Revisiting the origin of the preferential π-π stacking conformation of the (+)-8-phenylmenthyl acrylate

Abstracts

In this paper we report a theoretical study aiming to revisit the origin of the preferential π-π stacking conformation of the (+)-8-phenylmentyl acrylate (2). For this, we have applied several DFT and ab initio methods to calculate local minimum geometries, vibrational frequencies, thermochemical properties and ¹H NMR chemical shifts for 2 and the model compound 3-phenylpropyl acrylate (3). We have observed that the MPW1B95 functional was the most suitable method to explain ¹H NMR experimental data which show the stacking conformation of 2 (2S) is more stable that trans conformation (2T) and the stacking conformation of 3 (3S) is less stable that trans conformation (3T). After that, geometrical and energetic features of the intermolecular complex benzene...methylacrylate (4) have also been studied using MPW1B95 method. From our results, we have noticed that both steric and dispersion effects play a key role in the conformational equilibrium of 2.

conformational analysis; intramolecular π-π stacking interactions; MPW1B95 functional; chiral auxiliaries; enantioselective synthesis

Neste artigo reportamos um estudo teórico objetivando revisitar a origem da conformação π-π stacking do (+)-acrilato de 8-fenilmentila (2) ser a preferencial. Para isso, calculamos geometrias de mínimo local, freqüências vibracionais, propriedades termoquímicas e deslocamentos químicos de RMN de ¹H para 2 e para o composto modelo acrilato de 3-fenilpropila (3) usando vários métodos ab initio e de DFT. Observamos que o funcional MPW1B95 foi o método mais apropriado em explicar os dados experimentais de RMN de ¹H nos quais mostram que a conformação stacking de 2 (2S) é mais estável que a conformação trans (2T) e a conformação stacking de 3 (3S) é menos estável que a conformação trans (3T) . Após isso, detalhes geométricos e energéticos do complexo intermolecular benzeno...metilacrilato (4) também foram estudados usando o método MPW1B95. A partir dos nossos resultados percebemos que ambos os efeitos, estérico e de dispersão, desempenham papéis chave no equilíbrio conformacional de 2.

ARTICLE

Revisiting the origin of the preferential π-π stacking conformation of the (+)-8-phenylmenthyl acrylate

Saulo L. Capim; Sidney R. Santana; Boaz G. de Oliveira; Gerd B. Rocha^*; Mário L. A. A. Vasconcellos^*

Departamento de Química, Universidade Federal da Paraíba, Campus I, 58059-900 João Pessoa-PB, Brazil

ABSTRACT

In this paper we report a theoretical study aiming to revisit the origin of the preferential π-π stacking conformation of the (+)-8-phenylmentyl acrylate (2). For this, we have applied several DFT and ab initio methods to calculate local minimum geometries, vibrational frequencies, thermochemical properties and ¹H NMR chemical shifts for 2 and the model compound 3-phenylpropyl acrylate (3). We have observed that the MPW1B95 functional was the most suitable method to explain ¹H NMR experimental data which show the stacking conformation of 2 (2S) is more stable that trans conformation (2T) and the stacking conformation of 3 (3S) is less stable that trans conformation (3T). After that, geometrical and energetic features of the intermolecular complex benzene...methylacrylate (4) have also been studied using MPW1B95 method. From our results, we have noticed that both steric and dispersion effects play a key role in the conformational equilibrium of 2.

Keywords: conformational analysis, intramolecular π-π stacking interactions, MPW1B95 functional, chiral auxiliaries, enantioselective synthesis

RESUMO

Neste artigo reportamos um estudo teórico objetivando revisitar a origem da conformação π-π stacking do (+)-acrilato de 8-fenilmentila (2) ser a preferencial. Para isso, calculamos geometrias de mínimo local, freqüências vibracionais, propriedades termoquímicas e deslocamentos químicos de RMN de ¹H para 2 e para o composto modelo acrilato de 3-fenilpropila (3) usando vários métodos ab initio e de DFT. Observamos que o funcional MPW1B95 foi o método mais apropriado em explicar os dados experimentais de RMN de ¹H nos quais mostram que a conformação stacking de 2 (2S) é mais estável que a conformação trans (2T) e a conformação stacking de 3 (3S) é menos estável que a conformação trans (3T) . Após isso, detalhes geométricos e energéticos do complexo intermolecular benzeno...metilacrilato (4) também foram estudados usando o método MPW1B95. A partir dos nossos resultados percebemos que ambos os efeitos, estérico e de dispersão, desempenham papéis chave no equilíbrio conformacional de 2.

