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Conformation of bicyclo [n.1.0] Derivatives
Journal of Molecular Structure, 87 (1982) 53-64 THEOCHEM Elsevier Scientific Publishing Company, Amsterdam
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CONFORMATION OF BICYCLO [n.l.O] DERIVATIVES Part 3. Dioxa- and trioxa-bicyclo[ 5.1.01 octanes
GIORGIO ROBERTO Institute
FAVINI, DEMETRIO TODESCHINI of Physical
(Received
Chemistry,
PITEA, University
MANUELA
SOTTOCORNOLA
of Milan, Milan
and
(Italy)
21 April 1981)
ABSTRACT The conformational geometries and possible interconversion paths for some oxa derivatives of bicyclo[ 5.1.0] octane have been studied by the molecular mechanics method. The theoretical results are compared with the experimental data for the molecular geometry of bicyclo[ 5.1.01 octane and 3,5,8-trioxabicyclo[ 5.1.01 octane, the free energy of activation for cycloheptene epoxide and 3,5-dioxabicyclo[5.1.O]octane, the dipole moments and molar Kerr constants in solution for cycloheptene epoxide, 3,5-dioxaand 3,5,8-trioxabicyclo[ 5.l.Oloctane. INTRODUCTION
In Part 1 of this series [l] , quantum mechanical calculations of the semiempirical kind (MIND0/3 method [ 21) were performed in order to study the conformational equilibrium and the possible interconversion pathways of bicyclo[ 5.1.01 octane and cycloheptene epoxide. In Part 2 [3], the conformational geometries of norcarane and cyclohexene epoxide were studied by both quantum mechanical and molecular mechanics calculations in view of an extension of the research to some dioxa- and trioxa-bicyclooctanes. Conformational analysis of derivatives of this kind has received considerable attention from Gianni et al. [4], who have considered above all the effects of the introduction of a double bond or of an epoxide ring on the conformation of 1,3-dioxacycloheptanes. Their conclusions were supported by studies of low-temperature proton magnetic resonance spectra. However, the conformational geometries of these compounds are far from conclusively resolved, in spite of the X-ray crystal structure determination performed in our laboratories [5] on 3,5,8-trioxabicyclo[ 5.1.01 octane (1,3-dioxacyclohept-5-ene epoxide). In this paper, the molecular mechanics method has been chosen for a systematic study of the conformational properties of the following compounds: 3,5dioxabicyclo[ 5.1.01 octane (l), 3,5,8-trioxabicyclo[ 5.1.01 octane 0166-1280/82/0000-0000/$02.75
o 1982
Elsevier
Scientific
Publishing
Company
54
(2), 4,&dioxabicyclo[ 51.01 octane (3), together with bicyclo[5.1.0] octane (4) and cycloheptene epoxide (5) (previously studied only by the MIND0/3 method [l] ), and 4-oxabicyclo [ 5 .l .O] octane (6). Theoretical results have also been analysed on the grounds of experimental data for dipole moments and molar Kerr constants obtained simultaneously in our laboratories [ 61. CALCULATIONS
A modified version of the force field method of Schleyer-Andose-Mislow [ 73 was used, including the additional parameters suggested by Allinger and Chung [ 81 for oxa compounds. Difficulties were encountered with the pattern search minimization technique and, consequently, the steepest descent method already contained in the program was adopted. The minimization loop was terminated when the energy decrease relative to the preceding loop fell below 0.01 kcal mall’. The description of the electron density around an oxygen atom in molecular mechanics calculations has given rise to much discussion. In fact, the electron density may be considered to be spherical and, hence, centered on the oxygen nucleus, or the lone pairs of electrons may be treated explicitly. The former model was used recently in the WBFF force field [9] ; the latter model was preferred by other authors [8, lo] and adopted by us in Part 2 [ 31. An improved molecular mechanics version for systems containing oxygen atoms has been proposed [ 111 as an extension of the MM2 hydrocarbon force field [ 121. Since our program is related to Allinger’s MM1 force field [ 131, we preferred to leave unchanged the previous parameterization [ 81, which, moreover, supplied good results in Part 2 [ 31. In order to reduce the high values obtained for the bending strain and the steric energy of three-membered compounds, we decided to change the values of r. for C-C and C-O bond lengths and of 0 o for CCC, CC0 and COC bond angles in the three-membered ring by leaving unchanged the force constant values (both parameters should be varied at the same time). The new values (Table 1) were empirically obtained so as to fit experimental AH2.98 values of cyclopropane, ethylene oxide and their methyl derivatives. The decrease in r. (for C-C distance) and in B. values with respect to standard values is in line with the variation of the carbon hybridization, according to the theoretical models of Walsh [ 141 and Coulson and Moffitt
E151.
For molecules that contain two or more heteroatoms, it is necessary to consider the electrostatic interactions which occur between them, in addition to the non-bonded interactions described by the usual potential functions. To calculate the electrostatic interactions between the dipoles in the molecule, they can be placed at the midpoints of the bond concerned and the interaction evaluated by Jean’s equation [ 8, 161. Alternatively, electrostatic interactions may be calculated as coulombic interactions from the relationship [9, 171 E = 332.17 zij(qiqj/r@) kcal mall’, where qi and Q are the
55 TABLE Force
1 field parameters
for three-membered
Compound
Parameter
Bond C-C Angle C-C-C
Cyclopropane Methylcyclopropane 1,2-cis-Dimethylcyclopropane Ethylene oxide
Propene
oxide
aValues
of Table
rings
Bond C-O Angle CC-O Angle C-O-C
Value
AHi98
Expt.a
12.53
12.74
7.41 1.69 -12.66
6.19 0.60 -12.60
-18.78
-22.20
r0 = 1.472 so = 86.4
= 1.436 e0 = 84.7 8, = 83.0 r.
(kcal mol.I)
CalC.
1 in ref. 2.
partial charges on atoms i and j derivable from molecular orbital calculations (CNDO/B method), D is the dielectric constant and rij is the interatomic distance in a (between atoms i and j). Values in the range 1.5-5 have been suggested for the dielectric constant D [9, 11, 181; although the value chosen is not critical since electrostatic interactions represent a relatively small part of the non-bonded interactions. Since our program did not include electrostatic interactions in the calculation of the strain energy, we used the latter more simple procedure in order to evaluate the weight of the electrostatic interactions in the different molecular conformations. Theoretical dipole moments and molar Kerr constants were calculated by using the bond moments and the bond polarizabilities reported in Table 2 of ref. 2. For the C-O bond in a seven-membered ring, the values used were: 1-1= 0.59 D; b, = 0.89 A3; bT = b v - 0.46 A3. Details of the calculations will be described in ref. 6. All the calculations were carried out on a UNIVAC 1100/81 computer at CILEA, Milan. RESULTS
As in Part 1 [ 11, four C, symmetry forms were considered* (CC, BC, CB and BB), together with: a C1 form with a twist-boat conformation in the seven-membered ring; two transition states (TS/l and TS/2) with six coplanar atoms (1,2,3,5,6,7 positions in the molecular scheme of Fig. 1) intermediate in the symmetrical interconversion pathway between the BC and CB (TS/l) or between the CC and BB forms (TS/2); and two transition states (TS/3 and TS/4) with five coplanar atoms (2,3,4,5,6) intermediate in the symmetrical interconversion pathway between the CC and CB forms (TS/3) or between the BC and BB forms (TS/4). *The following abbreviations will be used throughout: chair-boat (CB); boat-boat (BB).
