 (1962).

33. W. A. Herrebout and B. J. van der Veken, J. Phys. Chem., 100, 9671-9677 (1996). I thank Dr. Michael Beachy (Schrodinger) for supplying this reference.

34. K. Yamanouchi, M. Sugie, H. Takeo, C. Matsumura, and K. Kuchitsu, J. Phys. Chem., 88,

2315-2323 (1984). An entropy difference calculated from moments of inertia and vibrational frequencies was used to correct the measured free-energy difference of -0.12 kcal/mol.

35. A. J. de Hoog, H. R. Buys, C. Altona, and E. Havinga, Tetrahedron, 25, 3365-3375 (1969).

Position of the equilibrium as a function of temperature was determined from conformationally averaged nmr coupling constants.

36. R. M. Clay, G. M. Kelle, and F. G. Riddell, J. Am. Chem. Soc., 95, 4632 (1973).

37. J. R. Durig, G. A. Guirgis, and D. A. C. Compton, J. Phys. Chem., 83, 1313-1323 (1979).

39. Average of values for nonpolar solvents cited in H. Booth and M. L. Jozefowicz, J. Chem.

Soc., Perkins Trans. II, 895-901 (1976).

40. R. W. Baldock and A. R. Katritzky, J. Chem. Soc. B, 1470-1477 (1968); see also R. A. Y.

Jones, A. R. Katritzky, A. C. Richards, R. J. Wyatt, R. J. Bishop, and L. E. Sutton, J. Chem. Soc.

B, 127-131 (1970).

41. P. J. Crowley, M. J. T. Robinson, and M. G. Ward, Tetrahedron, 33, 915-925 (1977). Kinetically-controlled protonation was used to trap conformers in quaternary salt form for nmr analysis.

42. R. K. Kakar, and C. R. Quade, J. Chem. Phys., 72, 4300-4307 (1980).

43. J. R. Durig, W. E. Bucy, C. J. Wurrey, and L. A. Carriera, J. Phys. Chem., 79, 988-993

(1975). The authors note that the value chosen for ∆H depends on the choice for a key line

assignment.

44. H. L. Fang and R. L. Swofford, Chem. Phys. Lett., 105, 5-11 (1984). Signal detection was by

photoacoustic spectroscopy.

45. E. Hirota, as cited in W. A. Lathan, L. Radom, W. J. Hehre, and J. A. Pople, J. Am. Chem. Soc., 95, 699-703 (1973). The reference to relative microwave intensities with no reference to

temperature dependence suggests that this measurement is ∆G, presumably corrected for the

two-fold statistical factor favoring the gauche conformer. For the preliminary study, see: S. Kondo

and E. Hirota, J. Mol. Spectrosc.,34, 97-107 1970). No follow-up study seems to have appeared.

46. E. L. Eliel and E. C. Gilbert, J. Am. Chem. Soc., 91, 5487-5495 (1969). The cited value was

measured for 4-t-butylcyclohexanol epimers equilibrated via Raney nickel catalysis.

47. J. A. Hirsch, in N. L. Allinger and E. L. Eliel, Eds., Topics in Stereochemistry, 1, 199-222

(1967). This often-cited value (cf. refs. 1, 2, 3b, and 5) is the free-energy difference Hirsch

recommends for nonpolar solvents, but has been criticized by Eliel and Gilbert46 _{as being too}

48. T. Kitagawa and T. Miyazawa, Bull. Chem. Soc., Jpn., 41, 1976 (1968).

49. J. F. Sullivan, T. J. Dickson, and J. R. Durig, Spectrochim. Acta, 42A, 113-122 (1986).

50. T. Beech, R. Gunde, P. Felder, and Hs. Günthard, Spectrochim. Acta., 41A, 319-339 (1985).

51. J. R. Durig and D. A. C. Compton, J. Chem. Phys., 69, 2028-2935 (1978). Note that this

value is incorrect and has been superseded by the Sullivan, Dickson and Durig result.49

52. H. Weiser, W. G. Laidlaw, P. J. Kruger, and H. Fuhrer, Spectrochim. Acta, 24A, 1055-1089

(1968). The listed uncertainty of ± 0.05 reflects a purely subjective assessment on our part of the data in Fig. 13 of this reference, and if anything is likely to be an overestimate.

53. F. R. Jensen, C. H. Bushweller, and B. H. Beck, J. Am. Chem. Soc.,91, 344-351 (1969).

54. E. L. Eliel and E. C. Gilbert, J. Am. Chem. Soc., 91, 5487-5495 (1969). This value was

measured for 4-t-butylmethoxycyclohexane using conformationally averaged nmr chemical

shifts.

