Dr C Gonçalo

Justino

; Justino

J Abel

PhD Vieira

Gonçalo C Justino

Abel J S C Vieira

Antioxidant Mechanisms of Quercetin and Myricetin in the Gas Phase and in Solution -a comparison and validation of semi-empirical methods

Keywords: Flavonoids, Antioxidant Mechanisms, Semi-empirical methods Flavonoids  Antioxidant Mechanism  Semi-empirical methods

Flavonoids have long been recognized for their general health-promoting properties, of which their antioxidant activity may play an important role. In this work we have studied the properties of two flavonols, quercetin and myricetin, using semi-empirical methods in order to validate the application of the recent Parametric Model 6 and to understand the fundamental difference between the two molecules. Their geometries have been optimized and important molecular properties have been calculated. The energetic of the possible antioxidant mechanisms have also been analyzed. The two studied flavonols do not differ significantly in their molecular properties, but the antioxidant mechanisms by which they may act in solution can be rather different. Moreover, we also show that the Parametric Model 6 can produce reliable information for this type of compounds.

Response to Reviewers: Reviewer #1: P.3 "Q" and "M" are used before they are defined. P.5 "Q" and "M" definitions should be given earlier in the paper. P.5 "... what is of extreme." should be ". which is of extreme ." P. 7 HAT has already been defined on p.2, BDE has already been defined. P.4 ". can be stabilized more effectively stabilized ." is very bad English »»» These issues have been properly adressed. P.5 ". determining the biological relevance of these compounds." Does not follow from the preceding part of the sentence. »»» It was an oversimplification of what was meant. We changed it to "indicating that they will be available to interact with surrounding radicals and other species" (pages 5/6).

, the absolute values obtained are strikingly different from those obtained by other authors at the DFT level." is utterly useless unless the DFT results are also presented. Do the authors intend the reader to stop, search for suitable DFT publications, do the comparison, and then resume reading? »»» We have now included these results in the tables and made the necessary comparisons. Table 6 was split in two -Table 6 for M and Table 7 for Q -and now contain the DFT acidities and BDE values 1 Antioxidant mechanisms of Quercetin and Myricetin in the gas phase and in solutiona comparison and validation of semiempirical methods

retrieved from the literature. We have also included a new table -Table 8 -which contains the deprotonation and H atom abstraction orders from the literature as well as from our work. P.8 For the authors to say that ". the calculated heats of formation of H+ and H*, that need to be further refined." is meaningless. They can say that PM6 gives very inaccurate values for these quantities. The implication that further refinement would give better values is not supported by any evidence. »»» As a consequence of this remark, as well as of the remarks of the Reviewer #2, we have repeated the calculations using the same method but under much more stringent conditions and also using other methods. These new calculations led to heats of formation of H* and H+ of, respectively, 217.99 (which is the accepted reference value, a parameter in the program) and 1303.16 kJ/mol, which differs about 15 % from the accepted reference value of 1530.17 kJ/mol. We have made the energetic analysis using both these values and the reference values, and found out that using the PM6 derived values leads to reactional energy changes that ressemble more closely the DFT ones, presumably by error cancelation.

This reviewer is not willing to re-review this article.

Reviewer #2: This paper addresses interesting and complex quentions concerning the reaction mechanisms of two flavanols. There are 3 significant issues that need to be addressed before publication, however.

1) The calculated homo-lumo gap for M increases in going from the gas phase to SCRF water whereas this number should get very much smaller. I suspect that the problem originates in using orbital energies to approximate IA and EP via Koopman's theorem. For molecules of this size, IP and EA should be evaluated properly from the total energies of the ions. Realistic values for IP-EA for these molecules are in the 2-3 eV range, though semi-empirical methods may overestimate this a bit. I am sure that experimental numbers from Cv are available and should be used for comparison to the calculated values in solution.

2) Semi-empirical methods are not the ones of choice for this problem -they are best for large systems that cant be done by other means. For these molecules I would start with DFT and try to do CCSD. At many points obtained results are compared to published DFT, sometimes they are very similar and sometimes very different. There is no analysis of the cases in which they are different, and no suggestion as to which is the most useful. The comment on page 8 about heats of formation for H and H+ are critical but not explored. I think that the problem is that the calculations have been asked to evaluate a poorly defined quantity and that a better measure should be found for addressing the experimental issues of relevance. In the end a much better case needs to be put for using semiempirical methods than has been presented. »»» In face of these two pertinent observations, we have repeated all the calculations using the PM6 methods with much more severe restrictions and a couple of other methods, such as the PM6DH (doi: 10.1021/ct9000922) and the semi-empirical methods implemented in Gaussian03 (AM1 and PM3), and the results of all the calculations are nearly coincidental. These new calculations led to heats of formation of H* and H+ of, respectively, 217.99 (which is the accepted reference value, a parameter in the program) and 1303.16 kJ/mol, which differs about 15 % from the accepted reference value of 1530.17 kJ/mol. We have made the energetic analysis using both these values and the reference values, and found out that using the PM6 derived values leads to reactional energy changes that ressemble more closely the DFT ones, presumably by error cancelation. The IP and EA were now computed using both the orbital approach and the energetic approach, and the results have been introduced in Table 2. As a consequence, the Results and Discussion section was greatly re-written.

3) The conclusions are very weak. The first paragraph just apologizes becauses the methods used are so bad, and the second paragraph, the one containing the interesting results, is very short. From reading the paper it seems that half of the tasks done in it have been done before and that what this paper offers is a complete view of the whole chemistry of the molecules. It is this positive feature, and the lessons learned, that need to dominate the conclusions.

»»» We have deeply re-written the conclusions to reflect all the comments of the reviewer. some minor comments; -use 2 or 3 significant figures throughou -give the full text along with symbols and acronyms in tables and figure captions -Q and M are undefined on first use on P 3 -"base" -> "basis" page 4 -"In face of" -> "Given" on page 4 »»» These issues have been properly addressed.

-"As can be seen from Table 6" on page 8 ... cant be seen as the DFT numbers being compared to are not in the table -page 8 bottom -which experimental results? What about alternative explanations? Its aspects like this that give the paper relevance and meaning and should be expanded.

»»» We have now included these results in the tables and made the necessary comparisons. Table 6 was split in two -Table 6 for M and Table 7 for Q -and now contain the DFT acidities and BDE values retrieved from the literature. We have also included a new table -Table 8 -which contains the deprotonation and H atom abstraction orders from the literature as well as from our work.

Introduction

Flavones and flavonols are two of the most important classes of compounds from the dietary phytochemicals, not only in terms of their greater abundance in the diet, but also due to the recognition of their in vitro antioxidant properties [START_REF] Manach | Polyphenols: food sources and bioavailability[END_REF][START_REF] Birt | Dietary agents in cancer prevention: flavonoids and isoflavonoids[END_REF][START_REF] Bors | Chemistry of the antioxidant effect of polyphenols[END_REF]. Moreover, several studies have shown that flavonoids contribute to the overall antioxidant capacity in vivo [START_REF] Halliwell | Health promotion by flavonoids, tocopherols, tocotrienols, and other phenols: direct or indirect effects? Antioxidant or not?[END_REF][START_REF] Williamson | Bioavailability and bioefficacy of polyphenols in humans. II. Review of 93 intervention studies[END_REF]. Besides their antioxidant activity, both flavonoid aglycones and glycosides can act as antifungal, insect antifeedants, antimicrobials and antivirals and anti-inflammatory, and are also of particular importance in chemotaxonomy [START_REF] Gomes | Molecular mechanisms of anti-inflammatory activity mediated by flavonoids[END_REF][START_REF] Friedman | Overview of antibacterial, antitoxin, antiviral, and antifungal activities of tea flavonoids and teas[END_REF][START_REF] Biesalski | 9: Polyphenols and inflammation: basic interactions[END_REF]. Associated with this, their identification in numerous herbs and infusions has also been the focus of several groups worldwide, particularly from regions where traditional medicine plays an important role [START_REF] Wang | Characterization of fifty-one flavonoids in a Chinese herbal prescription Longdan Xiegan Decoction by high-performance liquid chromatography coupled to electrospray ionization tandem mass spectrometry and photodiode array detection[END_REF][START_REF] Heinrich | Ethnobotany and natural products: the search for new molecules, new treatments of old diseases or a better understanding of indigenous cultures?[END_REF]. Recently, they have also received considerable interest in the food industry as food additives and as nutraceuticals because of their antioxidant and anticarcinogenic properties, among others [START_REF] Arts | A review of the epidemiological evidence on tea, flavonoids, and lung cancer[END_REF][START_REF] Tomar | Early life and adult exposure to isoflavones and breast cancer risk[END_REF][START_REF] Linseisen | Biomarkers of dietary intake of flavonoids and phenolic acids for studying diet-cancer relationship in humans[END_REF][START_REF] De Kok | Mechanisms of combined action of different chemopreventive dietary compounds: a review[END_REF].

Quercetin (3,5,7,3',4'-penta-hydroxyflavone) is one of the most important flavonoids in diet due to its abundance in foods and to its bioavailability [START_REF] Manach | Bioavailability and bioefficacy of polyphenols in humans. I. Review of 97 bioavailability studies[END_REF], and its antioxidant activity has been well studied [START_REF] Boots | Health effects of quercetin: from antioxidant to nutraceutical[END_REF]. On the other hand, several works have shown that myricetin (3,5,7,3',4',5'-hexa-hydroxyflavone) is a stronger antioxidant than quercetin, what has been attributed to the presence of the 5'-OH group that allows a further stabilization of the myricetin derived semi-quinone radical [START_REF] Oyama | Myricetin and quercetin, the flavonoid constituents of Ginkgo biloba extract, greatly reduce oxidative metabolism in both resting and Ca(2+)-loaded brain neurons[END_REF][START_REF] Gordon | Antioxidant activity of quercetin and myricetin in liposomes[END_REF]. Briefly, it has been found that myricetin is a stronger brain neuron oxidative stress and liposome oxidation inhibitor than quercetin.

Moreover, the pyrogallol moiety present in myricetin is a better superoxide scavenger than the catechol moiety present in quercetin [START_REF] Furuno | The contribution of the pyrogallol moiety to the superoxide radical scavenging activity of flavonoids[END_REF]. The structures of these flavonoids are presented in Fig. 1.

Several studies have pointed out the key factors determining the antioxidative potential of a compound, that include i) a low O-H bond dissociation enthalpy (BDE), easing H abstraction;

ii) a high ionization potential (IP), hampering oxygen reduction by the antioxidant; and iii) an adequate solubility [START_REF] Zhang | Substituent Effects on O-H Bond Dissociation Enthalpies and Ionization Potentials of Catechols: A DFT Study and Its Implications in the Rational Design of Phenolic Antioxidants and Elucidation of Structure-Activity Relationships for Flavonoid Antioxidants[END_REF]. Moreover, the stability of the antioxidant-derived radicals must also be considered, as unstable radicals may react with other molecules instead of terminating the radical reactions [START_REF] Zhang | Substituent Effects on O-H Bond Dissociation Enthalpies and Ionization Potentials of Catechols: A DFT Study and Its Implications in the Rational Design of Phenolic Antioxidants and Elucidation of Structure-Activity Relationships for Flavonoid Antioxidants[END_REF].

