Quantum Chemistry of C3H6O Molecules: Structure and Stability

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Quantum Chemistry of C3H6O Molecules: Structure and Stability, Isomerization Pathways, and Chirality Changing Mechanisms† Munusamy Elango, Glauciete S. Maciel, Federico Palazzetti, Andrea Lombardi, and Vincenzo Aquilanti* Dipartimento di Chimica, UniVersita di Perugia, 06123 Perugia, Italy ReceiVed: April 17, 2010; ReVised Manuscript ReceiVed: June 4, 2010

Electronic structure calculations were carried out to study the various isomers of formula C3H6O, as a part of our current quantum chemical and dynamical approaches to intra- and intermolecular kinetics for the CnH2nO (n ) 1, 2, 3) molecules. The usefulness of the GRRM (global reaction route mapping) program developed by Ohno and Maeda in predicting the structure of all isomers and of the transition states connecting them is fully exploited. All the isomers are identified as local minima on the MP2/CC-PVDZ potential energy surface. Acetone is the most stable isomer. In increasing order of stability the others are propanal, 2-propenol, 1-propenol, allyl alcohol, methyl vinyl ether, cyclopropanol, propylene oxide, and oxetane. Various isomerization paths connecting them are identified. All the transition states are fully characterized using intrinsic reaction coordinate calculations. The isomerization reactions may proceed through a single step or involve an intermediate species which is either a carbene or a diradical. Special attention is devoted to propylene oxide, a favorite molecule in current photochemical and stereodynamical studies because of its chiral nature. It is a rigid molecule, and chirality switching is found to be supported by its isomers. Two different chirality switching mechanisms which are assisted by propanal and allyl alcohol are presented. 1. Introduction Several isomers, which can be broadly classified as ketone, aldehyde, cyclic and acyclic alcohol, and cyclic and acyclic ether, correspond to the general formula C3H6O. The isomers containing the carbonyl group, acetone and propanal, are currently extensively studied regarding their photodissociation dynamics.1,2 The emerging “roaming mechanism” is also reported for the dissociation of acetone.1 Propylene oxide, also referred as methyl oxirane, has continuously received particular attention in the literature due to its chiral nature and is of particular relevance to us in relationship with current chirality changing experiments by aligned molecular beams.3 Recent work in this laboratory concerned molecules containing peroxidic and persulfidic bonds, characterizing the effect of substituents, and specifically considering processes of chirality changing isomerization by torsion.4-9 Our interest currently is about investigating systematically a sequence of other oxygencontaining organic molecules of general formula CnH2nO, where n ) 1, 2, 3.10 These molecules involve a series of decomposition and isomerization processes, which are the subject matter of many ongoing experimental research activities.11-16 For the (n ) 3) propylene oxide case, contrary to molecules corresponding to n ) 1 and 2, confirmation of its presence under interstellar condition has not been successful despite extensive search.17 Isomerization of propylene oxide has been studied by experiment accompanied by theoretical calculations.18 This chiral molecule has the important feature to be in a rather rigid conformation, if we exclude the free rotation of the methyl group. This property is rare in usual chiral molecules and simplifies considerably the study of the dynamics since multiple calculations at different conformations are avoided. No direct conversion channel with only one transition state exists between †

Part of the “Reinhard Schinke Festschrift”. * Corresponding author, [email protected].

the enantiomers of propylene oxide. Here, we have carried out an extensive study on the various isomerization paths and chirality exchange paths, respectively, providing ground for investigations of chiral exchange or switching mechanism reactions, for which considerable progress has been recorded in recent times.19 An overview of recent research carried out in our laboratories provides further background for the present work. The role of oxygen embedded in organic moieties is peculiar and relevant both for stable molecules and for reaction intermediates. For example, the significance of peroxidic and persulfidic bonds present in molecules and intermediates structures is well-known in ample fields of atmospheric chemistry, combustion chemistry, and biochemistry20,21 showing both inter- and intramolecular dynamical features. Besides intramolecular phenomena (wide amplitude anharmonic modes and isomerizations), these molecules also undergo simple mechanisms for chirality changing processes, and paramount interest is involved in these issues.22 The effect of substitutions of the hydrogens in H2O2 and H2S2 by alkyl groups or halogens7-9 has also been studied. Intermolecular interactions are of specific importance, with reference to the collisional mechanism of chiral effects both in gaseous streams and vortices and in scattering from surfaces.4 Our previous joint experimental and theoretical studies have been devoted to interactions of H2O and H2S with rare gases, for which state-of-the-art quantum chemical calculations have yielded complementary information on the interactions (specifically the anisotropies) with respect to molecular beam scattering experiments that measure essentially the isotropic forces,23,24 while experiments probe intermolecular interactions by scattering measurements.25 For a documentation of alignment and orientation effects, see refs 26-28 and references therein. Extending the theoretical studies to the rare gas interactions with H2O2 and H2S2, molecular dynamics simulations are documenting a possible mechanism of chiral biostereochemistry of