Introduction

Since 1975, when Corey and Ensley¹ used (+)-8-phenylmenthol (1) (Figure 1) for the preparation of the acrylate derivative (2) for enantioselective synthesis of prostaglandins, compound 1 has ranked among the most versatile chiral auxiliary in the toolbox of asymmetric organic synthesis, being especially useful for π-face-differentiation.² The presence of an aromatic nucleus is a salient feature common to many chiral auxiliaries, particularly those which provide the highest level of stereocontrol. The special stabilization in the stacking conformation (2S) by π-π dispersion interaction between the aromatic and the acrylate groups has emerged as one of the most attractive explanations.³ For example, Ulukanli et al.⁴ described the aziridination of compound 2 in high diastereoselectivity using 3-acetoxyamino-2-ethylquinazolinone. According to the transition state proposed by Ulukanli et al.,⁴ the reaction occurs selectively on the si face of the acrylate moiety of 2 due to hindrance of the aromatic benzene ring on the re face (see Scheme 1).

However, up to now there are some questions to be answered: is the attractive dispersion interaction between the phenyl group and the acrylate moiety in 2S (increasing its relative stability) the only effect which controls the preferential π-π stacking conformation of 2 (Figure 1)? Could it be the steric repulsion effect, e.g. between one of the methyl groups and the acrylate moiety in 2T,⁵ (increasing its relative energy) also an important effect to be considered? Or perhaps it is the case that both effects are controlling the preferential π-π stacking conformation of 2? As far as we know, there are no theoretical studies involving density functional theory (DFT) and ab initio methodologies aiming to evaluate the actual origin of the relative stabilities of 2S and 2T conformations.

A survey of the recent chemical literature reveals an explosion of interest in the theoretical studies of non-covalent intermolecular interactions, specially the π-π stacking ones.⁶ However, these kinds of studies for intramolecular π-π stacking interactions, using theoretical methods, are still very lacking.⁶

High-level quantum chemical calculations coupled with large basis sets covering large portions of correlation energy are required to describe accurately the non-covalent dispersion interactions.^7-9 For large structures or complexes, these high-level quantum chemical calculations cannot be carried out due to the high computational demand. For small or medium molecular structures we can apply second-order Møller-Plesset perturbation theory (MP2), which approximately accounts for uncoupled, two-body electron correlations. Unfortunately, some authors have detected that MP2 combined with an extended basis set tends to overestimate binding in non-covalent interactions.^10,11 On the other hand, DFT has been used as one of the most efficient theories to estimate non-covalent effects.^7-9,12,13 Recently, M. Swart et al.¹⁴ have surprisingly shown that the LSDA functional was the most effective to evaluate π-π stacking interaction, compared with others DFT methods, including the KT1 and KT2. At the same time, Moa et al.¹⁵ have performed DFT single-point calculations on the X-ray geometry of the quinone-hydroquinone (quinhydrone) intermolecular complex, and they were able to reproduce the experimental enthalpy when they used the method MPW1B95/6-311++G(2d,2p) with Cartesian d function for polarization atomic orbitals.

Then, in connection to our interests on developing new chiral auxiliaries,^16-20 synthesis²¹ and conformational studies²² of the new aromatic acrylate compounds to act as drugs,^23-25 we present in this paper a theoretical study involving DFT and ab initio methodologies aiming: (i) to discover which method is more suitable to estimate π-π stacking interactions between aromatic and acrylate moieties for medium-size systems and (ii) to evaluate if the intramolecular π-π stacking interactions really are the only effects that controls the conformation of (+)-8-phenylmenthyl acrylate (2).

Computational Details

First, we have used Hartree Fock (HF), MPW1B95,²⁶ M06,²⁷ M06-2X,²⁷ B97D²⁸ (this functional includes dispersion corrections) and MP2 in order to find the gas phase local minima of 2S, 2T, 3S and 3T (Figure 2). For this step, we have used the basis set 6-311++G(2d,2p) considering Cartesian d functions for polarization (6d opition in Gaussian input) for all calculations. All local minimum geometries were fully optimized without any symmetry constraints. After that, we have characterized each local minimum geometry by normal coordinate analysis at the corresponding theoretical level.

