J. Phys. Chem. 1981, 85, 2469-2475
2489
Conformations of Cyclooctane and Some Related Oxocanes Patrick W. Pakes,‘l Thomas C. Rounds,lb and Herbert L. Strauss‘ Department of Chemlstty, Unlversily of Callfornia, Berkeley, Callfornia 94720 (Received: Februaty 27, 198 1)
Calculations of the minimum-energy conformations of cyclooctane, 1,3-dioxocane, and 1,3,6-trioxocaneare presented. A potential energy function is determined that is consistent with the energies, geometries, and low-frequencyvibrations of these rings. The vibrational study is presented in the following paper. A model is developed that provides a representation for the interconversion of the conformations of eight-membered rings. The boat-chair form is the minimum-energy conformer for all three molecules. In the case of the oxocanes, the oxygen atoms have definite preferred positions.
Introduction The conformation of ring molecules have fascinated chemists for years. The intramolecular interactions that occur in rings are more difficult to unravel than those in straight chains, and their study is important in gaining insight into the forces that govern molecular structure in general. Elucidation of the minimum-energy conformers of the medium hydrocarbon rings has proven particularly challenging, and the results of our analyses for eightmembered and smaller rings were recently reviewed.2 Complete analyses of the six-3and seven-membered4rings indicate preferred geometries of the chair form in cyclohexane and the nonrigid twist-chair in cycloheptane. Conformationalcomplexity increases rather dramatically with increasing ring size. The eight-membered ring, cyclooctane (C&I16), has been the subject of a great deal of study.6 There are three low-energy conformations of cyclooctane, each of quite different shape and symmetry: the the boat-boat (D2&, and the boat-chair (C,) crown (DU), (Figure 1). All of these are somewhat nonrigid and can deform into a number of different conformations belonging to the same “family”. The barriers between families are high, perhaps 7-15 kcal/mol. The energy differences among the lowest-energy conformers are determined by a subtle balance of bonded and nonbonded forces. In an eight-membered ring, the hydrogens situated across the ring from one another might easily be found within the sum of their van der Waals radii. In a smaller ring such as cyclopentane or cyclohexane, the stiffness of the ring valence forces effectively prevents such a close approach. Furthermore, in conformations such as the crown or the boat-chair, the methylene groups are not in their unstrained staggered arrangements and the CCC ring angles tend to be larger than their unstrained 112’ value? adding torsional and ring strain contributions to the energy of the low-energy forms. Experimental investigations have led to a variety of conclusions. Nuclear magnetic resonance experiments in (1)(a) Materials Development Laboratory, General Motors Corp., Flint, MI 48556. (b) Department of Biological Chemistry, Harvard Medical School, Boston, MA 02115. (2)Rounds, T. C.; Strauss, H. L. Vib. Spectra Struct. 1978,7,238-68. (3)Pickett, H. M.; Straws, H. L. J. Am. Chem. SOC.1970,92,7281-90. (4)Bocian, D. F.;Strauss, H. L. J.am. Chem. SOC.1977,99,2876-82. (5) (a) Hendrickson, J. B. J. Am. Chem. SOC.1961,83,4537-47.(b) Ibid. 1964,86,4854-66.(c) Ibid. 1967,89,7036-46,7047-61. (d) Wiberg, K. B. Zbid. 1965,87,1070-8.(e) Bixon, M.; Lifson, S. Tetrahedron 1967, 23, 769-84. (0 Allinger, N.L.; Hirsch, J. A,; Miller, M. A.; Tyminski, I. J.; Van-Catledge, F. A. J. Am. Chem. SOC.1968,90,1199-210. (g) Allinger, N. L.; Tribble, M. T.; Miller, M. A.; Wertz, D. H. Zbid. 1971,93, 1637-48. (h) Anet, F. A. L.; Krane, J. Tetrahedron Lett. 1973, 50, 5029-32. (i) Engler, E.M.; Andme, J. D.; Schleyer,P. V. R. J. Am. Chem. SOC. 1973,95,8005-25. 0022-3654/81/2085-2469$01.25/0
isotropic6 and oriented’ solvents provide unambiguous evidence for the boat-chair and indicate the presence of a small amount of another form, probably of the crown family. A single conformation could not be reconciled with electron diffraction data? X-ray studiesghave shown the presence of the boat-chair, but only in substituted rings where barriers to interconversion are much higher. An early vibrational studylo arrived at the conclusion of a tub form for cyclooctane, which is now known to be incorrect. In this study, we provide a more detailed picture of the cyclooctane conformers by expressing the geometry of the conformers in simple coordinates and by using a potential function that reproduces the structural results (mostly NMR) and the vibrational spectra (following paper”). Cyclooctane by itself does not provide sufficient information to make firm vibrational assignments, and so we also investigate the mechanically similar molecules, 1,3dioxocane and 1,3,6-trioxocane. We have already published results on the related molecule cyclooctanone.12 The conformers for the cyclic ethers are basically the same as for cyclooctane except one must specify the location of the oxygen atoms. Some of the important conformers for the dioxo ether are shown in Figure 1. The possibilities for the trioxo ether are ~imi1ar.l~Nuclear magnetic resonance experiments on these m01ecules~~J~ establish the “boat-chair 1,3” for the dioxocane and the “boat-chair 1,3,6” and a crown form for the triooxocane as the lowest-energy conformations.