In this work we present a semi-empirical study, conducted using the PM6 Hamiltonian, in the gas phase and in the water phase, of quercetin, myricetin and their derived radical and anionic species, where we address the above-mentioned pre-requisites of a high antioxidant activity in order to determine which structural and electronic features are behind the higher antioxidant activity of myricetin and to elucidate the role of each of the three possible mechanisms underlying antioxidant activity, namely a) H atom abstraction (HAT), b) sequential proton loss electron transfer (SPLET) and c) single-electron transfer followed by proton transfer (SETPT) [START_REF] Litwinienko | Solvent effects on the rates and mechanisms of reaction of phenols with free radicals[END_REF]; these mechanisms are depicted in Fig. 2.

Computational details

In the present study, quercetin and myricetin molecules were considered theoretically by performing semi-empirical molecular orbital calculations both in the gas phase and in the water phase. The neutral forms and their anions, the radicals formed by H atom abstraction and the radical cations and radical anions of both flavonols were studied. Pre-optimization was performed under a Dreiding type molecular mechanics force field [START_REF] Mayo | DREIDING: a generic force field for molecular simulations[END_REF], implemented in the Marvin software and the Calculator plugins [START_REF]Marvin version 5.00 and Calculator Plugins for Marvin 500[END_REF]. The structures thus obtained were fully optimized using MOPAC2009 version 9.034 [START_REF] Mopac ; James | Computational Chemistry Version[END_REF]. Geometry was optimized using the Baker's Eigenvector Following routine [START_REF] Baker | An algorithm for the location of transition states[END_REF]. Geometry was considered to be fully optimized when the gradient norm was less than 0.01. Single point-calculations were then performed to compute the properties of the molecules. All computations were performed using the the restricted Hartree-Fock formalism.

The following semi-empirical Hamiltonians, as implemented in MOPAC2009, were used: Modified Neglect of Differential Overlap (MNDO) [START_REF] Dewar | Ground states of molecules. 38. The MNDO method. Approximations and parameters[END_REF], Austin Model 1 (AM1) [START_REF] Dewar | Development and use of quantum mechanical molecular models. 76. AM1: a new general purpose quantum mechanical molecular model[END_REF] and the derived Recife Model 1 (RM1) [START_REF] Rocha | RM1: A reparameterization of AM1 for H[END_REF], and the Parameterized Model 3 (PM3) [START_REF] Stewart | Optimization of parameters for semiempirical methods I[END_REF] and the new Parameterized Model 6 (PM6) Hamiltonian [START_REF] Stewart | Optimization of parameters for semiempirical methods V: Modification of NDDO approximations and application to 70 elements[END_REF]. Water phase optimizations and calculations were performed using the Conductor-like Screening Model, a continuum approach to the solvent effect [START_REF] Klamt | COSMO: a new approach to dielectric screening in solvents with explicit expressions for the screening energy and its gradient[END_REF]. In order to ensure that the obtained geometries corresponded to absolute energy minimums and not to local ones, quercetin (Q) and myricetin (M) were drawn with dihedral angles (the angle defined by the two planes that contain the B ring and the A and C rings) varying from -180 º to 180º in steps of 10 º and were subject to geometry optimization.

All optimizations converged to the same final structure, as presented hereafter. The dihedral angles obtained for all the computed species with the PM6 Hamiltonian vary between -1.7 º and 0.4 º . Both these findings are in agreement with previous results that the rotation around the C2-C1' bond does not constitute a rate limiting step for the antioxidant activity of these compounds due to the low energetic barrier associated with that rotation [START_REF] Antonczak | Electronic description of four flavonoids revisited by DFT method[END_REF].

The bond dissociation enthalpy (BDE), the proton affinity (PA), the electron transfer enthalpy from the anion (ETE) and the proton dissociation enthalpy from the radical cation (PDE) were calculated as differences between the heats of formation (H f ) of the products and the reactants (Fig. 2), where F-O • and F-O -are the radical and the anion derived of the antioxidant, F-OH, respectively. These values allow the analysis of the relevance of each of three proposed mechanisms of antioxidant activity, namely H atom transfer (HAT), quantifiable by the BDE, the single-electron transfer followed by proton transfer (SETPT), quantifiable by the ionization potential and the PDE, and the sequential proton loss electron transfer (SPLET), governed by the proton affinity and ETE [START_REF] Litwinienko | Solvent effects on the rates and mechanisms of reaction of phenols with free radicals[END_REF][START_REF] Fiorucci | DFT study of quercetin activated forms involved in antiradical, antioxidant, and prooxidant biological processes[END_REF][START_REF] Klein | DFT/B3LYP study of tocopherols and chromans antioxidant action energetics[END_REF], as shown in Fig. 2. The heats of formation used for H • and H + were, respectively, 217.99 (which is the actual reference value [START_REF] Lide | CRC Handbook Chemistry and Physics[END_REF]) and 1303.16 kJ mol -1 , as calculated with MOPAC2009; although the value for H + differs about 15% from the reference value (1530.17 kJ mol -1 [START_REF] Lide | CRC Handbook Chemistry and Physics[END_REF]), it generates results that are more similar to the DFT results from the literature.

The electronic density-derived properties were computed both from the orbital energies via Koopmans' theorem (and denoted with a subscript O) and from the total energies (denoted with a subscript E) of the species as follows:

IP E = H f (FOH •+ ) -H f (FOH), IP O = -E HOMO , EA E =H f (FOH) -H f (FOH •-)
and EA O = -E LUMO , where IP and EA stand for ionization potential and electron affinity, respectively. From these, global hardness () was computed as  = (IP -EA)/2, electronegativity () as  = (IP + EA)/2 and electrophilicity () as  =   /8 [36, 37. The energy difference between the LUMO and the HOMO was also computed using the orbital energies, as  G,O = E LUMO -E HOMO , and using the energetic values for electron affinities and ionization potentials, using

 G,E = IP E -EA E .

Results and discussion

Comparison of the performance of the different Hamiltonians

Table 1 lists the heats of formation computed using the PM6 Hamiltonians for quercetin and myricetin and their derived radicals and anions; results obtained with the other semi-empirical methods are presented as Supplementary Information. All methods indicate that the most acidic hydroxyl group is the 4' in both the gas phase and the water phase, and that the H atom more easily abstracted from quercetin is also the 4' in the gas phase and, in the water phase, either the 3' or the 4', though, except in the case of the AM1 method, always with very close heats of formation (with differences inferior to 1 kJ mol -1 ).

In the case of myricetin, the results with the MNDO, AM1 and RM1 methods show a high dispersion of values for the gas phase radicals and for the water phase anions. On the other hand, and considering the structure of myricetin, the most easily abstractable H atom appears to be the 4' one as the resulting radical is more efficiently stabilized due to the presence of the two neighboring OH groups. However, the mentioned methods indicate that the H atom to be firstly abstracted is the 3 one.

Results published in the literature [START_REF] Fiorucci | DFT study of quercetin activated forms involved in antiradical, antioxidant, and prooxidant biological processes[END_REF][START_REF] Mendoza-Wilson | CHIH-DFT study of the electronic properties and chemical reactivity of quercetin[END_REF][START_REF] Vasilescu | Quantum molecular modeling of quercetin -Simulation of the interaction with the free radical t-BuOO[END_REF][START_REF] Russo | Semiempirical molecular modeling into quercetin reactive site: structural, conformational, and electronic features[END_REF][START_REF] Leopoldini | Antioxidant Properties of Phenolic Compounds: H-Atom versus Electron Transfer Mechanism[END_REF][41][START_REF] Leopoldini | Density functional computations of the energetic and spectroscopic parameters of quercetin and its radicals in the gas phase and in solvent[END_REF][START_REF] Carpenter | Analysis of the geometry of the hydroxymethyl radical by the -different hybrids for different spins‖ natural bond orbital procedure[END_REF][START_REF] Reed | Natural localized molecular orbitals[END_REF] using several methods (ranging from the semiempirical AM1 to DFT methods with a 6-311++G(3df,2p) basis, which are presented as Supplementary Information) indicate that the most acidic OH group in quercetin is the 4' one and that the first H abstraction occurs from the 3-, 3'-or 4'-OH groups, and this variation does not appear to be method-dependent, although the 4' tends to predominate over gas phase studies and the 3-OH over the water phase studies. For myricetin, the few published results indicate that the 4'-OH group is the most acidic one in both phases. Given these results, we consider that the semi-empirical description of these two flavonoids obtained with the PM6 method, and, partially with the PM3 method, is in broad agreement with what has been published so far. Moreover, the results obtained are in agreement with what is expected from the structure of these flavonoids as both the radical and the anion formed from the 4'-OH group are the ones expected to be more stabilized by charge delocalization and resonance.

Geometry and molecular properties

The closed formulas of quercetin and myricetin are, respectively, C 15 H 10 O 7 and C 15 H 10 O 8 .

The optimized structures of myricetin in the gas and water phases are presented in Fig. 3. The dihedral angles O1C2C1'C2', formed between the plane containing the A and C rings and the plane containing the B ring, are close to zero, showing that both these molecules are very close to being fully planar. The X-ray structure of crystalline quercetin shows that the angle between the two planes is about 7º [START_REF] Cornard | Structural study of quercetin by vibrational and electronic spectroscopies combined with semiempirical calculations[END_REF]. Other works at the RHF level with STO-3G basis set [START_REF] Van Acker | A Quantum Chemical Explanation of the Antioxidant Activity of Flavonoids[END_REF] and with the semi-empirical PM3 method [START_REF] Vasilescu | Quantum molecular modeling of quercetin -Simulation of the interaction with the free radical t-BuOO[END_REF] have found that quercetin is planar; on the other hand, a work using the semi-empirical MNDO method has found it to be non-planar [START_REF] Yates | Semi-empirical molecular orbital calculations on tyrosine kinase inhibitors and structurally related compounds[END_REF]. Leopoldini et al. [41]calculations at the DFT level, using the B3LYP hybrid functional with the 6-311++G** basis set, have found that quercetin and myricetin are both planar, and also that the 4' anion of myricetin and all the quercetin anions are planar, thus allowing charge delocalization, with the concomitant enhancement of their antioxidant activity.