55. W. A. Herrebout, B. J. van der Veken, A. Wang, and J. R. Durig, J. Phys. Chem., 99,

578-585 (1995). I thank Prof. Alex MacKerell (Univ. Maryland) for supplying this reference. 56. A. L. Verma, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys., 60, 1540-1544 (1974).

57. J. R. Durig, A. Wang, W. Beshir, and T. S. Little, J. Raman. Spec., 22, 683-704 (1991).

58. R. K. Heenan and L. S. Bartell, J. Chem. Phys., 78, 1270-1274 (1983); W. F. Bradford, S. Fitzwater, and L. S. Bartell, J. Molec. Struct., 38, 185-194 (1977). These papers are cited by Allinger et al.7 _{as the basis for the value and the uncertainty listed in this table.}

59. M. Squillacote, R. S. Sheridan, O. L. Chapman, and F. A. L. Anet, J. Am. Chem. Soc., 97,

3244-3246 (1975); this result uses data from: F. A. L. Anet and A. J. Bourn, J. Am. Chem. Soc.,

89, 760-768 (1967).

61. T. L. Boates, thesis, Iowa State University, 1966, as cited by: E. J. Jacob, H. B. Thompson,

and L. S. Bartell, J. Chem. Phys., 47, 3736-3753. This value is reported as a ∆G, but has been corrected for the two-fold statistical factor in favor of the gauche conformer.

62. F. A. L. Anet and V. J. Basus, J. Am. Chem. Soc., 95, 4424-4426 (1973).

63. F. A. L. Anet and J. Krane, Isr. J. Chem., 20, 72-83 (1980). This result was measured by

nmr line-shape analysis at -145° and converted from ∆G = 0.5 kcal/mol by using a

force-field-calculated ∆S of 3.5 e.u. Use of the MP2/6-31G* estimate of 4.33 e.u. for ∆S (cf. ref. 1) would raise ∆H by an additional 0.1 kcal/mol.

64. J. R. Durig and D. A. C. Compton, J. Phys. Chem., 84, 773-781 (1980). We estimated the listed uncertainty of ± 0.02 kcal/mol from hand-drawn slopes for the five highest vs. four lowest temperature points in Fig. 3 of this reference.

65. D. Van Hemelrijk, L. Van den Enden, H. J. Greise, H. L. Sellers, and L. Schäfer, J. Am. Chem. Soc., 102, 2189-2195 (1980). The listed ∆H differs from the reported ∆H of 0.53

kcal/mol because it uses Durig and Compton's measured ∆S of 2.3 e.u. favoring skew (cf. ref. 64)

to make the full entropic correction (not just the symmetry-number correction of R ln2 = 1.18 e.u.) to the measured free-energy difference of 0.94 kcal/mol.

66. D. M. Golden, K. W. Egger, and S. W. Benson, J. Am. Chem. Soc., 86, 5416-5420 (1964).

67. Heat of combustion value cited in, but not correctly referenced by: N. L. Allinger, F. Li, and

L. Yan, J. Comput. Chem., 11, 848-867 (1990). The value listed here is from heats of formation

given in: Lange's Handbook of Chemistry, Fourteenth Edition, J. A. Dean, Ed., McGraw-Hill:

New York, NY, 1992. Measured heats of hydrogenation give similar values of 1.1 - 1.2

kcal/mol; see M. R. Ibrahim, Z. A. Fataftah, P. von R. Schleyer, and P. D. Stout, J. Comput.

1. T. A. Halgren and R. B. Nachbar, J. Comput. Chem., 17, 587-615 (1996).

2. K. Gundertofte, T. Liljefors, P.-O. Norrby, and I. Petterssen, J. Comput Chem., 17, 429-449 (1996).

3. (a) R. A. Friesner, R. B. Murphy, M. D. Beachy, M. N. Ringnalda, W. T. Pollard, B. D. Duneitz, and Y. Cao, J. Chem. Phys., submitted (1998); (b) R. B. Murphy, W. T. Pollard, and R. A. Friesner, J. Chem. Phys., 106, 5073-5084 (1997).

4. K. B. Wiberg, P. R. Rablen, and M. Marquez, J. Am. Chem. Soc., 114, 8654-8668 (1992).

5. (a) N. L. Allinger, F. Li, L. Yan, and J. C. Tai, J. Comput. Chem., 11, 868-895 (1990); (b) C.