Conformations of Cyclooctane As with the smaller rings, cyclopentane,16cyclohexane, and ~ycloheptane,~’ the cyclooctane conformations can be described in terms of the out-of-plane displacements zj of (6)Anet, F. A. L.; Basus, V. J. J. Am. Chem. SOC. 1973,95,4424-6. (7)Meiboom, S.;Hewitt, R. C.; Luz, 2. J. Chem. Phys. 1977,66, 4041-51. (8)Almeningen, A.; Bastiansen, 0.; Jensen, H. Acta Chem. Scand. 1966,20,2689-97. (9)Dunitz, J. D.; Magnoli, A. Chem. Commun.1966,166. (10)Bellis, H. E.;Slowinski, E. J., Jr. Spectrochim. Acta 1959,12, 1103-17. (11)Pakes, P. W.; Rounds, T. C.; Strauss, H. L. J.Phys. Chem., following paper in this issue. (12)Rounds, T. C.; Strauss, H. L. J. Chem. Phys. 1978,69,268-74. (13)Pakes, P. W. Ph.D. Dissertation, Univeraity of California, Berkelev. CA. 1979. (14)xnet, F. A. L. Top. Curr. Chem. 1974,45,169-220. (15)(a) Anet, F. A. L.; Degen, P. J. J. Am. Chem. SOC.1972,94, 1390-2. (b) Dales, J.; Ekeland, T.; Krane, J. Zbid. 1972,94, 1389-90. 1947, (16)Kilpatrick, J. E.; Pitzer, K. S.; Spitzer, R. J.Am. Chem. SOC. 69. 8-.-7-8-. . - - , -24. (17)Bocian, D. F.;Pickett, H. M.; Rounds, T. C.; Straws, H. L. J. Am. Chem. SOC.1975,97,687-95.
@ 1981 American Chemical Society
The Journal of Physical Chemistty, Vol. 85, No. 17, 1981
2470
I, 3
- DIOXOCANE
Pakes et at. OUT - O F
CONFORMATIONS
-
-
Boat Chair 2,4
Boat-Chair 1,3
+ 82"
o
t
+
o
-D -0. 3 t
06
+
4 3 t
++G5
=
-
0
E39
Boot-Choir 4,6
Boot -Choir 3, 5
- PLANE
-
IN PLANE
Boot
- Chair 2 , 8
QfJ
Twist Boat-Choir
E29
Crown
Twist Chair-Chair
r, E3u
Flguro 2. Ring bending-torsional symmetry coordlnates for the Infiniteslmal displacements of an eight-membered ring from Dahsymmetry.
Boot
- Boot
Flgure 1. Possible iow-energy conformations of 1,Mixocane. These are also the low-energy conformations of cyclooctane (ignorlng the placement of the oxygen atoms).
TABLE I: Abstract Coordinates of Cvclooctane Conformationsa crown chair-chair twist-chairchair boat-boat tub twist-tub chair twist-chair boat-chair twist-boatchair a
2,
e
...
The symmetry coordinates are shown in Figure 2 along with their irreducible representations in the Deh point group. The w1 coordinate represents a BzUcrownlike displacement, w2 and o3 are a degenerate Esu pair describing a boat-boat-like displacement, and w4 and w5 correspond to the degenerate Ea representation describing a twist-chair-like deformation. This equation can be written in an alternate form which is useful for discussing interconversions among conformers:
+
+
0 10 10
0 0 0
0 nn/2 (2n + l ) n / 4
0
zj = p{cos el cos (rj) sin cos O2 cos (aj/2 42) + sin d1 sin O2 cos (371'j/4 43)) j = 1, 2, ..., 8 (2)
0 0
where
90 90 90
0 0 0
nn/2 (2n + l ) a / 4 (2n + l)n/8 0 0 nn/2
0 0 0
.-.