Quercetin and myricetin, being constituted of an hydrophobic part, the phenyl rings, and an hydrophilic part, the hydroxylic groups, display an amphipathic behavior. The negative energies of solvation ( solv H f , Table 1) indicate that these flavonoids are soluble, although sparingly, in water; the derived radicals are also water soluble, which is of extreme importance as most of the reactions in which flavonoids participate occur in water or at water/lipid interfaces [START_REF] Erlejman | The interaction of flavonoids with membranes: potential determinant of flavonoid antioxidant effects[END_REF]. Moreover, the computed permanent dipole moments (μ 0 , Table 2) also indicate that both Q and M are relatively polarized systems, reflecting the polarized hydroxyl and carbonyl functions present in the structures and corroborating their water solubility.

The total dipole moment due to the presence of external fields is dependent on, besides μ 0 , the polarizability α and the first and second order hyperpolarizabilities, β and γ. The values obtained for Q and M, in water, are α M = 229.14 a.u., β M = 1606.44 a.u., γ M = 123548.86 a.u., and α Q = 225.03 a.u., β Q = 1868.56 a.u., γ Q = 125047.11 a.u., and indicate that these flavonoids are capable of polarizing other atoms or molecules and of accommodating themselves to the surrounding environment, indicating that they will be available to interact with surrounding radicals and other species [START_REF] Olivero-Verbel | Structure-Activity Relationships for The Anti-HIV Activity of Flavonoids[END_REF][START_REF] Bonin | Electric-Dipole Polarizabilities of Atoms Molecules and Clusters[END_REF]. However, the direction of the dipole varies strongly from species to species, thus it cannot be used as a descriptor of the activity of these compounds.

The high reactivity of these compounds is also characterized by a small energy gap,  G , between the HOMO and the LUMO and also by a low LUMO energy, that indicates that these compounds can behave as soft electrophiles [51][START_REF] Lewars | Computational Chemistry-Introduction to the Theory and Applications of Molecular and Quantum Mechanics[END_REF][START_REF] Hatch | Quantitative structure-activity relationship of flavonoids for inhibition of heterocyclic amine mutagenicity[END_REF]. The  G values obtained for Q and M are similar, indicating that their reactivity does not differ much. This similar reactivity has also been obtained by DFT computations [START_REF] Rasulev | A Quantitative Structure-Activity Relationship (QSAR) Study of the Antioxidant Activity of Flavonoids[END_REF] but the absolute values we obtained are roughly the double of the DFT ones. However, it must be noted that the energy derived  G values in water are, as expected, much smaller than those in the gas phase, a trend that is not observed with

 G,O values.
The ionization potentials and electron affinities of both Q and M have been computed both from the total energies and from the orbital energies (using Koopman's theorem). The results presented in Table 2 show that while all the values computed with the PM6 orbital values are substantially different than those obtained with a CHIH-DFT method, with differences ranging from 10 % to more than twice the DFT value, the PM6 values computed using the energies of the species involved in the processes (the neutral form and the radical cation and anion), the obtained values are in the same range of the values computed at the DFT level. Also, the obtained values also indicate that it is easier for these compounds to yield an electron than to acquire one, thus favoring their action as antioxidants (by reducing other species) than as putative pro-oxidants (by oxidizing other species).

A higher hardness index () is associated with a lower reactivity, and the results in Table 2 indicate that the energy-derived hardnesses of Q and M are lower in water than in the gas phase, thus suggesting a higher reactivity in the condensed phase, as expected from a lower ionization potential in water than in the gas phase, or in another words, an higher ability to provide an electron when in the gas phase.

The higher electron affinities of Q and M in water than in the gas phase also indicate that these compounds are more reactive in the condensed phase, where they have a higher ability to accommodate electrons from the solvent of from other species (as expressed from their higher electrophilicity).

However, the nucleophilic and electrophilic delocalizabilities, presented in Table 3, indicate that the reactivity of the two flavonoids, in terms of the most likely sites of electrophilic and nucleophilic attack, presents a striking difference: while myricetin is most likely to be attacked by electrophiles on the O atoms of the B ring OH groups (where Dn(r) hits its maximum values), quercetin is more likely to be attacked by electrophiles on hydroxylic O atoms of the A or C rings. On the other hand, the De(r) distribution is similar for both flavonoids in either phase.

In general, energy-derived properties present values that are more similar to their DFT analogues than orbital-derived properties. The best example is the ionization potential of Q and M. Also, the variations of the electron-derived properties, when comparing the gas phase and the water phases, are also more coherent with what is expected from the point of organic structure and reactivity and are also coherent with their DFT counterparts.

The IP and EA values of -tocopherol, a powerful antioxidant ubiquitous in mammal organisms, were also calculated using the PM6 method. In the water phase, the IP for tocopherol is 539.37 kJ mol -1 and the EA is 260.68 kJ mol -1 . In the gas phase, the calculated values are 684.26 and 26.44 kJ mol -1 , respectively.

The water phase ionization potential of tocopherol is smaller than the corresponding ones of Q and M, indicating that the two flavonoids are able to get an electron from either tocopherol. This agrees with the role of flavonoid on the transference of -radical character‖ from highly oxidant reactive species to antioxidants like tocopherol (and also ascorbate) that are regenerated from the diet (or, in the case of ascorbate, enzymatically) [START_REF] Chaudière | Intracellular Antioxidants: from Chemical to Biochemical Mechanisms[END_REF].

Charge and spin delocalization

It is commonly mentioned throughout the literature that planarity is important to the antioxidant activity of flavonoids because it allows charge (in the case of anions) or spin (in the case of radicals) delocalization over the entire molecule, thus contributing to the stabilization of these species. However, as it can be seen in Table 4, and in agreement with other results obtained at the DFT level by Fiorucci et al. [START_REF] Fiorucci | DFT study of quercetin activated forms involved in antiradical, antioxidant, and prooxidant biological processes[END_REF], charge delocalization is restricted to the ring from where the proton is abstracted and the C ringwhen deprotonation occurs from the B ring the resulting atomic charges are mainly located on B and C ring atoms, and when deprotonation occurs from the A ring atomic charges are mainly located on the A and C ring atoms. This effect is more evident in the water phase results than in the gas phase results.

Noticeably, the atomic charge of O atoms does not vary considerably between the neutral form and the anionic forms, and the excess charge is distributed mainly over the rings.

In the case of spin distribution (Table 5), spin accumulates essentially on the ring from where the H atom was abstracted, with only a small percentage of it being located on the central ring. The remarkable exception to this is the case of 3-O • radicals, where spin is also distributed throughout the B ring, which agrees with some published results that indicate that the 3-OH group of quercetin can be particularly important in the antioxidant activity of this flavonoid [START_REF] Leopoldini | Antioxidant Properties of Phenolic Compounds: H-Atom versus Electron Transfer Mechanism[END_REF]56].

It must be noted that the position of the OH group from where abstraction occurs is important abstraction from the 4'-OH group (which is para to the attachment position of the C ring) leads to a higher spin delocalization to the C ring than when it occurs from the 3' or 5'-OH groups (which are ortho to that position). This higher spin delocalization agrees with the abstraction order, where the 4'-OH H atom is the more prone to be removed. Charge delocalization to the C ring is also more prominent in the case of the 4'-O -anions.

All the above discussed characteristics are in agreement with the HOMO and LUMO distribution of quercetin [START_REF] Vasilescu | Quantum molecular modeling of quercetin -Simulation of the interaction with the free radical t-BuOO[END_REF] and myricetin (presented in Fig. 3). The HOMO orbitals are mainly disposed on the C2-C3 double bond, the 3-OH group and the B ring, in good agreement with the many experimental results that sustain the importance of those characteristics as key determinants of the flavonoids antioxidant activity (reviewed by Bors and Michel [START_REF] Bors | Chemistry of the antioxidant effect of polyphenols[END_REF]).

Energetics of the antioxidant processes

Flavonoids have been studied as antioxidants due to the ease with which an H atom can be abstracted from them by a radical, producing a flavonoid radical (F-O • ) that is more stable and less reactive than the original attacking radical. The HAT mechanism is primarily governed by the O-H bond dissociation enthalpy (BDE, the energy associated with the homolysis of a hydroxylic O-H bond). More recently, other mechanisms have been described that could be important for the formation of the flavonoid derived radicals, particularly the sequential proton loss electron transfer (SPLET) mechanism and the sequential electron transfer proton transfer (SETPT) mechanism [START_REF] Litwinienko | Solvent effects on the rates and mechanisms of reaction of phenols with free radicals[END_REF][START_REF] Fiorucci | DFT study of quercetin activated forms involved in antiradical, antioxidant, and prooxidant biological processes[END_REF][START_REF] Klein | DFT/B3LYP study of tocopherols and chromans antioxidant action energetics[END_REF].

The SPLET mechanism is expected to be relevant in proton-accepting solvents, as is water, and involves deprotonation of the flavonoid (measurable by proton affinity, PA) followed by electron transfer (measured by the electron transfer enthalpy, ETE) to produce the flavonoid radical. Oppositely, the SETPT mechanism involves formation of the flavonoid radical cation by electron loss from the neutral flavonoid (where the ionization potential, IP, becomes important) followed by deprotonation of the radical cation (describable by the proton dissociation enthalpy, PDE). The values computed for these reactions are presented in Table 6 for myricetin and Table 7 for quercetin. Table 8 summarized the orders of deprotonation and H atom abstraction for these compounds obtained with this study and also from published data from other authors.

Comparison of PM6 and DFT values

In the case of myricetin, the computed PA's were compared with the acidities calculated at various DFT levels [41,56], and the results differ at most 10 % in the gas phase (the average difference is ca. 5 %) and at most 30 % in the water phase due to the -outlier‖ value of the PA for the 3-OH group (the average difference is ca. 15 %). More interestingly, the PM6 results have the same behaviour as the DFT ones in the both phases.

The gas phase BDE values of myricetin were also compared to the available DFT ones [57],

and show a maximal deviation of 12 % with an average deviation of 6 %, and the values follow have the same behaviour in both cases.

The gas phase PA values of quercetin (Table 7) were compared to the corresponding acidities, enthalpy changes and Gibbs energy changes [START_REF] Fiorucci | DFT study of quercetin activated forms involved in antiradical, antioxidant, and prooxidant biological processes[END_REF]41,56], and a maximal 10 % deviation (with an average 5 % deviation) was found between the different sets of values and the PM6 ones; in the water phase the maximal deviation was of 13 % and the average deviation of 10 %. As before, the data show the same behaviour.

The gas phase BDE values also follow the same trends as the published ones [57, 58], with a global average deviation of 13 % and a maximal of 45 %; however, if we do not consider the G values presented in Table 8, those deviations fall to, respectively, to 10 % and 18 %; the larger deviations found with the Gibbs energy values are likely to come from differences in the entropic part of the Gibbs energy, which, although expectably small, may contribute to the overall deviations. The water phase BDE values also follow the same trends, with the exception of the PM6 value for the 3-OH BDE which is higher than expected from comparison with the other data, and show an average deviation of 5 % with a maximal deviation of 24 %. The distribution of the values discussed above is shown in Fig. 4.

