Quantum chemical calculations in the structural analysis of phloretin

Journal of Molecular Structure 930 (2009) 187–194

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Journal of Molecular Structure journal homepage: www.elsevier.com/locate/molstruc

Quantum chemical calculations in the structural analysis of phloretin Andrea Gómez-Zavaglia Department of Chemistry, University of Coimbra, P-3004-535 Coimbra, Portugal Centro de Investigación y Desarrollo en Criotecnología de Alimentos (Conicet La Plata, UNLP) RA-1900, Argentina

a r t i c l e

i n f o

Article history: Received 10 April 2009 Received in revised form 6 May 2009 Accepted 6 May 2009 Available online 13 May 2009 Keywords: Phloretin Cluster analysis H-bonds Conformational analysis Dendrogram

a b s t r a c t In this work, a conformational search on the molecule of phloretin [20 ,40 ,60 -Trihydroxy-3-(4-hydroxyphenyl)-propiophenone] has been performed. The molecule of phloretin has eight dihedral angles, four of them taking part in the carbon backbone and the other four, related with the orientation of the hydroxyl groups. A systematic search involving a random variation of the dihedral angles has been used to generate input structures for the quantum chemical calculations. Calculations at the DFT(B3LYP)/6311++G(d,p) level of theory permitted the identification of 58 local minima belonging to the C1 symmetry point group. The molecular structures of the conformers have been analyzed using hierarchical cluster analysis. This method allowed us to group conformers according to their similarities, and thus, to correlate the conformers’ stability with structural parameters. The dendrogram obtained from the hierarchical cluster analysis depicted two main clusters. Cluster I included all the conformers with relative energies lower than 25 kJ mol1 and cluster II, the remaining conformers. The possibility of forming intramolecular hydrogen bonds resulted the main factor contributing for the stability. Accordingly, all conformers depicting intramolecular H-bonds belong to cluster I. These conformations are clearly favored when the carbon backbone is as planar as possible. The values of the mC@O and mOH vibrational modes were compared among all the conformers of phloretin. The redshifts associated with intramolecular H-bonds were correlated with the H-bonds distances and energies. Ó 2009 Elsevier B.V. All rights reserved.

1. Introduction Flavonoids are natural products derived from 2-phenylchromen-4-one (flavone). They are widely distributed in plants and fulfill many functions, including the production of yellow or red/blue pigmentation in flowers and their protection from attack by microbes and insects. The anti-allergic, anti-inflammatory, antimicrobial and anti-cancer activity of flavonoids have attracted the attention of food manufacturers and consumers [1,2]. Phloretin [20 ,40 ,60 -trihydroxy-3-(4-hydroxyphenyl)-propiophenone or 3-(4-hydroxyphenyl)-1-(2,4,6-trihydroxyphenyl)-1-propanone] is a flavonoid known by its anti-oxidant activity and it is mainly present in apples. In this sense, the anti-oxidative properties of apples have been attributed to the phytochemicals present in the apple skin, namely phloretin [3,4]. The generation and abundance of reactive oxygen species is closely associated with the development and progression of atherosclerosis, and phloretin has an active role in avoiding the accumulation of these reactive oxygen species [5]. In its uncharged form, phloretin is known to be a powerful inhibitor of the glucose transport system in human red blood cell

E-mail address: [email protected] 0022-2860/$ - see front matter Ó 2009 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2009.05.014

membrane [6–8]. In addition, it affects the membrane transport of glycerol, urea, chloride and a great number of other charged and neutral substances. It also acts as an uncoupler of the mitochondrial oxidative phosphorylation [9]. From a physical chemistry point of view, phloretin is known to adsorb to lipid surfaces and alter the dipole potential of lipid monolayers and bilayers [9–11]. In this respect, the effect of phloretin on lipid membranes can be ascribed to its strong interaction with the phosphate groups of lipids, as demonstrated by the pronounced downward shift of the asymmetric vibration frequencies of lipid phosphates in the FTIR spectra [9–11]. The interaction of phloretin with lipids can be investigated from two points of view: (a) considering the lipid changes induced by phloretin, thus focusing the study on the lipids or (b) considering the conformations that the flavonoid may adopt in the interaction, thus focusing the study on the phloretin structure. Up to our knowledge, only the first approach (a) has been used to deal with the phloretin–lipid interaction. On the contrary, no attempts to investigate the molecular structure of phloretin have been reported hitherto. In this sense, quantum chemical calculations constitute a powerful method to deal with this issue. Taking into account the lack of fundamental information on phloretin, this work aims to shed light on the molecular structure of the compound, as a first step to understand its behavior and