Next, the optimized geometries obtained from MPW1B95 were used on several single point energy calculations on MPWB1K,²⁶ MPW1B95,²⁶ M06,²⁷ M06-2X,²⁷ B97D,²⁸ LSDA,²⁹ B3LYP,^30,31 B3LYP-D,³² B3PW91,³³ MPW1PW91,³⁴ HCTH,³⁵ PBE1PBE,^36.37 Hartree-Fock, second- and third-order Møller-Plesset perturbation theory (MP2 and MP3), Spin-component scaling MP2 (SCS-MP2)³⁸ and Spin-component scaling MP3 (SCS-MP3)³⁹ methodologies.

These calculations were carried out using GAUSSIAN 2003,⁴⁰ GAUSSIAN 2009⁴¹ and ORCA (only for B3LYP-D).⁴²

In order to verify the eficiency of MPW1B95 functional to predict the conformers for molecules 2 and 3, we have performed some calculation of ¹H NMR chemical shifts using gauge invariant atomic orbital GIAO methodology⁴³ on the MPW1B95 local minimum geometries of all studied conformers, including solvent effects through PCM⁴⁴ methodology considering chloroform as solvent. ¹H NMR chemical shifts calculation for Tetramethyl silane, TMS, considered as the reference, were carried out using the same method, basis set and PCM conditions.

Finally, for the non-covalent complex 4, we have performed calculations (geometry optimization and frequencies) using MPW1B95 and the same basis set with and without the counterpoise (CP) corrections for basis set superposition error (BSSE).^45,46

Results and Discussion

First, we will qualitatively describe geometrical features for the considered conformations of compounds 2 and 3 (see Figure 2) in order to simplify our discussions.

For compound 2 we have two clear situations: (i) in the conformation 2S the phenyl group make π-π stacking interaction with the methyl acrylate group while one of the benzylic methyl group is located in trans position, (ii) in the conformation 2T we have the phenyl group in trans position while one of the benzylic methyl is located interacting with the methyl acrylate group.

For compound 3 the situation is almost the same. The difference between conformations 3S and 3T is that in benzylic positions we now have hydrogen atoms, which present a smaller molecular volume.

It is important to notice that previous experimental data obtained by ¹H NMR spectra^1,47,48 (all spectra were obtained in deuterated chloroform and at room temperature) confirms that the 2S conformation is more stable than the 2T on (+)-8-phenylmentyl acrylate (2) and, the 3T conformation is more stable than 3S on 3-phenylpropyl acrylate (3).

In Figure 3 and table 1 we present the comparison between the ¹H NMR data for the hydrogen atoms H¹, H² and H³ in methyl acrylate (5),⁴⁷ 3-phenylpropyl acrylate⁴⁸ (3) and (+)-8-phenylmenthyl acrylate (2).¹ From these experimental data it is possible to point out which conformation is more stable for compounds 2 and 3.

We can note in table 1 that there is no significant shielding effect on H¹, H² and H³ in 3 when compared with the corresponding hydrogen H¹, H² and H³ in 5 (Δδ = 0.03 ppm for H¹; 0.01 for H² and 0.05 for H³). These data confirm that the conformation 3T is more stable than 3S on this equilibrium. Note that in the conformation 3S, the hydrogen atoms H¹, H² and H³ are positioned in the anisotropic shielding of the aromatic ring. So, if the conformation 3S was the most stable, we would expect the corresponding signals of H¹, H² and H³ at higher field, which does not occur.

On the other hand, in the same Table 1, we observed an important shielding effect on the hydrogen atoms H¹, H² and H³ in 2 compared with the corresponding hydrogen atoms H¹, H² and H³ in 5 (Δδ = 0.46 ppm for H¹; 0.39 for H² and 0.25 for H³ ). These data confirm that the conformation 2S is more stable that 2T on this equilibrium. We can note in Figure 2 that H¹, H² and H³ in 2S are disposed in anisotropic shielding of the aromatic ring, modifying the corresponding signals to higher field.

As can be seen from Figure 2, there are no steric effects in 3T between the benzylic and acrylate moieties due to the existence of the two hydrogen atoms in benzylic position. Thus, we have selected the molecule 3-phenylpropylacrylate (3) as a good model to indirectly evaluate the π-π stacking effect without the presence of steric effects observed in 2. From this point of view, an efficient theoretical method has to corroborate these experimental data.