The H atom transfer (HAT) mechanism

The water phase BDE values for quercetin indicate that H atom abstraction occurs primarily from the 3' and 4' OH groups, and the resulting radicals are ca. 70 kJ mol -1 more stable then the following one, from the 7-OH group. In the case of myricetin, H atom abstraction occurs primarily from the B ring OH groups, being the resulting radicals stabilized by the H bonds established with the oxygen atoms in that ring.

These results are in agreement with the established structure-activity relationships for the antioxidant activity of flavones, which point out the fundamental role of the B ring catechol (or pyrogallol) groups [START_REF] Bors | Chemistry of the antioxidant effect of polyphenols[END_REF]. Strikingly, the DFT results suggest that the 3-OH group of quercetin is the one more prone to suffer H atom abstraction in the water phase, in contrast with the gas phase DFT results that point out the 4' as the one most prone to yield H • .

In both flavonoids, the 3-OH H atom is the first one to be abstracted after the B ring H atoms have been removed, explaining experimental results that suggest that the C ring hydroxyl group, when present, potentiates the antioxidant activity that is mainly determined by the B ring OH groups and the C2-C3 double bond [59-62].

The sequential protol-loss electron-transfer (SPLET) mechanism

The SPLET mechanism is primarily governed by the ease of deprotonation, which can be described by the PA values, and secondarily by the ease of electron transfer from the anions, described by the ETE. Concerning the deprotonation step, which, as expected, is more favorable in water than in the gas phase, the PA values presented in Tables 6 and7 indicate that myricetin deprotonates slightly easier than quercetin. For quercetin, the most acidic proton is the 7-OH one, followed by the 4' one, which is in agreement with the majority of the DFT data available that show that these are two most acidic protons. In the case of myricetin, the PM6 results indicate that the 7-OH proton is also the most acidic one, followed by the 3-OH one in the gas phase and the 5-OH one in the water phase, in clear disagreement with the DFT results indicate that the 4' is the most acidic one followed by the 7 and 3' ones.

However, the results of Martins et al. [56] indicate that, in solution, flavones deprotonation occurs primarily from the 7-OH group, in agreement with our PM6 data. After deprotonation, the anions may proceed to form the corresponding radicals by electron transfer (measurable by ETE). The ETE values for the flavonoids are in the same order of magnitude, and follow the same trend for both flavonoids.

Considering the set of these results, the SPLET mechanism is expected to be more relevant for myricetin than for quercetin. More, taking into account that the more acidic protons are, in general, the same atoms that are more likely to be abstracted as H • , it is expectable that, in aqueous solutions, as are most of the biological environments that surround flavonoids in organisms, the SPLET mechanism will prevail over the HAT one.

The sequential electron-transfer proton-transfer (SETPT) mechanism

Electron removal from the neutral flavonoids, leading to the formation of the radical cations, is the first step of the SETPT mechanism. As it can be seen from the ionization potentials, this process is slightly more favorable for quercetin than for myricetin.

Contrarily to deprotonation, which occurs spontaneously in water, ionization requires an electron acceptor, thus being more likely to occur in the presence of such acceptors, as are proteins, or, in the case of flavonoid-solvent systems, in the presence of polar solvents, preferentially those able to establish H bonds with the flavonoid molecules, thus further stabilizing the radical cation [START_REF] Litwinienko | Solvent effects on the rates and mechanisms of reaction of phenols with free radicals[END_REF].

The radical cations of both flavonoids undergo a favorable deprotonation in aqueous solution, and the protons involved in these deprotonation are the same mentioned in the above analyzed mechanismsin myricetin, deprotonation of the radical cation occurs primarily from the central 4'-OH group in the B ring, followed by the neighboring two OH groups, and in quercetin it occurs from the 4'-OH and the 3'-OH groups.

Conclusion

In this work we have reported the results of a semi-empirical study of two flavonoids, quercetin and myricetin. Five different semi-empirical methods were employed, and the results obtained with the PM6 method are, in general, in good agreement with other results published using the density functional theory, thus validating the use of this method to study these compounds.

The PM6 calculations led to nearly planar structures of all the analyzed species, either neutral, radicals or anions, in agreement with results from other authors. Quite noticeably, the PM6 method is capable of reproducing the charge delocalization and the resonance characteristics of the flavonoids obtained by other authors using a DFT approach. The ionization potentials and the electron affinities computed using the PM6 results, as well as the other computed molecular properties (electronegativity, HOMO-LUMO gap, hardness, electrophilicity and permanent dipole moment) show trends that accompany the ones observed with DFT derived data. However, the PM6 values quite often differ from the DFT ones by more than 50 %; nevertheless, those differences became smaller when one uses the energies of the species involved instead of the energies of the orbitals.

The sites of H atom abstraction and the deprotonation orders are also in general agreement with the DFT data. In the case of quercetin, H atom abstraction is expected to occur from the 3' and 4' sites, with a possible contribution in the gas phase from the 3-OH group, which are the same three sites predicted to be more important by the DFT results. This is accompanied by the trends in the proton affinities (PA) and bond dissociation enthalpies (BDE), which are in general agreement with the trends observed for the same values obtained with the DFT procedures. Noticeably, the PM6-derived PA values are lower than the DFT ones while the PM6 BDE values are higher than the DFT ones, which indicates that the semi-empirical methods tend to overestimate the energetics of the anions and underestimate the energetic of the radicals when compared with the DFT methods. These results indicate that the semiempirical PM6 method can be used for, at least, a semi-quantitative approach to the energetic and molecular properties of these compounds. phase acidities of flavonoids. J Am Soc Mass Spectrom 15:848-861. Table 1 Heats of formation (in kJ mol -1 ) of quercetin (Q) and myricetin (M) and their derived radicals and anions obtained with the PM6 model. Δ solv H f values were calculated as Table 2 Computed properties for the quercetin (Q) and myricetin (M) neutral molecules in the gas and water phases obtained with the PM6 model; IPionization potential (in kJ mol -1 ); EAelectron affinity (in kJ mol -1 ); χelectronegativity;  Genergy gap between the highest occupied (HOMO) and lowest unoccupied (LUMO) molecular orbitals (in eV); molecular (or Parr and Pople absolute) hardness (in eV) ; molecular electrophilicity (in eV);  0permanent dipole moment (in Debye). Where available, literature data are included for comparison. The E and O indexes refer to data computed using an energy approach or an orbital approach, respectively. Adata taken from reference 54, obtained at the B3LYP/6-31G(d, p) level; Bdata taken from reference 37, using the CHIHDFT method with a CBSB4 basis set. 0,18 0,09 -0,27 -0,09 -0,18 0,18 0,09 -0,27 -0,09 -0,18 3-O - -0,06 -0,10 -0,84 -0,90 -0,94 -0,06 -0,08 -0,86 -0,92 -0,94 5-O - -0,58 -0,01 -0,42 -1,00 -0,43 -1,14 -0,21 0,36 -0,78 0,15 7-O - -0,50 0,01 -0,51 -1,01 -0,50 -0,51 0,02 -0,51 -1,02 -0,49 3'-O - 0,08 -0,78 -0,31 -0,22 -1,08 0,06 -0,75 -0,31 -0,25 -1,06 4'-O - 0,02 -0,60 -0,42 -0,40 -1,02 0,03 -0,62 -0,41 -0,38 -1,03 5'-O - 0,07 -0,77 -0,30 -0,23 -1,07 F-OH •+ 0,36 0,67 -0,03 0,33 0,64 0,39 0,38 0,03 0,43 0,42 3-O • 0,19 0,17 -0,36 -0,17 -0,19 0,18 0,18 -0,36 -0,18 -0,18 5-O • 0,08 0,09 -0,17 -0,09 -0,08 -0,38 -0,11 0,49 0,11 0,38 7-O • 0,08 0,11 -0,19 -0,11 -0,08 0,07 0,12 -0,19 -0,12 -0,07 3'-O • 0,20 0,07 -0,27 -0,07 -0,20 0,19 0,08 -0,27 -0,08 -0,19 4'-O • 0,19 0,08 -0,27 -0,08 -0,19 0,19 0,07 -0,27 -0,07 -0,19 5'-O • 0,19 0,08 -0,27 -0,08 -0,19

H f (X w )-H f (X g ) H f Q (g) H f M (g) F-
IP O IP E EA O EA E χ O χ E  G,O  G,E           0 M (
Water phase F-OH 0,22 0,10 -0,32 -0,10 -0,22 0,20 0,09 -0,33 -0,13 -0,24 5'-O - 0,10 -0,03 -1,07 -0,97 -1,10 0,09 0,00 -1,09 -1,00 -1,09 4'-O --0,63 0,06 -0,43 -1,06 -0,37 -0,63 0,07 -0,45 -1,07 -0,37 3'-O --0,64 0,07 -0,43 -1,07 -0,36 -0,65 0,08 -0,43 -1,08 -0,35 7-O - 0,20 -0,87 -0,33 -0,13 -1,20 0,20 -0,86 -0,34 -0,14 -1,20 5-O - 0,19 -0,83 -0,35 -0,17 -1,19 0,18 -0,81 -0,37 -0,19 -1,18 3-O - 0,20 -0,87 -0,33 -0,13 -1,20 F-OH •+ 0,24 0,95 -0,20 0,05 0,76 0,25 0,96 -0,20 0,05 0,76 5'-O • 0,23 0,27 -0,50 -0,27 -0,23 4'-O • -0,51 0,61 -0,10 -0,61 0,51 3'-O • -0,60 0,92 -0,32 -0,92 0,60 7-O • 0,22 0,07 -0,28 -0,07 -0,22 5-O • 0,22 0,06 -0,28 -0,06 -0,22 3-O • Adata taken from reference 33, obtained with a B3LYP method and a 6-31G* basis set for C and H atoms and a 6-31+G* basis set for O atoms; B acidity data taken from reference 41, obtained with a B3LYP method and a 6-311++G** basis set; Cdata taken from reference 56, obtained at the B3LYP/6-31G(d) level; Ddata taken from reference 56, obtained at the B3LYP/6-311G(2d,p) level; Edata taken from reference 61, obtained with a ONIOM-G3B3 method; Fdata taken from reference 62 using the B3P86 and the B3LYP methods with a 6-311+G(d,p) basis set.

Figure captions

doi: 10 .