10.1021/jp1034618  2010 American Chemical Society Published on Web 06/24/2010

Quantum Chemistry of C3H6O Molecules

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TABLE 1: Total Energy, Relative Energy, Potential Barrier, and Dipole Moments of All the Isomers and Transition States Connecting Them Obtained from the MP2/CC-PVDZ Level of Calculation µ (debye) molecules

Etotal (hartrees)

Erelative

1, acetone TS-1-3 TS-1-6b TS-1-11b 2, oxetane TS-2-10a 3, propylene oxide TS-3-5b TS-3-10b TS-3-12a TS-3-12b 4b, cyclopropanol TS-4b-4a TS-4b-13b 4a, cyclopropanol TS-4a-13a 5b, propanal TS-5b-7b TS-5b-8b TS-5b-5a TS-5b-13a 5a, propanal TS-5a-9a 6b, prop-1-en-2-ol TS-6b-6a TS-6b-13b 6a, prop-1-en-2-ol TS-6a-13a 7a, (1Z)-prop-1-en-1-ol TS-7a-7b 7b, (1Z)-prop-1-en-1-ol 8a, (1E)-prop-1-en-1-ol TS-8a-8b 8b, (1E)-prop-1-en-1-ol 9a, methyl vinyl ether TS-9a-11a TS-9a-12a TS-9a-9b 9b, methyl vinyl ether TS-9b-11b 10b, allyl alcohol TS-10a-10b 10a, allyl alcohol 10c, allyl alcohol 10d, allyl alcohol 10e, allyl alcohol 11a, methoxy methyl carbene TS-11a-11b 11b, methoxy methyl carbene 12a, diradical 12b, diradical 13a, ethyl carbene TS-13a-13b 13b, ethyl carbene

-192.5771755 -192.4081313 -192.4672427 -192.3846886 -192.5225909 -192.3843388 -192.5279462 -192.4005173 -192.4262110 -192.4262233 -192.4349494 -192.5266335 -192.5263907 -192.4330442 -192.5301077 -192.4382298 -192.5660165 -192.4491206 -192.4548062 -192.5644244 -192.4319646 -192.5685157 -192.3961033 -192.5539372 -192.5443757 -192.4141284 -192.5500127 -192.4189517 -192.5457912 -192.5411989 -192.5476841 -192.5441729 -192.5397613 -192.5477949 -192.5303395 -192.4133006 -192.4391603 -192.5197495 -192.5253760 -192.4197789 -192.5360136 -192.5299974 -192.5345475 -192.5368733 -192.5333723 -192.5331461 -192.4493731 -192.4150732 -192.4626626 -192.4605560 -192.4534067 -192.4771880 -192.4301339 -192.4726818

0.0 106.1 68.98 120.8 34.25 121.0 30.89 110.9 94.73 94.72 89.25 31.72 31.87 90.44 29.54 87.19 7.00 80.36 76.79 8.00 91.12 5.43 113.6 14.58 20.58 102.3 17.04 99.29 19.69 22.58 18.51 20.71 23.48 18.44 29.39 102.8 86.61 36.04 32.50 98.77 25.83 29.60 26.75 25.29 27.49 27.62 80.20 101.7 71.86 73.18 77.67 62.74 92.27 65.57

oriented reactants, acting through selective collisions. This may be of interest for the study of prebiotical systems, i.e., those which are assumed to have played a role in the origin of life.4,29 In the present systematic investigation of the different isomers of molecular formula C3H6O, we study properties of all stable isomers and potential barriers of transition states and characterize paths along the intrinsic reaction coordinates, employing quantum chemistry electronic structure calculations. The specific computational approaches employed here are described in section 2, and the results are given and discussed in section 3. Section 4 concludes the paper.

