Semiempirical SCF MO study of ring inversion in1,1,4,4,7,7-tetramethylcyclononane and trimeric acetone peroxide

I. Yavaria,*, M.R. Hosseini-Tabatabaeib, F. Nasiria

aDepartment of Chemistry, University of Tarbiat Modarres, P.O. Box 14155-4838, Tehran, IranbDepartment 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-tetramethyl-

1,2,4,5,7,8-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 mol21. 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 perox-

ide (2) are of interest because they are conformation-

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 confor-

mational 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],

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

0166-1280/01/$ - see front matter q 2001 Elsevier Science B.V. All rights reserved.

PII: S0166-1280(00)00688-6

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* Corresponding author. Tel.: 198-21-80066315; fax: 198-21-

8006544.

implemented on a VAX 4000-300 computer. Opti-

mal geometries were located by minimizing

energy, with respect to all geometrical coordi-

nates, 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

I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244240

Table 1

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

Compound Method Bond lengths (AÊ ) Bond angles (8) Dihedral angels (8)

C±CH2 CH2±CH2 CH2±C±CH2 C±CH2±CH2 C±CH2±CH2±C CH2±C±CH2±CH2

1 MNDO 1.57 1.55 114 119 2125 56

AM1 1.53 1.52 113 115 2129 57

PM3 1.54 1.53 110 114 2133 58

Expl. [4] 1.54 1.53 109 117 2129 56

C±O O±O O±C±O C±O±O C±O±O±C O±C±O±O

2 MNDO 1.43 1.29 109 116 2132 58

AM1 1.44 1.30 106 111 2138 59

PM3 1.41 1.55 110 109 2138 57

Expl. [3] 1.42 1.48 112 107 2135 57

Fig. 1. Calculated AM1 structural parameters (bond lengths in AÊ , bond angles and dihedral angles in degrees) in various geometries of 1. The

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 mol21) 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-hexaox-

acyclononane (2)

Compound Geometry MNDO AM1 PM3

DHf8 DDHf8a DHf8 DDHf8

a DDHf8 DDHf8a

1 TBC, D3 264.1 0.0 2286.5 0.0 2298.2 0.0

TCC, C2 246.3 17.8 2267.5 19.0 2287.8 10.4

TCB, C1 14.0 78.1 2202.8 83.7 2219.9 78.3

BC, Cs 5.4 69.5 2199.5 87.0 2226.5 71.7

2 TBC, D3 2293.7 0.0 2312.5 0.0 2395.1 0.0

TCC, C2 2287.0 6.7 2309.1 3.4 2394.9 0.2

TCB, C1 2264.6 29.1 2298.1 14.4 2369.5 25.6

BC, Cs 2197.6 96.1 2230.4 82.1 2332.2 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].

Fig. 2. Calculated AM1 structural parameters (bond lengths in AÊ , bond angles and dihedral angles in degrees) in various geometries of 2. The

CMe2 groups are shown by black circles.

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 3N-

6 and 3N-7 real vibrational frequencies, respec-

tively [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 1and 2 is generally quite good. However, the agreement

between the calculated oxygen±oxygen bond length

and the experimental value is rather weak. Most prob-

ably, this error results from exaggerated values for

lone-pair lone-pair repulsion terms at close inter-

atomic distances in the PM3 method, and

underestimated values of these repulsion terms in

the MNDO and AM1 methods.

The observation of an AA 0BB 0 spin system for the

methylene protons in the room temperature 1H NMR

spectrum of 1 shows unambiguously that this mole-

cule takes up the same (D3) conformation as in the

solid state and does not undergo ring inversion. The1H NMR spectrum of the methylene protons of the all-

cis isomer of trimeric chloroacetone peroxide shows

an AB quartet which remains sharp even at 1558C,

indicating that the free-energy barrier for enantiomer-

ization is higher than 80 kJ mol21, 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±244242

Fig. 3. Calculated AM1 pro®le (kJ mol21) for the enantiomerization of 1,1,4,4,7,7-hexamethylcyclononane (1).

trimeric acetone peroxide 2 are shown in Table 2 and

Figs. 1±4. For each compound, the TBC (D3) confor-

mation is calculated to have the lowest heat of forma-

tion (DHf8). As the twist-chair±chair, TCC,

conformers of 1 and 2 are 19.0 and 3.4 kJ mol21

higher than the corresponding TBC conformations,

they are not expected to be signi®cantly populated

at room temperature.

The conformational energy surfaces for ring inver-

sion of the TBC conformers of 1 and 2 were investi-

gated 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 confor-

mation with its mirror image via the TCC inter-

mediate, 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 nine-

membered 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

I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244 243

Fig. 4. Calculated AM1 pro®le (kJ mol21) for the enantiomerization of 3,3,6,6,9,9-hexamethyl-1,2,4,5,7,8-hexaoxacyclononane (2).

groups are replaced by oxygen atoms. Conse-

quently, conformations such as TCC have lower

heats of formation.

The other conformational feature of 1 and 2concerns 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 hetro-

cyclic trimeric acetone peroxide (2) from both struc-

tural and energetics points of view. Both compounds

take the symmetrical TBC, D3, conformation. The

calculated energy barriers for conformational enantio-

merization 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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I. Yavari et al. / Journal of Molecular Structure (Theochem) 538 (2001) 239±244244