 10 1016/j.jasms.2004.02.007 57. Li MJ, Liu L, Fu Y, Guo QX (2007) Accurate bond dissociation enthalpies of popular antioxidants predicted by the ONIOM-G3B3 method. THEOCHEM 815:1-9. doi:10.1016/j.theochem.2007.03.012 58. Trouillas P, Marsal P, Siri D, Lazzaroni R, Duroux JL (2006) A DFT study of the reactivity of OH groups in quercetin and taxifolin antioxidants: The specificity of the 3-OH site. Food Chem 97:679-688. doi:10.1016/j.foodchem.2005.05.042 59. Wolfe KL, Liu RH (2008) Structure-Activity Relationships of Flavonoids in the Cellular Antioxidant Activity Assay. J Agric Food Chem 56:8404-8411. doi:10.1021/jf8013074 60. Munoz-Munoz JL, Garcia-Molina F, Molina-Alarcón M, Tudela J, Carcía-Cánovas F, Rodríguez-López JN (2008) Kinetic Characterization of the Enzymatic and Chemical Oxidation of the Catechins in Green Tea. J Agric Food Chem 56:9215-9224. doi:10.1021/jf8012162 61. Tsimogiannis DI, Oreopoulou V (2005) The contribution of flavonoid C-ring on the DPPH free radical scavenging efficiency. A kinetic approach for the 3′,.1016/j.ifset.2005.09.001 62. Wang LF, Zhang HY (2004) Unexpected role of 5-OH in DPPH radical-scavenging activity of 4-thiaflavans. Revealed by theoretical calculations. Bioorg Med Chem Lett 14:2609-2611. doi:10.1016/j.bmcl.2004.02.066

Fig. 1 Fig. 2 Fig. 3 Fig. 4

 1234 Fig. 1Basic structure of quercetin and myricetin. The ring naming and atom numbering are shown

  Figure 1 Click here to download high resolution image

Table 3

 3 Nucleophilic -Dn(r)and electrophilic -Dn(r)delocalizabilities of the neutral quercetin (Q) and myricetin (M) molecules in the gas and water phases obtained with the PM6

	model
	M (g)		M (w)		Q (g)		Q (w)
	Dn(r)	De(r)	Dn(r)	De(r)	Dn(r)	De(r)	Dn(r)	De(r)
	O1

Table 4

 4 Sum of atomic charges for rings A (q A ), B (q B ) and C (q C ) and for the ring groups AC (q AC ) and BC (q BC ) computed for neutral quercetin and myricetin molecules in the gas and water phases using the PM6 model Myricetin Quercetin q A q B q C q AC q BC q A q B q C q AC q BC

	F-OH
	phase
	Gas

Table 5

 5 Sum of spin densities for rings A (s A ), B (s B ) and C (s C ) and for the ring groups AC (s AC ) and BC (s BC ) computed for neutral quercetin and myricetin molecules in the gas and water phases using the PM6 model

					Myricetin					Quercetin
			s A	s B	s C	s AC	s BC	s A	s B	s C	s AC	s BC
		F-OH •+ 0,03	0,65	0,33	0,35	0,97	0,04	0,51	0,45	0,49	0,96
	phase Gas	3-O • 5-O • 7-O • 3'-O • 4'-O •	0,05 0,86 0,97 0,00 0,00	0,30 0,01 0,00 0,98 0,88	0,65 0,13 0,03 0,02 0,12	0,70 0,99 1,00 0,02 0,12	0,95 0,14 0,03 1,00 1,00	0,04 0,86 0,97 0,00 0,00	0,30 0,01 0,00 0,98 0,98	0,65 0,13 0,03 0,01 0,02	0,70 0,99 1,00 0,02 0,02	0,96 0,14 0,03 1,00 1,00
		5'-O •	0,00	0,99	0,01	0,01	1,00
		F-OH •+ 0,00	0,89	0,10	0,11	1,00	0,00	0,89	0,11	0,11	1,00
	phase Water	5'-O • 4'-O • 3'-O • 7-O • 5-O •	0,05 0,08 0,08 0,00 0,00	0,29 0,28 0,27 0,97 0,89	0,66 0,64 0,65 0,03 0,11	0,71 0,72 0,73 0,03 0,11	0,95 0,92 0,92 1,00 1,00	0,04 0,03 0,01 0,00 0,00	0,34 0,56 0,86 0,97 0,97	0,62 0,41 0,13 0,03 0,03	0,66 0,44 0,14 0,03 0,03	0,96 0,97 0,99 1,00 1,00
		3-O •	0,00	0,98	0,02	0,02	1,00

Table 6

 6 Reaction energies (computed as differences of heats of formation) for the reactions involved in the various mechanisms of antioxidant activity of myricetin (M) in the gas and water phases. IPionization potential; PDEproton dissociation enthalpy; PAproton affinity; ETEelectron transfer enthalpy; BDEbond dissociation enthalpy.  ac Hacidity. All values are in kJ mol -1 . Where available, literature data are included

	for comparison
			IP	PDE	PA	 ac H A  ac H B  ac H C ETE BDE BDE D
		3		877.49 1305.54 1397.46 1425.91 1400.80 362.62 355.98 355.64
		5		965.85 1320.51 1415.45 1455.61 1425.91 436.02 444.34 416.73
	M(g)	7 3'	790.67	947.73 1281.79 1352.69 1396.62 1369.42 456.62 426.22 391.20 865.68 1321.55 1352.27 1398.71 1366.08 334.80 344.17 303.34
		4'		867.18 1318.09 1307.50 1344.74 1317.12 339.76 345.67 308.78
		5'		877.90 1361.37 1356.45 1401.64 1367.75 307.20 356.39 351.46
		3		1037.01 1106.53 1415.45	554.78 349.13
		5		1118.33 1103.59 1264.82	639.04 430.44
	M (w)	7 3'	624.30	1112.65 1101.54 1240.97 1034.37 1115.34 1248.51	635.41 424.76 543.33 346.49
		4'		1040.37 1123.20 1224.24	541.47 352.48
		5'		1029.69 1124.44 1249.34	529.55 341.81
	A -acidity data taken from reference 41, obtained with a B3LYP method and a 6-311++G** basis set; B
	-data taken from reference 56, obtained at the B3LYP/6-31G(d) level; C -data taken from reference 56,
	obtained at the B3LYP/6-311G(2d,p) level; D -data taken from reference 61, obtained with a ONIOM-
	G3B3 method.

Table 7

 7 Reaction energies (computed as differences of heats of formation) for the reactions involved in the various mechanisms of antioxidant activity of quercetin (Q) in the gas and water phases. IPionization potential; PDEproton dissociation enthalpy; PAproton affinity; ETEelectron transfer enthalpy; BDEbond dissociation enthalpy.  ac Hacidity. All values are in kJ mol -1 . Where available, literature data are included

	for comparison
			IP	PDE	PA	 r H ( r G) A  ac H B  ac H C  ac H D ETE BDE  r H ( r G) A BDE E BDE F
		3		881.41 1321.17	1385.74 (1387.41)	1393.69 1432.18 1410.01 344.42 353.40	322.59 (287.86)	357.73	350.20 (333.46)
	Q (g)	5 7	784.17 (682.41 33 )	973.02 1328.71 952.66 1288.94	1414.19 (1412.52) 1349.76 (1351.01)	1411.68 1458.96 1437.20 428.48 445.01 1349.34 1392.44 1373.19 447.90 424.65	384.93 (247.27) 347.27 (311.71)	417.98 389.95	415.47 (396.22) 370.70 (353.13)
		3'		886.66 1375.97	1357.29 (1368.17)	1352.69 1398.29 1366.49 294.86 358.65	303.34 (269.03)	342.25	322.17 (307.94)
		4'		864.61 1293.64	1328.42 (1331.35)	1324.24 1359.80 1336.37 355.14 336.60	292.88 (259.83)	329.28	312.13 (297.48)
		3		1036.94 1118.02	1213.78 (1206.25)	1254.36	540.17 346.01	322.59 (276.98)
	Q (w)	5 7	621.25 (696.66 36 )	1108.72 1130.02 1096.52 1096.45	1222.98 (1222.56) 1199.55 (1201.65)	1264.82 1240.97	599.96 340.65 621.32 328.45	366.94 (330.12) 365.68 (323.00)
		3'		1036.62 1134.68	1212.52 (1209.18)	1248.09	523.19 268.55	332.21 (289.53)
		4'		1033.15 1114.57	1197.88 (1194.53)	1254.78	539.83 265.07	319.24 (286.19)

Table S1 .

 S1 Heats of formation (in kJ/mol) of quercetin (Q) and derived radicals and anions obtained with the various semi-empirical methods employed. Columns to the right of each method (marked with #) present the ordering of H atom abstraction and of deprotonation. Δ solv H f values were calculated as H f (X w )-H f (X g ).

			MNDO	#	AM1	#	RM1	#	PM3	#
		Neutral -735.57		-847.56		-845.8		-910.21
		4'-O --1071.55 1	-1165.5	1	-1126	1 -1216.12 1
		3'-O --1029.87 2 -1144.91 2 -1084.28 2 -1173.32 4
		7-O -	-939.35	4	-1025.1	4 -1055.43 4 -1178.15 3
	H f (g) Q	5-O -3-O -Q •+	-910.54 -951.95 114.46	5 -1016.87 5 -1024.47 5 -1145.43 5 3 -1027.33 3 -1076.38 3 -1190.47 2 5.1 5.5 -156.86
		4'-O •	-758.44	1	-852.8	1	-815.65	1	-857.08	1
		3'-O •	-757.54	2	-852.78	2	-814.32	2	-855.47	2
		7-O •	-540.44	4	-659.23	4	-663.39	4	-693.84	4
		5-O •	-538.8	5	-637.26	5	-658.18	5	-689.61	5
		3-O •	-606.31	3	-700.96	3	-737.38	3	-778.08	3
			MNDO	#	AM1	#	RM1	#	PM3	#
		Neutral -792.8		-917.87		-900.64		-986.47
		4'-O --1309.56 1 -1421.63 1 -1357.97 1 -1468.89 1
		3'-O --1294.24 2 -1408.53 2	-1342.3	2 -1455.82 2
		7-O -	-1166.55 4 -1264.23 4 -1282.99 4 -1421.77 4
	H f (w) Q	5-O -3-O -Q •+	-1160.18 5 -1275.06 3 -1268.19 5 -1414.58 5 -1172.29 3 -1255.5 5 -1291.56 3 -1428.2 3 -138.85 -292.05 -231.58 -318.85
		4'-O •	-810.85	1	-908.64	2	-864.47	1	-926.03	1
		3'-O •	-810.46	2	-954.65	1	-863.67	2	-925.48	2
		7-O •	-597.93	5	-746.25	5	-724.71	5	-769.55	5
		5-O •	-615.43	4	-765.73	4	-733.61	4	-788.12	4
		3-O •	-666.62	3	-806.19	3	-797.05	3	-856.24	3
			MNDO		AM1		RM1		PM3
		Neutral	-57.23		-70.31		-54.84		-76.26
		4'-O -	-238.02		-256.13		-231.97		-252.76
		3'-O -	-264.36		-263.62		-258.03		-282.5
		7-O -	-227.2		-239.13		-227.56		-243.62
	Q H f Δ solv	5-O -3-O -Q •+	-249.64 -220.34 -253.3		-258.19 -228.17 -297.14		-243.72 -215.19 -237.08		-269.15 -237.72 -161.99
		4'-O •	-52.4		-55.84		-48.82		-68.95
		3'-O •	-52.92		-101.87		-49.36		-70
		7-O •	-57.49		-87.02		-61.32		-75.72
		5-O •	-76.63		-128.48		-75.43		-98.51
		3-O •	-60.31		-105.23		-59.67		-78.16

Table S2 .