Eact

calcd

exptl

3.23

2.91

2.17

1.93

2.31

2.00

1.60

1.46

106.1 68.98 120.8 86.75 79.96 63.84 63.83 58.36 0.15 58.73 1.64 57.65 3.17 73.35 69.79 0.99 84.12 2.94

2.52

108.2 0.54 5.99 87.73 2.41 82.24 1.77 2.88 1.36 1.86 2.77 1.22 0.98

0.96

73.44 57.22 6.65 1.91 66.26 1.69

1.55

3.78 1.89 1.66 1.76 1.77 21.52

29.52

2. Computational Details Chemical reactions involve intermediates, transition states, stable reactants, and products. It is important to locate all these features in order to have a complete picture of reaction mechanisms. In this work, the achievement of this goal was made possible by an anharmonic downward distortion (ADD) following the method developed by Ohno and Maeda to characterize all the species involved in reaction mechanism.30-32 It is an uphill walking approach along reaction pathways from an equilibrium structure to transition states and dissociation

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Figure 1. Optimized geometries of various closed shell isomers of C3H6O obtained from MP2/CC-PVDZ calculations. The bond lengths are given in angstroms.

channels, implemented in their GRRM program. This method has been found to produce a successful application in many cases.33 We have used the program to identify various isomers, transition states connecting them, and intermediates of interest. All the electronic structure calculations were carried out using the Gaussian 98 suite of programs.34 The geometries of all the species presented in this article were optimized using the CCPVDZ basis set at the Møller-Plesset second-order perturbation (MP2) level of theory. Harmonic frequency analysis verified the nature of the stationary points as minima (all real frequencies) or as transition structures (with one imaginary frequency). Intrinsic reaction coordinate (IRC) calculation procedure available in the ADD-following method was carried out to confirm

that the transition state structures connect the proper reactants and products. 3. Results and Discussion In the present work, we have used the entries 1, 2, 3, ..., etc., to label the different isomers of C3H6O. The conformational isomers are identified by the notations a, b, c, ..., etc. A transition state connecting the stable structures x and y is referred to as TS-x-y. Table 1 contains the name, total energy, relative energy, potential barrier, and dipole moment for all the isomers of C3H6O. The optimized structures of all the closed shell isomers are presented in Figure 1. On the basis of the structures

Quantum Chemistry of C3H6O Molecules shown in Figure 1 and the data summarized in Table 1, the structure and stability of the isomers are discussed. Cyclic Isomers. It is evident from the molecular formula C3H6O that cyclic isomers of ring size three and four are feasible. There are three cyclic isomers 2, 3, and 4, of which 4 has two conformations 4a and 4b. Isomer 2, generally known as oxetane, has a four-membered CCCO ring. It has a Cs plane of symmetry, and it is less stable than isomer 1 (acetone, the most stable isomer) by 34.25 kcal/mol. The CCCO ring is not flat and is puckered by about 10.0° from the plane. Most of the research interest in the oxetane molecule stems primarily from the fact that the effective ring puckering potential possesses a small barrier to ring planarity.35-39 In the case of saturated fourmembered ring molecules ring strain tends to make the ring planar. In oxetane, the preferred staggered positions of the hydrogen atoms on the adjacent methylene groups tend to pucker the ring. The barrier to planarity obtained from the present calculation is less than 1.0 kcal/mol. Isomer 3, propylene oxide, also known as methyl oxirane, is the smallest cyclic ether known.18 This is a chiral molecule and has two enantiomers. It has the important characteristic to be in a rigid conformation, if we exclude the free rotation of the methyl group.40 Energetically it is 30.89 kcal/mol less stable than 1. Cyclopropanol exists in two conformations 4a and 4b, and both of them have Cs symmetry. It is interesting to notice that 4a and 4b are separated by less than 2.0 kcal/mol of energy.41 The most stable form, 4a, belongs to a conformation wherein the dihedral angle of HOCH chain of atoms is 76°. The other conformer 4b exists with a HCOH dihedral angle of exactly 180°. Acyclic Isomers. There are about seven acyclic isomers of C3H6O. All of them can be classified into two ways, isomers with CdC bond and isomers with CdO bond. Isomers with CdO bond are acetone and propanal. The isomers with CdC bond are (Z)- and (E)-1-propenol, 2-propenol, allyl alcohol, and methyl vinyl ether. Acetone, 1, represents the most stable geometry among all the isomers. It has a C2V point group symmetry.42 The next stable conformer, propanal, exists in two conformations: a cis form (5a) with a planar CCCO backbone and a gauche form (5b) with the CdO group rotated out of the plane.43,44 For the neutral molecule, the gauche form is 1.57 kcal/mol higher in energy than the cis, and the cis-to-gauche interconversion barrier is calculated as 2.57 kcal/mol. Conformers 5a and 5b belong to different symmetry groups, Cs and C1 respectively. Allyl alcohol can assume different conformations owing to the free rotation of O-H group and C-C single bond.45 Later in the text a detailed discussion is given on the conformations of allyl alcohol. The most stable conformation for allyl alcohol is isomer 10b. In this conformation, the hydrogen of the O-H is rightly placed between the oxygen atom and the CdC double bond. Methyl vinyl ether has two conformations 9a and 9b which are essentially produced by the rotation of the methoxy group.46 Both the isomers have C1 symmetry. The more crowded cis conformer (9a) is the most stable structure. Steric effects should favor a trans conformation, but the cis conformation is more stable. This conformational preference is understood in terms of nonbonded attractive interactions between the methyl group and the CdC double bond.46 The isomers 9a and 9b are less stable than isomer 1 by ∼30.0 kcal/mol. The difference in energy between them is found to be 3.83 kcal/mol by experiments.46 The computed energy difference between cis and trans conformation is predicted to be 3.11 kcal/mol. Two enolic isomers are possible for C3H6O. They are essentially 1-propenol and 2-propenol, the enolic forms of 5 and 1, respectively.