Initially, we have performed geometry optimizations for the ground states of the conformers 2T, 2S using HF method with the basis set 6-311++G(2d,2p) considering Cartesian d functions for polarization. We have found Δε_2S-2T = 0.00 kcal mol^-1 for relative total energy for these conformations. This finding confirms that the Hartree-Fock method underestimate the π-π stacking interaction, in discordance to the ¹H NMR data which show the 2S conformation is more stable than 2T. This result was already expected since the ab initio Hartree-Fock method does not consider electron correlation and it cannot accurately measure the π-π stacking interactions. Thus, this method is more appropriate to evaluate the steric effect contributions than π-π stacking.

Then we have performed geometry optimizations for the ground states of conformers 3T, 3S using MP2 method and the same basis set. We have found Δε_3S-3T = -2.73 kcal mol^-1 for the relative total energy for these conformations. This finding also confirms that the MP2 method overestimate the π-π stacking interaction, in discordance to the ¹H NMR data which show the 3T conformation is more stable than 3S.

As a preliminary conclusion, neither Hartree-Fock nor MP2 are good methods to study the conformational equilibria for these compounds.

On these grounds, we have decided to investigate the efficiency of some recent DFT methods to describe the conformational equilibria for the molecules 2 and 3.

So, we have used the DFT methods MPW1B95, M06, M06-2X and B97D with the same basis set to find the ground state minima for 2T, 2S, 3T and 3S conformations.

Table 2 shows gas phase relative total energies (Δε), gas phase relative total energies including thermal corrections (Δε^thermal) and gas phase relative Gibbs energy (ΔGº, T = 298.15K and p = 1.0 atm) to (+)-8-phenylmenthyl acrylate (2) trans (2T) and stacking (2S) conformations, and to 3-phenylpropylacrylate (3) trans (3T) and stacking (3S) conformation (values in kcal mol^-1) using the following DFT methods: MPW1B95, M06, M06-2X and B97D. Table 2 still shows the relative conformational populations (in percentage) corresponding to 3T 3S inter-conversion equilibrium. Conformational equilibrium population [3T] can be evaluated from the equilibrium constant expression using the well-known equation (equation 1).

The conformational equilibrium population for 3S can be easily obtained keeping in mind that [3S] = 1 - [3T].

Negative values for Δε, Δε^thermal and ΔG properties indicate that the conformation stacking (S) is preferable to the corresponding trans (T) conformation and the positive one indicate the trans conformation (T) as the preferable in such equilibrium.

From both calculated Δε, Δε^thermal results it can be seen that the MPW1B95 is the only DFT method capable to correctly predict the relative stability between the studied conformations of molecules 2 and 3. Indeed, this theoretical method predicts that the 2S is the most stable conformer in the conformational equilibrium for 2 and 3T is the most stable conformer in the conformational equilibrium for 3, corresponding to negative Δε_2S-2T and and positive Δε_3S-3T and values.

Our results for gas phase relative Gibbs energies show that the M06 and B97D methods incorrectly predict the conformational equilibrium for the molecule 2 (ΔG_2S-2T > 0), indicating a lacking of π-π stacking interaction on its conformational equilibrium in contrast to ¹H NMR experimental values shown in Table 1.

Based in the results for Gibbs energies, both DFT methods, M06-2X and MPW1B95 correctly predict the conformational equilibria for compounds 2 and 3 ( ΔG _2S-2T < 0 and ΔG _3S-3T > 0). However, the value of ΔG _3S-3T = +0.72 kcal mol^-1 calculated using M06-2X method results in the equilibrium population for 3S of 22.88%. Considering this population on the conformational equilibrium of the molecule 3, ¹H NMR data through its anisotropic shielding would show the existence of stacking conformation and this evidence is not observed from the data presented in Table 1. On the other hand, MPW1B95 predicts ΔG _3S-3T = +4.41 kcal mol^-1, corresponding to [3T] = 99.94% for the trans conformation of this molecule. These results are fully consistent with the experimental observations: a complete lacking of anisotropic shielding in the ¹H NMR spectra of 3, as we can see in Table 1.

