Carbohydrate Research 407 (2015) 34e41
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Spectroscopic and structural studies on lactose species in aqueous solution combining the HATR and Raman spectra with SCRF calculations rquez a, Alicia Beatriz Brizuela b, Lilian Davies c, María Jimena Ma n a, * Silvia Antonia Branda a nica, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucuma n, Ayacucho Catedra de Química General, Instituto de Química Inorga n, Tucuma n, Argentina 471, 4000 San Miguel de Tucuma b n, San Lorenzo Catedra de Bromatología, Instituto de Bioquímica Aplicada, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucuma n, Tucuma n, Argentina 456, 4000 San Miguel de Tucuma c Instituto de Investigaciones para la Industria Química (INIQUI, CONICET), Universidad Nacional de Salta, Av. Bolivia 5150, 4400 Salta, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2014 Received in revised form 23 January 2015 Accepted 26 January 2015 Available online 31 January 2015
In this work, the a and b isomers, the a-lactose monohydrate and dihydrate and the dimeric species of lactose were studied from the spectroscopic point of view in gas and aqueous solution phases combining the infrared, Horizontal Attenuated Total Reflectance (HATR) and Raman spectra with the density functional theory (DFT) calculations. Aqueous saturated solutions of a-lactose monohydrate and solutions at different molar concentrations of a-lactose monohydrate in water were completely characterized by infrared, HATR and Raman spectroscopies. For all the species in solution, the solvent effects were studied using the solvation polarizable continuum (PCM) and solvation (SM) models and, then, their corresponding solvation energies were predicted. The vibrational spectra of those species in aqueous solution were completely assigned by employing the Scaled Quantum Mechanics Force Field (SQMFF) methodology and the self-consistent reaction field (SCRF) calculations. The stabilities of all those species were studied by using the natural bond orbital (NBO), and atoms in molecules (AIM) calculations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Lactose Vibrational spectra Molecular structure Force field DFT calculations
1. Introduction The milk sugar is well-known as lactose whose chemical name is 4-O-b-D-Galactopyranosyl-a-D-glucopyranose.1e11 Different studies show that structurally in an aqueous solution of this disaccharide their two, a and b isomers, are present in a continuous and a reversible equilibrium called mutarotation.3,6,9 Both isomers have different solubilities in water and only differ in the orientation of the OH group at the position C1 in the glucose unit and, the proportion of each form is determined by the temperature.9 Hence, the studies of the physical chemistry properties of diverse systems of lactose in water or in different solvents are of pharmaceutical and industrial interest to know the involved solute-solvent and solutesolute interactions and the type of system formed.3e5,7,8,10e12 In particular, the inter-conversion of lactose solutions and the crystallization process are important characteristics in the fabrication of
* Corresponding author. Tel.: þ54 381 4247752; fax: þ54 381 4248169. n). E-mail address: [email protected] (S.A. Branda http://dx.doi.org/10.1016/j.carres.2015.01.019 0008-6215/© 2015 Elsevier Ltd. All rights reserved.
