Semiempirical SCF MO study of ring inversion in 1,1,4,4,7,7-tetramethylcyclononane and trimeric acetone peroxide

Journal of Molecular Structure (Theochem) 538 (2001) 239±244

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Semiempirical SCF MO study of ring inversion in 1,1,4,4,7,7-tetramethylcyclononane and trimeric acetone peroxide I. Yavari a,*, M.R. Hosseini-Tabatabaei b, F. Nasiri a b

a Department of Chemistry, University of Tarbiat Modarres, P.O. Box 14155-4838, Tehran, Iran Department of Chemistry, Science and Research Campus, Islamic Azad University, Ponak, Tehran, Iran

Received 10 February 2000; revised 4 August 2000; accepted 7 August 2000

Abstract An investigation employing the MNDO, AM1, and PM3 semiempirical SCF MO methods to calculate structure optimization and conformational interconversion pathways for 1,1,4,4,7,7-tetramethylcyclononane (1) and 3,3,6,6,9,9-tetramethyl1,2,4,5,7,8-hexaoxa- cyclononane (trimeric acetone peroxide, (2) has been undertaken. Both compounds take the symmetrical TBC (D3) conformation. Compounds 1 and 2 are expected to have chiral stability at room temperature as their conformational racemization energies are higher than 80 kJ mol 21. q 2001 Elsevier Science B.V. All rights reserved. Keywords: Medium rings; Conformational analysis; Stereochemistry; Semiempirical

1. Introduction Cyclononane [1] presented some interesting conformational features. The calculated energy levels of the three minimum-energy conformations, TBC (D3), TCB (C2), and TCC (C2), are such that one would expect the molecule to exist largely in the TBC conformation, especially at low temperature. However, NMR results [2] disclosed the existence of two minor conformers (TCB and TCC) and also indicated that these conformers have substantially higher entropy than the symmetrical TBC. In fact, it was estimated that, at room temperature, cyclononane should contain as much as 50% of the TCB conformer and 10% TCC in addition to 40% of TBC. 1,1,4,4,7,7-Tetramethylcyclononane (1) and the heterocyclic nine-membered trimeric acetone peroxide (2) are of interest because they are conformation* Corresponding author. Tel.: 198-21-80066315; fax: 198-218006544.

ally homogeneous and both take the D3 conformation [3,4]. This is not unexpected, as gem-dimethyl groups tend to occupy those ring positions which are on twofold axes [5]. Only the D3 conformer has three ring positions of twofold symmetry which ®ts the constitutional symmetry of compounds 1 and 2. We present the results of MNDO (Modi®ed Neglect of Diatomic Overlap), AM1 (Austin Model 1), and PM3 (Parametric Method Number 3) semiempirical SCF MO calculations [6±8] on 1 and 2 that allow interesting conclusions to be drawn about the conformational properties of these molecules. 2. Calculations Initial estimates of the geometry of structures 1 and 2 were obtained by a molecular-mechanics program pcmodel (88.0) [9] followed by full minimization using semiempirical MNDO, AM1, and PM3 methods in the mopac 6.0 computer program [10,11],

0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved. PII: S 0166-128 0(00)00688-6

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I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244

Table 1 Calculated semiempirical and experimental structural parameters in TBC conformer of 1 and 2 Compound

Method

Ê) Bond lengths (A

Bond angles (8)

C±CH2

CH2 ±CH2

CH2 ±C±CH2

C±CH2 ±CH2

C±CH2 ±CH2 ±C

CH2 ±C±CH2 ±CH2

Dihedral angels (8)

1

MNDO AM1 PM3 Expl. [4]

1.57 1.53 1.54 1.54

1.55 1.52 1.53 1.53

114 113 110 109

119 115 114 117

2125 2129 2133 2129

56 57 58 56

2

MNDO AM1 PM3 Expl. [3]

C±O 1.43 1.44 1.41 1.42

O±O 1.29 1.30 1.55 1.48

O±C±O 109 106 110 112

C±O±O 116 111 109 107

C±O±O±C 2132 2138 2138 2135

O±C±O±O 58 59 57 57

implemented on a VAX 4000-300 computer. Optimal geometries were located by minimizing energy, with respect to all geometrical coordinates, and without imposing any symmetry

constraints. The structure of the transition-state geometries were obtained using the optimized geometries of the equilibrium structures according to the procedure of Dewar et al. (keyword

Ê , bond angles and dihedral angles in degrees) in various geometries of 1. The Fig. 1. Calculated AM1 structural parameters (bond lengths in A CMe2 groups are shown by black circles.

I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244

241

Table 2 Calculated energies (kJ mol 21) in various geometries of 1,1,4,4,7,7-hexamethylcyclononane (1) and 3,3,6,6,9,9-hexamethyl 1,2,4,5,7,8-hexaoxacyclononane (2) Compound

Geometry

MNDO DHf8

AM1 DDHf8

a

PM3

DHf8

DDHf8

a

DDHf8

DDHf8 a

1

TBC, D3 TCC, C2 TCB, C1 BC, Cs

264.1 246.3 14.0 5.4

0.0 17.8 78.1 69.5

2286.5 2267.5 2202.8 2199.5

0.0 19.0 83.7 87.0

2298.2 2287.8 2219.9 2226.5

0.0 10.4 78.3 71.7

2

TBC, D3 TCC, C2 TCB, C1 BC, Cs

2293.7 2287.0 2264.6 2197.6

0.0 6.7 29.1 96.1

2312.5 2309.1 2298.1 2230.4

0.0 3.4 14.4 82.1

2395.1 2394.9 2369.5 2332.2

0.0 0.2 25.6 62.9

a

The standard strain energy in each geometry of a molecule is de®ned as the difference between the standard heats of formation (DHf8) for that geometry and the most stable conformation of the molecule [16].