From these results, we have considered the MPW1B95 method to be the most efficient in correctly describing conformational equilibria of molecules 2 and 3. For this reason, on the following steps of our study we have decided to verify which methods produce gas phase relative total energies for 2 and 3 conformers in accordance with experimental data. So, we have carried out single point energy calculation using MPW1B95 ground state geometries.

This same strategy was carried out by Swart et al.¹⁴ and Moa et al.,¹⁵ where they have used a theoretically predicted conformation from a reference method in order to evaluate several different computational methods performing single point calculations.

In Table 3 we present gas phase relative total energies obtained from single point calculations to 2T and 2S , and to 3T and 3S considering several ab initio and DFT methods.

In Table 3 we can observe that HF method predicts total energy for 3T 5.74 kcal mol^-1 lower than 3S (entry 1). On the other hand, 2T and 2S conformations have similar energies (= +0.50 kcal mol^-1). These results indicate that there is no steric effect between the benzylic hydrogen atoms and the acrylate moiety on 3T conformation (see Figure 2). Differently, there is a steric effect between one of the benzylic methyl groups and the acrylate moiety on the 2T conformation and a steric effect between phenyl and acrylate groups in the 2S conformation. So, considering only the steric effects, the energies of 2T and 2S are almost equal. Thus, any method capable to catch π-π stacking interaction effects should indicate more stability for the 2S than 2T.

The DFT methods: LSDA, B3LYP-D, MPW1BK, MPW1B95, M06, M06-2X and B97D indicates that 2S is lower in energy than 2T (see Table 3). The ab initio methods MP2, MP3 and their spin-component-correction versions (SCS-MP2 and SCS-MP3) also indicate conformation 2S as the most stable. The DFT methods B3LYP, B3PW91, HCTH and MPW1PW91 were not efficient to estimate π-π stacking interaction on 2.

Differently from the analysis for 2, LSDA, MP2, B97D and B3LYP-D methods show erroneously that the conformation 3S is more stable than 3T. Surprisingly, spin-component-correction versions of both MP2 and MP3 erroneously predicted conformation 3S as the most stable. Since ¹H NMR experimental data in Table 1 confirms that conformation 3S is not more stable than 3T on the equilibrium, this evidence points out that LSDA, B3LYP-D, B97D, MP2, SCS-MP2 and SCS-MP3 methods are overestimating the π-π stacking effect in this case.

In fact, as reported by Moa et al.,¹⁵ the Truhlar's DFT methods MPWB1K and MPW1B95 were efficient methods to count the contribution of the π-π stacking effects for compounds 2 and 3. The same results were observed when we used MP3 method to calculate gas phase relative total energy. However, MP3 calculations for large molecules are of prohibitive computational expense.

Calculation of NMR chemical shifts can be used to bring forth more information about conformational equilibria for compounds 2 and 3.

For this, we have carried out proton chemical shift calculations using gauge invariant atomic orbital (GIAO) methodology⁴³ and MPW1B95 gas phase ground state geometries considering solvent effects through PCM model.⁴⁴ These results are presented in Table 4. The hydrogen atoms shown in table 4 are the same highlighted in Figure 3 and their experimental ¹H NMR chemical shifts data are in Table 1.

A comparison between the predicted chemical shifts and the corresponding experimental ones (respectively, Table 4 and Table 1) show that, despite this non quantitative concordance, we can see the same trends between these data. As it should be expected, all hydrogen atoms for conformation 2S become more shielded than the corresponding ones in conformation 2T. This same evidence could be observed for the hydrogen atoms of the molecule 3.

In a last step, we have decided to predict the minimum geometry of the benzene···methyl-acrylate complex 4 (Figure 4) in order to measure the π-π stacking without steric interferences. For this calculation we have used MPW1B95/6-311G++(2d,2p) (with Cartesian d functions for polarization atomic orbitals) which was the best theoretical method to study these compounds. In this part, our goal was to accurately measure the total formation energy (ΔE^cs) for this complex where the benzene and methyl acrylate are in parallel position to each other, as occurs in 2S.

Note that in complex 4 there are no relevant steric interactions such as the ones in 2, so the calculated value of the ΔE^cs serve as a good estimation to the dispersion effects that occur in the conformation 2S.