compressible lactose in hard tablets.10,11 On the other hand, the presence of lactose in protein complexes such as lectins, is of importance in diverse biological processes because they provide tools for deciphering the biological information stored in the sugar code, as reported by Mikeska et al.13 In this context, a technique easy and common to identify and quantify the different systems containing lactose is the vibrational spectroscopy, as reported in the literature.14e16 So far, a vibrational study of lactose was reported by Gafour et al.16 but, the vibrational spectra and the completed assignments for the different forms of lactose in aqueous media were not reported. Hence, the goals of this paper are the structural and vibrational studies of the different species of lactose in gas and aqueous solution phases in order to know their structural and vibrational properties and to perform the complete assignments of their vibrational spectra. For these purposes, aqueous saturated solutions of a-lactose monohydrate and solutions at different molar concentrations of lactose in water were completely characterized by infrared, HATR and Raman spectroscopies. Simultaneously, the theoretical initial structures of a and b-lactose and of a-lactose monohydrate and dihydrate and the dimeric species were
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modelled according to the experimental structures reported by Fries et al.1 and Smith et al.2 for a-lactose monohydrated. All the structures were optimized in both media by using the hybrid B3LYP/6-31G* method17,18 while the solvent effects were studied by using the SCRF method with the PCM and SM models.19e21 The nature and topological properties of the b-1,4 glycosidic bonds were studied by using the NBO22,23 calculations and the AIM theory.24,25 Furthermore, the harmonic frequencies of the three species of lactose were also calculated and the vibrational spectra were completely assigned by combining the normal coordinate analysis with the SQMFF methodology.26 2. Experimental methods A pure commercial sample of a-lactose monohydrate was used. Due to the low solubility of lactose in water (18.9049 g at 25 C), as reported by Palani et al.4 only was possible to prepare solutions at molar concentrations 0.5 and 0.1 M of lactose in water. Both solutions were characterized by HATR and Raman spectroscopies. In addition, the FTIR spectrum in the region of 4000e400 cm1 was recorded by putting one drop of a water saturated solution of lactose between KRS5 windows. All spectra were recorded with a resolution of 4 cm1 and 100 scans. HATR spectra of those two solutions of lactose were also performed by a cell with a top plate fitted with a ZnS crystal using pure water as a background. Liquid samples for Raman measurements with saturated solution of lactose and solutions of lactose 0.5 and 0.1 M in water were performed with a 10 mm path length glass cuvette, the sample holder has a reflective recess that increases the intensity of the spectra. FTIR GX1 Perkin Elmer spectrometer, equipped with Raman accessory was used for all measurements. Raman has an Nd-YAG* laser (excitation line of 1064 nm, 1900 mW of laser power) and an InGaAs detector cooled at liquid nitrogen temperature. The FTRaman spectra were recorded in the 3500e100 cm1 region. 3. Computational details The theoretical initial structures of a and b-lactose, of a-lactose monohydrate and dihydrate and of the dimeric form were modelled according to the experimental structures reported by Fries et al.1 and Smith et al.2 for a-lactose monohydrated with the GaussView program.27 The structures in gas and aqueous solution phases were optimized by using the hybrid B3LYP/6-31G* level of theory15,16 employing the Gaussian 09 program.28 Fig. 1 shows the structures of a and b-lactose together with the labelling of the atoms while the corresponding to a-lactose monohydrate is given in Fig. 2 together with a comparison with the experimental structure determinate by X-ray diffraction by Fries et al.1 These three structures in aqueous solution were optimized by means of the SCRF method,19,20 as implemented in the PCM model using the Gaussian 09 program package.28 Here, the solvation energies for the different species in solution were calculated with the solvation SM model21 and the obtained values were corrected by the total non electrostatic terms due to the cavitation, dispersion and repulsion energies, as reported for diverse molecules in aqueous solution.29e34 In addition, the total energy calculated for lactose monohydrate by using the 6-31G* basis set was corrected for Basis Set Superposition Error (BSSE) by the standard BoyseBernardi counterpoise method.35 The molecular electrostatic potentials and the atomic charges derived from MerzeKollman (MK)36 were computed for all the species in both media by using the 6-31G* basis set while, the NBO 3.1 program,23 was used to calculate the natural atomic charges (NPA), the bond orders expressed as Wiberg indexes and, the stabilization energies. The topological properties were calculated by using the AIM2000 program.25 On the other hand, the force fields
Fig. 1. Theoretical structures of a-Lactose and b-Lactose anhydrous and atoms numbering corresponding. The circle indicates the difference between both structures.