90
90 90 90 -64 or -69 116 - 6 4 or - 6 9 nn/4 116 and e in degrees; 9, and @3 in radians.
el +
5
p
(2n + l ) n / 8 nn/4 (n - 2)n/4
=
(E i= 1 w
tan dl = ol/p
j w
0 Iel I.rr
( n - 2)n/8 n = 0, 1,
the methylene groups from a planar reference geometry.'hllg These displacement coordinates give z j = w1 cos (aj)+ w2 cos (aj/2)+ w3 sin (aj/2) + j = 1, 2, ..., 8 (1) w4 cos (3.rrj/4) + o5 sin (37rj/4) (18) Pickett, H. M.; Strauss, H. L. J. Chem. Phys. 1971,55,324-34.
tan 42 = 0 3 / 0 2
0 I42
tan 43 = 0 5 / 0 4
43 5 2a
Coordinate p represents the overall deviation from planarity of a given structure; el specifies the relative amount (19) For a discussion of alternate coordinate systems, see: Offenbach, J. L.; Strauss, H. L.; Graveron-Demilly, D. J. Chem. Phys. 1978, 69,
3441-2.
The Journal of Physical Chemistry, Vol. 85, No. 17, 198 1 2471
Conformations of Cyciooctane
Tub
Figure 3. Spherical conformational energy surface for cyciooctane. The coordinate O2 is held at 0 and the value of 4 Is arbitrary. The 0 coordinate Is the 0, of eq 2.
of crown character and O2 represents the relative amounts of boat-boat to twist-twist character. Additionally, 42and 43describe the contributions of bending and twisting of the structure. The specification of the standard conformations of cyclooctane in terms of these coordinates is found in Table I. Some of the values of O1 and O2 are not fixed by symmetry, but are calculated as described below. The many conformations of cyclooctane cannot be pictured on any simple three-dimensional figure since they are described by five coordinates. However, a combination of three of the coordinates can be pictured on the surface of a sphere and a combination of four on the surface of a torus. The complete conformational energy surface can be imagined as combining these projections. The crown and boat-boat families of conformers involve variations of coordinates 01,02, and p with the other two coordinates held fixed at zero. These three coordinates can be considered as a spherical polar system, and the potential surface for these two families can be mapped on the surface of a sphere as shown in Figure 3. This conformational sphere is very similar in its symmetry to that of ~yclohexane.~ The planar form with p = 0 is represented by the origin of the sphere. The two crown forms are located at the poles, each conformer being the inverted form of the other. The chair-chair and twist-chair-chair occur at values of O1 N 10'. A variation of $z constitutes the pseudorotation path for the chair-chair family. Along the equator of the sphere at O1 = 90°, the boatboat family is represented. As required by symmetry, there are four equivalent boat-boat conformers at values of 42 = O', M O O , and 180°, and four equivalent tub forms at d2 = k45' and *135'. Eight twist-tub conformers appear between the boat-boat and tub forms as 42is swept around the equator. The most important family energetically is the boatchair. The transition barrier between the boat-chair and ~~ twist-boat-chair has been calculated at 1.7 k ~ a l / r n o l .The boat-chair, twist-boat-chair pseudorotation path is given by 43 = 4 + 43' 42 = 24 + 42' (3) with 01' 64' and 6," N 69'. Such a pseudorotation with a variation in two coordinates simultaneously is best visualized as a path on a torus as discussed previously for cyc10heptane.l~For cyclooctane, the radii of the torus are p sin O1 cos O2 and p sin O1 sin OB One boat-chair conformer has 42 = 0 and 43 = 90' as shown in Figure 4. The next
k)
(d)
Figure 4. Relationships of the symmetry components of the displacements of the boat-chair form of cyclooctane. One boat-chair consists of a comblnatlon of a and c. The boat-chair form next on the pseudorotationpath is made up of b and d. The appropriate value of 4 for each form is given.
62
Flgure 5. Rectangular projection of a torus showing the boat-chairtwist-boat-chair pseudorotation pathway.
boat-chair on the pseudorotation path is then at d2 = 90' and 43 = 135O (Figure 4). A twist-boat conformer is at 42 45' and 43= 112.5'. The conformational torus can be cut to form a re~tangle,'~ and this gives the map of Figure 5. For every conformation with a nonzero value of w1 or O1 there is an "inverted" form at -olor 7~ - 01. This means that there is an inverted pseudorotation path which has ?r - 01,visualized as a toroidal path which looks just the same. Since the barrier to inversion is high, a given molecule pseudorotates on one torus at a time with only occasional jumps between tori.
Potential Function and Calculations The potential energy is expressed in terms of the ge-
2472
The Journal of Physical Chemistry, Vol. 85, No. 17, 1981
Pakes et al.