 S2 Heats of formation (in kJ/mol) of myricetin (M) and derived radicals and anions obtained with the various semi-empirical methods employed. Columns to the right of each method (marked with #) present the ordering of H atom abstraction and of deprotonation. Δ solv H f values were calculated as H f (X w )-H f (X g ). -1103.[START_REF] Lide | CRC Handbook Chemistry and Physics[END_REF] 6 -1619.35 2 -1172.98 4 -1650.86 5 4'-O --1497.14 3 -1629.11 1 -1545.83 1 -1646.46 6

			MNDO	#	AM1	#	RM1	#	PM3	#
		Neutral -1060.27		-1046.7		-1031.56		-1135.22
		5'-O --1112.31 5 -1241.45 4 -1243.89 3 -1359.98 5
		4'-O --1260.98 1 -1340.15 2 -1313.89 1 -1388.94 1
		3'-O --1225.25 2 -1298.31 3 -1239.38 5 -1361.35 4
		7-O -	-1128.33 4 -1220.68 5 -1240.23 4 -1385.79 2
	H f (g) M	5-O -3-O -M •+	-1098.8 -1139.76 3 -1364.78 1 -1261.58 2 -1372.39 3 6 -1172.76 6 -1208.75 6 -1324.44 6 21.95 42.02 8.28 -333.69
		5'-O •	-682.5	4	-831.61	3	-760.25	4	-731.81	5
		4'-O •	-950.58	1 -1045.89 1 -1009.37 1 -1041.04 1
		3'-O •	-681.19	5	-831.73	2	-757.54	5	-764.76	4
		7-O •	-882.29	2	-567.26	6	-853.9	2	-933.41	2
		5-O •	-878.14	3	-574.26	5	-845.91	3	-924.17	3
		3-O •	-673.87	6	-787.77	4	-748.69	6	-686.45	6
			MNDO	#	AM1	#	RM1	#	PM3	#
		Neutral -1137.25		-808.95		-1090.09		-1234.87
		5'-O 3'-O --1323.78 4	-1532.6	4 -1371.19 3	-1651.3	4
	(w) M H f	7-O -5-O -3-O -M •+ 5'-O •	-1508.2 -1502.9 -1108.21 5 -1612.95 3 -1166.23 5 -1660.11 3 1 -1137.43 6 -1472.28 2 -1669.31 1 2 -1158.69 5 -998.85 6 -1661.56 2 -229.25 -647.01 -544.02 -597.06 -995.37 3 -1108.83 3 -1047.37 3 -1109.96 2
		4'-O • -1006.36 2 -1108.83 2 -1061.73 2 -1115.98 1
		3'-O •	-992.37	4 -1105.57 4	-1045.9	4 -1107.69 3
		7-O •	-939.22	6	-1047.4	5	-996.72	6 -1018.17 5
		5-O •	-957.07	5 -1134.74 1 -1005.07 5 -1007.22 6
		3-O •	-1009.98 1	-854.79	6 -1066.05 1 -1102.69 4
			MNDO		AM1		RM1		PM3
		Neutral	-76.97		237.75		-58.52		-99.65
		4'-O -	8.96		-377.9		70.9		-290.87
		3'-O -	-236.16		-288.95		-231.94		-257.52
	M H f Δ solv	7-O -5-O -3-O -Q •+ 4'-O •	-98.52 -379.87 -404.1 31.55 -251.2		-234.29 83.25 14.07 -248.17 -689.03		-131.81 -232.05 209.9 95.36 -552.31		-289.95 -283.51 -337.11 -287.72 -263.37
		3'-O •	-312.87		-277.21		-287.12		-378.16
		7-O •	-55.79		-62.94		-52.36		-74.94
		5-O •	-311.17		-273.83		-288.37		-342.93
		3-O •	-56.93		-480.15		-142.82		-84.76

-

Acknowledgments G. C. J. would like to acknowledge a post-doctoral grant from Fundação para a Ciência e a Tecnologia (SFRH/BPD/2006/27563). The authors would also like to thank Dr. Marta Corvo and one of the reviewers for very significant discussions.

Table 8 Order of H atom abstraction and deprotonation of hydroxylic H atoms of quercetin (Q) and myricetin (M) in the gas and water phases obtained with the PM6 model. Data from the literature is also included for comparison Table S1. Heats of formation (in kJ/mol) of quercetin (Q) and derived radicals and anions obtained with the various semi-empirical methods employed.

Table S2. Heats of formation (in kJ/mol) of myricetin (M) and derived radicals and anions obtained with the various semi-empirical methods employed.

Table S3. Dihedral angles (in degrees) of quercetin (Q) and myricetin (M) obtained with the semiempirical methods employed.

Supplementary Material

Click here to download attachment to manuscript: tables_sup_mat_2.doc Table S3. Dihedral angles (in degrees) of quercetin (Q) and myricetin (M) obtained with the semiempirical methods employed.

Myricetin


Benoît Minisini
email: bminisini@ismans.fr

Sylvain Chavand

François Rudolph Barthelery

Ph Benoit Minisini

Benoît Minisini

François Tsobnang

Keywords: dodecyltrimethylammonium, electrostatic charges, quantum calculations Dodecyltrimethylammonium  Electrostatic charges  Quantum calculations

come

Introduction

Since the nineties there has been a growing interest in cationic surfactants due to their important implications in new technologies such as the room temperature ionic liquids [1] or nanomaterials [2]. From the same date the molecular modelling simulations were intensively carried out for different purposes well detailed in different reviews [3][4][5]. Among the different methods available, in spite of the simulated size and time limitations, atomistic methods are still considered as the most precise techniques to study surfactants systems. The main characteristics of the atomistic method rely on an accurate treatment of the van der Waals and Coulombic interactions. Therefore, the parameterization of the partial atomic charges is crucial in the evaluation of numerical results when a quantitative comparison with experimental data is required. This statement is perfectly illustrated by the works of Heinz et al. dealing with the experimental determination of the partial atomic charges of silicates [6] and the impact of the partial charges on the surface energy calculations [7]. However from our knowledge, there are no any experimental techniques available to measure the electrostatic charges of surfactants. Consequently, numerical methods remain the most accurate means to evaluate these charges. In general, the charges of alkylammonium ions are directly taken from existing force fields such as COMPASS [8][9][10][11] or ffgmx [12]. When UFF [13][14][15][16][17] and Dreiding [16][17][18][19][20][21][22][23] force fields are used the charges are often evaluated from the charge equilibration method [14,15,[18][19][20][21][22]. Otherwise, the charges for NH 4 + , CH 3 NH 3 + and (CH 3 ) 4 N + evaluated by Jorgensen et Gao [24] in 1986 owing to a population analysis on wave functions obtained at HF/6-31G* level are extensively used for more recent atomistic simulation studies [25][26][27][28][29]. At the beginning of the nineties, Böcker et al. [30] used the same level of theory to evaluate the charge distribution on ethyltrimethylammonium ion, once again their results were used as a reference for more recent atomistic simulation studies [31][32].

More recently a method deriving the charge from electrostatic potential calculated at a HF/6-31G* level was used to evaluate the atomic partial charges of hexylammonium [34], hexytrimethylammoium [34], dodecyltrimethylammonium [33,34] and octyltrimethylammonium [35] ions. However, as far as we know, the only results including the correlation effects were obtained for cetylpiridinium ion [36] from B3LYP/SVP calculations.

From these previous works we can notice an important dispersion of the values of the atomic charges. For example, the nitrogen charges cover a range of values from -0.628e [37] to 0.20e [34] for alkyltrimethylammonium ion. Moreover, the charges were in some cases only calculated for the headgroup and consequently the charges of the alkyl group of the tail were fixed at zero. However, from a study of charge distribution in ionic surfactant performed with semiempirical methods, Huibers [38] have shown that 10% of the positive charge could reside on the tail.

Consequently, the aim of this work was to compare the charge distributions in dodecyltrimethylammonium ion (CH 3 (CH 2 ) 11 (CH 3 ) 3 N + ) obtained with different methods.

The wave functions and the electrostatic potential determinations were performed using HF, MP2, LDA, GGA, B3LYP theories and the 6-31++G(d,p) basis set on geometry previously optimized with the B3LYP theory and 6-31++G(d,p) basis set. After a comparison of the electrostatic potential, we compared the atomic partial charges calculated according to three methods from electrostatic potentials, natural population analysis and the atomic polar tensor analysis. These results were also compared to those obtained from charge equilibration methods and those available in COMPASS force field.

Methodology

The linear geometry of dodecyltrimethylammonium ion was optimized using the GAUSSIAN98 [START_REF] Frisch | Gaussian 98, Revision A7[END_REF] program at the B3LYP/6-31++g(d,p) level. The SCF convergence on the density matrix was set up at 10 -8 a.u whereas the Berny algorithm [START_REF] Peng | [END_REF] was used for the optimization with the criteria for convergence being a maximum force less than 45 10 -5 a.u and a rms force less than 3 10 -4 a.u. Then the molecular electrostatic potential(MEP) and the atomic population were evaluated, using Hartree-Fock (HF) [41], second order Moller-Plesset perturbation theory (MP2) [42], local density approximation(LDA) [43], generalized gradient approximation(GGA) with the PBE [44] exchange correlation functional and B3LYP [45][46] hybrid exchange correlation functional with 6-31++g(d,p) basis set, on the previously optimized geometry using the GAUSSIAN03 [START_REF] Frisch | Gaussian 03, Revision C.02. Gaussian Inc[END_REF] program. Population analyses were first evaluated using three methods based on the fit of the molecular electrostatic potential under the constraint of reproducing the dipole moment. The CHELP [48] method was used with the atomic radii defined by Francl and five shells leading to 2892 points to fit. The CHELPG [49] method was used with the atomic radii defined by Breneman. The grid spacing and the outer grid radius were 0.

Results and discussion

The structure of the optimized dodecyltrimethylammonium ion and the molecular electrostatic potential mapped on the electron density surface is presented in Fig. 1. An isodensity value of 0.002 e/Bohr 3 was chosen. This mapped surface was created from the results obtained at B3LYP level with a color scale varying from 0 kcal mol -1 (red) to 127 kcal mol -1 (blue). From these results, the molecule can be clearly divided into three parts. The blue region on the right represents an important electrophilic region with an important positive electrostatic potential.