J. Casewit, K. S. Colwell, and A. K. Rappé, J. Am. Chem. Soc., 114, 10035-100046 (1992). 6. R. B. Murphy, M. D. Beachy, R. A. Friesner, and M. N. Ringnalda, J. Chem. Phys., 103,

1481-1490 (1995).

7. N. L. Allinger, Y. H. Yuh, and J.-H. Lii, J. Am Chem. Soc., 111, 8551-8566 (1989). See also N. L. Allinger and L. Yan, J. Am. Chem. Soc., 115, 11918-11925 (1993), and references therein. 8. G. D. Smith and R. L. Jaffe. J. Phys. Chem., 100, 18718-18724 (1996).

9. Average of values in: S. Ataka, H. Takeuchi, and M. Tasumi, J. Mol. Struct., 113, 147-160 (1984), and F. A. L. Anet and M. Squillacote, J. Am. Chem. Soc., 97, 3243-3244 (1974). 10. S. Ataka, H. Takeuchi, and M. Tasumi, J. Mol. Struct., 113, 147-160 (1984).

11

.

T. Drakenberg and S. Forsén, Chem. Commun., 1404-1405 (1971). This result is from a difference in enthalpies of activation for isomerization in C2H4Cl2 as determined by nmr

line-shape analysis.

12. W. H. Hocking, Naturforsch., 31a, 1113-1121 (1976).

13. B. P. van Eijck and F. B. van Duijneveldt, J. Mol. Struct., 39, 157-163 (1977).

15. S. Ruschin and S. H. Bauer, J. Phys. Chem., 84, 3061-3064 (1980).

16. J. M. Riveros and E. B. Wilson Jr., J. Chem. Phys., 46, 4605-4612 (1967). This quantity is reported to be the "energy difference" between the lowest vibrational levels, but its calculation from measured microwave intensities at a single temperature suggests that it may be a free-energy difference, presumably corrected for the two-fold statistical factor favoring the C-O-C-C gauche conformer; no later report on this measurement appears to have been made.

17. J. R. Durig, D. A. C. Compton, and A. Q. McArver, J. Chem. Phys., 73, 719-724 (1980).

18. G. Sbrana and V. Schettino, J. Molec. Spectrosc., 33, 100-108 (1970). This value contributes

to the composite value of 0.95 kcal/mol cited in ref. 1. For other references, see: P. van Nuffel, L. van den Enden, C. van Alsenoy, and H. J. Geise, J. Mol. Struct., 116, 99-118 (1984).

19. T. Shimanouchi, Y. Abe, and M. Makami, Spectrochim. Acta A, 24A, 1037-1053 (1968). 20. Y. N. Panchenko, A. V. Abramenkov and C. W. Bock, J. Mol. Struct., 140, 87-92 (1985). 21. J. R. Durig, W. E. Bucy, and A. R. H. Cole, Can. J. Phys., 53, 1832-1837 (1975).

22. L. Carreira, J. Chem. Phys., 62, 3851-3854 (1975).

23. Y. N. Panchenko, V. I. Pupyshev, A. V. Abramenkov, M. Traetteberg, and S. J. Cyvin, J. Mol. Struct., 130, 355-359 (1985).

24. C. E. Blom and A. Bauder, Chem. Phys. Lett., 88, 55-58 (1982). Note that this value

supersedes the earlier result of 1.6 kcal/mol obtained by C. E. Blom, R. P. Müller and Hs. H. Günthard, Chem. Phys. Lett., 73, 483-486 (1980).

25. E. J. Bair, W. Goetz, and D. A. Ramsay, Can. J. Phys., 49, 2710-2717 (1971). A note added

in proof to this paper reports a correction, agreed to by the original authors, to the value of 2.00 ± 0.11 kcal/mol published by: A. C. P. Alves, J. Christoffersen, and J. M. Hollas, Mol. Phys., 20, 625-644 (1971); 21, 384 (1971).

26. P. Huber-Wälchi and Hs. H. Günthard, Chem. Phys. Lett., 30, 347-351. This result and the

cited uncertainty were obtained from the relative intensity vs. 1/T plots in Fig. 3. The authors appear to incorrectly label their determinations as ∆G.

27. K. T. Hirano, S. Nonoyama, T. Miyajima, Y. Kurita, T. Kawamura, and H. Sato, J. Chem. Soc., Chem. Commun., 1986, 606-607.