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mechanisms of action in more complex environments (i.e., biological environments). In order to assess the molecular structure of phloretin, a systematic conformational study of the compound in the gaseous phase has been carried out. With its 34 atoms, phloretin is a large molecule rich in low-energy conformational minima. In this work, an effort was made to systematically search the most relevant conformers. This search involved a random variation of the relevant dihedral angles to generate more structures, which were subsequently subjected to minimization. The molecular structures of the located conformers have then been analyzed using hierarchical cluster analysis. This method allowed us to group conformers according to similarities, and thus, to correlate the conformers’ stability, hydrogen bonding properties and mC@O and mOH vibrational frequencies. 2. Materials and methods 2.1. Computational methodology The semi-empirical PM3 method was used to perform a systematic preliminary conformational search on the phloretin potential energies surfaces (PES). It provided a quick assessment of the energy conformers suitable for further analysis. This conformational search was carried out using HyperChem Conformational Search module (CyberChem, Inc. Ó 2004) [12]. Taking into account the high flexibility of the phloretin molecule, a random search appeared as the most appropriate way to perform a conformational analysis [13–15]. In this approach, the generation of new starting conformations for the energy minimization uses a random variation of the dihedral angles of previously found conformers [13,14]. The method searches on until all given starting geometries have been used or no new minima are generated. In this work, eight dihedral angles defining conformational isomers of phloretin were considered in the random search: C2C1C13C16, C1C13C16C19, C13C16C19C21, C16C19C21C23, C21C22O29H30, C25C26O31H32, C21C23O33H34 and C3C4O11H12 (see Scheme 1). Conformations with energies lower than 75 kJ mol1 were stored while higher-energy conformations or duplicate structures were discarded. The structures obtained from the random search served as start point for the construction of the input files later used in the quantum chemical calculations. The quantum chemical calculations were performed with Gaussian 98 [16] at the DFT level of theory, using the 6-

311++G(d,p) basis set [17]. The three-parameter density hybrid functional abbreviated as B3LYP, which includes Becke’s gradient exchange correction [18] and the Lee, Yang and Parr [19] and Vosko, Wilk and Nusair correlation functionals, was selected for calculations [20]. Conformations were optimized using the Geometry Direct Inversion of the Invariant Subspace (GDIIS) method [21]. The optimized structures of all conformers were confirmed to correspond to true minimum energy conformations on the PES. The calculated frequencies were considered as obtained in calculation, without any further scaling. 2.2. Cluster analysis After obtaining the optimized structures of the conformers of phloretin, a double entrance table was constructed as follows: All dihedrals defining the conformers were considered for the analysis. For each dihedral angle, different columns corresponding to specific ranges of its possible values were built. The following ranges were considered: (a) for C2C1C13C16: 80–95° and 50–55°, (b) for C1C13C16C19: ca. 60°, ca. 90° and 180°, (c) for C13C16C19C21: ca. 120°, ca. 140°, ca. 160°, ca. 45°, ca. 60°, ca. 75°, ca. 90°, ca. 120°, ca. 180°, (d) for C16C19C21C23: ca. 0°, 40–50°, 55–75°, ca. 120°, ca. 155°, ca. 180°, (e) for C21C22O29H30: ca. 0° and ca. 180°, (f) for C25C26O31H32: ca. 0° and ca. 180°, (g) for C21C23O33H34: ca. 0° and ca. 180°, (h) for C3C4O11H12: ca. 0° and ca. 180°. The ranges were defined according to the values obtained for the dihedrals considered in all the conformers. Symmetry related conformers were discarded. Once defined the column ranges for all the dihedrals, the presence or absence of a given dihedral value was assigned as 1 and 0, respectively. For example, if the dihedral C16C19C21C23 is ca. 120°, 0 will be the value assigned to the columns corresponding to the ranges ca. 0°, 40–50°, 55–75°, ca. 155° and ca. 180°, and 1, the value assigned to the column corresponding to ca. 120°. The comparison among conformers was carried out using the simple-matching coefficient (Ssm), which was calculated as

Ring A

Ring B 34 20

7 14,15

33

8

28 13

6

19

1

5 4

16

3

11

23 21

2

17,18 29

22

25 24

32

26

10 31 12

9

30

27

3-(4-hydroxyphenyl)-1-(2,4,6-trihydroxyphenyl)propan-1-one Scheme 1.