chair-chair
(CC);
boat-chair
(BC);
56
k7 TS/4
Fig.1.Interconversion pathways. TABLE2 Geometrical
parameters
of 3,5-dioxabicyclo[5.1.O]octane (1)
cc Bondlength C,--c* C,0, 0,-C, C,-C, C,-C" Cl--H, C,-Hna
CB
BC 1.530 1.403 1.405 1.506 1.508 1.101 1.101
1.529 1.404 1.405 1.508 1.507 1.102 1.101
C, 1.528 1.409 1.405 1.504 1.507 1.100 1,101
1.534/1.533 1.407/1.408 1.406/1.405 1.507 1.510/1.503 1.100/1.101 1.101
Bond angle (” ) 115.6 114.3 110.1 119.9 118.7 118.5 117.5 113.0 104.3 106.9
117.7 114.1 108.8 118.5 123.6 118.6 115.0 114.0 107.6 107.2
115.1 114.6 114.0 119.5 115.2 118.3 116.7 115.1 104.4 106.5
109.9 130.0 112.8 108.0 -125.5 83.6 -79.2 0.0
106.1 145.1 105.1 114.5 -33.5 -70.6 89.4 0.0
110.9 123.5 121.7 103.8 -133.9 25.8 67.6 0.0
c,c,o,
CP,C, O,C,O, C,C,C, C,C,C* H&H, C,C,H, C,C,H, H&H, H,C,H., Dihedral 01
0 Y Wtll WI2 a23 w34 WI7
111.5/114.6 112.5/112.9 109.9 116.4/120.5 118.4/119.2 118.5 116.8D14.8 114.1/115.3 104.2l107.6 109.6
angle (“)
aAveragedvalue.
108.9/-108.3 -111.4/34.2 97.u91.7 -49.0/-50.7 4.7
57 TABLE 3 Geometrical parameters of 3,5,8-trioxabicyclo[5.l.O]octane
Bondlength c,--c, c,--0, oi-c, c,-c, c,--0, c,--H, c,--H,b Bond
angle
c,c*o,
c*o,c. o,c,o, o,c,c, CFIC2 Osc,H, c&,H, HncnHnb
ExPt.a BC
BC
C,
(2) BC
C,
ExPLa BC
Dihedralangle(O) 1.524/1.521 1.408/1.404 1.405/1.408 1.474 1.436/1.436 1.103/1.104 1.104
1.532 1.407 1.405 1.473 1.436 1.104 1.103
1.496
1.420 1.405 1.457 1.449
; Y Wlil 109.1/-107.8 WI2 -120.8/38.2 *23 98.3/85.5 w34 -42.3/-53.5 WI7 10.8
105.1 143.8 103.8 114.7 -31.1 -71.5 90.3 0.0
105.4 148.1 105.7 118.2 -38.4 -64.2 88.1 0.0
(“)
109.1/116.7 112.0/113.3 112.2 114.8/124.4 118.0/120.4 110.5/108.9 116.9/115.3 107.5
117.1 113.1 108.4 118.1 123.9 109.4 115.1 107.4
116.4 114.4 112.3 119.1 127.0 113.5 116.6 109.0
aValues from ref. 5. bAveraged value.
Geometrical parameters calculated for the most stable conformations of compounds l-6 are given in Tables 24 together with experimental data (where available) and previous theoretical values. Geometrical parameters of the other conformations and of the transition states are available on request (to the authors). The calculated heats of formation of all the conformations and transition states are collected in Table 8. Dipole moments and molar Kerr constants for the most stable conformations are given in Table 9 and compared with experimental data. TABLE 4 Geometrical parameters of 4,&dioxabicyclo[
cc Bond
length
Ck-c, c*-C, c,*, CL--C, c,--0" c,--H, C,-H,a
BC
5.1.01 octane (3) cc
C,
(rr,
Dihedral
1.525 1.525 1.410 1.475 1.436 1.104 1.100
Bond angle(") c,c,c, 117.8 c&%0, 112.2 c,o,c, 114.1 O&,C, 123.5 C&,C, 119.6 O&,H, 110.5 c,c,H, 114.3 Hnc,Hna 106.4
aAveraged value.
1.534 1.526 1.412 1.472 1.436 1.105 1.101
118.2 111.3 115.1 119.1 124.9 109.2 114.5 107.4
1.52311.522 1.524/1.519 1.411/1.413 1.472 1.436/1.436 1.104/1.105 1.100
106.0/115.4 112.9/113.2 116.2 115.4/122.3 122.41123.8 109.5/108.5 115.5/114.9 106.2
angle
113.6 131.7 113.1 107.1 -126.4 79.9 -76.7 0.0
BC
C,
(“)
105.9 143.2 104.5 115.5 -30.2 -67.7 86.6 0.0
114.1p112.9 -118.2/45.1 94.0178.5 42.2/-51.1 8.2
58 TABLE 5 Geometrical parameters of bicyclo[ 5.1.01 octane (4) (CC form) MIND0/3(1)
Force field method This work
Bond length (A) C,--c* C;-c, G--c, C,-c, C,--c, C,-H, C,-H,C Bond angle c,c,c, c,w, c,c,cs c,c,c, c,c,c, C&P, C,C,H, H&t& I-WnH,C Dihedral
(“)
1.536 1.532 1.535 1.506 1.508 1.102 1.099
Expt.b
Previousa
1.540 1.542 1.543 1.534 1.539
1.506 1.516 1.516 1.670 1.479 1.115 1.120
113.5 113.9 113.8 119.7 119.0 116.9 113.6 118.3 106.1
112.0 113.8 115.1 118.3 117.4 115.3 113.8 118.9 105.0
121.6 121.5 132.2 121.7 118.4 117.5 98.3 106.3 101.4
109.5 122.6
118.2 108.6
123.7 133.2 144.4 99.0 -125.7 68.2 -42.5
1.503 1.546 1.522 1.511 1.507
113.3 112.4 118.2 121.4 119.3 120.5 115.0 119.0 107.5
angle (“)
; Y *a1 * 12 w 23 w34
122.3 108.4 -135.6 83.9 -66.3
119.2 107.5 -138.6 85.4 -62.3
111.4 121.5 118.0 108.0 -137.7 81.5 -64.1
aRef. 18. bRef. 19. ‘Averaged value. DISCUSSION
A preliminary investigation of the results obtained for bicyclo[ 5.1.0]octane and cycloheptene epoxide is interesting since a conformational study for the two molecules was previously accomplished by quantum mechanical calculations [ 11. The CC conformation of compound 4 appears to be once again the most stable; the calculated geometrical parameters are in good agreement with experimental data (Table 5); only the C,-C, distance is somewhat overestimated. An improvement is also achieved in the heat of formation (-0.21 kcal mol-’ calculated in this work; -3.8 kcai mol-’ experimental [ 201 ; 3.14 kcal mol-’ calculated in the previous work [1] ). The interconversion between the CC and BC forms should follow pathway c (Fig. 1) with an
59
TABLE 6 Geometrical parameters of cycloheptene
epoxide (5)
Force field method cc Bond length (A) C,--C* C*-c, C,-C, C,--C, C,--0, Cl-H, C,-Hnb
BC
1.528 1.530 1.533 1.472 1.436 1.104 1.099
1.536 1.530 1.532 1.472 1.436 1.106 1.099
MIND0/3 BP
C, 1.52511.527 1.52911.524 1.534/1.539 1.473 1.43611.436 1.104/1.105 1.099
1.500 1.520 1.519 1.616 1.356 1.122 1.122
Bond angle (” )
c*CA
119.2 112.9 112.8 124.7 121.8 109.8 113.8 106.0
119.0 111.4 112.6 119.2 126.7 109.0 113.9 106.6
114.3 133.6 116.9 109.4 -127.0 77.2 -72.6 0.0
105.3 144.6 107.1 117.7 -31.7 -66.8 83.9 0.0
c,w, w,c, o,c,c, c,c,c, O&P, C,C,H,
W3nb
108.0/117.0 109.5/110.6 116.2 117.31123.2 122.61124.4 109.7/108.3 115.0/114.5 105.7
122.7 111.9 120.8 127.7 117.9
Dihedral angle (“) p” Y Will WI2 w23 *34 *17
117.9
113.5/-113.4 -121.6143.4 93.7178.7 -40.9/-49.2 6.7
133.1 143.0 99.4 -5.7 -70.3 43.8 0.0
=For the other forms see Table 3 in ref. 1. bAveraged value.