TABLE 11: Parameters Used in RingBending Potential -~
CCCC 15.0 COCC 14.0 COCO 14.0 OCCC-15.0
CCC 61.660 CCO 82.967 OC0119.606 COC 73.324
T,ltcal/mol CCCC CCCO OCCO COCO
cocc
CCCC1000.0 CCO 0 OCO 0 COC 0
cccc - 10.0 ccco - 10.0 OCCO 0 coco 0 cocc 0
A, kcal/mol B , kcd A6/mol
l/ro, A-l
3.60 (HH) 2.00 (OH) fixed geometrical parameters
rcc = 1.532 A rco = 1.430 A rcH = 1.107 a
45.90
eoccc = 112.60 e One = 104.0°a eocco = 109.50 eooco = 109.50 eococ = 112.60 e0HCH = 104.00
a Angle between oxygen nonbonded electrons.
ometry of the ring in internal coordinates. The potential used is 8
V(r,$,7)=
C {Hi($i -
$j')'
L=l
($'+I - $i+l')
\ I
/'I5
K , kcal/(mol rad2)
1.65 2.42 1.724 1.85 1.012
3300
I\
+ Qi($j
Ki($i - $i')($i+l
i+4
+ F,($j - $io) X + Ti COS 37i + - $i+I') COS 7i + 4
C C
j=i+3 m = l mod 8
(Ae-'ijmlro - B/rijm6)) (4)
where $i are the instantaneous values of the eight ring bond angles and the $io are the equilibrium values which they would have if the ring were opened. The ri are the torsional angles, For cyclooctane, the rijm are the distances between nonbonded hydrogen atoms attached to carbon atoms i and j . The index m labels the four pairs of interactions. This term accounts for 1,4and 1,5 interactions involving hydrogen atoms attached to carbon atoms 3 and 4 atoms removed from each other, respectively. Additionally, this term accounts for oxygen-hydrogen interactions in the case of the cyclic ethers. A complete list of parameters used in eq 4 appears in Table 11. In calculations, the carbon-carbon bond lengths were held fixed at 1.54 A and the carbon-hydrogen bond lengths at 1.107 A.* The positions of the hydrogen atoms were calculated by using a bisector model with a fixed HCH angle of 104'. For cyclooctane and the cyclic ethers, the +tioused were the same as those of Picket and Strauss in their study of cyclohexane and some related ~xepanes.~ The force constants were first transferred from the ring-bending potential that proved successful for the seven-membered-ringcycloheptane and related ~xepanes.~ However, application of this potential to cyclooctane gave low-energy boat-boat forms with 1,5H atoms that came much closer than the sum of their van der Waal's distances. Since the boat-boat can be formed with ring and torsional angles close to those of the unstrained cyclohexane it is this conformation that is favored by a potential function transferred from smaller rings if the nonbonded interactions are not hard enough. Consequently, the nonbonded interaction was made harderz0(which changes (20) See the discuasion in: Altona, C.; Faber, D. H. Top. CUW.Chem. 1974,45,1-38. Our parameters are close to those oE Williams, D. E. J. Chem. Phys. 1966,45,377&8.
Flgure 8. Definition of the five out-of-plane coordinates al, a2,a3, a,,and 6 and the five in-plane coordinates PI, P2, b3,p,, and y,*.
TABLE 111: Symmetry Adapted Linear Combinations of the In-Plane Coordinates Q(6) ' / 4 ( 0 1 t P Z t P3 04) '/4(@2 t P4 - P I - E 3 Q(7) Q(8) '/2(04P2) Q(9)" 50r1 Q(10) */2(P3 - Pl) a This coordinate was multiplied by a factor of 50 for ease of minimization. TABLE IV: Coordinates of the Boat-Chair Pseudorotation of Cyclooctane
9,
@3
01
02
p
E , kcd/mol
-180.0 -90.0 0.0 90.0 180.0 - 90.0 0.0 90.0 180.0
-180.0 -135.0 -90.0 -45.0 0.0 45.0 90.0 135.0 180.0
68.4 62.1 68.4 63.7 68.4 62.1 68.4 63.7 68.4
52.9 70.5 53.0 68.9 53.0 70.5 53.0 68.9 53.0
56.4 46.4 56.4 46.5 56.4 46.4 56.3 46.5 56.4
12.564 12.564 12.564 12.564 12.564 12.564 12.564 12.564 12.564
both A and ro)and a quartic term added to the ring angle bend. The 2-fold term used in earlier calculations on cyclooctanone12was dropped as it favored the crown forms over the boat-chair in cyclooctane. The value of the 3-fold CCCC torsional term in Table I1 is not particularly well-defined. Calculated vibrational frequencies of the boat-chair form of cyclooctane were insensitive to the increase of this 3-fold term by 10%. However, the relative energies between the crown forms and the boat-chair were found to increase rapidly with an increase in the 3-fold term. This 3-fold term, as well as the rest of the terms appearing in Table I1 not discussed, were fixed at approximately the values used in the seven-membered-ring potential. For the cyclic ethers, 1,4 and 1,5 interactions between hydrogen atoms and nonbonded electrons of oxygen atoms were calculated with the same bisector model that was used for placement of the hydrogen atoms. This model was used to locate the center of density for the nonbonded electrons, keeping a fixed angle of 104' between them and with the center of electron density placed 0.5 A away from the oxygen atoms. In other words, the center of electron density was located at the same positions as for hydrogen atoms in a methylene roup in the ring, but with " b o n d length shorter by 0.5 . In the cycloheptane study: the center of nonbonded electron density was placed at the coordinates of the oxygen atoms themselves. But here a "harder" oxygen-hydrogen interaction was needed to ensure that the boat-boat forms for the cyclic ethers would not be favored. The five in-plane deformation and five out-of-plane deformation coordinates were taken as shown in Figure 6 and Table 111. These 10 coordinates were transformed
R
The Journal of Physical Chemistry, Vol. 85, No. 17, 1981 2473
Conformations of Cyclooctane
TABLE V: Geometries of Eight-Membered Ringsa bond angles
$1
$2
$3
$4
$5
$6
Ijl?