Ê , bond angles and dihedral angles in degrees) in various geometries of 2. The Fig. 2. Calculated AM1 structural parameters (bond lengths in A CMe2 groups are shown by black circles.

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I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244

Fig. 3. Calculated AM1 pro®le (kJ mol 21) for the enantiomerization of 1,1,4,4,7,7-hexamethylcyclononane (1).

SADDLE) [12]. All geometries were characterized as stationary points, and true local energy-minima and transition states on the potential energy surface were found using keyword FORCE. All energy-minima and transition-state geometries obtained in this work are calculated to have 3N6 and 3N-7 real vibrational frequencies, respectively [13,14]. 3. Results and discussion 1,1,4,4,7,7-Hexamethylcyclononane (1) and trimeric acetone peroxide (2) have been the subject of X-ray crystallographic investigations [3,4]. In order to gauge MNDO, AM1, and PM3 reliabilities for these ring systems, we have optimized the geometry of compounds 1 and 2 without restriction. As shown in Table 1, the agreement between the experimental data and the calculated quantities for compounds 1 and 2 is generally quite good. However, the agreement

between the calculated oxygen±oxygen bond length and the experimental value is rather weak. Most probably, this error results from exaggerated values for lone-pair lone-pair repulsion terms at close interatomic distances in the PM3 method, and underestimated values of these repulsion terms in the MNDO and AM1 methods. The observation of an AA 0 BB 0 spin system for the methylene protons in the room temperature 1H NMR spectrum of 1 shows unambiguously that this molecule takes up the same (D3) conformation as in the solid state and does not undergo ring inversion. The 1 H NMR spectrum of the methylene protons of the allcis isomer of trimeric chloroacetone peroxide shows an AB quartet which remains sharp even at 1558C, indicating that the free-energy barrier for enantiomerization is higher than 80 kJ mol 21, and that trimeric ketone peroxides are potentially resolvable at room temperature [15]. The results of semiempirical calculations for various geometries of hexamethylcyclononane 1 and

I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244

243

Fig. 4. Calculated AM1 pro®le (kJ mol 21) for the enantiomerization of 3,3,6,6,9,9-hexamethyl-1,2,4,5,7,8-hexaoxacyclononane (2).

trimeric acetone peroxide 2 are shown in Table 2 and Figs. 1±4. For each compound, the TBC (D3) conformation is calculated to have the lowest heat of formation (DHf8). As the twist-chair±chair, TCC, conformers of 1 and 2 are 19.0 and 3.4 kJ mol 21 higher than the corresponding TBC conformations, they are not expected to be signi®cantly populated at room temperature. The conformational energy surfaces for ring inversion of the TBC conformers of 1 and 2 were investigated in detail. The results are shown in Table 2 and Figs. 3 and 4. For each compound, there are two distinct transition states which are required to describe conformational enantiomerization of the chiral TBC geometries. The structural parameters for the energy minima and transition-state geometries of 1 and 2 are shown in Figs. 1 and 2. Having found a conformational transition state linking two conformations, we still need to determine

whether this transition state in on the lowest energy path. Since the potential energy surface is highly multidimentional, it is not possible to explore all possibilities, but we have carried out suf®cient calculations to feel con®dent that the lowest energy path, or something close to it, has been obtained in each case. Degenerate interconversion of the TBC conformation with its mirror image via the TCC intermediate, is found to be the lowest energy conformational process. If this process is fast the time-averaged symmetry of the TBC conformation becomes D3h, which is the maximum symmetry allowed by the chemical structure of these ninemembered rings. Two signi®cant differences can be anticipated between the conformational features of 1 and 2. The ®rst derives from the fact that van der Walls repulsion should diminish in 2, as the methylene

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groups are replaced by oxygen atoms. Consequently, conformations such as TCC have lower heats of formation. The other conformational feature of 1 and 2 concerns their ¯exibilities. The ease with which the C±CH2 ±CH2 ±C torsions in 1 can be deformed compared to the C±O±O±C moieties in 2. Thus, the barrier separating the TBC conformer of 2 from its mirror image should be higher than that required for the same conformational change in 1. 4. Conclusions Semiempirical SCF MO calculations provide a fairly clear picture of the conformations of 1,1,4,4,7,7-tetramethylcyclononane (1) and the hetrocyclic trimeric acetone peroxide (2) from both structural and energetics points of view. Both compounds take the symmetrical TBC, D3, conformation. The calculated energy barriers for conformational enantiomerization of the chiral TBC conformers are quite high. Thus, compounds 1 and 2 are expected to have chiral stability at room temperature.

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