energy barrier of 10.3 kcal mol-‘. The CB conformer, which is at a lower energy than the BC conformation, should also be present in the conformational equilibrium. In cycloheptene epoxide (5), a similar strain energy was found for the BC and C, conformers, whereas that of the CC form is slightly higher. The results of a CNDO/B calculation made with the geometries obtained by the force field method indicate that the BC form is more stable than the C, form by about 1.3 kcal mol-‘. These results confirm the preferred orientation of the oxiranic ring already found in the previous paper [ 11. The energy barrier in the interconversion process between the BC and C, forms through TS/l (pathway b) should be ca. 9.3 kcal mol-’ and that between the CC and C, forms through TS/3 (pathway d) ca. 5.3 kcal mol-‘. The free energy of activation (7.5-7.9 kcal mol-’ at 157-150 K) calculated from the observed NMR spectra [21] is halfway between the two energy barrier values.
60
TABLE7 Geometrical parameters of4-oxabicyclo[5.1.0]octane (6)
cc Bond
length
Cl--C2 C,--c, C,--0, C,-C, C,-C, C,-H, C,-Hna
cc
CB
Bond angle (O ) c,w, 111.6 C&O, 112.5 C,O,C, 114.9 C,C,C, 119.7 C,C,C* 118.0 C,C,H, 117.1 C,C,H, 113.7 HnCnHna 108.9
(A)
1.531 1.526 1.412 1.506 1.508 1.101 1.099
1.535 1.532 1.407 1.508 1.509 1.100 1.099
cc
CB Dihedral
114.7 112.6 115.1 120.6 116.7 117.7 114.0 107.6
angle
CB (” )
110.0 111.6 121.7 124.0 115.5 117.3 107.2 105.2 -133.8 -133.4 85.6 23.4 -73.9 71.6
01
P Y wg1 WI2 W2J a24
aAveragedvalue. The dipole moments calculated for the three conformations are nearly equal and in good agreement with the experimental values. On the other hand, the molar Kerr constants are strongly dependent on the molecular con.. formation. The measured value of ,(,K,) can be regarded as an average value connected with the molar Kerr constants of the individual forms by the relation: ,(,K,) = Cy=, Xi(mKi) where Xi is the molar fraction of the ith conformer [ 221. By considering a BC + C1 equilibrium in solution the following composition may be obtained from the values reported in Table 9: 89.5% (C,)-10.5% (BC). Even if the CC form is present, the equilibrium concentration of the three conformers in solution can be calculated from the relative conformational energies determined by the molecular mechanics method (the calculation is approximate because free enthalpy differences should be considered [23] ). The equilibrium mixture would be: 54.4% (Cl)-34.0% (BC)-11.6% (CC), for which a molar Kerr constant of -31.09 is calculated. This is close to the measured value (-25.46 f 1.70). TABLE8 Heatsof formation Form cc BC CB BB C, TS/l TS/2 TS/3 TS/4
1 -50.89 -50.75 -50.11 -35.34 -53.56 -48.18 -40.98 -40.37 -36.14
(AH;‘*)
inkcalmolP for compounds l-6 2 -78.15 -80.77 -75.25 -69.02 -82.32 -77.05 -75.32 -69.76 -58.20
3 -51.82 -51.82 -45.21 -44.80 -51.01 -42.68 -43.46 -40.79 -31.75
4 -0.21 4.24 1.85 14.27 3.23 8.04 11.99 10.09 13.31
5 -25.58 -26.22 -22.43 -18.25 -26.50 -17.24 -18.10 -20.25 -10.90
6 -24.89 -21.21 -22.51 -15.05 -21.05 -15.87 -14.41 -10.65 -8.33
61 TABLE
9
Dipole
moments
Compound
Form
1
2
(D) and molar Kerr constants Calculateda NX
cc BC CB
l&u,
lO’*,K
-3.54
-1.93 1.94 -0.73 --0.01
1.93 2.01 1.62 0.09
2.22
C,
-0.04 0.51 1.45 0.08
cc BC C,
0.0 0.0 0.13
0.80 -0.01 -0.67
1.34 3.81 1.70
1.56 3.81 1.83
2.48 + 0.05
0.15 0.19 0.16
2.13 1.11 1.59
2.13 1.13 1.60
1.74 1.84 1.78 1.69
1.98 1.96 1.98 1.97
0.14 -0.66 -0.99 -0.12
0.95 1.00 1.24 0.96
cc BC C,
0.0 0.0 -0.04
5
cc BC CB c,
0.0 0.0 0.0 0.0
cc BC CB C,
0.0 0.0 0.0 -0.01
aThe reference
-0.95 -0.66 -0.88 -1.00 0.94 0.75 -0.75 0.95
axes are directed
Expt.
talc.