This region includes the nitrogen atoms, the three methyl groups and the two first alkyl groups of the tail. The second region of green color spreading from Met2 to Met7 means that the electrostatic potential is significantly positive in this area. The color in the last region, including the rest of the tail, ranges from greenish yellow to orangish yellow. Consequently, even if it is close to zero the electrostatic potential remains positive even far away from the headgroup. The same division is visible from the results obtained with the two ab initio methods and the three density functional theory methods. However, the net maximal value of the positive electrostatic potential (V max ) is different in function of the methods. For an isodensity value of 0.002 e/bohr 3 , V max ranges from 124 kcal mol -1 to 132 kcal mol -1 . The most positive values are obtained for the HF methods. The value of V max is also basis set dependant since V Max obtained at the HF/6-31g(d) level is 3 kcal mol -1 higher than the value obtained at the HF/6-31g++(d) level. The lowest value of V max is obtained with the LDA calculation whereas GGA and hybrid results are close together.

Table 1 and Table 2 present the atomic partial charges evaluated with the different methods.

The results obtained with the HF/6-31G(d) are not presented but can be given on demand. As observed in previous works [34,37], the sign of the nitrogen partial charge depends on the methods of evaluation. Thus all the methods based on the fitting of the electrostatic potential gave a positive nitrogen value varying from 0.05|e| to 0.32|e| respectively for the MK scheme at the LDA-6.31++G(d,p) level and the CHELP scheme at the HF-6-31++G(d,p) level. The CHELPG nitrogen charge is, on average on the chemistry models, 0.1|e| and 0.17|e| more positive than the values obtained with the CHELP and the MK schemes. This difference is not due to a bad fitting technique since for all these methods, the maximum root mean square (rms) and the relative rms (rrms) are small with the most important value being 0.00233 u.a and 0.02751% respectively. This discrepancy has already been revealed [59] and could be attributed to the different van der Waals radii used in the three schemes, the nitrogen van der Waals radius is 1.50, 1.67 and 1.70 Bohr for the MK, CHELP and CHELPG methods respectively, and the choice of the points used in the least-squares fit of the electrostatic potential. More recent methods such as CHELP-BOW [60] could be tested to see the effect of the inclusion of fit potential points inside the van der Waals surface. On the other hand the nitrogen charges evaluated by NPA and APT are negative. However, the calculated values are less negative than the atomic charges used in commercial force fields. Concerning the charge of the carbon atoms in the methyl groups, all the methods but APT give negative values. We can also notice that the NPA method is the only one which does not make the distinction between the three methyl groups. In all the others methods the atomic charges of the two methyl groups equivalent by mirror symmetry and which include C 1 and C 2 carbon atoms are the same and are different from the methyl group which include the C 3 carbon atom. The negative atomic charges on nitrogen and carbon atoms and the distinction between the three methyl groups do not agree with the distribution of the electrostatic potential visible in Fig. 1.

The electrostatic potential is positive all around the headgroup, consequently we expected to have a positive atomic charge on all the atoms present in the headgroup. Moreover, the potential is more positive close to the nitrogen atom than the hydrogen atoms but all the methods gave an atomic charge on the nitrogen atom less important than on the hydrogen atoms.

From a more global point of view, it is interesting to evaluate the global charge of the headgroup to compare this value with the common model using a point unit charge at the headgroup. The α methylene group linking the headgroup to the tail has been included in the reported values. It appears that the charge is less than 1|e| for all the methods. With the exception of the exceptionally low value of 0.379|e| obtained with the semi empirical method Qeq the charges range from 0.78|e| to 0.95|e|. This last value calculated with the other semiempirical method Gasteiger1.0 was relatively close to that evaluated with the NPA method ranging from 0.92|e| to 0.93|e|. Then, the charges calculated from the APT and CHELP methods ranged from 0.85|e| to 0.87|e| and finally, the MK and CHELPG methods gave some values between 0.77|e| and 0.80|e|. In general for the same method of calculation the charges follow this order HF>B3LYP>PBE>LDA. The CHELP method is sensitive to the exchange correlation term with a maximal difference of 0.02|e| contrary of the NPA method with a difference of less than 0.009|e|. Consequently, we can say that the charge of the headgroup is more sensitive to the way atomic charges are determined than to the quantum chemical model. The most important discrepancy is that of 17% between the MK charges and the NPA evaluated at the B3LYP level. It is difficult to know if a method is better than another but we could be sure that such an important difference of charge affects the solubility of the molecule. Compared to a point unit charge model, all of the calculations lead to a delocalization of the positive charge on the tail as observed by Huibers [38] owing to semiempirical quantum calculation. To evaluate the expansion of this distribution we plotted the distribution of the alkyl groups charges along the tail.

Fig. 2 represents the distribution for the charges estimated from the electrostatic potential evaluated at the B3LYP level, the other results give similar shape with slightly different charges and are not represented for better visibility. We can see that the least square fit lead to an odd-even effect with a set of alternative positive and negative alkyl group charges. This behaviour seems unrealistic compared to the electrostatic potential monotonous decreasing along the tail. The concept of charge alternation was put in evidence by Pople and Gordon [61] at the end of the sixty's. P. Poltizer et al. [62] reviewed the controversial experimental and numerical data of the seventy's and performed some calculations on fluorine hydrocarbon at the beginning of the eighty's. Relying on this review, their results and the work of Weinstein et al. [63], they concluded that alternating atomic charges are not inconsistent with an electrostatic potential without sign of alternation. Moreover, if we sum up the partial charges of the first four alkyl groups we find a charge of 0.19|e|, 0.16|e| and 0.11|e| respectively for MK, CHELPG and CHELP method. The sum of the partial charges on Met5, Met6 and Met7 was close to 0.3|e| for all the methods whereas the sum of the last four alkyl groups lead to a charge of 0|e|. Consequently, even if the partial charges of the alkyl group seemed wrong the distribution of the charge along the tail was consistent with the electrostatic potential.

This delocalization is also visible on Fig. 3 representing the distribution of the partial charge evaluated with the APT and NPA methods. The evolution of the charge along the tail was very similar whereas the methods are completely different from a technical point of view. In both cases we had a low partial charge on Met1 and then a greater charge on Met2 followed by a monotonous decrease of the partial charges until Met8. As in Fig. 2, we can see an odd even effect but only on the last four methyl groups. The sums of the partial charges on the last four alkyl groups were 0.02|e| and 0.01|e| respectively for APT and NPA. This result is in agreement with the positive electrostatic potential visible at the end of the tail in Fig. 1.

As expected the partial charges given in commercial force fields did not take into account the distribution of the positive charge on the tail, Fig. 4. The semiempirical method Gasteiger gave a positive charge delocalized on the first two alkyl groups whereas Qeq delocalized more than 60% of the charge all along the tail, the last alkyl group having a charge higher than 0.10|e|. Consequently, from these results, the Qeq method did not seem appropriate for the evaluation of the atomic partial charge in the dodecyltrimethylammonium.

With regard to the results on a whole it is obvious that all the tested methods provided different distributions of the partial charges. However, it is complicated to conclude which method is the best due to the difficulty in finding the quality criteria. Nevertheless, these partial charges are intended to be used as input parameters in atomistic simulations.

Consequently, it would be interesting to see if the discrepancies induced by the different models of atomic partial charges are within the range for statistical error generated by molecular dynamic simulations.

Conclusions

The electrostatic potential of dodecyltrimethylammonium ion was evaluated at different level for various theories. Then, the influence of the methods for deriving atomic charges from the electrostatic potential was analyzed. The results were compared to other quantum techniques, Distribution of the derived partial charges from electrostatic potential along the 13 alkyl tail. Met X stands for the X th methylene group composed of C tX and the two 14 H tX atoms define d in Table 1 and2 15 16 Fig. 3 Distribution of partial charges estimated from the natural population analysis 17 (NPA) and the Cioslowki's atomic polar tensor (APT) along the alkyl tail 18 19 Fig. 4 Distribution of partial charges estimated from semiempirical method Qeq and 20 Gasteiger and available in COMPASS force field 21

  the natural population analysis (NPA), the Cioslowki's atomic polar tensor (APT) and semi empirical methods. From the electrostatic potential, the molecule can clearly be divided into three parts in function of the values ranging from 0 to 127 kcal mol -1 . The partial charges evaluated with the NPA and APT methods represent pretty well the monotonous decrease of the electrostatic potential along the tail. The same is true for the methods based on the fitting of the electrostatic potential giving some unrealistic negative partial charges along the tail. It is clear from the results that the different methods provide different estimations of the atomic charges. However, further investigations are now necessary to assess the influence of these different distributions of charge on the results obtained with atomistic simulation.

Figure captions 8 Fig. 1 12 Fig. 2

 81122 Figure captions

4

 4 Figure 1 Click here to download high resolution image

  3 Bohr and 2.8 Bohr respectively resulting in 25882 points to fit.

	used around the van der Waals envelope defined by the Merz-Kollman atomic radii. The
	default density of grid points provided 1861 points used for the fitting. The Natural
	Population Analysis [52, 53] (NPA) and the Cioslowki's Atomic Polar Tensor [54, 55] (APT)
	were also considered. These results were compared to less demanding methods such as the
	charge equilibration methods available in the Materials Studio software package[56] (version
	4.2). Qeq_charge 1.1 [57] and Gasteiger 1.0 [58] methods were used with a convergence limit
	of 5*10 -6 |e|.
	Concerning the MK [50, 51] method, 4 shells, with scaling factor ranging from 1.4 to 2, were