and their corresponding frequencies were also calculated using the same level approximation in order to perform the complete vibrational assignments. For these purposes, the natural internal coordinates for both anhydrous and monohydrated species were defined like those reported for sucrose,34 the same are summarized in Tables S1, S2 and S3 (Supplementary data), respectively. Afterwards, the resultant force fields expressed in Cartesian coordinates were transformed to natural internal coordinates by means of the Molvib program.37 In general; the completed assignments of the three species were performed considering the potential energy distribution (PED) components 10% while for those strongly coupled modes the PED contributions of 8 and 9% were also considered. Furthermore, two additional species of lactose, the alactose dimer and a-lactose di-hydrate, were also considered only in the vibrational analysis because there are bands in the infrared and Raman spectra not attributed to a and b-lactose and to alactose monohydrate. The vibrational assignment for the dihydrate (Fig. S1a) was performed taking into account the SQM methodology and the internal coordinates for the monohydrate presented in Table S2 and the nine additional coordinates summarized in Table S3. For the dimeric species (Fig. S1b), the complete assignment was performed by using the GaussView program.27
4. Results and discussion 4.1. Geometry optimization Table S4 shows the total energies and dipole moment values for the optimized a and b-lactose and a-lactose monohydrate
36
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Fig. 2. Experimental (upper) and theoretical (bottom) structures and atoms numbering for a-Lactose monohydrate. In both structures the water molecules are indicated with a ‘w’ letter.
structures in gas phase and in aqueous solutions by using the B3LYP/6-31G* method. The obtained values are compared with those reported for the species neutral, di-hydrate and pentahydrate of sucrose in the two media and at the same level of theory. Here, the more important results obtained are: (i) that the blactose structure in both media have higher energy values than the corresponding to a-lactose form confirming that both species are present in aqueous solution in an equilibrium, as reported by different authors,3,6,9 (ii) that the optimization of a-lactose monohydrate in the gas phase produce imaginary frequencies indicating this way that this form can to exit in solid phase or in aqueous solution and, (iii) that the a-lactose isomer in solution is more stable than b-lactose, showing thus that the proportions of each isomer in the equilibrium are different being higher the presence of a-isomer than b with a relative energy between them of 1.57 kJ/ mol. Hence, the population a/b-lactose ratio in solution is 65/35, a result similar to those reported in the literature from 62/38 to 58/42 between 0 C and 100 C.38 Another very important result is that despite sucrose has a different structure from lactose, as observed in Fig. S2, the energy values for a-Lactose anhydrous only in solution is similar to sucrose anhydrous, as can be seen in Table S4. This observation is justified because sucrose is hydrolysed in solution to glucose and fructose while lactose is hydrolysed to galactose and glucose. Moreover, in aqueous solution, glucose has two hydrates: penta-hydrate and di-hydrate, as sucrose while fructose has two hydrates: penta-hydrate and mono-hydrate. Thus, probably the rigidity of fructose compared to that of glucose and sucrose justify in these species the different hydrate formed in solution.39,40
Analysing the dipole moments, we observed that the values for the species of lactose in solution are slightly higher than in the gas phase, as expected because the species are hydrated in a solution but, the values are also different from sucrose species. Probably, in part the different solubilities between lactose and sucrose in water or the presence of both forms of lactose justify the latter observation. On the other hand, the dipole moment value for a-lactose monohydrate in solution is lower than in the gas phase indicating clearly that the role of water in the lactose molecule is different from sucrose. Evidently, the water mobility has influence on the properties of lactose in solution. Table 1 shows a comparison between the calculated geometrical parameters for the three forms derived from lactose with the corresponding experimental values reported by Fries et al.1 The comparisons between the experimental and theoretical values were