J. Phys. Chem. A, Vol. 114, No. 36, 2010 9867 2-Propenol, the third most stable isomer of C3H6O, exists in two conformations 6a and 6b. The structural parameters and energies of these two conformers are very similar. 1-Propenol has two constitutional stereoisomers (E)- and (Z)-1-propenol. The isomers 7a and 7b are two conformations of (Z)-1-propenol. They differ from each other by the orientation of the hydroxyl group. Similarly 8a and 8b are the two conformations of (E)1-propenol. Due to the similarity in the structural parameters, these isomers have the same stability. Calculations were also carried out on carbenes and diradicals which are energetically less stable than the isomers discussed before. These species are more than 60 kcal/mol energetically unstable compared to the most stable acetone. They are so reactive that they could not be isolated under the usual experimental conditions even if they are produced. These molecules act as intermediates in the isomerization between closed shell isomers of C3H6O. Isomerization Paths for C3H6O Isomers. In this section, we discuss the various isomerization paths obtained from the GRRM program. All the reaction paths were completely characterized using the intrinsic reaction coordinate (IRC) method available in the GRRM program.30-32 The IRC calculation using the GRRM method is easy to use and it follows on either side of the transition structure until it finds the stable geometry. The isomerization reaction of various isomers either is single step or involves an intermediate. The intermediates are mainly carbenes and diradical species. It is interesting to note that interconversion is possible between all the isomers. It is evident from the results that a single molecule can isomerize into more than one molecule. The GRRM program is very effective in predicting various isomers, the reaction paths between them, and the respective transition states. A summary of the isomerization reactions obtained for all the isomers is listed below. The italic letters correspond to isomerization involving intermediates.

acetone f propylene oxide | 2-propenol | methyl Vinyl ether (1) propylene oxide f allyl alcohol | propanal | methyl Vinyl ether (2) propanal f allyl methyl vinyl ether | cyclopropanol| (Z)/ (E)-1-propenol|2-propenol (3) 2-propenol f cyclopropanol

(4)

allyl alcohol f oxetane

(5)

All these interconversions are presented in Figures 2-5 along with transition state geometries and potential barriers. The isomerization reactions are discussed based on these figures. Figure 2. Propanal (5a) interconverts to methyl vinyl ether (9a) via a concerted transition state TS-5a-9a. The reaction coordinate for this isomerization is the migration of a methyl group from carbon atom to oxygen atom. The calculated potential barrier for this isomerization is 108 kcal/mol. Isomers 9a and 9b are two conformers of methyl vinyl ether which can interconvert easily by the rotation of the methoxy group through the transition state TS-9a-9b. The calculated CCOC torsion angle in the transition state is 75°. Isomerization of methyl vinyl ether 9b to acetone 1 is not a single-step reaction. It involves an intermediate which is a carbene 11b. This intermediate is

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Figure 2. Energy profile along the intrinsic reaction paths for isomerization paths for C3H6O isomers as obtained from the MP2/CC-PVDZ level of calculation.

