Journal of Molecular Structure (Theo&em), 204 (1990) 219-227 Elsevier Science Publishers B.V., Amsterdam - Printed in The Netherlands

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A GRADIENT AB INITIO STUDY OF THE GEOMETRICAL TRENDS OF 1,2-DIOXOCYCLOPENTANE AND OTHER CYCLIC PEROXIDES

LUIS CARBALLEIRA, RICARDO A. MOSQUERA and MIGUEL A. RfOS

Departamento de Quimica F&a, Unioersidad de Santiago, Santiago de Compostela, Galicia (Spain)

(Received 27 January 1989)

ABSTRACT

The geometries of certain conformations of 1,2-dioxocyclopentane, 1,2-dioxocyclohexane and 2,3-dioxobicyclo [2.2.l]heptane have been obtained by complete optimization at the SCF level using the 4-21G and 4-21G(O*) bases. The results for 1,2-dioxocyclohexane are compared with microwave findings, and a new set of geometric parameters derived from the ab initio parameters is used for fitting to the experimental rotation constants.

INTRODUCTION

In an earlier systematic study [l-3] of the conformation of alkyl peroxides aimed at the construction of a molecular-mechanics [ 41 force field, it was con- cluded that it would be desirable for the geometries of certain cyclic compounds to be studied by ab initio methods with complete optimization in order to sup- plement currently available information [ 5,6]. We have accordingly used such methods to study 1,2dioxocyclopentane (dioxolane, DOCP), 1,2-dioxocyclo- hexane (dioxane, DOCH) and 2,3dioxobicyclo [2.2.l]heptane (DOBH). DOCP has previously been studied by microwave spectroscopy (although without its complete geometry being reported ) [ 71, and by ab initio methods with incomplete optimization using the bases 4-31G and 6-31G and aimed at determining the potential hypersurface and the number of conformers of the molecule [ 81. While the only available structural data concerning DOCH and DOBH are estimations of the C-O-O-C dihedral angle from the photoelec- tronic spectra [ 9,101 and molecular-mechanics calculations [ 2,3] carried out using a set of parameters [ 1,3] expressly incorporated into the original MM2(80) program [ll].

The calculations were performed using the method [ 121 and program de- veloped by Pulay [ 131 using the bases 4-21G [ 141 and 4-21G (0*) [ 151 and the usual convergence criteria [ 161. Knowing the limitations of bond-length

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calculations with these bases and in the presence of important electron-cor- relation effects, our interest centred mainly on the results concerning the di- hedral and valency angles, for which 4-21G (0* ) has proved reliable in studies of a number of linear peroxides [ 1,3,15]. The influence of the bond lengths on these angles was estimated by comparing the results of 4-21G//4-21G and 4-21G(O*)//4-21G(O*) studies.

RESULTS AND DISCUSSION

1,2-Dioxocycbpentan (Fig. 1)

In view of Cremer’s recent ab initio results [ 81, a single twist conformer with C, symmetry was considered. The geometry of this conformer was optimized subject only to the constraints imposed by its symmetry. Table 1 lists both the 4-21G//4-21G and 4-21G(O*)//4_21G(O*) results. In general, the inclusion of polarization functions for the oxygen atoms affected bond lengths more than other geometrical elements. Whereas bond lengths and dihedral angles involv- ing oxygen atoms were more affected than other elements of these types, the most affected valency angle was C5-C4-C3.

The use of polarization functions reduced the O-O bond length by 0.0617 A and the C-O distances by 0.0389 A as compared with an increase of just 0.0005 A in the C-C distances. The C-H bonds involving C3 or C5 were much more affected than the C-H bonds. The fact that the 4-21G (0*) the axial bonds C3- H7 and C5-HlO were longer than the corresponding equatorial bonds C3-H6 and C5-Hll (1.0866 as against 1.0797 A) may be interpreted as reflecting the anomeric effect of the oxygen atoms’ lone pairs [ 17,181.