expressed by means of the root mean of square deviations (rmsd) and the values are also presented in Table 1. Note that between the a and b-isomers few changes are observed in the bond length (between 0.009 and 0.028 Å) and angles (between 1.2 and 1.7 ), as expected because the only difference between both species is the position of an OH group while the higher difference are observed in the C4eC5eC6eO32 dihedral angles. For a-lactose monohydrate in solution the better correlations are obtained for the bond length in gas phase (0.010 Å) while the higher variations are observed in the dihedral angles (82.7e83.1 ) of this species probably due to the water mobility, as above mentioned. Besides, for the three species in solution practically the inter-glycosidic bond angle (C1eO7eC21) do not change, as observed by Desai et al.41 for sucrose octasulfate and by Brizuela et al. for sucrose,34 due to a limited conformational mobility as a consequence of the electrostatic repulsions. In general, for the a-lactose monohydrate in aqueous solution have observed the higher changes in the geometrical parameters, which are related to the sites in which occur the H bonds with the water molecules. For the species a and b-lactose similar correlations in the geometrical parameters are observed. Table S5 shows the molecular volumes and calculated solvation energies for all the forms derived from lactose in different media by using the B3LYP/6-31G* method. Here, the Moldraw program42 was used to calculate the volume variations. For the monohydrate, the higher volume variation in the solution is observed, indicating probably strong solutesolvent interactions, as reported for sucrose by Gupta and Singh.43 4.2. Molecular electrostatic potentials and atomic charges For the three species of lactose the molecular electrostatic potentials, the atomic derived from the ESPs (MK)36 and the natural atomic charges (NPA) and, the bond orders expressed as Wiberg indexes were calculated by using B3LYP/6-31G*Method. These parameters are of importance to analyse the electrostatic forces of packing of a solute hydrated among water molecules because they determine the compaction of the hydration layer, as reported by Birch.44 Tables S6 and S7 show the calculated molecular electrostatic potential and the two atomic charges studied for the three lactose species, respectively. The exhaustive analysis of the molecular electrostatic potential values reveals that (i) the higher values in all the species are observed on the O atoms and, particularly, the low values are observed on the O10 atoms belonging to the galactose rings of all the species and on the O34 atoms belonging to a OH group, (ii) the value corresponding to the O7 atom for b-lactose decrease in solution while the value corresponding to this atom for a-lactose monohydrate increase in that medium, (iii) a similar variation is observed in the O10 atoms belonging to the C5eO10eC1 angles of the galactose rings of the two species, a and b-lactose and a-lactose monohydrate, (iv) the
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Table 1 Comparison of calculated geometrical parameters for lactose with the corresponding experimental values B3LYP/6-31G*a Parameter
Expb
a-Lactose anhydrous
b-Lactose anhydrous
a-Lactose monohydrate
Gas
PCM
Gas
PCM
Gas
PCM
Bond lengths (Å) C1eO7 O10eC1 C1eC2 C2eC3 C3eC4 C4eC5 C5eO10 C4eO34 C2eO8 C3eO9 C5eC6 C6eO32 C21eO7 C20eC21 C20eO30 C19eO30 C19eC26 C22eC26 C21eC22 C19eO36 C26eO28 C22eO24 C20eC39 C39eO43 RMSD
1.380 1.436 1.526 1.537 1.532 1.538 1.423 1.434 1.415 1.420 1.520 1.420 1.437 1.541 1.431 1.419 1.527 1.530 1.534 1.406 1.412 1.423 1.528 1.422 0.012
1.396 1.433 1.526 1.536 1.532 1.535 1.442 1.434 1.424 1.425 1.517 1.428 1.441 1.539 1.438 1.420 1.527 1.529 1.536 1.410 1.424 1.426 1.524 1.427 0.010
1.381 1.436 1.526 1.537 1.532 1.538 1.424 1.434 1.415 1.420 1.520 1.419 1.436 1.542 1.420 1.428 1.530 1.531 1.533 1.386 1.413 1.420 1.530 1.419 0.011
1.396 1.433 1.535 1.540 1.535 1.533 1.440 1.435 1.424 1.423 1.517 1.428 1.439 1.540 1.432 1.427 1.527 1.528 1.535 1.401 1.424 1.425 1.524 1.427 0.009
1.380 1.443 1.525 1.536 1.531 1.538 1.432 1.433 1.415 1.420 1.529 1.414 1.440 1.534 1.426 1.436 1.531 1.533 1.537 1.388 1.413 1.426 1.521 1.438 0.010
1.396 1.433 1.534 1.540 1.536 1.533 1.440 1.436 1.424 1.423 1.517 1.428 1.441 1.539 1.435 1.429 1.528 1.528 1.535 1.401 1.425 1.426 1.426 1.525 0.028
1.389 1.427 1.517 1.523 1.533 1.536 1.448 1.429 1.425 1.433 1.514 1.419 1.437 1.525 1.425 1.443 1.531 1.516 1.533 1.387 1.429 1.434 1.514 1.430
