Acta Chini. Slov. 2002, 49, 111-120.
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THEORETICAL STUDY OF SUBSTITUTED TRIOXANES: frans-3,6-DIMETHOXY-l,2,4-TRIOXANE
N. Jorge, M. E. Gomez-Vara
Area de Fisicoquimica, F ACENA, UNNE, Av. Libertad 5300, 3400 Corrientes, Argentina
L. F. R. Cafferata
Programa LADECOR, Departamento de Quimica, Facultad de Ciencias Exactas, UNLP, Calles 47 y
115, 1900 La Plata, Argentina
E. A. Castro*
CEQUINOR, Departamento de Quimica, Facultad de Ciencias Exactas, UNLP, C C 962, 1900 La Plata,
Argentina
Received 05-06-2001
Abstract
We report the calculation of a theoretical study of the ?rara-3,6-dimethoxy-l,2,4-trioxane molecule through the employment of the AMI and PM3 semiempirical methods in order to determine the geometrical structure of the trans a-a and e-e and eis a-e and e-a isomers. The relative energetic stabilities are discussed on the basis of several purely electronic and stereoelectronic effects. Predictions derived from both methods are quite similar.
Introduction
The all encompassing study of organic peroxides comprehends a large number of
chemical issues, from biological like themes (involving, for example, the metabolic oxidation processes), up to disinfection action and pigment manufacture. " In biological systems organic peroxides are specially important, since they take part in cellular decaying transformations caused by an enzymatic self-oxidation due to intermediate peroxidic chemical species.
An important peroxide within family of 1,2,4-trioxanes is natural product derived from Artemisia annua, ' which is a very powerful antimalarial drug with a rather low human toxicity . This compound is the so called Qinghaosu (Artemisinina or Arteannuin) and it was derived from research on Chinese medical traditional practices. " The antimalarial activity of the Artemisia annua extract can be associated to the presence of the ring in 1,2,4-trioxane within the molecules of these compounds. The specific antimalarial action of these compounds is discussed in the previous references.
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Owing to this reason during these last years several research groups have synthetized many new compounds having a ring of 1,2,4-trioxane by way of different methods. a' ' Since there exists a real scarcity of structural information about this sort of chemical compounds, in the following we present the results of a conformational study of both isomers resorting to the semiempirical AMI and PM3 molecular orbital methods.
Results and Discussion
Calculations   were   made   resorting   to   the   HYPERCHEM"   package   and
computations were run in a PENTIUM 4 of lGhz and 512 Mbytes of RAM. Although some critics have arisen regarding the predictive capabilities of the PM3 and AMI methods to reproduce the energetics of internal rotations, this seems not to be the case for the present calculations.
We have not included results derived from the action of environmental effects since some previous calculations using explicit solvent models do not change significantly the results obtained from the isolated molecule model.
We examine the trans a-a and e-e, and eis a-e and e-a isomers, analyzing their relative stabilities. The stereoelectronic (anomeric and exoanomeric) effects are discussed as well as their their significant roles in the stabilization of the trans isomer, where both methoxyl groups are located at the axial position.
The theoretical analysis derived from both methods shows that trans diaxial isomer is the preferred one with respect to the eis isomer, in close agreement with experimental results. In fact, there is a conformational equilibrium between the synclinal and antiperiplanar forms in the trans diaxial isomer. We present results on the rotational barriers of the methoxyl group calculated via both methods and we discuss the stabilization of one conformer with respect the other one, in terms of interactions depending on the orientation of the free electron pairs attached to the exocyclic oxygen atom on the C-0 endo bonds/antibonds.
The stability of the trans axial-axial isomers when the substituent has free electron pairs can be attributable to the existence of interactions involving free electron pairs located at the substituent,  '    besides the proper interactions of the free electron
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pairs of the ring oxygen atoms. The importance of the stereoelectronic effect exerted by
1 7
the substituent has not been taking into account in previous papers.
We give in Table 1 the heats of formation of the trans a-a and e-e and eis a-e isomers in the chair and twist forms of the 3,6-dimethoxy-l,2,4-trioxane. From the examination of the energetic results we verify that the most stable conformer is the trans axial - axial with the chair geometry.
Table 1. Heats of formation (kcal/mol) of 3,6-dimethoxy-l,2,4-trioxane isomers.
Isomers	Chair		Twist	
	AMI	PM3	AMI	PM3
TRANS         a-a                -161.22         -150.36         -156.14         -146.31
CIS               a-e                -153.73          -147.53         -158.49         -148.82
TRANS          e-e                -152.61          -146.84         -156.14         -146.31
A(AH) (aa-ee)= 8.61 kcal/mol conversion axial-equatorial (AMI). A(AH) (aa-ee)= 3.52 kcal/mol conversion axial-equatorial (PM3).
This energy difference reveals the anomeric effect since it stabilizes the isomer having the metoxyl group at the axial position. The effect is more noticeable from AMI calculations.