As mentioned above, the valency angle for which the two sets of results differ most is C5-C4-C3, which is over 2’ narrower using the 4-21G (0* ) than using the 4-21G basis. The discrepancies in the other valency angles are all about 0.5” for ring angles and about 1.0” for angles involving hydrogen atoms. In keeping with the anomeric effect noted above [ 181, the C-O-H angles involv- ing axial hydrogen atoms (H7-C3-02 and HlO-C5-01) are wider than those involving equatorial hydrogens (H6-C3-02 and Hll-C5-01 ), with values of

Fig. 1. Structure of 1,2-dioxocyclopentane (DOCP).

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TABLE 1

Geometry of 1,2-dioxocyclopentane (Fig. 1) as obtained by 4-21G//4-21G and 4-21G(0*)//4- 2lG(O*) calculations

4-21G(O*) 4-21G 4-21G(O*) 4-21G

Bond lengths (A) 02-01 C3-02 c4-c3 c5-01 c5-c4 H6-C3 H7-C3 H&-C4 H9-C4 HlO-C5 Hll-C5

Bond angles (“) C3-02-01 C4-C3-02 C5-01-02 c5-c4-c3 c4-c5-01 H6-C3-02 H6-C3-C4 H7-C3-02 H7-C3-C4 H7-C3-H6 H8-C4-C3 H8-C4-C5 H9-C4-C3 H9-C4-C5 H9-C4-H8 HlO-C5-01 HlO-C5-C4

1.4132 1.4749 1.4294 1.4683 1.5483 1.5478 1.4294 1.4683 1.5483 1.5478 1.0797 1.0772 1.0806 1.0772 1.0795 1.0792 1.0795 1.0792 1.0806 1.0772 1.0797 1.0772

102.46 101.93 104.29 104.67 102.46 101.93 100.28 102.37 104.29 104.67 106.93 106.01 113.72 113.82 110.00 109.04 111.43 111.94 110.19 110.89 112.20 111.74 111.50 110.99 111.50 110.99 112.20 111.74 108.99 108.93 110.00 109.04 111.43 111.94

Hll-C5-01 106.93 106.01 Hll-C5-C4 113.72 113.82 Hll-C5-HlO 110.19 110.89

C3-02-Ol-C5 52.61 50.16 C4-C3-02-01 -41.50 -40.01 H6-C3-02-01 - 162.25 - 160.64 H7-C3-02-01 78.10 79.92 C5-C4-C3-02 15.39 15.20 C5-C4-C3-H6 131.50 130.49 C5-C4-C3-H7 - 103.24 - 102.77 H8-C4-C3-02 - 103.06 - 103.64 H8-C4-C3-H6 13.04 11.65 H8-C4-C3-H7 138.31 138.39 H9-C4-C3-02 134.36 134.55 H9-C4-C3-H6 - 109.54 - 110.16 H9-C4-C3-H7 15.73 16.58 C4-C5-01-02 -41.50 -40.01 HlO-C5-01-02 78.10 79.92 Hll-C5-01-02 - 162.25 - 160.64 Ol-c5-c4-c3 15.39 15.20 01-C5-C4-H8 134.36 134.55 Ol-C5-C4-H9 - 103.06 - 103.64 HlO-C5-C4-C3 - 103.24 - 102.77 HlO-C5-C4-H8 15.73 16.58 HlO-C5-C4-H9 138.31 138.39 Hll-C5-C4-C3 131.50 130.49 Hll-C5-C4-H8 - 109.54 - 110.16 Hll-C5-C4-H9 13.04 11.65

110.00” as compared with 106.93” using 4-21G (O*) and 109.04” as compared with 106.01’ using 4-21G.

The only dihedral angle for which the two bases afford values differing by more than 2’ is C5-Ol-02-C3. The discrepancies as regards the other angles decrease with the number of oxygen atoms involved in the central bond.