(4) (3) (5) (4) (4) (4) (4) (4) (3) (4) (4) (5) (4) (5) (5) (4) (5) (5) (4) (4) (3) (4) (4) (5)
C1eO10eC5 C10eC5eC4 C5eC4eC3 C4eC3eC2 C3eC2eC1 C2eC1eO10 O7eC1eC2 O10eC1eO7 C1eO7eC21 O7eC21eC20 C21eC20eO30 C20eO30eC19 O30eC19eC26 C19eC26eC22 C26eC22eC21 C22eC21eC20 C5eC6eO32 C20eC39eO43 RMSD
114.5 111.2 109.4 111.9 109.9 108.2 109.2 108.0 118.2 105.1 111.0 114.8 108.8 110.5 110.0 111.2 107.3 112.9 1.7
113.5 110.0 109.4 111.5 110.1 108.6 108.8 107.7 117.7 105.7 110.6 115.0 109.1 111.3 110.6 111.3 108.2 112.5 1.3
114.6 111.2 109.5 111.8 109.9 108.3 109.2 108.0 118.3 105.6 110.6 114.6 107.5 110.4 111.1 110.4 107.3 113.2 1.7
113.1 109.7 110.3 111.6 110.3 109.4 108.6 107.7 117.8 105.9 110.2 113.7 108.4 110.6 111.5 110.7 108.1 112.5 1.2
115.7 111.0 109.8 111.5 110.0 108.4 109.1 108.0 118.6 106.1 109.3 113.0 107.1 110.8 111.1 109.2 112.8 110.5 1.7
113.2 109.9 110.5 111.6 110.1 109.2 108.7 107.7 117.7 105.8 110.6 114.8 108.3 111.1 110.7 111.2 108.3 112.5 1.3
112.2 109.0 108.9 110.9 110.9 111.2 107.7 107.0 117.1 107.0 107.9 114.1 109.7 110.9 110.3 111.1 110.3 111.2
(0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2)
O10eC1eO7eC21 C2eC1eO7eC21 C1eO7eC21eC20 O10eC5eC6eO32 C4eC5eC6eO32 O30eC20eC39eO43 C21eC20eC39eO43 O30eC20eC21eO7 RMSD
90.4 151.9 157.0 65.4 171.9 70.7 167.0 172.5 82.8
89.4 152.8 151.6 65.5 172.9 64.8 173.7 172.2 82.9
90.2 152.0 156.5 65.1 172.2 68.3 169.6 172.7 82.8
88.8 152.6 151.6 65.9 172.8 64.7 174.0 172.6 82.9
87.0 155.1 153.7 65.8 171.7 70.0 168.3 176.7 82.7
89.5 152.1 152.8 65.0 173.7 64.2 174.2 172.2 83.1
92.6 146.2 143.0 59.4 (3) 178.7 (3) 63.2 (4) 177.6 (3)
a b
This work. From Ref. 1.
values corresponding to the O30 atoms belonging to the C19eO30eC20 angles of the glucose rings of a-lactose and its monohydrate increase in aqueous medium while the value of that atom in b-lactose decrease in solution, (v) in the monohydrate, the high molecular electrostatic potential value observed on the O36 atom in solution is justified by the hydration due to the H bonds with the water molecules, (vi) the molecular electrostatic potential value observed on the O46 atom belonging to the water molecule of the monohydrated species decrease in solution as a consequence of
the hydration and, finally (vi) the less negative molecular electrostatic potential values are observed, in the H35 atoms of the three species in agreeing with the lower values on the O34 atoms belonging to an O24eH35 groups. Fig. S3 shows the strong red colours on the O28, O36 and O43 atoms due to their high negative electrostatic potential values, being they nucleophilic sites, while the blue colours on the H17, H18, H33 and H35 atoms show the less negative electrostatic potential sites, which are electrophilic sites. Note the change in the colourations of the atoms for a-lactose
38
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monohydrate in solution as a consequence of the hydration, especially the strong blue colour on the water molecule, as can be seen in Fig. S4. In Table S7 can be observed the atomic MK and natural charges for the three species of lactose in gas and aqueous solution phases by using the 6-31G* basis set. The complete examination of both charges shows that in general the natural atomic charges for the three lactose species have higher values than the other ones and that for a-lactose the most negative MK values are localized on the O9, O24 and O43 atoms in gas phase increasing the O24 atom its value in solution while the other ones decrease the values in this medium. A similar relation is observed in b-lactose for the most negative MK values localized on the O9, O28 and O43 atoms while, for a-lactose monohydrate the higher MK value is localized on the O36 atom that significantly decrease in solution due to the formation of H bonds with water molecules. Note that the O36eH37 group is linked to the water molecule in this monohydrate compound. On the other hand, for a-lactose the most positive MK value is localized on the H35 atom in the gas phase decreasing its value in solution while on the C1 atom is observed a MK charge value of 0.610 in gas phase decreasing appreciably up to 0.573 in solution. A similar observation is found since b-lactose with a MK value on the C1 atom of 0.494 in gas phase. These sites in the galactose rings of a and b-lactose are strongly related to the hydration due to that two O atoms are linked to those C1 atoms. In the a-lactose monohydrate, the high positive MK charges are observed on the H37 and C1 atoms decreasing in both cases their value in the solution. Furthermore, from the three CeOeC inter-bonds for