Figure 3. Energy profile along the intrinsic reaction paths for isomerization paths for C3H6O isomers as obtained from the MP2/CC-PVDZ level of calculation.

formed from 9b through a transition state TS-9b-11b where a hydrogen atom is shifted between the carbon atoms of the double bond. The potential barrier for the formation of 11b is found to be 66.3 kcal/mol. The most stable isomer 1 is formed from 11b via the transition state TS-11b-1. The reaction coordinate is

the migration of a methyl group from oxygen atom to the carbon atom. The calculated potential barrier for this transformation is 48.9 kcal/mol. Acetone interconverts to the 2-propenol via TS1-6b with a potential barrier of 68.9 kcal/mol. Rotation of the hydroxyl group in 2-propenol gives rise to the two conformers



Figure 4. Energy profile along the intrinsic reaction paths for isomerization paths for C3H6O isomers as obtained from the MP2/CC-PVDZ level of calculations. The dotted line corresponds to the energy of the most stable isomer 1.

Figure 5. Energy profile along the intrinsic reaction paths for isomerization paths for C3H6O isomers as obtained from the MP2/CC-PVDZ level of calculations. The dotted line corresponds to the energy of the most stable isomer 1.

6a and 6b. The potential barrier to conversion of 6b to 6a is 5.9 kcal/mol. Figure 3. Oxetane, the only four-membered cyclic isomer, interconverts to allyl alcohol 10c via a concerted transition state TS-2-10c. The potential barrier for this reaction is 86.75 kcal/mol. In the process, the C-O bond of the ring ruptures and a hydrogen atom is migrated from a carbon atom to the oxygen in a concerted manner. The isomer 10c isomerizes to 10b via a rotational transition state TS10c-10b. Propylene oxide is formed from allyl alcohol

through TS-3-10b. The reaction coordinate for this interconversion is the formation of an ether ring and simultaneous migration of a hydrogen atom of the hydroxyl group to the carbon atom. The calculated potential barrier for this isomerization is 68.9 kcal/mol. Propylene oxide isomerizes to acetone via the transition state TS-1-3. This conversion requires a potential barrier of 78.1 kcal/mol. This reaction involves breaking of the ether ring and migration of a hydrogen atom in a concerted manner. Propylene oxide can also isomerize to give methyl vinyl ether, and this conversion