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Ssm ¼ ða þ cÞ=ða þ b þ cÞ where a and c correspond to the number of matching present and absent angle values, respectively, and b represents the number of non-matching angle values between pairs of conformers. The Ssm between any pair of conformers was computed. The matrix of the Ssm correlation coefficients was clustered by the unweighted average linkage method [22–25] using SYSTAT (version 12.0). 3. Results Phloretin has eight internal rotational axes that can give rise to different conformers. But, which are the most relevant ones in determining the global stability of a given conformer? The answer of this question becomes important when one attempts to understand the behavior of phloretin in more complex chemical or biochemical environments. After optimizing the structures obtained from the random search at the DFT(B3LYP)/6-311++G(d,p) level of theory 58 conformational isomers were found, all of them belonging to the C1 symmetry point group. Table 1 presents the calculated relative energies and dipolar moments of all the conformers calculated at the DFT(B3LYP)/ 6-311G++(d,p) level of theory. The values corresponding to the dihedral angles determining the conformational structures are provided in Table S1. In view of the huge number of conformers, the correlation between structure and molecular properties requires a systematic analysis that can be achieved using hierarchical cluster analysis. This type of analysis allows grouping conformers according to their similarity. In principle, all dihedrals obtained from calculations can be considered as parameters for cluster analysis. The more parameters included, the more reliable the analysis is. However, it is important to take into account that the simplematching coefficient (Ssm) is a non-weighed algorithm, thus all parameters have exactly the same weight. For this reason, as soon as the number of parameters increases, the importance of each one individually, decreases. Hence, only eight dihedrals defining conformational isomers were included in the cluster analysis. Fig. 1 depicts the dendrogram obtained from the cluster analysis of the phloretin’s conformers. Two main clusters, named I and II, displaying a similarity of 78.2% (Ssm = 0.782) were observed. Cluster I includes 30 conformers with relative energies lower than 25 kJ mol1. This cluster is composed of two subclusters, the first one (A), mainly including conformers with relative energies lower than 12–15 kJ mol1, and the other one (B), including conformers with relative energies within 12–25 kJ mol1. This indicates that within cluster I, it is also possible to find slight differences among the 30 most stable conformational isomers of phloretin. Cluster II is composed of the remaining 28 conformers, all of them with relative energies higher than 50 kJ mol1. It is interesting to note that within each cluster (I and II), the relative energies of the conformers increase gradually, covering all the energy range defining the cluster. However, a great jump separates both clusters: no conformers within the range 25–50 kJ mol1 were found. The careful observation of the structures corresponding to conformers of cluster I indicates that all of them contain intramolecular hydrogen bonds, clearly contributing to their stabilization. These intramolecular hydrogen bondings always involve the carbonyl oxygen as acceptor (O20) and either H30 or H34 as donors. The orientation of H30 or H34 addressed to the carbonyl oxygen is conditioned by the values of the dihedral angles defined by the carbon backbone (C2C1C13C16, C1C13C16C19, C13C16C19C21 and C16C19C21C23). Among these dihedrals, C16C19C21C23 is the most relevant one. If it adopts values of 0 or 180 degrees, intramolecular Hbonds can be formed. If this dihedral angle is different from 0 or 180 degrees, the planarity is broken and the formation of H-bonds,

Table 1 Relative energies, including zero point vibrational contributions and dipolar moments for the various conformers of phloretina. Conformer

DFT(B3LYP)/6-311++G(d,p) DE ZPE

Dipolar moment

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

0.00b 3.41 4.22 4.64 4.86 5.22 8.22 9.20 9.62 10.07 10.32 10.37 11.33 12.14 12.32 12.49 13.16 13.53 15.08 15.54 15.66 16.41 16.86 17.75 17.84 17.89 19.18 19.31 24.41 25.93 53.32 53.34 53.72 53.85 56.33 56.48 56.70 56.88 57.61 57.94 58.36 58.75 59.29 59.60 59.63 59.97 64.21 65.21 65.94 66.10 66.55 66.26 66.83 66.86 68.61 69.12 71.71 72.09