0.0 0.0 0.0 0.02
3
6
PLY
Expt. P
/J
?- 0.02
-14.16 8.08
-30.06 -157.50 -24.40
-21.49
k 0.75
-66.85
2 1.85
-25.46
t 1.70
-41.70 -9.80 -25.72 3.87 2.10 * 0.01
-58.18 16.61 -21.61 -10.74 -4.21 -23.21 1.09
as follows
6 7
_______-_+y
1
:
!I
2
;
The preferred conformations of 3,5&trioxabicyclo[ 5.1.01 octane (2) are the C, and BC forms, as for compound 5. The calculated energy difference is 1.55 kcal mol-’ (by the force field method) and 0.82 kcal mol-’ (by the CNDO/B method for the same geometries). The electrostatic interaction between pairs of point charges calculated by the force field method stabilizes the C, conformer by a further 4.3/D kcal mol-‘. The solid compound, prepared by us following the procedure described in the literature [ 241, was recrystallized from petroleum ether as the BC conformer, as was established by the X-ray crystal structure determination [ 51. The agreement between calculated and measured geometric parameters is very satisfactory (Table 3). The proton magnetic resonance spectrum of compound 2 remains unchanged until -160°C; this fact has been justified by suggesting that the
62
molecule might be in a twist-boat conformation (C,) even allowing for the existence of an equilibrium BC + CC with a low energy barrier [4] . This equilibrium is precluded by our theoretical results, although an equilibrium BC =+ C1 with an energy barrier of about 7 kcal mall’ (through TS/l and CB as intermediates) is considered to be feasible. Supporting evidence for the presence of the twist-boat conformation has been inferred from the values of the coupling constants measured for the e3co- and e&o-isopropyl derivatives of compound 2 in deuterioacetone as 10% solutions [4]. Moreover, the experimental values of the dipole moment and of the molar Kerr constant in carbon tetrachloride as 25°C (Table 9) are halfway between those calculated for the Cl and BC forms. The following equilibrium compositions, may therefore, be estimated: 75% (Cl)-25% (BC) from P values and 68% (C,)-32% (BC) from ,K values. A higher percentage of the twist-boat conformation is expected from the relative energies of the two conformers. In any case, the C1 form should be preferred in solution while the BC form is favoured in the crystalline state. It is also interesting to note that the P and ,K values calculated for the BC form are almost identical using both the force field method and crystal geometries; this fact confirms the dependence of p and ,K on the conformation, whereas the dependence on bond distances and angles is slight. As far as the conformation of compound 1 is concerned, the results are rather contrasting. Force field calculations indicate that the C, form is more stable by 2.7-2.8 kcal mol-’ than the CC and BC forms; further stabilization is caused by electrostatic interactions (2.1/D and 2.7/D kcal mall’, respectively). The results obtained here for compounds 4 and 5, together with the knowledge that cycloheptene is more stable in the chair than in the twistboat conformation [25], indicate that the strain imposed by the cyclopropyl ring is not sufficient to raise the energy of the chair conformation (in the seven-membered ring) above that of the twist-boat form. On the other hand, the strain imposed by the epoxide ring makes the energies of the two forms almost equal. The anomeric effect [ 261 connected with dioxa substitution should increase the energy of the chair conformation (in which C-O bonds are synperiplanar) in compound 1 more than that of the twist-boat conformation (in which the C-O bonds are oriented gauche). However, experimental results show that this increase is small. In fact: (a) the dipole moment and molar Kerr constant values support a BC conformation for compound 1 in Ccl, solution (Table 9); (b) the coupling constants between the C, and C2 hydrogens of the 4-isopropyl derivatives are consistent with a chair conformation of the seven membered ring (CC for the exo-isomer and BC for the endo-isomer [4] ); (c) the two molecules in the asymmetric unit of the crystals of syn-B,&dichloro-4-phenyl-3,5-dioxabicyclo[ 5.1.01 octane [ 271 have the seven-membered ring in the chair conformation with the dichloromethylene group in the least-sterically restricted site (CC); and (d) the activation energy of 10.7 kcal mall’ calculated for the interconversion of BC to CC forms for compound 1, from the coalescence temperature in the proton
63
NMR spectra [4], is consistent with the energy barrier calculated for pathway c of Fig. 1 (10.5 kcal mol-‘). One can only guess that the anomeric effect is somewhat overestimated in our force field program and/or that the calculation of the electrostatic interactions is inadequate. This hypothesis should also justify the high value calculated for the equilibrium concentration of the C1 conformation of compound 2 (see above). The results obtained for compounds 3 and 6 are in line with those of the other compounds. 4-Oxa substitution in the bicyclo[ 5.1.01 octane molecule does not significantly modify the energy differences between the most stable (CC) and the other conformers nor the height of the barrier to interconversion between the CC and BC forms (10.5 kcal mall’), even if, in this case, pathway b is preferred to pathway c, followed by compound 4. 4-Oxa substitution in the cycloheptene epoxide molecule makes the strain energies of the CC, BC and C1 forms even more similar. Greater stabilization (by about 1 kcal mol-‘) is found for the BC conformer by CNDO/B calculations or by considering the electrostatic interactions, in agreement with the results obtained for compound 5. The energy barrier to the interconversion process between the BC and C1 forms through TS/l is 9.1 kcal mall’ (9.3 kcal mol-’ in compound 5); that between the CC and C1 forms is 8.4 kcal mol-’ via pathway b (7.5 kcal mall’ in compound 5) and 11.0 kcal mol-’ via pathway d (5.3 kcal mol-’ in compound 5). The theoretical dipole moments and, especially, the molar Kerr constants calculated for the conformers of compounds 3 and 6 are somewhat different; a conformational analysis for these species will only be possible when the necessary experimental data become available. ACKNOWLEDGEMENTS
Financial support from the Italian C.N.R. is gratefully acknowledged. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14
R. Todeschini and G. Favini, J. Mol. Struct., 64 (1980) 47. R. G. Bingham, M. J. S. Dewar and D. H. Lo, J. Am. Chem. Sot., 97 (1975) 1285. R. Todeschini, D. Pitea and G. Favini, J. Mol. Struct., 71 (1981) 279. M. H. Gianni, R. Cody, M. R. Asthana, K. Wursthom, P. Patanode and H. G. Kuivila, J. Org. Chem., 42 (1977) 365. T. Pilati and M. Simonetta, Cryst. Struct. Comm., 10 (1981) 265. D. Pitea, F. Gatti and G. Favini, to be published. QCPE program 348. N. L. Alhnger and D. Y. Chung, J. Am. Chem. Sot., 98 (1976) 6798. M. J. Bovill, D. J. Chadwick, I. 0. Sutherland and D. Watkin, J. Chem. Sot., Perkin Trans. 2, (1980) 1529. M. A. Robb, W. J. Haines and I. G. Csizmadia, J. Am. Chem. Sot., 95 (1973) 42. N. L. Allinger, S. H. M. Chang, D. H. Glaser and H. Honig, Isr. J. Chem., 20 (1980) 51. N. L. Allinger, J. Am. Chem. Sot., 99 (1977) 8127. D. H. Wertz and N. L. Ailinger, Tetrahedron, 30 (1974) 1579. A. D. Walsh, Trans. Faraday Sot., 45 (1949) 179.