The above comparison of 4-21G and 4-21G(O*) results suggest that even quite large variations in the O-O and C-O bond lengths have relatively little effect on most of the other geometrical parameters of the ring, the only excep- tions being the valency angle C-C-C and the dihedral angle C-O-O-C.

222

TABLE 2

Rotational constants of 1,2-dioxocyclopentane: values obtained experimentally [7] and by cal- culation from theoretical geometries with and without alteration of O-O and/or C-O distances to fit the experimental values A, B and C

A (MHz) B C %A %B %C RMS

M.W. [7] 7500.0 7326.4 4209.8 _ _

4-21G(O*) 7524.0 7468.8 4260.6 0.32 2.19 1.21 96.1 4-21G 7293.2 7211.7 4099.3 2.76 1.59 2.62 151.2 MM2 [2,3] 7576.2 7337.4 4261.2 1.02 0.12 1.22 53.3

4-21G(O*)* 7494.1 7335.2 4211.1 0.08 0.09 0.03 5.3 4-21Gb 7505.2 7329.7 4191.8 0.07 0.02 0.43 10.9 MM2” [2,3] 7503.5 7331.6 4236.6 0.05 0.04 0.69 17.0

‘Corrected bond lengths: O-O = 1.4560 A, C-O = 1.4329 A. bCorrected bond lengths: O-O = 1.4479 A, C-O = 1.4353 8. ‘Corrected bond length: C-O= 1.432 A.

In the absence of any more detailed experimental data with which to com- pare the above results, the rotation constants deduced from microwave studies [ 71 are compared in Table 2 with those calculated from the geometries given in Table 1. On the whole, the constants calculated from geometries obtained using polarization functions are closer to the experimental values than those calculated using 4-21G, but in both cases the agreement can be improved by at least one order of magnitude by forcing different values for the geometrical elements for which the two bases differ most strikingly, the O-O and C-O bond lengths. Thus the 4-21G (O* ) //4-21G (0* ) geometry gives rotational con- stants within + 7 MHz of the experimental values if the O-O and C-O dis- tances are changed to 1.4560 and 1.4329 A, respectively, while the largest error of the values given by the 4-21G//4-21G geometry is only 18.0 MHz if the O- 0 distance is changed to 1.4479 A and the C-O distances to 1.4353 A. Although many geometries give rotational constants agreeing with the experimental findings, it should be noted that the differences between the bond lengths sub- stituted in the geometries obtained with the two bases are only 0.0081 A for the O-O bond and 0.0024 A for the C-O bonds; such proximity suggests that the true values lie somewhere within these ranges. The value substituted for the O-O distance in the 4-21G(O*) geometry, 1.4560 A, would furthermore appear to be in keeping with the O-O distance of 1.457 A in dimethylperoxide [ 201 if the difference between the physical significance of rg, r, and r, struc- tures is taken into account [ 191.

1,2-Dioxocyclohxane (Fig. 2)

The geometry of the chair conformation of 1,2dioxocyclohexane was opti- mized subject only to the preservation of C, symmetry. The results (Table 3 )

223

Fig. 2. Structure of 1,2-dioxocyclohexane (DOCH).

show a slight distortion towards a half-chair form, the parameter 19 [ 211 having a value of 12.5 o when 4-21G (0*) is used and 12.9’ for 4-21G. This allows the widening of the C-O-O-C angle, which is considerably greater than is usual for a cyclohexane, a finding that agrees qualitatively, though not quantita- tively, with the experimental values deduced [ 9,101 from the photoelectronic spectrum of the molecule (Table 4).

In DOCP, the inclusion of polarization functions for the oxygen atoms chiefly affects the O-O and C-O bond lengths, which are shortened by 0.0602 and 0.0376 A, respectively. The C-C distances are changed by no more than about 0.004 A and the C-H distances by about 0.003 A.