28. W. C. Harris, J. R. Holtzclaw, and V. F. Kalasinsky, J. Chem. Phys., 67, 3330-3338 (1977).

29. Average of values in Table 5 of: K. Kveseth, Acta Chem. Scand. A, 29, 307-311 (1975).

30. K. Tanabe, Spectrochim. Acta, 28A, 407-424 (1972). An entropy difference calculated from

symmetry numbers, moments of inertia, and vibrational frequencies was used to correct the measured free-energy difference.

31. J. R. Durig, S. E. Godbey, and J. F. Sullivan, J. Chem. Phys., 80, 5983-5993 (1984). 32. E. Hirota, J. Chem. Phys., 37, 283-291 (1962).

33. W. A. Herrebout and B. J. van der Veken, J. Phys. Chem., 100, 9671-9677 (1996). I thank Dr. Michael Beachy (Schrodinger) for supplying this reference.

34. K. Yamanouchi, M. Sugie, H. Takeo, C. Matsumura, and K. Kuchitsu, J. Phys. Chem., 88, 2315-2323 (1984). An entropy difference calculated from moments of inertia and vibrational frequencies was used to correct the measured free-energy difference of -0.12 kcal/mol.

35. A. J. de Hoog, H. R. Buys, C. Altona, and E. Havinga, Tetrahedron, 25, 3365-3375 (1969).

Position of the equilibrium as a function of temperature was determined from conformationally averaged nmr coupling constants.

36. R. M. Clay, G. M. Kelle, and F. G. Riddell, J. Am. Chem. Soc., 95, 4632 (1973).

37. J. R. Durig, G. A. Guirgis, and D. A. C. Compton, J. Phys. Chem., 83, 1313-1323 (1979).

39. Average of values for nonpolar solvents cited in H. Booth and M. L. Jozefowicz, J. Chem.

Soc., Perkins Trans. II, 895-901 (1976).

40. R. W. Baldock and A. R. Katritzky, J. Chem. Soc. B, 1470-1477 (1968); see also R. A. Y.

Jones, A. R. Katritzky, A. C. Richards, R. J. Wyatt, R. J. Bishop, and L. E. Sutton, J. Chem. Soc. B, 127-131 (1970).

41. P. J. Crowley, M. J. T. Robinson, and M. G. Ward, Tetrahedron, 33, 915-925 (1977). Kinetically-controlled protonation was used to trap conformers in quaternary salt form for nmr analysis.

42. R. K. Kakar, and C. R. Quade, J. Chem. Phys., 72, 4300-4307 (1980).

43. J. R. Durig, W. E. Bucy, C. J. Wurrey, and L. A. Carriera, J. Phys. Chem., 79, 988-993

(1975). The authors note that the value chosen for ∆H depends on the choice for a key line assignment.

44. H. L. Fang and R. L. Swofford, Chem. Phys. Lett., 105, 5-11 (1984). Signal detection was by

photoacoustic spectroscopy.

45. E. Hirota, as cited in W. A. Lathan, L. Radom, W. J. Hehre, and J. A. Pople, J. Am. Chem. Soc., 95, 699-703 (1973). The reference to relative microwave intensities with no reference to temperature dependence suggests that this measurement is ∆G, presumably corrected for the two-fold statistical factor favoring the gauche conformer. For the preliminary study, see: S. Kondo and E. Hirota, J. Mol. Spectrosc., 34, 97-107 1970). No follow-up study seems to have appeared. 46. E. L. Eliel and E. C. Gilbert, J. Am. Chem. Soc., 91, 5487-5495 (1969). The cited value was

measured for 4-t-butylcyclohexanol epimers equilibrated via Raney nickel catalysis.

47. J. A. Hirsch, in N. L. Allinger and E. L. Eliel, Eds., Topics in Stereochemistry, 1, 199-222

(1967). This often-cited value (cf. refs. 1, 2, 3b, and 5) is the free-energy difference Hirsch recommends for nonpolar solvents, but has been criticized by Eliel and Gilbert46 _{as being too} low because it averages in early determinations they believed to be unreliable.