3.66 3.10 4.70 2.31 5.76 5.00 4.91 7.12 4.63 4.45 7.11 3.31 1.86 1.33 2.78 4.16 3.39 5.51 6.29 5.91 0.49 2.38 2.54 1.35 5.10 2.46 3.48 5.15 2.10 4.47 1.51 4.82 4.51 3.71 4.50 2.59 4.75 3.06 4.44 4.97 5.07 5.91 3.45 3.76 5.82 6.42 3.76 3.10 4.19 5.50 4.46 5.84 2.82 5.66 3.13 3.23 3.99 2.91

a

Energies in kJ mol1, dipolar moments in Debyes. Total energy with zero point vibrational energy contribution. The value corresponding to Conformer 1 is 2510425.499 kJ mol1. b

avoided. This happens in the conformers belonging to cluster II (Table S1). The effect of the other dihedrals on the global stability of the conformers can be also analyzed. In general, one can observe that the most stable conformers correspond to the most planar structures. Only the dihedral angles taking part in the carbon backbone contribute to the planarity of the conformers. The dihedral C2C1C13C16 determines the orientation of ring A (see Scheme 1), which is almost perpendicular (+90 or 90 de-

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A

I

B

II

12 10 19 20 8 3 2 1 5 7 6 11 9 4 28 16 13 27 24 26 17 18 14 15 30 29 25 23 22 21 47 31 36 38 53 34 58 57 55 56 52 40 39 50 51 54 42 35 37 41 32 33 46 44 43 45 49 48

100

95.0

90.0

85.0

80.0

75.0

Distances Fig. 1. Dendrogram obtained after unweighted average linkage method analysis of the simple-matching coefficient obtained taking into account the following dihedral angles of the molecule of phloretin: C2C1C13C16, C1C13C16C19, C13C16C19C21, C16C19C21C23, C21C22O29H30, C25C26O31H32, C21C23O33H34 and C3C4O11H12. Similarities are expressed as distances: 1.0 represents 100% similarity and 0.0 represents 0% similarity.

grees) to the dihedral C1C13C16C19 in all the conformers analyzed. This indicates that this dihedral does not have any influence on the global stability of the conformers. The values of dihedrals C1C13C16C19 and C13C16 C19C21 (connecting single bonds carbon chains) do not follow a clear pattern. The more planar the structure these dihedrals define, the more stable the conformer is. However, the non-planarity around these dihe-

drals does not destabilize the conformers in a specific way. In fact, these dihedrals can be far from the planarity in both low- and highenergy conformers. If we intend to rationalize how the four dihedrals from the backbone condition the stability of a given conformer, we can state that C2C1C13C16 does not have any influence, C16C19C21C23 stabilizes a conformer when it is planar (because of the H-bonds), and

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regarding the dihedrals C1C13C16C19 and C13C16 C19C21, the most stable structures have both dihedrals planar and the less stable ones have both dihedrals far from the planarity. Hence, the global stability of a given conformer results mostly from a balance among the conformations around the dihedral angles defined by the carbon backbone. The orientation of the hydroxyl groups also influence the relative stability of the conformers, especially the dihedrals C21C22O29H30 and C21C23O33H34, which are the ones potentially involved in intramolecular H-bondings. The orientation of dihedrals C25C26O31H32 and C3C4O11H12 do not contribute significantly to the relative energies of the conformers because H32 and H12 have no possibility to be involved in any H-bonding. Finally, the description of two conformers, the most and less stable ones (Conformer 1 and 58, respectively) is shown as an example of how the dihedrals contribute to the stabilization of the conformers (Fig. S1). In Conformer 1, C2C1C13C16, remained close to 90 degrees and the other three dihedrals taking part in the carbon backbone are close to 180 degrees (planar). In particular, the planarity of C16C19C21C23 allowed the formation of an intramolecular H-bond (O20  H34). In Conformer 58, all dihedrals taking part in the carbon backbone are clearly far from the planarity and no H-bonds could be formed.

A

3.1. Correlation of the calculated vibrational spectra with selected geometrical parameters As explained in the previous section, the most stable conformers (conformers belonging to cluster I in Fig. 1) have intramolecular H-bondings. These intramolecular H-bonds always involve the carbonyl oxygen as acceptor (O20) and either H30 or H34 as donors, depending on the rotation around the C19C21 bond. It is well known the strong influence of H-bonds on the vibrational spectra. Taking into account the high number of phloretin conformers and the fact that in a single conformer, both free group and hydrogen bonded OH groups can coexist, it is interesting to analyze how these interactions affect the vibrational spectra. Fig. 2A depicts the values corresponding to the calculated mC@O vibrational modes for each conformer of phloretin. In the plot, two groups of conformers are observed, the first one (full squares) corresponding to low mC@O (ca. 1640 cm1) and the second one, to high mC@O (ca. 1750 cm1). The low carbonyl stretching frequencies indicate the participation of the C@O group in H-bonds. Fig. 2B depicts the values corresponding to the mO29H30 and mO33H34 vibrational modes for each conformer. For each vibration, two main groups were observed: the first one, including mOH within the range 3100–3300 cm1 (full squares) and the second one,