64 15 16 17 18 19 20 21 22 23 24 25 26 27
C. A. Coulson and W. E. Moffitt, Philos. Mag., 40 (1949) 1. J. Lehn and G. Ouriason, Bull. Sot. Chim. Fr., (1963) 1113. L. J. Collins and D. N. Kirk, Tetrahedron Lett., (1970) 1547. D. E. Brant and P. J. Flory, J. Am. Chem. Sot., 87 (1965) 2791. R. A. Kershaw, Jr., Diss. Abstr. Int., B35 (1975) 5456. S. Chang, D. McNally, S. Shary-Tehrany, M. J. Hickey and R. H. Body, J. Am. Chem sot., 92 (1970) 3109. K. L. Servis, E. A. Noe, N. R. Easton, Jr. and F. A. L. Anet, J. Am. Chem. Sot., 96 (1974) 4185. M. J. Aroney, Angew. Chem., Int. Ed. Engl., 16 (1977) 663. Y. Brunel, C. Coulombeau and A. Rassat, Nouv. J. Chim., 4 (1980) 663. K. C. Brannock and G. Lappin, J. Org. Chem., 21 (1956) 1366. G. Favini and A. Nava, Theor. Chim. Acta (Berlin), 31 (1973) 261. S. Wolfe, J. Chem. Sot. B, 13 (1971) 136. G. R. Clark and G. J. Palenik, J. Chem. Sot., Perkin Trans. 2, (1973) 194.
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Printed
in The Netherlands
CONFORMATION OF BICYCLO [n.l.O] DERIVATIVES Part 3. Dioxa- and trioxa-bicyclo[ 5.1.01 octanes
GIORGIO ROBERTO Institute
FAVINI, DEMETRIO TODESCHINI of Physical
(Received
Chemistry,
PITEA, University
MANUELA
SOTTOCORNOLA
of Milan, Milan
and
(Italy)
21 April 1981)
ABSTRACT The conformational geometries and possible interconversion paths for some oxa derivatives of bicyclo[ 5.1.0] octane have been studied by the molecular mechanics method. The theoretical results are compared with the experimental data for the molecular geometry of bicyclo[ 5.1.01 octane and 3,5,8-trioxabicyclo[ 5.1.01 octane, the free energy of activation for cycloheptene epoxide and 3,5-dioxabicyclo[5.1.O]octane, the dipole moments and molar Kerr constants in solution for cycloheptene epoxide, 3,5-dioxaand 3,5,8-trioxabicyclo[ 5.l.Oloctane. INTRODUCTION
In Part 1 of this series [l] , quantum mechanical calculations of the semiempirical kind (MIND0/3 method [ 21) were performed in order to study the conformational equilibrium and the possible interconversion pathways of bicyclo[ 5.1.01 octane and cycloheptene epoxide. In Part 2 [3], the conformational geometries of norcarane and cyclohexene epoxide were studied by both quantum mechanical and molecular mechanics calculations in view of an extension of the research to some dioxa- and trioxa-bicyclooctanes. Conformational analysis of derivatives of this kind has received considerable attention from Gianni et al. [4], who have considered above all the effects of the introduction of a double bond or of an epoxide ring on the conformation of 1,3-dioxacycloheptanes. Their conclusions were supported by studies of low-temperature proton magnetic resonance spectra. However, the conformational geometries of these compounds are far from conclusively resolved, in spite of the X-ray crystal structure determination performed in our laboratories [5] on 3,5,8-trioxabicyclo[ 5.1.01 octane (1,3-dioxacyclohept-5-ene epoxide). In this paper, the molecular mechanics method has been chosen for a systematic study of the conformational properties of the following compounds: 3,5dioxabicyclo[ 5.1.01 octane (l), 3,5,8-trioxabicyclo[ 5.1.01 octane 0166-1280/82/0000-0000/$02.75
o 1982
Elsevier
Scientific
Publishing
Company
54
(2), 4,&dioxabicyclo[ 51.01 octane (3), together with bicyclo[5.1.0] octane (4) and cycloheptene epoxide (5) (previously studied only by the MIND0/3 method [l] ), and 4-oxabicyclo [ 5 .l .O] octane (6). Theoretical results have also been analysed on the grounds of experimental data for dipole moments and molar Kerr constants obtained simultaneously in our laboratories [ 61. CALCULATIONS
A modified version of the force field method of Schleyer-Andose-Mislow [ 73 was used, including the additional parameters suggested by Allinger and Chung [ 81 for oxa compounds. Difficulties were encountered with the pattern search minimization technique and, consequently, the steepest descent method already contained in the program was adopted. The minimization loop was terminated when the energy decrease relative to the preceding loop fell below 0.01 kcal mall’. The description of the electron density around an oxygen atom in molecular mechanics calculations has given rise to much discussion. In fact, the electron density may be considered to be spherical and, hence, centered on the oxygen nucleus, or the lone pairs of electrons may be treated explicitly. The former model was used recently in the WBFF force field [9] ; the latter model was preferred by other authors [8, lo] and adopted by us in Part 2 [ 31. An improved molecular mechanics version for systems containing oxygen atoms has been proposed [ 111 as an extension of the MM2 hydrocarbon force field [ 121. Since our program is related to Allinger’s MM1 force field [ 131, we preferred to leave unchanged the previous parameterization [ 81, which, moreover, supplied good results in Part 2 [ 31. In order to reduce the high values obtained for the bending strain and the steric energy of three-membered compounds, we decided to change the values of r. for C-C and C-O bond lengths and of 0 o for CCC, CC0 and COC bond angles in the three-membered ring by leaving unchanged the force constant values (both parameters should be varied at the same time). The new values (Table 1) were empirically obtained so as to fit experimental AH2.98 values of cyclopropane, ethylene oxide and their methyl derivatives. The decrease in r. (for C-C distance) and in B. values with respect to standard values is in line with the variation of the carbon hybridization, according to the theoretical models of Walsh [ 141 and Coulson and Moffitt
E151.
For molecules that contain two or more heteroatoms, it is necessary to consider the electrostatic interactions which occur between them, in addition to the non-bonded interactions described by the usual potential functions. To calculate the electrostatic interactions between the dipoles in the molecule, they can be placed at the midpoints of the bond concerned and the interaction evaluated by Jean’s equation [ 8, 161. Alternatively, electrostatic interactions may be calculated as coulombic interactions from the relationship [9, 171 E = 332.17 zij(qiqj/r@) kcal mall’, where qi and Q are the
55 TABLE Force
1 field parameters
for three-membered
Compound
Parameter
Bond C-C Angle C-C-C
Cyclopropane Methylcyclopropane 1,2-cis-Dimethylcyclopropane Ethylene oxide
Propene
oxide
aValues
of Table
rings
Bond C-O Angle CC-O Angle C-O-C
Value
AHi98
Expt.a
12.53
12.74
7.41 1.69 -12.66
6.19 0.60 -12.60
-18.78
-22.20
r0 = 1.472 so = 86.4
= 1.436 e0 = 84.7 8, = 83.0 r.