48. T. Kitagawa and T. Miyazawa, Bull. Chem. Soc., Jpn., 41, 1976 (1968).

49. J. F. Sullivan, T. J. Dickson, and J. R. Durig, Spectrochim. Acta, 42A, 113-122 (1986).

50. T. Beech, R. Gunde, P. Felder, and Hs. Günthard, Spectrochim. Acta., 41A, 319-339 (1985).

51. J. R. Durig and D. A. C. Compton, J. Chem. Phys., 69, 2028-2935 (1978). Note that this

value is incorrect and has been superseded by the Sullivan, Dickson and Durig result.49

52. H. Weiser, W. G. Laidlaw, P. J. Kruger, and H. Fuhrer, Spectrochim. Acta, 24A, 1055-1089

(1968). The listed uncertainty of ± 0.05 reflects a purely subjective assessment on our part of the data in Fig. 13 of this reference, and if anything is likely to be an overestimate.

53. F. R. Jensen, C. H. Bushweller, and B. H. Beck, J. Am. Chem. Soc., 91, 344-351 (1969).

54. E. L. Eliel and E. C. Gilbert, J. Am. Chem. Soc., 91, 5487-5495 (1969). This value was measured for 4-t-butylmethoxycyclohexane using conformationally averaged nmr chemical shifts.

55. W. A. Herrebout, B. J. van der Veken, A. Wang, and J. R. Durig, J. Phys. Chem., 99, 578-585 (1995). I thank Prof. Alex MacKerell (Univ. Maryland) for supplying this reference. 56. A. L. Verma, W. F. Murphy, and H. J. Bernstein, J. Chem. Phys., 60, 1540-1544 (1974).

57. J. R. Durig, A. Wang, W. Beshir, and T. S. Little, J. Raman. Spec., 22, 683-704 (1991).

58. R. K. Heenan and L. S. Bartell, J. Chem. Phys., 78, 1270-1274 (1983); W. F. Bradford, S. Fitzwater, and L. S. Bartell, J. Molec. Struct., 38, 185-194 (1977). These papers are cited by Allinger et al.7 _{as the basis for the value and the uncertainty listed in this table.}

59. M. Squillacote, R. S. Sheridan, O. L. Chapman, and F. A. L. Anet, J. Am. Chem. Soc., 97, 3244-3246 (1975); this result uses data from: F. A. L. Anet and A. J. Bourn, J. Am. Chem. Soc., 89, 760-768 (1967).

61. T. L. Boates, thesis, Iowa State University, 1966, as cited by: E. J. Jacob, H. B. Thompson,

and L. S. Bartell, J. Chem. Phys., 47, 3736-3753. This value is reported as a ∆G, but has been corrected for the two-fold statistical factor in favor of the gauche conformer.

62. F. A. L. Anet and V. J. Basus, J. Am. Chem. Soc., 95, 4424-4426 (1973).

63. F. A. L. Anet and J. Krane, Isr. J. Chem., 20, 72-83 (1980). This result was measured by

nmr line-shape analysis at -145° and converted from ∆G = 0.5 kcal/mol by using a force-field-calculated ∆S of 3.5 e.u. Use of the MP2/6-31G* estimate of 4.33 e.u. for ∆S (cf. ref. 1) would raise ∆H by an additional 0.1 kcal/mol.

64. J. R. Durig and D. A. C. Compton, J. Phys. Chem., 84, 773-781 (1980). We estimated the listed uncertainty of ± 0.02 kcal/mol from hand-drawn slopes for the five highest vs. four lowest temperature points in Fig. 3 of this reference.

65. D. Van Hemelrijk, L. Van den Enden, H. J. Greise, H. L. Sellers, and L. Schäfer, J. Am. Chem. Soc., 102, 2189-2195 (1980). The listed ∆H differs from the reported ∆H of 0.53

kcal/mol because it uses Durig and Compton's measured ∆S of 2.3 e.u. favoring skew (cf. ref. 64) to make the full entropic correction (not just the symmetry-number correction of R ln2 = 1.18 e.u.) to the measured free-energy difference of 0.94 kcal/mol.

66. D. M. Golden, K. W. Egger, and S. W. Benson, J. Am. Chem. Soc., 86, 5416-5420 (1964). 67. Heat of combustion value cited in, but not correctly referenced by: N. L. Allinger, F. Li, and L. Yan, J. Comput. Chem., 11, 848-867 (1990). The value listed here is from heats of formation given in: Lange's Handbook of Chemistry, Fourteenth Edition, J. A. Dean, Ed., McGraw-Hill: New York, NY, 1992. Measured heats of hydrogenation give similar values of 1.1 - 1.2 kcal/mol; see M. R. Ibrahim, Z. A. Fataftah, P. von R. Schleyer, and P. D. Stout, J. Comput. Chem., 8, 1131-1138 (1987), and references therein.