1780 1760 1740

ν

1720 1700 1680 1660

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

1640

Conformer

31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

Conformer 3100

3200

3200

3300

3300

3400

3400

3500

3500

3600

3600

3700

3700

3800

3800

3800

3800

3700

3700

3600

3600

3500

3500

3400

3400

3300

3300

3200

3200

3100

3100 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58

3100

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

νO29H30

νO33H34

B

Conformer Fig. 2. (A) Plot showing the values of the mC@O vibrational mode for each conformer of phloretin. Full squares correspond to carbonyl groups involved in H-bonds, opened squares, to carbonyl groups not involved in H-bonds. (B) mO29H30 and mO33H34 frequencies for the conformers of phloretin. Full squares correspond to H-bonded OH groups; opened squares, to free OH groups.

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Dm=cm1 ¼ 0:025½rHO =nm5:6

A

νC=O / cm

-1

1644

1642

1640

1638

1636 158

160

162

164

...

distance =O20 H30 or H34 /pm

B

3280 3260 3240 3220

-1

3200 3180 3160 3140 3120 3100 3080 158

160

162

164

...

distance =O20 H30 or H34 /pm

C

ð1Þ

From the optimized geometries of all the conformers depicting intramolecular H-bonds, the redshifts corresponding to the mOH vibrational modes were estimated. The values obtained were compared with the ones obtained from the calculated vibrational spectra (Table S2). Taking into account that the correlation depicted in Eq. (1) is empirical and it was obtained from intermolecular Hbonds, the correspondence obtained can be considered acceptable. The use of Eq. (1) to calculate redshifts from quantum chemically calculated H-bond distances has two main advantages. From one side, among compounds presenting several H-bonded OH groups, the assignment of the mOH vibrational modes to a specific OH group may be facilitated. From the other side, the vibrational calculations are time consuming and require more important computational resources, particularly for large compounds with biological relevance, such as sugars, oligosaccharides, etc. In these cases, obtaining the mOH redshifts corresponding to each specific OH group from the optimized geometries certainly contributes to save computational time and efforts. The use of quantum chemical calculations offers another interesting advantage: the possibility of selectively deuterate the molecule under study very easily. Taking into consideration this possibility, the molecule of phloretin has been selectively deuter-

1648

1646

νOH / cm

including mOH at ca. 3840 cm1 (opened squares). The first group corresponds to H-bonded OH groups, whereas the second one joins OH not involved in H-bonds (free OH groups). It is important to point out that for each conformer, two mOH, corresponding to the two OH groups (O29H30 and O33H34) were plotted. Among conformers having H-bonds, one of the mOH is typical from H-bonded OH groups (in the range 3100–3300 cm1) and the other mOH, corresponds to free OH groups (ca. 3840 cm1). Among conformers without H-bonds, both mOH occur at ca. 3840 cm1. It is worth mentioning that among H-bonded OH groups, the OH stretching mode occurs at considerably lower wavenumbers and in a larger range (3100–3300 cm1). This reflects differences in the strength of the H-bonds corresponding to the different conformers. Since the O11H12 and O31H32 groups do not take part in any Hbond, their predicted mOH frequencies are similar and typical of free OH groups (ca. 3840 cm1, as predicted by the calculation). Among the conformers containing intramolecular H-bonds, the H-bond distances (O20  H30 or O20  H34) were correlated with the frequencies corresponding to mC@O and mOH modes (Fig. 3A and C). According to Fig. 3A, no correlation was found between the mC@O redshift and the H-bond distance, indicating that vibrational coupling is also important in determining the frequency of the mC@O mode, at least in some of the conformers. In spite of that, a good correspondence was found when the angle O30H34O20 (or O29H30O20) was correlated with the H-bond distance. In this case, it was observed that the closer the angle to 150° is, the shorter the distance (the stronger the H-bond) (Fig. 3B). On the other hand, the values corresponding to the mOH frequencies correlate well with the H-bonds distances, as shown in Fig. 3C. The hydrogen bonds strength and their influence on specific vibrational modes and on the H-bond distances have been analyzed in detail by Rozenberg and co-workers [26–30]. These authors have obtained different empirical correlations that allow the estimation of specific vibrational frequency red or blue shifts from the values of the H-bond distances, and also the estimation of the energies associated to the H-bonds from the frequency values of the OH stretching or torsional modes [27–29]. One of these empirical correlations relates the redshift of the mOH vibrational modes with the H-bond distance:

150.0

149.5

O30H34O20or O29H30O20 / degrees

192

149.0

148.5

148.0

147.5

147.0 158

160

162

164

...

distance =O20 H30 or H34 /pm Fig. 3. (A) Plot correlating the mC@O values and the H-bond distance for all the conformers with intramolecular H-bondings. (B) Plot correlating the O30H34O20 or O29H30O20 angle with the H-bond distance for all the conformers with intramolecular H-bondings. C: Plot correlating the shift of the mOH values and the H-bond distance for all the conformers with intramolecular H-bondings.

ated in the groups taking part in H-bondings and the vibrational spectra were calculated at the DFT(B3LYP)/6-311++G(d,p) level of

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theory for the chosen isotopomers. The values corresponding to the mOD vibrations were also included in Table 2. According to Rozenberg et al. [28,31], the energy associated to H-bonds can be estimated from the following Equation: 

DH ¼ 1:92 ½ðDmOHÞ  40

2

ΔH = =1.92* [(νOH) - 40] (Eq. 2)

40

ð2Þ -1

2

50

1

DH ¼ 0:67  104 Ds2 2

2 Y

ð3Þ

2

where Ds = s  s0 . The subscripts H and O indicate the values corresponding to torsions from H-bonded and free molecules,

Table 2 Hydrogen bond distances and stretching vibrations of the OH, OD and C@O groups.

30

Δ

where DH is the enthalpy in kJ mol and DmOH = mo  mY. The subscripts O and H denote the values of mOH (in cm1) for free molecules and H-bonded, respectively. For the estimation of DH among the non-deuterated conformers, a value of 3840 cm1, corresponding to the average mOH values of free OH groups, was used for mo. For the deuterated conformers, a value of 2795 cm1 was considered as the average mOD value for OD groups not involved in Dbonds. This value, as well as the quantum chemically calculated mOD vibrational modes for each deuterated conformer were corp rected by the isotopic factor of deuterium ( 2) before the applicap 1 tion of Eq. (2). Hence, a value of 3953 cm (2795 cm1 2) was considered for mo in the case of H-bonds in deuterated molecules. The different reference values for m0 in H or D containing molecules is a result of different zero point energies and vibrational couplings. The approximations considered for mOHo and mDHo result very useful because they allow estimating the redshifts of mOH and mOD among conformers with intramolecular H-bonds of D-bonds. From the values obtained for DmOH and DmOD, the enthalpies were calculated according to Eq. (2). Fig. 4 depicts the plot of DH vs the calculated frequency redshifts. As shown for the first time here, Rozenberg et al. correlation Eq. (2) can also be applied for deuterated OD groups. Rozenberg et al. [26] have also reported that the H-bond energies can be as well correlated with the out-of-plane torsional vibration s(OH), according to Eq. (3):

20

10

0 200

400

600

800

1000

-1

Shift νOH ; νOD / cm

Fig. 4. Correlation between DH and the shift mOH (full circles) or mOD (opened circles) for the conformers with intramolecular H-bonds or D-bonds. Eq. (2) was considered to correlate DH values with the mOH shift.

respectively, with DH in kJ mol1 and s in cm1 [26]. According to Lake and Thompson [26,32] a value of 200 cm1, defined for gas phase can be assumed for s0 in alcohols. In the case of torsions, the value of 200 cm1 was preferred instead of the calculated value for the sOH among the non-H bonded conformers because vibrational coupling makes the selection of just one frequency, a difficult task for the phloretin molecule. The values obtained for the H-bond enthalpies using both Eqs. (2) and (3) are comparable and attained values of ca. 32– 37 kJ mol1 and 29–36 kJ mol1, respectively (Table 3). These values demonstrate that the intramolecular H-bonds in all conformers

Table 3 Comparison of the H-bonds energies calculated from the DmOH and DsOH vibrational modes, according to Eqs. (2) and (3) (see text).

Conformer

H-bond distance/pm

mOH/cm1

mC@O/cm1

mOD/cm1

Conformer

DH (from DmOH) (kJ mol1)

DH (from DsOH) (kJ mol1)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

159.0 159.0 159.2 157.6 159.6 157.6 159.7 159.8 158.3 157.7 158.3 157.8 159.9 162.5 162.7 160.7 163.5 163.4 158.5 158.5 160.9 161.0 161.6 160.5 161.7 160.3 161.2 161.0 159.7 160.4

3146.9 3156.2 3159.4 3096.7 3175.4 3096.3 3185.1 3188.4 3128.4 3094.9 3127.9 3099.9 3210.7 3228.5 3233.1 3240.3 3261.1 3260.8 3130.5 3132.6 3229.3 3232.3 3257.2 3193.0 3260.6 3190.2 3222.6 3220.3 3188.2 3215.6