(kcal mol.I)
CalC.
1 in ref. 2.
partial charges on atoms i and j derivable from molecular orbital calculations (CNDO/B method), D is the dielectric constant and rij is the interatomic distance in a (between atoms i and j). Values in the range 1.5-5 have been suggested for the dielectric constant D [9, 11, 181; although the value chosen is not critical since electrostatic interactions represent a relatively small part of the non-bonded interactions. Since our program did not include electrostatic interactions in the calculation of the strain energy, we used the latter more simple procedure in order to evaluate the weight of the electrostatic interactions in the different molecular conformations. Theoretical dipole moments and molar Kerr constants were calculated by using the bond moments and the bond polarizabilities reported in Table 2 of ref. 2. For the C-O bond in a seven-membered ring, the values used were: 1-1= 0.59 D; b, = 0.89 A3; bT = b v - 0.46 A3. Details of the calculations will be described in ref. 6. All the calculations were carried out on a UNIVAC 1100/81 computer at CILEA, Milan. RESULTS
As in Part 1 [ 11, four C, symmetry forms were considered* (CC, BC, CB and BB), together with: a C1 form with a twist-boat conformation in the seven-membered ring; two transition states (TS/l and TS/2) with six coplanar atoms (1,2,3,5,6,7 positions in the molecular scheme of Fig. 1) intermediate in the symmetrical interconversion pathway between the BC and CB (TS/l) or between the CC and BB forms (TS/2); and two transition states (TS/3 and TS/4) with five coplanar atoms (2,3,4,5,6) intermediate in the symmetrical interconversion pathway between the CC and CB forms (TS/3) or between the BC and BB forms (TS/4). *The following abbreviations will be used throughout: chair-boat (CB); boat-boat (BB).
chair-chair
(CC);
boat-chair
(BC);
56
k7 TS/4
Fig.1.Interconversion pathways. TABLE2 Geometrical
parameters
of 3,5-dioxabicyclo[5.1.O]octane (1)
cc Bondlength C,--c* C,0, 0,-C, C,-C, C,-C" Cl--H, C,-Hna
CB
BC 1.530 1.403 1.405 1.506 1.508 1.101 1.101
1.529 1.404 1.405 1.508 1.507 1.102 1.101
C, 1.528 1.409 1.405 1.504 1.507 1.100 1,101
1.534/1.533 1.407/1.408 1.406/1.405 1.507 1.510/1.503 1.100/1.101 1.101
Bond angle (” ) 115.6 114.3 110.1 119.9 118.7 118.5 117.5 113.0 104.3 106.9
117.7 114.1 108.8 118.5 123.6 118.6 115.0 114.0 107.6 107.2
115.1 114.6 114.0 119.5 115.2 118.3 116.7 115.1 104.4 106.5
109.9 130.0 112.8 108.0 -125.5 83.6 -79.2 0.0
106.1 145.1 105.1 114.5 -33.5 -70.6 89.4 0.0
110.9 123.5 121.7 103.8 -133.9 25.8 67.6 0.0
c,c,o,
CP,C, O,C,O, C,C,C, C,C,C* H&H, C,C,H, C,C,H, H&H, H,C,H., Dihedral 01
0 Y Wtll WI2 a23 w34 WI7
111.5/114.6 112.5/112.9 109.9 116.4/120.5 118.4/119.2 118.5 116.8D14.8 114.1/115.3 104.2l107.6 109.6
angle (“)
aAveragedvalue.
108.9/-108.3 -111.4/34.2 97.u91.7 -49.0/-50.7 4.7
57 TABLE 3 Geometrical parameters of 3,5,8-trioxabicyclo[5.l.O]octane
Bondlength c,--c, c,--0, oi-c, c,-c, c,--0, c,--H, c,--H,b Bond
angle
c,c*o,
c*o,c. o,c,o, o,c,c, CFIC2 Osc,H, c&,H, HncnHnb
ExPt.a BC
BC
C,
(2) BC
C,
ExPLa BC
Dihedralangle(O) 1.524/1.521 1.408/1.404 1.405/1.408 1.474 1.436/1.436 1.103/1.104 1.104
1.532 1.407 1.405 1.473 1.436 1.104 1.103
1.496
1.420 1.405 1.457 1.449
; Y Wlil 109.1/-107.8 WI2 -120.8/38.2 *23 98.3/85.5 w34 -42.3/-53.5 WI7 10.8
105.1 143.8 103.8 114.7 -31.1 -71.5 90.3 0.0
105.4 148.1 105.7 118.2 -38.4 -64.2 88.1 0.0
(“)
109.1/116.7 112.0/113.3 112.2 114.8/124.4 118.0/120.4 110.5/108.9 116.9/115.3 107.5
117.1 113.1 108.4 118.1 123.9 109.4 115.1 107.4
116.4 114.4 112.3 119.1 127.0 113.5 116.6 109.0
aValues from ref. 5. bAveraged value.
Geometrical parameters calculated for the most stable conformations of compounds l-6 are given in Tables 24 together with experimental data (where available) and previous theoretical values. Geometrical parameters of the other conformations and of the transition states are available on request (to the authors). The calculated heats of formation of all the conformations and transition states are collected in Table 8. Dipole moments and molar Kerr constants for the most stable conformations are given in Table 9 and compared with experimental data. TABLE 4 Geometrical parameters of 4,&dioxabicyclo[
cc Bond
length
Ck-c, c*-C, c,*, CL--C, c,--0" c,--H, C,-H,a
BC
5.1.01 octane (3) cc
C,
(rr,
Dihedral
1.525 1.525 1.410 1.475 1.436 1.104 1.100
Bond angle(") c,c,c, 117.8 c&%0, 112.2 c,o,c, 114.1 O&,C, 123.5 C&,C, 119.6 O&,H, 110.5 c,c,H, 114.3 Hnc,Hna 106.4
aAveraged value.