the three lactose species the high negative MK values are observed in the O30 atoms belonging to the glucose rings (C19eO30eC20), being higher the MK values in the monohydrate. In relation to the natural charges, different results are obtained for the three species of lactose. Thus, the results of the CeOeC inter-bonds of the three lactose species show the difference with the MK charges because the high negative natural charge values in the gas phase are observed on the O10 atoms corresponding to the galactose rings (C1eO10eC5) decreasing their value in aqueous solution. For a-lactose monohydrate the high negative charge values are observed on the O24 and O46 atoms while for both a and b-lactose the higher negative charge values are observed in the O24 atoms. In reference to the positive charges, for a and b-lactose the higher values are observed on the H25 atoms while for the monohydrate the higher values are observed in the H37 atoms, as expected because the water molecule of the monohydrate is linked to lactose through these atoms. In these latter cases the values decrease in solution due to the hydration. Thus, these studies on the molecular electrostatic potentials and the two atomic charges reveals different sites of formation of H bonds in alactose, b-lactose and a-lactose monohydrate. 4.3. NBO and AIM studies To investigate the charge transfers of the two galactose and glucose rings and its stabilization energies the most important delocalizations and the bond orders related to the different bonds for the three lactose species in both media were calculated by using of NBO calculations.23 Thus, the bond orders, expressed as Wiberg indexes and the energetic properties for a-lactose, b-lactose and alactose monohydrate can be observed in Tables S8 and S9, respectively. The total inspection of the bond orders shows that: (i) the bond orders for the three CeOeC inter-bonds in the three lactose species present the higher values having the O7 atom the higher values in the three species in gas phase, which decrease in solution, (ii) for the monohydrate, the values for the O10 and O30 atoms increase in solution, in relation on the values in gas phase while for a and b-Lactose anhydrous the values for the O30 atoms in the gas phase decreasing slightly in solution, (iii) in general in the three
species, the values for the O atoms decrease in solution probably due to the H bond formation in these regions, (iv) analysing the bond orders corresponding to the atoms involved in the OH groups, for a and b-lactose the O9 atoms have higher values while for alactose monohydrate the O28, O32 and O43 atoms have the same values in gas phase but notable change in solution toward lower values and, finally (v) the bond orders of the H atoms linked to C atoms in sp3 hybridation present the higher values, as expected because they are strongly bonded while, those H atoms belonging to OH groups have the lowest values, having the lower values in the gas phase the H25 atoms of a and b-lactose and the H37 atom of alactose monohydrate increasing slightly their values in the solution. Note that the lower bond order values for the O46 atoms corresponding to the water molecule of the monohydrate are justified due to the H bonds linked to a-lactose. Here, the results for the monohydrate are in accordance with those found by means of the molecular electrostatic potential and the MK charges while for aand b-lactose different results are obtained. Checking the main delocalization energies for the three lactose species presented in Table S9 in gas and aqueous solution phases, we observed that a-lactose in solution is more stable than in the gas phase and than b-lactose in solution but this latter species is more stable in gas phase because it has a total contribution of 640.51 kJ/ mol. Thus, the presence only in a-lactose of the LP(2) O36/s*C19eH38 charge transfers in the two media due to the lone pairs of the O36 atoms justify the difference between both species. On the other hand, the closer values in DETotal for a and b-lactose in solution support the equilibrium that exists between both species in solution. Note that the higher contributions of the stabilization energies to the total stabilization energy are observed in the monohydrated species, as indicated in Table S9, thus this species is the most stable form of lactose in both media. The topological properties for a-lactose, b-lactose and a-lactose monohydrate were calculated by using the AIM2000 program.24 This way, the analysis of the electron density distribution, r(r) in the