The interconversion barrier chair (aa) - chair (ee) should pass through an intermediate twist conformation and the interconversion chair/twist is equal to 5.08 kcal/mol, according to the AMI method (for comparison purposes it is suitable to point out that the value corresponding to cyclohexane is equal to 5.5 kcal/mol). The energy barrier calculated with PM3 method is 4.05 kcal/mol.
The most stable geometries calculated with the AMI and PM3 methods are shown in Figures 1 and 2. The rather similar appearance of the equilibrium geometries must be considered carefully. In fact, although the general pattern in nearly the same, specific figures associated with the bond lengths and bond angles present some significant differences. These details can be seen in Table 2 where we display the geometrical parameters derived from the AMI method: bond lengths, bond angles and dihedral angles, for the trans axial - axial of the title compound in the chair and twist geometries, together with the geometrical parameters obtained from the PM3 method.
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Figure 1. Chair conformation of trans diaxial isomer via the AMI method.
H
iiyN
J, Oexo
H    , \   O-i—02
Co----°4\\ /H10
Oexo
Pl2
H      H
H
Figure 2. Chair conformation oî trans diaxial isomer via the PM3 method.
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Table 2. Geometrical parameters of trans diaxial 3,6-dimethoxy-l,2,4-trioxane obtained for AMI and PM3 methods.
	AMI		MNDO-PM3	
	Twist	Chair	Twist	Chair
Bond length (A)				
O1-O2	1.283	1.291	1.545	1.576
c3-o2	1.443	1.428	1.396	1.373
C3-O4	1.397	1.397	1.405	1.408
*^3"'-'exo	1.404	1.401	1.403	1.403
Oexo-Ci2	1.422	1.422	1.405	1.405
C3-H10	1.117	1.120	1.114	1.112
Bond angle (degrees)				
C3-O4-C5	114.96	114.86	116.10	116.54
o2-c3-o4	110.33	109.45	113.77	111.91
OrCVCs	109.75	110.25	112.97	112.83
04-C3-Oexo	104.87	105.28	108.15	110.59
O4-C3-H10	109.62	109.07	105.34	105.99
02-C3-Oexo	102.02	108.43	95.73	105.12
O2-C3-H10	113.09	107.30	115.70	105.58
C3-Oexo-Ci2	113.78	113.92	115.49	115.30
Torsion angle (degrees)				
C6-Oi-02-C3	65.09	-58.85	63.68	-54.86
C6-C5-O4-C3	59.39	48.62	57.21	47.60
02-C3-04-C5	-30.63	-53.80	-27.01	-55.52
02-C3-Oexo-Cl2	-81.07	-73.81	-143.75	-152.82
04-C3-Oexo-Cl2	163.84	169.13	98.91	86.21
C5-04-C3-Oexo	78.53	62.55	78.01	61.32
(VO2-C3-CU	-143.67	-55.63	-145.21	-64.57
0l-02-C3-04	-32.65	58.71	-32.49	55.42
AMI   method  describes   quite  well  stereoelectronic   effects,  but  predicted conformation differs from the experimental data, since there are some differences in bond lengths and bond angles. A bond angle (C3-O2-C3-O4) = 0.031Â Exp A bond angle (C3-O2-C3-O4) = 0.011Â Abond angle (CVCs-CWMCVCs-CU) = 3.15° AExp.bond angle (04-C3-OeXo)-(02-C3-OeXO) = 1.90°
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The stability order of the isomers of 3,6-dimethoxy-l,2,4-trioxane is analyzed taking into consideration the four factor chosen previously in similar works " plus two additional stereoelectronic properties:
a)   The syn-axial effect arising from the nonbonding repulsion between the free electron pairs located on the non-adjacent oxygen atoms. Assuming a tetrahedrical hibridization for the oxygen atom belonging to the ring, the repulsions between 1,5 syn-axial free electron pairs are smaller in the twist than in the chair form, because the free electron pairs momenta are less parallel in the first than in the second structure. This effect is magnified with the decrease of the O-C-0 bond angle and the increase of the X-C-X' bond angle, where X = methoxyl and X' = hydrogen.
b)   The torsion angle around the 0-0 bond favours the twist form, since this the less strained conformation. Results are given in Table 2.
c)   The steric effect, according the methoxyl group is located at the equatorial or axial position8.
d)   The anomeric effect that free electron pairs of the endocyclic oxygen atoms exert on the C-Oendo and C-Oexo bonds when the methoxyl group is at the axial position.
e)   The exoanomeric effect that oxygen free electron pairs of the substituent exert on the C-Oendo in the synclinal and antiperiplanar conformations. As stated before, the methoxyl group rotational barrier around the C(ring) - 0(methoxyl) bond must be rather low (i.e. 1-3 kcal/mol ) and the exoanomeric effect must increase this barrier height in around additional 2 kcal/mol   .
We present in Table 3 the energy minima corresponding to the methoxyl group rotation around the C-Oexo bond calculated by the AMI and PM3 methods. Regarding the first procedure the synclinal conformer with two anomeric effects and one anomeric effect is the most stable isomer, and the difference is 2.6 kcal/mol. The PM3 results is quite similar to this because the energy difference is 2.3 kcal/mol.