1.534 1.526 1.412 1.472 1.436 1.105 1.101
118.2 111.3 115.1 119.1 124.9 109.2 114.5 107.4
1.52311.522 1.524/1.519 1.411/1.413 1.472 1.436/1.436 1.104/1.105 1.100
106.0/115.4 112.9/113.2 116.2 115.4/122.3 122.41123.8 109.5/108.5 115.5/114.9 106.2
angle
113.6 131.7 113.1 107.1 -126.4 79.9 -76.7 0.0
BC
C,
(“)
105.9 143.2 104.5 115.5 -30.2 -67.7 86.6 0.0
114.1p112.9 -118.2/45.1 94.0178.5 42.2/-51.1 8.2
58 TABLE 5 Geometrical parameters of bicyclo[ 5.1.01 octane (4) (CC form) MIND0/3(1)
Force field method This work
Bond length (A) C,--c* C;-c, G--c, C,-c, C,--c, C,-H, C,-H,C Bond angle c,c,c, c,w, c,c,cs c,c,c, c,c,c, C&P, C,C,H, H&t& I-WnH,C Dihedral
(“)
1.536 1.532 1.535 1.506 1.508 1.102 1.099
Expt.b
Previousa
1.540 1.542 1.543 1.534 1.539
1.506 1.516 1.516 1.670 1.479 1.115 1.120
113.5 113.9 113.8 119.7 119.0 116.9 113.6 118.3 106.1
112.0 113.8 115.1 118.3 117.4 115.3 113.8 118.9 105.0
121.6 121.5 132.2 121.7 118.4 117.5 98.3 106.3 101.4
109.5 122.6
118.2 108.6
123.7 133.2 144.4 99.0 -125.7 68.2 -42.5
1.503 1.546 1.522 1.511 1.507
113.3 112.4 118.2 121.4 119.3 120.5 115.0 119.0 107.5
angle (“)
; Y *a1 * 12 w 23 w34
122.3 108.4 -135.6 83.9 -66.3
119.2 107.5 -138.6 85.4 -62.3
111.4 121.5 118.0 108.0 -137.7 81.5 -64.1
aRef. 18. bRef. 19. ‘Averaged value. DISCUSSION
A preliminary investigation of the results obtained for bicyclo[ 5.1.0]octane and cycloheptene epoxide is interesting since a conformational study for the two molecules was previously accomplished by quantum mechanical calculations [ 11. The CC conformation of compound 4 appears to be once again the most stable; the calculated geometrical parameters are in good agreement with experimental data (Table 5); only the C,-C, distance is somewhat overestimated. An improvement is also achieved in the heat of formation (-0.21 kcal mol-’ calculated in this work; -3.8 kcai mol-’ experimental [ 201 ; 3.14 kcal mol-’ calculated in the previous work [1] ). The interconversion between the CC and BC forms should follow pathway c (Fig. 1) with an
59
TABLE 6 Geometrical parameters of cycloheptene
epoxide (5)
Force field method cc Bond length (A) C,--C* C*-c, C,-C, C,--C, C,--0, Cl-H, C,-Hnb
BC
1.528 1.530 1.533 1.472 1.436 1.104 1.099
1.536 1.530 1.532 1.472 1.436 1.106 1.099
MIND0/3 BP
C, 1.52511.527 1.52911.524 1.534/1.539 1.473 1.43611.436 1.104/1.105 1.099
1.500 1.520 1.519 1.616 1.356 1.122 1.122
Bond angle (” )
c*CA
119.2 112.9 112.8 124.7 121.8 109.8 113.8 106.0
119.0 111.4 112.6 119.2 126.7 109.0 113.9 106.6
114.3 133.6 116.9 109.4 -127.0 77.2 -72.6 0.0
105.3 144.6 107.1 117.7 -31.7 -66.8 83.9 0.0
c,w, w,c, o,c,c, c,c,c, O&P, C,C,H,
W3nb
108.0/117.0 109.5/110.6 116.2 117.31123.2 122.61124.4 109.7/108.3 115.0/114.5 105.7
122.7 111.9 120.8 127.7 117.9
Dihedral angle (“) p” Y Will WI2 w23 *34 *17
117.9
113.5/-113.4 -121.6143.4 93.7178.7 -40.9/-49.2 6.7
133.1 143.0 99.4 -5.7 -70.3 43.8 0.0
=For the other forms see Table 3 in ref. 1. bAveraged value.
energy barrier of 10.3 kcal mol-‘. The CB conformer, which is at a lower energy than the BC conformation, should also be present in the conformational equilibrium. In cycloheptene epoxide (5), a similar strain energy was found for the BC and C, conformers, whereas that of the CC form is slightly higher. The results of a CNDO/B calculation made with the geometries obtained by the force field method indicate that the BC form is more stable than the C, form by about 1.3 kcal mol-‘. These results confirm the preferred orientation of the oxiranic ring already found in the previous paper [ 11. The energy barrier in the interconversion process between the BC and C, forms through TS/l (pathway b) should be ca. 9.3 kcal mol-’ and that between the CC and C, forms through TS/3 (pathway d) ca. 5.3 kcal mol-‘. The free energy of activation (7.5-7.9 kcal mol-’ at 157-150 K) calculated from the observed NMR spectra [21] is halfway between the two energy barrier values.
60
TABLE7 Geometrical parameters of4-oxabicyclo[5.1.0]octane (6)
cc Bond
length
Cl--C2 C,--c, C,--0, C,-C, C,-C, C,-H, C,-Hna
cc
CB
Bond angle (O ) c,w, 111.6 C&O, 112.5 C,O,C, 114.9 C,C,C, 119.7 C,C,C* 118.0 C,C,H, 117.1 C,C,H, 113.7 HnCnHna 108.9
(A)
1.531 1.526 1.412 1.506 1.508 1.101 1.099
1.535 1.532 1.407 1.508 1.509 1.100 1.099
cc
CB Dihedral
114.7 112.6 115.1 120.6 116.7 117.7 114.0 107.6
angle
CB (” )
110.0 111.6 121.7 124.0 115.5 117.3 107.2 105.2 -133.8 -133.4 85.6 23.4 -73.9 71.6
01
P Y wg1 WI2 W2J a24
aAveragedvalue. The dipole moments calculated for the three conformations are nearly equal and in good agreement with the experimental values. On the other hand, the molar Kerr constants are strongly dependent on the molecular con.. formation. The measured value of ,(,K,) can be regarded as an average value connected with the molar Kerr constants of the individual forms by the relation: ,(,K,) = Cy=, Xi(mKi) where Xi is the molar fraction of the ith conformer [ 221. By considering a BC + C1 equilibrium in solution the following composition may be obtained from the values reported in Table 9: 89.5% (C,)-10.5% (BC). Even if the CC form is present, the equilibrium concentration of the three conformers in solution can be calculated from the relative conformational energies determined by the molecular mechanics method (the calculation is approximate because free enthalpy differences should be considered [23] ). The equilibrium mixture would be: 54.4% (Cl)-34.0% (BC)-11.6% (CC), for which a molar Kerr constant of -31.09 is calculated. This is close to the measured value (-25.46 f 1.70). TABLE8 Heatsof formation Form cc BC CB BB C, TS/l TS/2 TS/3 TS/4
1 -50.89 -50.75 -50.11 -35.34 -53.56 -48.18 -40.98 -40.37 -36.14
(AH;‘*)
inkcalmolP for compounds l-6 2 -78.15 -80.77 -75.25 -69.02 -82.32 -77.05 -75.32 -69.76 -58.20
3 -51.82 -51.82 -45.21 -44.80 -51.01 -42.68 -43.46 -40.79 -31.75
4 -0.21 4.24 1.85 14.27 3.23 8.04 11.99 10.09 13.31
5 -25.58 -26.22 -22.43 -18.25 -26.50 -17.24 -18.10 -20.25 -10.90
6 -24.89 -21.21 -22.51 -15.05 -21.05 -15.87 -14.41 -10.65 -8.33
61 TABLE
9
Dipole
moments
Compound
Form
1
2
(D) and molar Kerr constants Calculateda NX
cc BC CB
l&u,
lO’*,K
-3.54
-1.93 1.94 -0.73 --0.01
1.93 2.01 1.62 0.09
2.22
C,
-0.04 0.51 1.45 0.08
cc BC C,
0.0 0.0 0.13
0.80 -0.01 -0.67
1.34 3.81 1.70
1.56 3.81 1.83
2.48 + 0.05
0.15 0.19 0.16
2.13 1.11 1.59
2.13 1.13 1.60
1.74 1.84 1.78 1.69
1.98 1.96 1.98 1.97
0.14 -0.66 -0.99 -0.12
0.95 1.00 1.24 0.96
cc BC C,
0.0 0.0 -0.04
5
cc BC CB c,
0.0 0.0 0.0 0.0
cc BC CB C,
0.0 0.0 0.0 -0.01
aThe reference
-0.95 -0.66 -0.88 -1.00 0.94 0.75 -0.75 0.95
axes are directed
Expt.