$8
Cyclooctane boat-chair twist-boat-chair crown chair-chair twist-chair-chair boat-boat ( D 2 d) boat-boat ( C , ) chair twist-chair
116.6 116.9 115.4 115.8 115.8 118.4 117.1 118.0 116.7
117.6 113.9 115.4 115.4 115.7 119.6 117.9 118.0 117.0
115.5 113.7 115.4 114.0 114.1 118.4 117.1 113.7 116.7
boat-chair 1,3 boat-chair 2,4 boat-chair 3,5 boat-chair 4,6 boat-chair 2,8 twist-boat-chair crown twist-chair-chair boat-boat
116.1 114.5 115.6 116.7 111.9 110.9 116.2 114.9 116.9
111.0 117.8 112.2 117.1 119.9 113.3 114.2 109.6 111.7
114.2 110.4 115.0 111.4 113.7 109.3 116.2 112.4 117.3
boat-chair 1,3,6 boat-chair 2,4,7 boat-chair 3,5,8 boat-chair 1,4,6 boat-chair 2,5,8 twist-boat-chair crown twist-chair-chair boat-boat
115.9 113.1 113.0 115.9 112.4 111.3 115.8 111.3 116.0
111.2 118.4 114.0 113.2 120.8 115.7 112.5 116.1 111.5
114.5 110.6 115.8 111.4 114.0 109.4 115.8 111.9 117.7
boat-chair twist-boat-chair crown chair-chair twist-chair-chair boat-boat ( D z d ) boat-boat ( C , ) chair twist-chair
- 63.8
-47.6 - 88.4 -76.5 -63.7 -51.5 -34.1 0.7 40.2
-43.9 117.1 88.4 98.6 85.4 -51.5 -66.6 -76.9 40.2
101.6 -48.2 -88.4 - 98.6 -110.7 51.5 34.1 118.2 -107.4
boat-chair 1,3 boat-chair 2,4 boat-chair 3,5 boat-chair 4,6 boat-chair 2,8 twist-boat-chair crown twist-chair-chair boat-boat
- 68.8
- 55.8
-63.9 -53.2 - 60.2 - 71.6 - 53.7 -92.7 -59.7 -62.7
-45.2 - 60.8 -43.1 -39.6 122.9 92.7 97.1 - 60.9
112.5 116.6 118.3 108.6 95.4 -39.6 - 91.4 -127.7 63.0
boat-chair 1,3,6 boat-chair 2,4,7 boat-chair 3,5,8 boat-chair 1,4,6 boat-chair 2,5,8 twist-boat-chair crown twist-chair-chair boat-boat
-65.3 -63.6 - 59.2 -74.3 - 66.4 - 52.9 -91.5 - 66.7 - 50.3
-55.7 -43.5 - 53.8 -38.9 - 39.4 121.6 91.5 83.6 - 64.6
109.3 111.7 110.6 105.5 99.9 - 39.3 - 92.0 -111.3 46.6
114.8 116.9 115.4 115.4 114.2 119.6 117.9 114.0 109.5
117.7 116.1 115.4 115.8 115.8 118.4 117.1 118.0 116.7
114.8 115.2 115.4 115.4 115.7 119.6 117.9 118.0 117.0
115.5 115.3 115.4 114.0 114.1 118.4 117.1 113.7 116.7
117.6 116.2 115.4 115.4 114.2 119.6 117.9 114.0 109.5
116.6 113.7 117.4 112.0 119.4 116.8 114.8 116.0 117.2
114.5 116.5 112.8 115.2 116.1 116.5 109.6 115.0 117.7
115.2 116.2 116.6 111.4 113.7 112.4 114.8 116.2 116.4
113.5 119.2 117.7 117.1 119.9 115.3 112.3 114.6 113.9
112.5 113.0 118.1 112.1 118.5 115.7 110.5 114.5 114.9
113.7 110.4 112.0 115.2 111.2 111.3 111.6 111.0 119.6
110.9 115.4 113.5 111.4 114.0 111.0 110.5 110.1 112.4
113.1 113.0 119.8 113.2 120.8 114.1 111.6 114.1 113.2
67.9 93.1 - 88.4 -76.5 -63.7 -51.5 - 34.1 -0.7 -40.2
-101.6 - 91.5 88.4 98.6 85.4 -51.5 - 66.6 76.9 - 40.2
43.9 92.7 - 88.4 -98.6 -110.7 51.5 34.1 -118.2 107.4
63.8 -48.0 88.4 76.5 85.1 51.5 66.6 75.8 -- 107.4
60.9 65.8 69.9 78.2 59.9 85.7 -89.1 -59.7 -47.3
-97.7 - 90.7 - 99.8 -108.6 - 95.4 -81.3 89.1 83.3 - 52.1
42.6 37.4 40.9 43.1 39.6 101.1 - 90.9 -107.3 46.5
73.7 65.6 60.9 60.2 71.6 - 60.4 91.4 77.2 66.6
74.4 64.8 68.7 76.4 75.7 101.0 - 97.1 -71.6 - 32.6
- 109.4
40.1 53.9 44.2 38.9 39.4 98.1 -91.1 -116.4 39.9
72.4 59.8 61.4 74.3 66.4 - 55.7 92.0 95.7 73.6
1,3-Dioxocaneb
110.5 113.3 109.7 115.2 116.1 115.9 112.3 110.0 115.3
1,3,6-Trioxocane
110.7 114.3 109.9 115.2 111.2 112.3 111.5 110.1 116.6
Cyclooctane
-67.9 -47.7 88.4 76.5 85.1 51.5 66.6 -75.8 107.4
1,3-Dioxocaneb
-62.5 -77.5 -70.5 -18.2 -59.9 -51.8 90.9 84.4 46.9
1,3,6-Trioxocane
a
All values in degrees.
-64.9 -73.2 -68.6 -76.4 -75.7 - 60.6 91.1 96.5 58.7
- 107.4
-103.2 -105.5 -99.9 - 87.7 97.1 82.3 - 67.3