bond critical points (BCPs), the values of the Laplacian, V2r(r), the eigenvalues (l1, l2, l3) of the Hessian matrix at these points matrix and, the l1/l3 ratio are calculated. Table S10 shows the values obtained in the two studied media for a-lactose and blactose species at the B3LYP/6-31G* level of theory while Table S11 summarizes the values for a-lactose monohydrate. The whole inspections of these parameters demonstrate the following points: (i) in all the cases the l1/l30 suggesting that the interactions are those called closed-shell interactions, which are typical of hydrogen bonds interactions (O/H),45 (ii) for a-lactose in both media is observed three H bonds interactions, which, in the gas phase are the O8/H41, O32/H25 and O34/H18 interactions while in solution two interactions are different (O8/H41, O10/H25 and O32/H25), (iii) for b-lactose is observed four H bonds interactions in both media, whose properties slightly increase in solution and finally, (iv) for the monohydrate in the gas phase are observing a total of seven H bonds interactions while only five are present in solution, whose properties have higher values in the solution, explaining this way the high stability of this species in both media, as revealed by the NBO study. Figs. S5, S6 and S7 show the details of the molecular model for a-lactose, b-lactose and alactose monohydrate, respectively in solution with the geometry of all their BCPs. 4.4. HOMOeLUMO studies It is known that lactose has particular physical chemistry properties, as compared with other sugars6 and, for this reason; it is broadly used in the industries, being the major application in the pharmaceutical industry. Here, the highest occupied molecular
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orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gaps46 for all the lactose forms in the different media were calculated by using the B3LYP/6-31G* method and the results are given in Table S12. The knowledge of these properties is important to understand the fact that lactose exists in two isomeric forms and their different behaviours and properties in both media. The inspection of the results show that b-lactose anhydrous has an energy gap of 7.2790 eV indicating that it is a species slight less reactive in solution than a-lactose anhydrous (7.1974 eV). This difference probably explains the different proportions of each form in aqueous solution while, a-lactose in solution is more reactive than in the gas phase (7.2682 eV) because in this medium it is in equilibrium with the b-lactose form. For the monohydrate, the values show the low reactivity in solution (7.0994 eV) than the other ones while in gas phase this species has a low reactivity (7.5294 eV). Thus, the reactivity orders according to the gap values in solution follow the tendency: a-lactose monohydrate>a-lactose>b-lactose. Comparing lactose with sucrose, the values for sucrose in the gas phase of 7.79878 eV and, in aqueous solution of 7.79797 eV show clearly that it is less reactive than lactose due to the di-hydrate and penta-hydrate formation in solution.34 This study demonstrates clearly that from the three lactose forms, the b-lactose species is chemically most stable and inert, in accordance with data reported in the literature.6,47 4.5. Vibrational analysis A comparison between the experimental infrared spectrum of
a-lactose monohydrate in solid phase and the HATR spectra in an aqueous saturated solution and in an aqueous solution at 0.5 M concentration can be seen in Fig. 3 while the experimental infrared spectrum of a-Lactose monohydrate in solid phase compared with the corresponding theoretical infrared spectra of a- and b-Lactose anhydrous, a-Lactose monohydrate and the dimer at B3LYP/6-31G* level of theory are presented in Fig. S8. The Raman spectra of a solution concentrated of the sample in water compared with the corresponding to aqueous solutions of 0.5 and 0.1 M concentrations are observed in Fig. 4. The optimized a- and b-lactose and a-lactose monohydrate and dihydrate structures have C1 symmetries, presenting the first two structures 129 normal vibration modes while the monohydrate has 138 normal vibration modes and the dihydrate 147 normal vibration modes, where all the vibration normal modes in the four species are active in both spectra. The observed and calculated SQM
Fig. 3. Experimental HATR spectrum of a-Lactose monohydrate in aqueous saturated solution (upper) compared with the corresponding to an aqueous solution at 0.5 M concentration (medium) and in the solid phase (bottom).