1644.7 1645.5 1646.2 1639.0 1644.1 1639.4 1645.1 1646.0 1638.1 1644.4 1638.7 1644.1 1645.0 1637.1 1638.0 1646.4 1638.4 1638.9 1644.8 1644.2 1645.7 1646.6 1647.0 1637.2 1647.9 1637.7 1638.3 1638.8 1643.9 1645.1

2298.3 2304.9 2307.4 2263.1 2318.5 2262.8 2325.4 2327.7 2285.9 2261.2 2285.5 2265.2 2344.0 2356.3 2359.6 2364.9 2379.5 2379.4 2285.5 2287.5 2357.0 2359.1 2376.8 2331.2 2379.3 2329.2 2352.1 2350.2 2327.6 2347.6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

35.41 35.16 35.07 36.75 34.63 36.76 34.36 34.27 35.91 36.79 35.92 36.66 33.64 33.12 32.99 32.78 32.17 32.17 35.85 35.80 33.10 33.02 32.28 34.14 32.18 34.22 33.30 33.36 34.37 33.50

35.67 35.41 35.31 36.98 34.89 36.99 34.62 34.52 36.13 37.05 36.15 36.90 33.88 33.38 33.25 33.03 32.42 32.43 36.15 36.07 33.35 33.27 32.54 34.39 32.43 34.47 33.55 33.63 34.53 33.73

194

A. Gómez-Zavaglia / Journal of Molecular Structure 930 (2009) 187–194

of phloretin are considerably strong. The real significance of these values can be understood when compared with the ones of glycolic (CH2OHCOOH), oxalic (HOOC@COOH) acid, pyruvic (CH3COCOOH) acids, glycine and dimethylglycine which were found to be are much lower (8.8, 7.6, 12, 24.8 and 26.0 kJ mol1, respectively [33–37].

References

4. Conclusions

[6] [7] [8] [9] [10]

Quantum chemical calculations in large flexible molecules still represent a challenge. The high number of combinations of conformationally relevant dihedral angles makes it an extremely complicated task if no systematic investigation is carried out. In this work, a systematic conformational search has been performed on the phloretin molecule followed by hierarchical cluster analysis. Cluster analysis has been extensively used in many fields in Biology and Biochemistry, but, to the best of our knowledge, it is the first time that this approach is used in the structural comparison of conformers of flexible molecules. This comparison allowed us to group conformers according similarities and correlate the most significant structural parameters with their relative energies. This first analysis definitely facilitated a deeper investigation on the influence of each dihedral angle on the global stability of the conformers. Based on previously reported empirical equations [26–31], the redshifts corresponding to mOH and sOH vibrational modes could be correlated with the distances and strength of the hydrogen bondings. The possibility of correctly estimating frequency shifts from specific geometrical parameters is a useful tool because it allows theoretical predictions of vibrational frequencies without the need to execute vibrational calculations, which for large flexible compounds are in many cases still constrained in terms of computational resources. Acknowledgements This work was supported by ANCPCyT (Project PICT(2006)/ 00068) and CYTED (Network 108RT0362). AGZ is member of the Research Carreer Conicet, Argentina.

[1] [2] [3] [4] [5]

[11] [12] [13] [14] [15] [16]

[17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]

Appendix A. Supplementary data Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2009.05.014.

[35] [36] [37]