Numbering is keyed t o the conformations that appear in Figure 1.
to (1) Cartesian coordinates, (2) the valence coordinates of the potential function (eq 4), and (3) the z-displacement symmetry coordinates of eq 1. The symmetry coordinates can be uniquely defined in terms of the CY’S and the 6 of Figure 6 for infinitesimal deformations from the planar form. For finite displacements, the z, of eq 1 are rather nonlinear functions of the ring parameters, and this causes the calculated values of p , el, 02, &, and cp3 to vary some-
what from ideal relationships such as those of Table I. The preliminary conformational calculations were done by specifying the five out-of-plane oi and then by minimizing with respect to the in-plane coordinates of Table 111. These calculations determined the initial values for the boat-chair, crown, and boat-boat forms. Then more
2474
The Journal of Physical Chemistry, Vol. 85, No. 77, 1981
Pakes et at.
TABLE VI: Energiesu of Eight-Membered Rings (kcal/mol) EQ
ET
Cyclooctane boat-chair twist-boat-chair crownb chair-chair twist-chair-chairb boat-boat ( D 2 d ) b boat-boat (C,) chair twist-chair
2.232 0.479 1.490 0.312 1.212 0.295 1.058 0.237 0.929 0.203 6.224 1.486 3.645 0.874 2.317 0.409 2.412 0.102 EH
EF
0.219 0.103 0.048 0.044 0.039 1.320 0.449 0.317 0.202 EQ
6.635 10.153 12.135 11.811 11.280 1.268 5.571 15.466 15.055 ET
-0.136 -0.078 -0.005 -0.018 -0.026 -0.616 -0.356 -0.193 -0.219
9.429 11.980 13.685 13.132 12.425 9.682 10.183 18.316 17.552
1.615 1.519 2.373 - 0.087 - 0.175 - 0.084 0.190 -0.177 0.532 -0.193 7.150 -0.235 4.873 0.392 2.588 - 0.074 1.574 - 0.074
~ E B O N D Eh”
EK
EkG
12.564 14.266 13.426 13.145 12.764 16.597 15.448 20.830 19.052 ZE
1.702 0.862 0.581 0.200 4.033 2.884 8.266 6.488 AEBC
1.3
1,3-Dioxocane boat-chair 1,3 boat-chair 2,4 boat-chair 3,5 boat-chair 4,6 boat-chair 2,8 twist-boat-chair crown twist-chair-chair boat-boat
1.338 3.056 2.084 1.769 4.835 1.303 2.154 1.457 3.581 EH
0.091 0.095 0.169 0.183 0.497 0.146 0.116 0.047 0.280 EF
0.119 0.217 0.364 0.202 0.606 0.115 0.130 0.095 0.529 The energies are for the terms of eq 4. boat-chair 1,3,6 boat-chair 2,4,7 boat-chair 3,5,8 boat-chair 1,4,6 boat-chair 2,5,8 twist-boat-chair crown twist-chair-chair boat-boat
1.097 2.250 3.443 1.652 5.273 0.933 1.070 0.739 4.665
0.029 0.209 0.094 0.099 0.225 0.064 0.012 0.020 0.127 EQ
5.617 7.568 8.625 7.029 7.896 7.728 14.629 11.406 1.710
-0.038 -0.119 -0.078 -0.094 -0.064 -0.034 0.002 -0.004 -0.176
1.070 1.434 7.037 1.744 10.809 1.793 1.738 10.894 1.353 0.906 8.986 2.038 13.389 3.189 1.520 2.402 -0.113 9.207 16.913 - 0.235 - 0.088 0.949 12.926 - 0.253 5.446 5.522 - 0.262
9.541 14.346 13.985 11.930 18.098 11.496 16.590 13.622 10.706
ET E K ~ E B O N DEff4H, OH 1,3,6-Trioxocane
Ehk, OH
ZE
1.293 2.152 2.689 1.312 3.293 2.720 -0.273 -0.276 0.276
1.554 1.839 1.831 1.918 1.758 -0.123 - 0.083 0.795 5.769
9.312 12.799 15.303 12.306 18.000 11.269 13.482 12.402 13.829
5.249 6.341 6.976 7.222 7.070 7.624 12.638 11.049 2.590
6.465 8.808 10.783 9.076 12.949 8.672 13.838 11.833 7.784
4.805 4.444 2.389 8.557 1.955 7.049 4.081 1.165
AEBC
1.3.6
3.487 5.991 2.996 8.689 1.957 4.170 3.090 4.517
Saddle points on the energy surface.