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Table 3. Heats of formation (kcal/mol) of trans-coniormsx diaxial 3,6-dimethoxy-l,2,4-trioxane.
Conformer trans	AMI	PM3	ATj#(a) AH      AMI	ATT#(b) AH     PM3
Synclinal Antiperiplanar	-161.22 -158.62	-150.36 -147.92	-158,55	-146,72
(a) and (b) activation enthalpies of the conversion synclinal-antiperiplanar.
The rotation barrier of the methoxyl group around the C(ring) - 0(methoxyi), calculated via AMI method is a rather small value: 2.67 kcal/mol. PM3 prediction is equal to 3.64 kcal/mol.
The AMI semiempirical method reveals a shortening of the C-Oexo bond, which is larger in the anti conformer than in the synclinal isomer, which makes evident the studied stereoelectronic interactions. The lengthened C-Oendo bond corresponds to a state of affairs where the methoxyl oxygen free electron pairs locate at a antiperiplanar position with respect to such atom. This situation is associated to the synclinal conformer and it is shown in the Figure 3. In the antiperiplanar conformer the methoxyl oxygen free electron pairs ar located at an antiperiplanar position with respect to each C-Oendo bond. Geometrical parameters of trans diaxial 3,6-dimethoxy-l,2,4-trioxane with a chair conformation obtained from AMI method for antiperiplanar and synclinical geometries are given in Table 4 together with available experimental data.
Figure 3. Synclinal conformer.
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Table 4. Geometrical parameters of trans diaxial 3,6-dimethoxy-l,2,4-trioxano (chair) obtained from AMI method from conformers synclinal, antiperiplanar and experimental values.
	Experimental	Synclinal	Antiperiplanar
Bond length (A)			
O1-O2	1.467	1.291	1.292
c3-o2	1.412	1.422	1.425
C3-O4	1.401	1.397	1.398
Bond angle (degrees)			
o2-c3.-o4	110.10	109.45	111.79
Cs-CVOi	107.90	110.25	109.21
c5-o4-c3	115.00	114.83	118.14
02-Oi-C6	107.31	114.10	113.31
Oexo-C3-C>4	111.60	105.28	112.48
Oexo"C3-02	109.91	108.43	111.49
C3-Oexo-CMe	110.20	113.92	120.00
C6-Oexo-CMe	-	114.05	114.05
Torsion angle (degrees)			
C6-C5-O4-C3	-45.90	48.62	37.58
C6-Oi-02-C3	71.50	-58.85	-60.65
c5-o4-c3-o2	54.80	-53.80	-39.38
02-Oi-C6-C5	-62.31	50.63	54.25
Conclusions
PM3 semiempirical method predicts the same general results as AMI does, but the
difference among bond lengths between both conformers are lower and it is due to the deficient description of the C-0 bond lengths arising from this method.
For this sort of compounds we can state that the secondary stereoelectronic effect of n —> a* type generated by the free electron pairs belonging to the peroxidic oxygen atoms on the methoxyl group C-0 antibond, located at axial position, yields an important stabilization effect on the trans diaxial form.
Although AMI method describes incorrectly the 0-0 bond distances with respect to the PM3 method, numerical results show that variations in C-Oendo and C-Oexo bond lengths are given quite well from the first method, which also happens with the remaining peroxides molecules.
Regarding the equilibrium between synclinal and antiperiplanar conformers, although there is some experimental evidence in similar compounds with five-membered rings   (for   example,   2-methoxy-l,3-dioxolane)   that   synclynal   -ö-   antiperiplanar
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equilibrium in solution favours the antiperiplanar form, in this compound it is found the lower energy form corresponds to the synclinal isomer.
Theoretical calculations show that for the title compound although the anti conformer is electronically favoured from two exoanomeric interactions that methoxyl oxygen free electron pairs exert on the C-0 ring antibonds, steric repulsion arising when the methoxyl methyl group is located at an antiperiplanar position with respect to the C-H bond, and consequently the synclinal conformer is the most stable isomer.
The most remarkable fact is the stability of trans axial-axial isomers when the substituent possesses free electron pairs, can be attributable to the existence of stereoelectronic interactions which are specific of the free electron pairs attached to the oxygen atoms located into the ring.
Acknowledgment
The authors thank very much the useful comments of an anonymous referee, whose
remarks and suggestions has been helpful to improve the final version of this paper.
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Povzetek
Z uporabo AMI in PM3 semiempiriènih metod smo študirali ?ra«s-3,6-dimetoksi-l,2,4-trioksansko molekulo z namenom doloèiti prostorske strukture trans a-a in e-e ter eis a-e in e-a izomerov. Relativno stabilnost smo poskusili doloèiti z upoštevanjem èistih elektronskih in stereoelektronskih efektov. Obe metodi dasta približno enake rezultate.
N. Jorge, M. E. Gómez-Vara, L. F. R. Cafferata, E. A. Castro: Theoretical study of substituted...