Y. Yamamoto, R.B. Gaynor, J. Clin. Invest. 107 (2001) 135. T.P.T. Cushnie, A.J. Lamb, Int. J. Antimicrob. Agents 26 (2005) 343. M.V. Eberhardt, C.Y. Lee, R.H. Liu, Nature 405 (2000) 903. K.W. Lee, Y.J. Kim, D.O. Kim, H.J. Lee, C.Y. Lee, J. Agric. Food Chem. 51 (2003) 6516. V. Stangl, M. Lorenz, A. Ludwig, N. Grimbo, C. Guether, W. Sanad, S. Ziemer, P. Martus, G. Baumann, K. Stang, J. Nutr. 135 (2005) 172. P.G. LeFevre, J.K. Marshall, J. Biol. Chem. 234 (1959) 3022. C. Xiao, J.P. Cant, Am. J. Physiol. Cell Physiol. 285 (2003) C1226. M.M. Raja, N.K. Tyagi, R.K.H. Kinne, J. Biol. Chem. 278 (2003) 49154. R. Cseh, R. Benz, Biophys. J. 77 (1999) 1477. S. Diaz, F. Lairión, J. Arroyo, A.C. Biondi de Lopez, E. Disalvo, Langmuir 17 (2001) 852. F. Lairión, E. Disalvo, Langmuir 20 (2004) 9151. HyperChem Conformational Search module, Tools for Molecular Modeling, Hypercube, Inc., 2002. M. Saunders, J. Am. Chem. Soc. 109 (1987) 3150. M. Saunders, K.N. Houk, Y.-D. Wu, W.C. Still, J.M. Lipton, G. Chang, W.C. Guidal, J. Am. Chem. Soc. 112 (1990) 1419. A.E. Howard, P.A. Kollman, J. Med. Chem. 31 (1988) 1669. M. Frisch, G. Trucks, H. Schlegel, G. Scuseria, M. Robb, J. Cheeseman, V. Zakrzewski, J. Montgomery, R. Stratmann, K. Burant, S. Dapprich, J. Millam, A. Daniels, K. Kudin, M. Strain, O. Farkas, J. Tomasi, V. Barone, M. Cossi, R. Cammi, B. Mennucci, C. Pomelli, C. Adamo, S. Clifford, J. Ochterski, G. Petersson, P. Ayala, Q. Cui, K. Morokuma, D. Malick, A. Rabuck, K. Raghavachari, J. Foresman, J. Cioslowski, J. Ortiz, A. Baboul, B. Stefanov, G. Liu, A. Liashenko, P. Piskorz, I. Komaromi, R. Gomperts, R. Martin, D. Fox, T. Keith, M. Al-Laham, C. Peng, A. Nanayakkara, M. Challacombe, P. Gill, B. Johnson, W. Chen, M. Wong, J. Andres, C. Gonzalez, M. Head-Gordon, S. Replogle, J. Pople, Gaussian 98, revision A.9, Gaussian Inc., Pittsburgh, PA, 1998. M. Frisch, M. Head-Gordon, J. Pople, Chem. Phys. Lett. 166 (1990) 281. A. Becke, Phys. Rev. A 38 (1988) 3098. C. Lee, W. Yang, R. Parr, Phys. Rev. B. 37 (1988) 785. S. Vosko, L. Wilk, M. Nusair, Can. J. Phys. 58 (1980) 1200. P. Csaszar, P. Pulay, J. Mol. Struct. (THEOCHEM) 114 (1984) 31. R. Sokal, C. Michener, Univ. Kansas Sci. Bull. 38 (1958) 1409. A. Gómez-Zavaglia, A. Abraham, S. Giorgieri, G.L. De Antoni, J. Dairy Sci. 82 (1999) 870. A. Gómez-Zavaglia, G. Kociubinski, P. Pérez, G.L. De Antoni, J. Food Prot. 61 (1998) 865. P.J. De Urraza, A. Go´mez-Zavaglia, M.E. Lozano, V. Romanowski, G.L. De Antoni, J. Dairy Res. 67 (2000) 381. M. Rozenberg, A. Loewenschuss, Y. Marcus, Carbohydr. Res. 394 (1997) 183. M. Rozenberg, A. Loewenschuss, Y. Marcus, Carbohydr. Res. 328 (2000) 307. M. Rozenberg, G. Shoham, I. Reva, R. Fausto, Phys. Chem. Chem. Phys. 7 (2005) 2376. M. Rozenberg, Spectrochim. Acta A 52 (1996) 1559. M. Rozenberg, G. Shoham, I. Reva, R. Fausto, Spectrochim. Acta A 60 (2004) 463. A.V. Iogansen, Spectrochim. Acta A 55 (1999) 1585. R.F. Lake, H.W. Thompson, Proc. R. Soc. London 291 (1966) 469. R. Fausto, E.M.S. Maçôas, J. Mol. Struct. (THEOCHEM) 563/564 (2001) 29. S. Jarmelo, T.M.R. Maria, M.L.P. Leitão, R. Fausto, Phys. Chem. Chem. Phys. 3 (2001) 387. I. Reva, S. Stepanian, L. Adamowicz, R. Fausto, J. Phys. Chem. 105 (2001) 4773. S.G. Stepanian, I.D. Reva, E.D. Radchenko, M.T.S. Rosado, M.L.T.S. Duarte, R. Fausto, L. Adamowicz, J. Phys. Chem. 102 (1998) 1041. A. Gómez Zavaglia, I. Reva, R. Fausto, Phys. Chem. Chem. Phys. 5 (2003) 41.