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is assisted by a diradical intermediate. The potential barrier for the formation of diradical via TS-3-12a is 63.83 kcal/ mol. The formation of 9a from the intermediate 12a is found to occur via TS-9a-12a with a potential barrier of 22.63 kcal/mol. Figure 4. Propanal 5b interconverts to the enolic forms (Z)and (E)-1-propenol. 5b isomerizes to 8b via TS-5b-8b with a potential barrier of 69.79 kcal/mol. Similarly 7b is formed from 5b via TS-5b-7b and the potential barrier for this reaction is 73.35 kcal/mol. Both the isomerizations involve the migration of a hydrogen atom from carbon to oxygen. Isomers 7b and 8b can isomerize to their conformers 7a and 8a, respectively. The reaction coordinate for the isomerization is the rotation of the hydroxyl group. Propanal 5b can also interconvert to the chiral isomer 3 via TS-5b-3 with a potential barrier of 103.9 kcal/ mol. Figure 5. The isomerization reaction of 2-propenol, 6b, to give rise to cyclopropanol, 4b, is assisted by ethyl carbene as intermediate. For the formation of 13b from 6b via TS-6b-13b has a potential barrier of 87.73 kcal/mol. The reaction coordinate is the migration of a methyl group between the carbon atoms. The carbene 13b then isomerizes to cyclopropanol 4b via TS4b-13b with a potential barrier of 24.87 kcal/mol. The two conformers of cyclopropanol, 4a and 4b, can interconvert easily as the potential barrier is much lower. Ring-Opening Mechanisms in Propylene Oxide. Propylene oxide is a three-membered ring in which an oxygen atom replaces a -CH2 group in methylcyclopropane. The ring has strain energy of ∼27 kcal/mol, and it is kinetically unstable. Being asymmetrical, unlike ethylene oxide which has only one isomerization channel (ethylene oxide to acetaldehyde), propylene oxide has about four isomerization channels, when it is brought to high temperatures.18 The isomerization channels are discussed in detail in the previous section. It is evident that the isomerization reaction involves the rupture of ether ring. While the rupture of the C-O bond results in the formation of propanal, allyl alcohol, and acetone, rupture of the C-C bond gives rise to methyl vinyl ether. In a theoretical study on the isomerization of propylene oxide,18 it has been reported that the formation of methyl vinyl ether involves two intermediates, which are essentially diradicals. Here, we report an interesting observation about the ring-opening mechanism of propylene oxide. It is found that the ether ring opens in two different ways as presented in Figure 6. The transition states for both types of ring opening are successfully identified and verified using intrinsic reaction coordinate calculations. According to type I, the C-C bond breaks, followed by the clockwise rotation of the two C-O bonds which results in the formation of diradical 12a. The potential barrier for this reaction is found to be 63.83 kcal/mol. On the other hand, in a type II mechanism, the C-C bond breaks, followed by the anticlockwise rotation of the two C-O bonds to form 12b. The potential barrier for this reaction is 58.36 kcal/mol. It should be noted that the potential barrier for the formation of 12a is higher than 12b, but 12a is more stable than 12b by ∼5 kcal/mol (see Figure 7) at this level of calculation. However, regarding the results obtained for this ring opening of the propylene oxide by a homolytic breaking of the original C-C bond leading to diradicals 12a and 12b, the reaction proceeds in the singlet ground state of the molecule. It is known that RHF calculations currently may not give an adequate description of the open-shell singlet configuration character of diradicals, in particular for degenerate or quasi-degenerate

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Figure 6. Two kinds of ring-opening mechanisms in propylene oxide as calculated using the MP2/CC-PVDZ level of theory.

Figure 7. A plot of the variation of energy along the intrinsic reaction coordinate for the ring-opening mechanism in propylene oxide, as obtained from the MP2/CC-PVDZ level of calculation.

molecular orbitals. Also, perturbative second-order calculations are known not to improve the description. Accordingly, we have performed test calculations for both radicals using the ROHF method, obtaining single point energies at the top of the two barriers and for the two products. While the energies at the top of the two barriers were unchanged, as well as for the 12b radical, the energy for the 12a radical was higher, so that the energy difference in the products decreased from 4.5 to 0.95 kcal/mol.



Figure 8. The chirality changing mechanism in propylene oxide via propanal as intermediate.

The present observation suggests a modification in the mechanism proposed by Lifshitz et al. for the formation of methyl vinyl ether from propylene oxide.18 The mechanism, which is simpler than the formation of diradical 12a from propylene oxide, will be followed by the migration of hydrogen atom to form methyl vinyl ether. It is worth mentioning that the GRRM program is helpful in understanding interesting features of reaction mechanisms. Chirality Changing Paths in Propylene Oxide. Molecular chirality is a pervasive phenomenon in nature and has fascinated chemists and physicists alike. Chiral molecules are classified into three groups depending on their chiralities, that is, axial, helical, and point chiralities. In this paper, we present the results of a theoretical study on the chiral exchange reaction of propylene oxide possessing point chirality. This molecule has two stable configurations: they are referred as P and M for the rest of the discussion.47 In a hydrogen peroxide system, for example, the chirality switching is achieved by rotation of a O-O single bond. This is not possible with propylene oxide as the ether ring is a rigid system. Therefore, it is necessary to break the ether ring in order to achieve chirality switching in propylene oxide. Here, we present two mechanisms for the chirality switching in propylene oxide, one assisted by propanol (presented in Figure 8) and the second assisted by allyl alcohol (presented in Figure 9).