The calculated π-π stacking energy ΔE^cs for this complex 4 (Figure 4) was -1.30 kcal mol^-1 (-0.95 kcal mol^-1, considering the BSSE correction = 0.35 kcal mol^-1)⁴⁹ (Table 5). Considering the relative total energies of all conformers of 2 and 3 (Tables 2 and 3), we believe that this π-π stacking stabilization energy is not large enough to overcome the larger stability of the 3T conformation in comparison to 3S, due to the inexistence of steric effects on 3T.

The observation that Δε _2S-2T = 0.00 kcal mol^-1 (obtained by HF//HF) and Δε _2S-2T = +0.50 kcal mol^-1 (obtained by HF//MPW1B95) points out that the steric effects on 2T and 2S are practically the same. Therefore the obtained value of -0.95 kcal mol^-1 suggests that the dispersion contribution is crucial for the relative stability of the conformation 2S on the conformational equilibrium of 2.

Conclusions

The study described in the present manuscript was performed by applying nearly two dozen different quantum chemical to calculate local minimum geometries, frequencies, thermochemical properties and ¹H NMR chemical shifts for (+)-8-phenylmentyl acrylate (2) and 3-phenylpropyl acrylate (3). These calculations were applied aiming to revisit the origin of the preferential π-π stacking conformation of the 2.

Based on our theoretical results we have presented more evidences that point neither Hartree-Fock nor Møller-Plesset perturbation theory (MP2) methods as able to accurately treat π-π stacking interactions (respectively, underestimating and overestimating these effects).

Additionally, we have a clear proof that, differently than what were observed by Swart et al.,¹⁴ the LSDA functional indeed overestimates π-π stacking interaction in these molecules (2 and 3) as well as the recent DFT methods B97D, M06 and M06-2X which were developed to treat dispersion effects.

Our results from Gibbs energies and equilibrium populations for stacking and trans conformations of 2 and 3 show that the MPW1B95 is really the most suitable method to evaluate the contributions between the π-π stacking and steric effects, as were reported by Moa et al.¹⁵

We believe that considering the dispersion π-π stacking interactions as the only origin to the high efficiency of 2 for asymmetric reactions is not correct. Two pivotal effects (the repulsive steric and attractive π-π stacking dispersion) have to be considered for the analysis of the origin of the great efficiency of 2 in asymmetric reactions.

The steric effect between the benzylic methyl group and the acrylate moiety in 2 disfavors the 2T conformer in comparison to 2S. At same time, the steric effect between phenyl and acrylate groups disfavors the 2S conformation in comparison to 2T. These two opposite steric effects seem to be compensated by each other.

On the other hand, because of the stabilizing π-π stacking intramolecular interaction between the phenyl group and acrylate moiety, the 2S conformer is favored in comparison to 2T. Then, there is a balance of these two effects (dispersion and steric), favoring the 2S conformation.

The π-π stacking interaction is really decisive (but not the only effect) to lead 2S as the more important conformer in equilibrium of (+)-8-phenylmentyl acrylate (2).

We believe that the calculated π-π stacking interaction energy for the intermolecular benzene...acrylate complex 4 (-0.95 kcal mol^-1) could be used to estimate the intramolecular π-π stacking interactions on 2S and 3S. This energy is large enough to shift the conformational equilibrium to 2S. However, it is not strong enough to make 3S conformation the most stable.

We hope that this study can provide new insights to rational design of new chiral auxiliaries for enantioselective synthesis.

Supplementary Information

Supplementary data are available free of charge at http://jbcs.sbq.org.br, as PDF file.

Acknowledgments

We would like to thank FAPESQ (Fundação de Amparo à Pesquisa do Estado da Paraíba), CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico) and INCT-INAMI (Instituto Nacional de Ciência e Tecnologia de Nanotecnologia para Marcadores Integrados). We also thank to G. A. U. Carvalho for reviewing our manuscript in English.

Submitted: September 23, 2009

Published online: May 27, 2010

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• ⁴⁷
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  » link
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• ⁴⁹
  Curiously, in the Truhlar's paper (see reference 12 and 13) and quinhydrone complex calculation (see reference 15) the BSSE correction were not performed. However, we are sure that the kind of correction is pivotal to obtain accuracy of the calculation.

Publication Dates

• Publication in this collection
  16 Sept 2010
• Date of issue
  2010

History

• Received
  23 Sept 2009
• Accepted
  27 May 2010