The valency angles given by 4-21G(O*) for the ring are mostly wider than those given by 4-21G (although by no more than lo ) , the exceptions being the C-C-C angles, which are 0.9” narrower. The differences as regards the H-C- O and H-C-H angles are also less than l”, and become less with increasing distance from the oxygen atoms. The fact that H7-C3-02 is wider than H8- C3-02 regardless of which basis is used suggests, as for DOCP, the existence of an anomeric effect [ 181, although in this case the effect is not apparent in the C3-H bond lengths.

The two sets of results also differ little as regards the dihedral angles (Table 4). The greatest differences are in the angles around the C4-C3 and C6-C5 bonds, while the C-O-O-C angles differ by only 0.82 ‘.

The above findings are analogous to those for DOCP in showing that large changes in the O-O and C-O distances have relatively little effect on the other geometrical elements of the molecule.

2,3-Dioxobicyct!o[2.2.l]heptane (Fig. 3)

The geometry of the C, conformation of 2,3dioxobicyclo [ 2.2.11 heptane was optimized preserving its symmetry throughout the computations. 4-21G//4-

224

TABLE 3

Geometry of 1,2-dioxocyclohexane (Fig. 2) as obtained by 4-21G//4-21G and 4-21G(0*)//4- 2lG(O*) calculations

21-4G(O*) 4-21G 4-21G(O*) 4-21G

Bond lengths (A) 02-01 C3-02 c4-c3 c5-c4 C6-01 C6-C5 H7-C3 H8-C3 H9-C4 HlO-C4 Hll-C5 H12-C5 H13-C6 H14-C6

Bond angles (“) C3-02-01 C4-C3-02 c5-c4-c3 C6-01-02 C6-C5-C4 C5-C6-01 H7-C3-02 H7-C3-C4 H8-C3-02 H8-C3-C4 H8-C3-H7 H9-C4-C3 H9-C4-C5 HlO-C4-C3 HlO-C4-C5 HlO-C4-H9 Hll-C5-C4 Hll-C5-C6 H12-C&C4 H12-C5-C6 H12-C5-Hll H13-C6-01 H13-C6-C5 H14-C6-01 H14-C6-C5 H14-C6-H13

1.4117 1.4719 1.4288 1.4664 1.5355 1.5319 1.5407 1.5425 1.4288 1.4664 1.5355 1.5319 1.0815 1.0786 1.0821 1.0795 1.0833 1.0829 1.0827 1.0828 1.0833 1.0829 1.0827 1.0828 1.0815 1.0786 1.0821 1.0795

106.38 105.64 109.43 108.76 109.06 109.98 106.38 105.64 109.06 109.98 109.43 108.76 109.36 108.58 111.48 112.19 105.28 104.53 111.62 112.28 109.47 110.14 108.49 108.47 109.67 109.65 110.37 109.98 111.06 110.62 108.14 108.10 109.67 109.65 108.49 108.47 111.06 110.62 110.37 109.98 108.14 108.10 109.36 108.58 111.48 112.19 105.28 104.53 111.62 112.28 109.47 110.14

Torsional angles (“) C3-02-Ol-C6 C4-C3-02-01 H7-C3-02-01 H8-C3-02-01 C5-C4-C3-02 C5-C4-C3-H7 C5-C4-C3-H8 H9-C4-C3-02 H9-C4-C3-H7 H9-C4-C3-H8 HlO-C4-C3-02 HlO-C4-C3-H7 HlO-C4-C3-H8 C6-C5-C4-C3 C6-C5-C4-H9 C6-C5-C4-HlO Hll-C5-C4-C3 Hll-C5-C4-H9 Hll-C5-C4-HlO H12-C5-C4-C3 H12-C5-C4-H9 H12-C5-C4-HlO C5-C6-01-02 H13-C6-01-02 H14-C6-01-02 Ol-C6-C5-C4 Ol-C6-C5-Hll Ol-C6-C5-H12 H13-C6-C5-C4 H13-C6-C5-Hll H13-C6-C5-H12 H14-C6-C5-C4 H14-C6-C5-Hll H14-C6-C5-H12