A detailed conformational analysis on propanal and allyl alcohol is essential to understand more about the chirality switching in propylene oxide. In Figure 10, it is shown that there are two torsional angles which essentially control the various conformations in propanal and allyl alcohol. In the case of propanal, the torsion of the aldehydic group around the C2-C4 bond is defined by the dihedral angle R ) O1C2C4C7, while the torsion of the methyl group around the C4-C7 bond may be defined by the dihedral angle β ) C2C4C7H8. In the case of allyl alcohol, the torsion of the hydroxyl group around O2-C3 bond is defined by the dihedral angle R ) H1O2C3C6, while the torsion around the C3-C6 bond may be defined by the dihedral angle β ) O2C3C6C8. A scan on the potential energy surface of allyl alcohol is shown in (a). It is found that there are five stable conformations for allyl alcohol. They are 10a, 10b, 10c, 10d, and 10e. The corresponding torsion angles R and β are provided in the figure. Similarly it is found that there are two stable conformations for propanal, 5a and 5b. Chirality Switching via Propanal. Figure 8 presents the mechanism for the chirality switching in propylene oxide assisted by propanal. 5a, the cis form of propanal, is assumed to be the origin. The direction of the rotation of the central C-C bond, more precisely the torsion angle R, can be the right-hand or left-hand side. The left-hand side rotation results

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Figure 9. The chirality changing mechanism in propylene oxide via allyl alcohol as intermediate.

in the formation of a gauche-M. The potential barrier for this rotation is calculated as 1.0 kcal/mol. The next step is the formation of propylene oxide-M from gauche-M via the transition state TS-1-M. It is worth mentioning that gauche-M is called as pro-chiral molecule since a chiral molecule is formed from it. On the other hand, the righthand side rotation results in the formation of a gauche-P. The potential barrier is 1.0 kcal/mol. Propylene oxide-P is formed from gauche-P via TS-1-P. It is interesting to mention that the two transition states, TS-1-M and TS-1-P are mirror images of each other with identical geometrical parameters and energy. This type of mirror image transition state structure is known in the literature.48 With the geometrical parameters, energetics predicted for left-hand side is identical to the right-hand side. Chirality Switching via Allyl Alcohol. Figure 9 presents the mechanism for the chirality switching in propylene oxide assisted by allyl alcohol. The conformer 10a with the torsion angles R and β of 0.0° and 180.0°, respectively, is the origin of the chirality switching pathway. Starting from the molecule 10a, the C-C single bond is rotated on either side which

results in the formation of intermediate 10e-M on the lefthand side and 10e-P on the right-hand side. The hydroxyl group rotation in conformers 10e-P and 10e-M results in the formation of 10b-P and 10b-M on respective sides. These two intermediates are referred to as prochiral. In the last step, the allyl alcohol conformers 10b-M and 10b-P cycle to the respective enantiomer of propylene oxide, M and P. As observed in the case of propanal, the transition states TS2-M and TS-2-P are mirror images with identical geometrical parameters and energetic. Chirality switching via simple rotation is known for many molecules including hydrogen peroxide. Considerable progress on the research of chirality switching is being made. Therefore, chirality switching via breaking or forming chemical bonds seems to be important when it comes to cyclic rigid chiral molecules. 4. Concluding Remarks Here we list what we consider the most salient features which have emerged from this work. The GRRM method is a useful tool in modeling chemical reactions, as evident from



Figure 10. Potential energy scan on the various conformations of allyl alcohol obtained from MP2/CC-PVDZ calculations. The two torsional angles are shown as a red arrow (R) and blue arrow (β).

the present study on C3H6O molecules. Despite the complexity of the number of the isomers and of their interconversion paths, the method comprehensively provides all the important details. There are 10 closed shell isomers of molecular formula C3H6O. All the possible reaction paths for the interconversion among various isomers are predicted. The interconversion either takes place in a single step or involves an intermediate. The reactive intermediates involved in these reactions are carbenes and diradicals. It is found that the migration of hydrogen atom, hydroxyl group, methyl group, and formation/breakdown of the cyclic molecules result in the interconversions among the isomers. The ring-opening mechanism of propylene oxide is found to follow two mechanisms, resulting in two biradicals. Two different

chirality switching mechanisms in propylene oxide which are assisted respectively by propanal and allyl alcohol have been illustrated. Acknowledgment. The authors are grateful to Professor Koichi Ohno for his advice on the use of the GRRM program. We thank an anonymous referee for pointing out the need of additional calculations for the diradical systems. They also thank MIUR (the Italian Ministry for University and Research) and ASI (the Italian Space Agency). M. Elango thanks MIUR for a fellowship. References and Notes (1) Goncharov, V.; Herath, N.; Suits, A. G. J. Phys. Chem. A 2008, 112, 9423.

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