talc.
0.0 0.0 0.0 0.02
3
6
PLY
Expt. P
/J
?- 0.02
-14.16 8.08
-30.06 -157.50 -24.40
-21.49
k 0.75
-66.85
2 1.85
-25.46
t 1.70
-41.70 -9.80 -25.72 3.87 2.10 * 0.01
-58.18 16.61 -21.61 -10.74 -4.21 -23.21 1.09
as follows
6 7
_______-_+y
1
:
!I
2
;
The preferred conformations of 3,5&trioxabicyclo[ 5.1.01 octane (2) are the C, and BC forms, as for compound 5. The calculated energy difference is 1.55 kcal mol-’ (by the force field method) and 0.82 kcal mol-’ (by the CNDO/B method for the same geometries). The electrostatic interaction between pairs of point charges calculated by the force field method stabilizes the C, conformer by a further 4.3/D kcal mol-‘. The solid compound, prepared by us following the procedure described in the literature [ 241, was recrystallized from petroleum ether as the BC conformer, as was established by the X-ray crystal structure determination [ 51. The agreement between calculated and measured geometric parameters is very satisfactory (Table 3). The proton magnetic resonance spectrum of compound 2 remains unchanged until -160°C; this fact has been justified by suggesting that the
62
molecule might be in a twist-boat conformation (C,) even allowing for the existence of an equilibrium BC + CC with a low energy barrier [4] . This equilibrium is precluded by our theoretical results, although an equilibrium BC =+ C1 with an energy barrier of about 7 kcal mall’ (through TS/l and CB as intermediates) is considered to be feasible. Supporting evidence for the presence of the twist-boat conformation has been inferred from the values of the coupling constants measured for the e3co- and e&o-isopropyl derivatives of compound 2 in deuterioacetone as 10% solutions [4]. Moreover, the experimental values of the dipole moment and of the molar Kerr constant in carbon tetrachloride as 25°C (Table 9) are halfway between those calculated for the Cl and BC forms. The following equilibrium compositions, may therefore, be estimated: 75% (Cl)-25% (BC) from P values and 68% (C,)-32% (BC) from ,K values. A higher percentage of the twist-boat conformation is expected from the relative energies of the two conformers. In any case, the C1 form should be preferred in solution while the BC form is favoured in the crystalline state. It is also interesting to note that the P and ,K values calculated for the BC form are almost identical using both the force field method and crystal geometries; this fact confirms the dependence of p and ,K on the conformation, whereas the dependence on bond distances and angles is slight. As far as the conformation of compound 1 is concerned, the results are rather contrasting. Force field calculations indicate that the C, form is more stable by 2.7-2.8 kcal mol-’ than the CC and BC forms; further stabilization is caused by electrostatic interactions (2.1/D and 2.7/D kcal mall’, respectively). The results obtained here for compounds 4 and 5, together with the knowledge that cycloheptene is more stable in the chair than in the twistboat conformation [25], indicate that the strain imposed by the cyclopropyl ring is not sufficient to raise the energy of the chair conformation (in the seven-membered ring) above that of the twist-boat form. On the other hand, the strain imposed by the epoxide ring makes the energies of the two forms almost equal. The anomeric effect [ 261 connected with dioxa substitution should increase the energy of the chair conformation (in which C-O bonds are synperiplanar) in compound 1 more than that of the twist-boat conformation (in which the C-O bonds are oriented gauche). However, experimental results show that this increase is small. In fact: (a) the dipole moment and molar Kerr constant values support a BC conformation for compound 1 in Ccl, solution (Table 9); (b) the coupling constants between the C, and C2 hydrogens of the 4-isopropyl derivatives are consistent with a chair conformation of the seven membered ring (CC for the exo-isomer and BC for the endo-isomer [4] ); (c) the two molecules in the asymmetric unit of the crystals of syn-B,&dichloro-4-phenyl-3,5-dioxabicyclo[ 5.1.01 octane [ 271 have the seven-membered ring in the chair conformation with the dichloromethylene group in the least-sterically restricted site (CC); and (d) the activation energy of 10.7 kcal mall’ calculated for the interconversion of BC to CC forms for compound 1, from the coalescence temperature in the proton
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NMR spectra [4], is consistent with the energy barrier calculated for pathway c of Fig. 1 (10.5 kcal mol-‘). One can only guess that the anomeric effect is somewhat overestimated in our force field program and/or that the calculation of the electrostatic interactions is inadequate. This hypothesis should also justify the high value calculated for the equilibrium concentration of the C1 conformation of compound 2 (see above). The results obtained for compounds 3 and 6 are in line with those of the other compounds. 4-Oxa substitution in the bicyclo[ 5.1.01 octane molecule does not significantly modify the energy differences between the most stable (CC) and the other conformers nor the height of the barrier to interconversion between the CC and BC forms (10.5 kcal mall’), even if, in this case, pathway b is preferred to pathway c, followed by compound 4. 4-Oxa substitution in the cycloheptene epoxide molecule makes the strain energies of the CC, BC and C1 forms even more similar. Greater stabilization (by about 1 kcal mol-‘) is found for the BC conformer by CNDO/B calculations or by considering the electrostatic interactions, in agreement with the results obtained for compound 5. The energy barrier to the interconversion process between the BC and C1 forms through TS/l is 9.1 kcal mall’ (9.3 kcal mol-’ in compound 5); that between the CC and C1 forms is 8.4 kcal mol-’ via pathway b (7.5 kcal mall’ in compound 5) and 11.0 kcal mol-’ via pathway d (5.3 kcal mol-’ in compound 5). The theoretical dipole moments and, especially, the molar Kerr constants calculated for the conformers of compounds 3 and 6 are somewhat different; a conformational analysis for these species will only be possible when the necessary experimental data become available. ACKNOWLEDGEMENTS
Financial support from the Italian C.N.R. is gratefully acknowledged. REFERENCES 1 2 3 4 5 6 7 8 9 10 11 12 13 14
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