- 76.11 - 75.29 68.79 68.49

- 53.59 - 53.85 - 171.12 - 171.40

- 54.50 - 55.55 66.61 64.58

- 170.63 - 170.74 64.91 64.35

- 173.99 - 175.52 -51.22 - 50.83

- 176.76 - 177.62 - 55.66 -57.49

67.11 67.19 46.33 48.36

-72.35 - 70.83 168.18 170.04

- 72.35 - 70.83 168.97 169.98 49.50 50.85

168.18 170.04 49.50 50.85

- 69.97 - 68.28 68.79 68.49

- 53.59 - 53.85 - 171.12 - 171.40 - 54.50 - 55.55

64.91 64.35 - 176.76 - 177.62

66.61 64.58 - 173.99 - 175.52 - 55.66 -57.49

- 170.63 - 170.74 - 51.22 - 50.83

67.11 67.19

225

TABLE 4

The C-O-O-C dihedral angle (in degrees) of various cyclic peroxides as calculated and as esti- mated from their photoelectronic spectra

Compound Photoelectron spectroscopy

17981

4-ZlG(O*) 4-21G MM2 [2,3]

DOCP 50 52.6 50.2 53.1 DOCH 88 76.1 75.3 76.5 DOBH 0 0.0 0.0 0.0

Fig. 3. Structure of 2,3-dioxobicyclo [Z.Z.l]heptane (DOBH).

21G and 4-21G (0*) //4-21G (0*) calculations afforded considerably sub-te- trahedral C4-C7-Cl angles of 92.4” and 90.9” respectively. All the valency angles of the ring were likewise sub-tetrahedral, whereas supra-tetrahedral values were obtained for valency angles involving hydrogen atoms. As for DOCP and DOCH, the main discrepancies between the geometries calculated using the two bases concern the O-O and C-O bond lengths, the other chief differ- ence being in this case the 1.5” between the calculated C4-C7-Cl angles. The rigidity of DOBH is probably responsible for the fact that the inclusion of polarization functions shortens the O-O bond less (0.0575 A) and the C-O bond more (0.0439 A) than in DOCP and DOCH. No other bond length changes by more than 0.005 A, although it is worth noting that the largest change among C-H bonds is the lengthening (by 0.0022 A) of those involving bridgehead carbon atoms (Table 5).

The dihedral angle C-O-O-C is determined by the symmetry of the molecule and agrees with the interpretation of the photoelectronic spectrum [lo] and earlier molecular mechanics calculations [ 2,3] (Table 4).

226

TABLE 5

Geometryof2,3-dioxobicyclo[2.2.1]hept.ane (Fig.3) asobtainedby4-21G//4-21Gand4-21G(0*)//4-2lG(O*) calculations

4-21G(O*) 4-21G 4-21G(O*) 4-21G

Bond lengths (A) 02-Cl 03-02 c4-03 c5-c4 C6-Cl C6-C5 c7-Cl c7-c4 HS-Cl H9-C4 HlO-C5 Hll-C5 H12-C6 H13-C6 H14-C7 H15-C7

Bond angles (“) 03-02-Cl C4-03-02 c5-c4-03 C6-Cl-02 C6-C5-C4 C5-C6-Cl C7-Cl-02 C7-Cl-C6 c7-c4-03 c7-c4-c5 c4-c7-Cl H8-Cl-02 Ha-Cl-C6 H8-Cl-C7 H9-C4-03 H9-C4-C5 H9-C4-C7 HlO-C5-C4 HlO-C5-C6 Hll-C5-C4 Hll-C5-C6 Hll-C5-HlO H12-C6-Cl H12-C6-C5 H13-C6-Cl H13-C6-C5 H13-C6-H12 H14-C7-Cl H14-C7-C4 H15-C7-Cl H15-C7-C4 H15-C7-H14