complete minimizations were carried out. In order to locate the most stable conformers, the method of steepest descents with a variable step gradient was employed.21 For cyclooctane, the geometry of the boat-chair represented a global minimum in potential energy. For the cyclic ethers, the “boat-chair 1,3” and “boat-chair 1,3,6” were global minima. The energy minimizations were carried out to 0.005 kcal/mol and for most of the conformations converged without difficulty. Table IV illustrates the nonlinearity of the coordinates of eq 1 as they are expressed in terms of the geometrical coordinates of Figure 6. At each boat-chair conformation defied by fixed values of 42and &, the values of the other eight coordinates were found by minimization starting from approximately correct initial values. In contrast to our experience with the smaller rings, we had difficulty in locating minima for some of the cyclooctane conformations. The problem of converging on false minima in gradient searches is well-known.22 Particular problems were found with the crown family (crown, chair-chair, and twist-chair-chair) and with the boat-boat conformation. The crown is at a saddle point because it is a minimum with respect to only some of the coordin a t e ~ . The ~ ~ energy of the boat-boat form is a strong (21) Williams, J. E.; Stang, P. J.; Schleyer, P.v.R. Annu. Reu. Phys. Chem. 1968,19, 531-58. (22) Wilde, D. J. “Optimum Seeking Methods”; Prentice-Hall: Englewood Cliffs, NJ, 1965. (23) The exact geometries of the tub and twist-tub conformers were not found because of the nonlinearity of the coordinate system and the fact that they are not at local minima. However, coordinates of eq 1 corresponding to these configurations were minimized, resulting in energies of 12.1 and 11.8 kcal/mol for the tub and the twist-tub, respectively, relative to the energy of the boat-chair. Both forms were ruled out as minimum-energy conformers.
function of the 1,5 H repulsion, and the minimization programs tended to hang up in the process of twisting the molecule in an attempt to make small adjustments in the H-H distances. This twisting of the ring led to a lowerenergy conformer. In the tables we refer to the “ideal” boat-boat with DZdsymmetry and the twisted boat-boat with only C2 symmetry. The geometries, energies, and energy distributions of the various cyclooctane and oxocane conformations are listed in Tables V and VI. The coordinates of Figure 6 and the rotational constants for these conformers may be found in ref 13. The potential energy distributions provide useful information, but this partitioning cannot be assigned exact physical meaning since different force fields yield different partitions.20 Nevertheless, by comparison, the members of the crown and chair families suffer predominately from torsional strain and the boat-boat family from unfavorable 1,5 interactions. The boat-chair forms for all three molecules represent the best compromise among all of the investigated sources of strain. The substituted rings show highly preferred positions for the oxygen atoms. These preferred positions are precisely the ones that serve to eliminate unfavorable nonbonded interactions through the substitution of an oxygen atom for a methylene group. Interestingly, the COCOC framework in dimethoxymethane has the same geometry about the oxygen atoms, that is, a + gauche, + gauche conformation.“” Thus the interactions among the groups immediately about the oxygen favor this geometry even (24) (a) Dale, J.; Ekeland, T.Acta Chem. Scand. 1973,27, 1519-25.
(b)Dale, J.; Ekeland, T.; Krane, J. J. Am. Chem. SOC.1972,94,1389-90. (25) Astrup, E. C. Acta Chem. Scand. 1971,25, 1494.