Table 1

 1 Atomic partial charges calculated in the framework of the density functional theory 1

	2
				LDA-6-31++G(d,p)			PBE-6-31++G(d,p)			B3LYP-6-31++G(d,p)
			MK	CHELP CHELPG	NPA	MK	CHELP CHELPG	NPA	MK	CHELP CHELPG	NPA	APT
	N	N	0.05	0.23	0.14	-0.29	0.10	0.26	0.17	-0.31	0.11	0.27	0.18	-0.33 -0.43
	C 1 C 1 -0.41 -0.09	-0.28	-0.54	-0.38 -0.07	-0.25	-0.48	-0.35	-0.05	-0.22	-0.45 0.17
	H 1a H 1a 0.21	0.08	0.16	0.29	0.19	0.07	0.14	0.27	0.18	0.06	0.13	0.26	0.04
	H 1b H 1b 0.23	0.10	0.17	0.29	0.21	0.09	0.16	0.27	0.20	0.08	0.15	0.26	0.05
	H 1c H 1c 0.20	0.09	0.16	0.29	0.19	0.08	0.14	0.27	0.18	0.08	0.13	0.26	0.05
	C 2 C 2 -0.41 -0.08	-0.28	-0.54	-0.38 -0.06	-0.25	-0.48	-0.35	-0.05	-0.22	-0.45 0.17
	H 2a H 2a 0.23	0.10	0.17	0.29	0.21	0.09	0.16	0.27	0.20	0.08	0.15	0.26	0.05
	H 2b H 2b 0.21	0.08	0.16	0.29	0.19	0.07	0.14	0.27	0.18	0.06	0.13	0.26	0.04
	H 2c H 2c 0.21	0.09	0.16	0.29	0.19	0.08	0.14	0.27	0.18	0.08	0.13	0.26	0.05
	C 3 C 3 -0.53 -0.34	-0.32	-0.54	-0.48 -0.30	-0.28	-0.48	-0.45	-0.28	-0.25	-0.45 0.19
	H 3a H 3a 0.24	0.15	0.17	0.29	0.22	0.13	0.15	0.27	0.21	0.12	0.14	0.26	0.05
	H 3b H 3b 0.24	0.15	0.17	0.29	0.22	0.13	0.15	0.27	0.21	0.12	0.14	0.26	0.05
	H 3c H 3c 0.25	0.18	0.17	0.29	0.23	0.16	0.16	0.27	0.22	0.15	0.15	0.26	0.04
	C α	C -0.24 0.08	-0.19	-0.30	-0.21	0.09	-0.16	-0.26	-0.19	0.10	-0.15	-0.23 0.34
	H α H	0.16	0.02	0.12	0.28	0.14	0.02	0.11	0.27	0.14	0.01	0.10	0.26	0.00
	H α H	0.16	0.02	0.12	0.28	0.14	0.02	0.11	0.27	0.14	0.01	0.10	0.26	0.00
	C t1 C	0.04	0.18	0.07	-0.54	0.05	0.19	0.08	-0.50	0.06	0.20	0.09	-0.48 0.00
	H t1 H	0.05 -0.06	0.02	0.27	0.04	-0.06	0.01	0.25	0.03	-0.07	0.01	0.24 -0.01
	H t1 H	0.05 -0.06	0.02	0.27	0.04	-0.06	0.01	0.25	0.03	-0.07	0.01	0.24 -0.01
	C t2 C -0.08 -0.08	0.00	-0.51	-0.05 -0.05	0.03	-0.47	-0.04	-0.04	0.04	-0.45 0.13
	H t2 H	0.05	0.01	0.02	0.26	0.04	0.00	0.01	0.25	0.03	-0.01	0.00	0.23 -0.03
	H t2 H	0.05	0.01	0.02	0.26	0.03	0.00	0.01	0.25	0.03	-0.01	0.00	0.23 -0.03
	C t3 C -0.06 0.19	-0.07	-0.51	-0.04	0.20	-0.05	-0.47	-0.02	0.22	-0.03	-0.45 0.11
	H t4 H	0.03 -0.04	0.02	0.26	0.02	-0.05	0.01	0.24	0.01	-0.05	0.00	0.23 -0.04
	H t4 H	0.03 -0.04	0.02	0.26	0.02	-0.05	0.01	0.24	0.01	-0.05	0.01	0.23 -0.04
	C t15 C	0.06	0.07	0.04	-0.51	0.08	0.09	0.06	-0.47	0.09	0.10	0.07	-0.45 0.10
	H t5 H	0.00 -0.04	0.00	0.26	-0.01 -0.05	-0.01	0.24	-0.02	-0.06	-0.02	0.23 -0.04
	H t5 H	0.00 -0.04	0.00	0.26	-0.01 -0.05	-0.01	0.24	-0.02	-0.06	-0.02	0.23 -0.04
	C t6 C -0.05 0.05	0.02	-0.51	-0.03	0.07	0.04	-0.47	-0.01	0.09	0.06	-0.44 0.10
	H t6 H	0.02 -0.05	0.00	0.26	0.00	-0.06	-0.01	0.24	0.00	-0.06	-0.02	0.23 -0.05
	H t6 H	0.02 -0.05	0.00	0.26	0.00	-0.06	-0.01	0.24	0.00	-0.06	-0.02	0.23 -0.05

Table 2

 2 Atomic partial charges calculated at the Hartree Fock and post Hartree Fock level 4 of theory, semi empirical level and given by commercial force field 5

	6
			HF-6-31++G(d,p)			MP2-6-31++G(d,p)		Semi empirical	Force field
		MK	CHELP CHELPG	NPA	MK	CHELP CHELPG	NPA	Gasteiger	Qeq	COMPASS
	N	0.15	0.32	0.22	-0.41	0,15	0,32	0,22	-0,41	0.14	-0.40	-0.628
	C 1 -0.38 -0.08	-0.25	-0.37	-0,38 -0,08	-0,25	-0,37	0.02	-0.25	0.248
	H 1a 0.19	0.07	0.14	0.24	0,19	0,07	0,14	0,24	0.06	0.15	0.053
	H 1b 0.21	0.09	0.15	0.24	0,21	0,09	0,15	0,24	0.06	0.15	0.053
	H 1c 0.19	0.08	0.14	0.24	0,19	0,08	0,14	0,24	0.06	0.15	0.053
	C 2 -0.38 -0.08	-0.25	-0.37	-0,38 -0,08	-0,25	-0,37	0.02	-0.25	0.248
	H 2a 0.21	0.09	0.16	0.24	0,21	0,09	0,15	0,24	0.06	0.16	0.053
	H 2b 0.19	0.07	0.14	0.24	0,19	0,07	0,14	0,24	0.06	0.15	0.053
	H 2c 0.19	0.08	0.14	0.24	0,19	0,08	0,14	0,24	0.06	0.15	0.053
	C 3 -0.51 -0.33	-0.28	-0.37	-0,51 -0,33	-0,28	-0,37	0.02	-0.27	0.248
	H 3a 0.22	0.13	0.15	0.24	0,22	0,13	0,15	0,24	0.06	0.15	0.053
	H 3b 0.22	0.13	0.15	0.24	0,22	0,13	0,15	0,24	0.06	0.16	0.053
	H 3c 0.23	0.16	0.16	0.24	0,23	0,16	0,16	0,24	0.06	0.16	0.053
	C α -0.23 0.11	-0.17	-0.17	-0,23	0,11	-0,17	-0,17	0.04	-0.13	0.301
	H α 0.15	0.01	0.11	0.24	0,15	0,01	0,11	0,24	0.07	0.16	0.053
	H α 0.15	0.01	0.11	0.24	0,15	0,01	0,11	0,24	0.07	0.16	0.053
	C t1 0.07	0.20	0.10	-0.44	0,07	0,20	0,10	-0,44	-0.02	-0.28	-0.106
	H t1 0.03 -0.07	0.00	0.22	0,03	-0,07	0,00	0,22	0.03	0.16	0.053
	H t1 0.03 -0.07	0.00	0.22	0,03	-0,07	0,00	0,22	0.03	0.16	0.053
	C t2 -0.05 -0.05	0.04	-0.41	-0,05 -0,05	0,04	-0,41	-0.05	-0.31	-0.106
	H t2 0.03	0.00	0.00	0.22	0,03	0,00	0,00	0,22	0.03	0.17	0.053
	H t2 0.03	0.00	0.00	0.22	0,03	0,00	0,00	0,22	0.03	0.17	0.053
	C t3 -0.03 0.21	-0.05	-0.41	-0,03	0,21	-0,05	-0,41	-0.05	-0.29	-0.106
	H t4 0.01 -0.05	0.01	0.21	0,01	-0,05	0,01	0,21	0.03	0.17	0.053
	H t4 0.01 -0.05	0.01	0.21	0,01	-0,05	0,01	0,21	0.03	0.17	0.053
	C t15 0.09	0.10	0.07	-0.41	0,09	0,10	0,07	-0,41	-0.05	-0.29	-0.106
	H t5 -0.02 -0.06	-0.02	0.21	-0,02 -0,06	-0,02	0,21	0.03	0.17	0.053
	H t5 -0.02 -0.06	-0.02	0.21	-0,02 -0,06	-0,02	0,21	0.03	0.17	0.053
	C t6 -0.02 0.07	0.05	-0.41	-0,02	0,07	0,05	-0,41	-0.05	-0.30	-0.106
	H t6 0.00 -0.06	-0.02	0.21	0,00	-0,06	-0,02	0,21	0.03	0.17	0.053
	H t6 0.00 -0.06	-0.02	0.21	0,00	-0,06	-0,02	0,21	0.03	0.17	0.053
	C t7 0.02	0.26	0.03	-0.41	0,02	0,26	0,03	-0,41	-0.05	-0.29	-0.106
	H t7 -0.01 -0.08	-0.02	0.21	-0,01 -0,08	-0,02	0,21	0.03	0.17	0.053
	H t7 -0.01 -0.08	-0.02	0.21	-0,01 -0,08	-0,02	0,21	0.03	0.17	0.053
	C t8 0.10	0.09	0.10	-0.41	0,10	0,09	0,10	-0,41	-0.05	-0.30	-0.106
	H t8 -0.03 -0.05	-0.03	0.20	-0,03 -0,05	-0,03	0,20	0.03	0.17	0.053
	H t8 -0.03 -0.05	-0.03	0.20	-0,02 -0,05	-0,03	0,20	0.03	0.17	0.053
	C t9 -0.07 0.03	-0.02	-0.41	-0,06	0,03	-0,02	-0,41	-0.05	-0.30	-0.106
	H t9 0.00 -0.05	-0.01	0.20	0,00	-0,05	-0,01	0,20	0.03	0.17	0.053
	H t9 0.00 -0.05	-0.01	0.20	0,00	-0,05	-0,01	0,20	0.03	0.17	0.053
	C t10 0.00	0.22	0.03	-0.41	0,00	0,22	0,03	-0,41	-0.05	-0.28	-0.106
	H t10 0.00 -0.07	-0.01	0.20	0,00	-0,07	-0,01	0,20	0.03	0.18	0.053
	H t10 0.00 -0.07	-0.01	0.20	0,00	-0,07	-0,01	0,20	0.03	0.18	0.053
	C t11 0.19	0.20	0.19	-0.42	0,19	0,20	0,18	-0,42	-0.06	-0.30	-0.106
	H t11 -0.03 -0.07	-0.04	0.20	-0,03 -0,07	-0,04	0,20	0.03	0.18	0.053
	H t11 -0.03 -0.07	-0.04	0.20	-0,03 -0,07	-0,04	0,20	0.03	0.18	0.053
	C t12 -0.28 -0.09	-0.21	-0.60	-0,28 -0,09	-0,21	-0,60	-0.07	-0.41	-0.159
	H t12 0.06 -0.01	0.04	0.20	0,06	-0,01	0,04	0,20	0.02	0.17	0.053
	H t12 0.06 -0.01	0.04	0.20	0,06	-0,01	0,04	0,20	0.02	0.17	0.053
	H t12 0.07	0.03	0.05	0.21	0,07	0,03	0,05	0,21	0.02	0.17	0.053