1.4363 1.4802 1.4410 1.4985 1.4363 1.4802 1.5424 1.5377 1.5424 1.5377 1.5705 1.5712 1.5340 1.5321 1.5340 1.5321 1.0771 1.0749 1.0771 1.0749 1.0813 1.0812 1.0786 1.0780 1.0813 1.0812 1.0786 1.0780 1.0777 1.0772 1.0786 1.0790

105.05 103.95 105.05 103.95 107.17 106.37 107.17 106.37 101.52 102.03 101.52 102.03 101.84 101.68 103.59 103.99 101.84 101.68 103.59 103.99 90.92 92.43

107.61 106.78 116.83 117.64 118.36 118.68 107.61 106.78 116.83 117.64 118.36 118.68 111.27 111.03 111.94 111.81 110.46 110.32 112.30 112.24 109.25 109.27 111.27 111.03 111.94 111.81 110.40 110.32 112.30 112.25 109.25 109.27 112.88 112.93 112.88 112.93 113.46 112.82 113.46 112.82 111.76 111.63

Torsional angles (“) 03-02-Cl-C6 03-02-Cl-C7 03-02-Cl-H8 C4-03-02-Cl C5-C4-03-02 C7-C4-03-02 H9-C4-03-02 C6-C5-C4-03 C6-C5-C4-C7 C6-C5-C4-H9 HlO-C5-C4-03 HlO-C5-C4-C7 HlO-C5-C4-H9 Hll-C5-C4-03 Hll-C5-C4-C7 Hll-C5-C4-H9 C5-C6-Cl-02 C5-C6-Cl-C7 C5-C6-Cl-H8 H12-C6-Cl-02 H12-C6-Cl-C7 H12-C6-Cl-H8 H13-C6-Cl-02 H13-C6-Cl-C7 H13-C6-Cl-H8 Cl-C6-C5-C4 Cl-C6-C5-HlO Cl-C6-C5-Hll H12-C6-C5-C4 H12-C6-C5-HlO H12-C6-C5-Hll H13-C6-C5-C4 H13-C6-C5-HlO H13-C6-C5-Hll C4-C7-Cl-02 C4-C7-Cl-C6 C4-C7-Cl-H8 H14-C7-Cl-02 H14-C7-Cl-C6 H14-C7-Cl-H8 H15-C7-Cl-02 H15-C7-Cl-C6 H15-C7-Cl-H8 Cl-c7-c4-03 Cl-c7-c4-c5 Cl-C7-C4-H9 H14-C7-C4-03 H14-C7-C4-C5 H14-C7-C4-H9 H15-C7-C4-03 H15-C7-C4-C5 H15-C7-C4-H9

72.57 72.74 - 35.86 - 35.81

- 161.01 - 160.85 0 0

- 72.57 - 72.74 35.86 35.81

161.01 160.85 70.11 71.37

-37.09 - 35.53 - 169.16 - 169.06 - 170.65 - 169.36

82.16 83.74 -49.91 -49.79 -49.16 - 48.08

- 156.36 - 154.98 71.57 71.49

-70.11 - 71.37 37.09 35.53

169.16 169.06 170.65 169.36

-82.16 -83.74 49.91 49.79 49.16 48.08

156.36 154.98 -71.57 - 71.49

0 0 - 118.77 - 118.71

117.91 118.08 118.77 118.71

0 0 - 123.32 -123.21 - 117.91 - 118.08

123.32 123.21 0 0

53.76 55.15 -57.41 -55.22 171.43 171.83

-61.63 -61.05 - 172.79 -171.42

56.04 55.64 169.93 171.19 58.76 60.82

- 72.40 -72.12 -53.76 -55.15

57.41 55.22 - 171.43 - 171.83

61.63 61.05 172.79 171.42

- 56.04 -55.64 - 169.93 - 171.19 - 58.76 - 60.82

72.40 72.12

227

ACKNOWLEDGEMENTS

The authors thank Dr. C. van Alsenoy for his invaluable help. This work was partly supported by the Xunta de Galicia and by an F.P.I. grant awarded to R.A.M. by the Spanish Ministry of Education and Science.

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