The Journal of Physical Chemlstty, Vol. 85, No. 17, 198 1 2475
Conformations of Cyclooctane
TABLE VII: Comparison of Cyclooctane Structures 01
thisstudy ref I
63.7 66.2
02
70.0 71.8
@2
90.0 90.0
@B
P
135.0 135.0
46.5 46.8
TABLE VIII: Comparison of Results for the Conformationsa relative strain energies, kcal/mol conformation
ref 5c
ref 5d
ref 5f
ref 5h
ref this 5i study
0 0 0 0 0 boat-chair twist-boat-chair 2.0 1.7 t wist-chair-chair 1.7 -.0.25 2.20 0.8 0.1 2.8 2.09 1.5 0.2 crown chair-chair 2.25 1.8 1.9 boat-boat 1.4 4.44 >2.00 2.8 >2.00 2.8 twist-tub 0.9 11.2 10.8 8.96 tub 0.5 chair 8.3 7.7 twist -c hair 8.7 6.09
0 1.70 0.20 0.86 0.58 2.88 8.27 6.49
a The results of ref 5 are for the symmetrical conformers of Figure 1. Some minima found in this study were of lower symmetry. See text.
in the absence of a closed ring. The other than the boat-chair conformers reported in the tables for the cyclic ethers represent the lowest energy of all forms calculated by pseudorotation of the structure.
Comparison with Other Results This study provides a model of cyclooctane and related molecules which has been fit to reproduce the boat-chair as found by both NMR and vibrational spectroscopy. The model can be tested by comparison of the detailed NMR structure with the calculated one (considered below), by comparison of the observed frequencies with the calculated ones (considered in ref l l ) , and by comparison with other calculations. The NMR findings of Anet6 were based solely on symmetry considerations, but in the work of Meiboom, Hewitt, and Luz7 a liquid crystalline solvent was used, which provides data on the direct dipolar interactions of the magnetic nuclei. These interactions are simply related to molecular geometry and lead to both quantitative and qualitative information regarding the conformation of cyclooctane. Meiboom et al. calculated the magnitude of the dipolar interactions for a variety of configurations,and the observed spectrum was only consistent with a boatchair. In their fit, they constrained all CCC bond angles to the same value. Their reported structure has bond angles of 118' and torsional angles of 69.2", 35.8', and -95.3O. To provide a basis for comparison with this work, their structure was put in terms of the out-of-plane abstract coordinates, and these are shown in Table VII. The two structures agree quite closely, differing only in small geometric details. A summary of various strain-energy calculations is shown in Table VIII. There is general agreement as to
the sequence of conformers in terms of relative energies, but the absolute magnitudes differ. For example, in this study, the twist-chair-chair was found to be of nearly the same energy as that of the boat-chair. The same result was found in the calculations of Wiberg" and Engler, Andose, and von R. Schleyer.6i The latter authors have been somewhat critical of previous strain calculations; they suggest that excessive constraints in the minimization may have resulted in a larger calculated energy difference between conformers. It should be pointed out that in this study a constraint was imposed on the hydrogen atoms which prevents a complete relaxation of the molecular structure during minimization. It was also observed that the energy difference between the boat-chair and twistchair-chair could be manipulated by changing the value of the 3-fold torsional barrier, with little change in calculated frequencies. The conclusions for the boat-chair 1,3for the dioxocane and the boat chair 1,3,6 for the trioxocane are in accord with the NMR evidence. However, the NMR studies have also seen an appreciable amount of another conformer with about the same population over the entire investigated temperature range for the trioxocane. This conformer is thought to be a member of the crown family. It is difficult to reconcile this observation with our calculation since we would suggest a crown family conformer with both a higher energy and a higher entropy than the boat chair. However, it is possible that these factors nearly cancel to provide the observed temperature independence of the NMR intensities.
Summary and Conclusions A model was developed that provides a representation for the interconversion of eight-membered rings. This representation yields an excellent method for computing dynamic properties of the rings, and its projections on the sphere and torus are useful visualizations. A ring-bending potential energy expression was characterized which provides information that is consistent with the energies, geometries, and low-frequencyvibrations of the three rings studied. The potential indicates the boat-chair as the minimum energy form for all three rings with preferred positions for the oxygen atoms in the case of the oxocanes. The information obtained is consistent with all prevailing evidence with the exception of the NMR evidence for the crown form of the trioxocane. More work needs to be done to resolve this discrepancy. The potential function presented here is undoubtedly not unique since each of the three properties of energies, geometries, and vibrations can be independently varied through manipulation of the force constants.20 Acknowledgment. We acknowledge Drs. David F. Bocian and Janet L. Offenbach for many helpful discussions regarding calculations of ring molecules. We gratefully acknowledge support from the National Science Foundation.