39
Fig. 4. Experimental Raman spectra of a-Lactose monohydrate in aqueous saturated solution (upper) and in aqueous solution at 0.5 (medium) and 0.1 M (bottom) concentrations.
wavenumbers for these four lactose species by using 6-31G* basis set together with the corresponding assignments are given in Table S13 while the PED contributions for the two anhydrous species of lactose and its monohydrate in aqueous solution are shown in Tables S14, S15 and S16, respectively. A rigorous comparison between the experimental Raman spectra of saturated solutions of a-lactose monohydrate in the water with that corresponding to sucrose in water at room temperature can be seen at different wavenumbers in Figs. S9 and S10. The vibrational assignment for a-lactose dihydrate was performed by using the calculated SQM26 wavenumbers and, for comparison they are included in Table S13. In the higher wavenumbers region (Figs.S8eS9), in the OH stretchings region, the spectrum of sucrose shows bands broad and intense with undefined bands assigned to CH2 and CH stretchings while in the Raman spectrum of lactose it is possible to observe bands with low intensities in the OH region and bands clearly defined in the CH2 and CH stretchings region. The numbers of OH groups are the same in both molecules but the total quantity of CeH bonds in lactose is ten while in sucrose is eight (Fig. S2). Note that the bands attributed to these vibration modes are clearly observed in the higher wavenumbers region for lactose while, on the contrary, these differences for sucrose in the water are evidently attributed to the high solubility of sucrose in this solvent, in relation to lactose, that favours the formation of both hydrates in the 4000e3000 cm1 region supporting, this way, the strong intensity observed in the IR spectrum of sucrose in aqueous solution. Another comparison between the theoretical infrared of a-lactose with that corresponding to the b-form in aqueous solution at B3LYP/6-31G* level of theory in two different regions are observed in Figs. S11 and S12. Here, as a consequence of the different positions of the OH groups in both spectra in the same region are observed bands but with diverse forms and intensities such as, those observed in the 3100e2900 and 1500e1400 cm1 regions. On the other hand, Figs. S13 and S14 show the comparisons between the theoretical infrared spectra of a-lactose and a-lactose monohydrate in aqueous solution at B3LYP/6-31G* level of theory. Here, the bands attributed to the vibration modes due to the water molecule are clearly evidenced in the two regions presented. Another interesting comparisons are the theoretical infrared spectra of a-lactose monohydrate and dihydrate in aqueous solution at the B3LYP/6-31G* level of theory, which are given in
40
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4000e3000 and 1800e0 cm1 regions in Figs. S15 and S16, respectively. At this point in the two regions, the dihydrate shows the bands more intense than the monohydrate with notable shifting of the bands toward lower wavenumbers, as expected because that form presents two water molecules. The complete vibrational analysis for all the lactose species were performed taking into account the assignment previous reported in solid phase,16 with the results of our calculations and by comparison with similar molecules.16,34,48e52 Later, a discussion related to the assignments of the most important groups is presented below. 4.5.1. Band assignments 4.5.1.1. OeH modes. For all the species of lactose, the OeH stretching modes are predicted as pure modes between 3645 and 3189 cm1 where the modes corresponding to the water molecules are predicted to higher wavenumbers than the other ones, as observed in Table S13, hence, these modes are associated with the observed HATR and Raman bands between 3588 and 3216 cm1. Note that in the IR spectrum of the dimer (Fig. S8) the bands related to these groups appear with lower intensities due to the H bond formation of these groups while in the other lactose forms those modes are observed more intense. The OH deformation modes in the forms studied of lactose those modes are assigned between 1464 and 1140 cm1 while the out-of-plane deformation modes (tOH or gOH) are predicted between 657 and 149 cm1, hence, those modes are assigned to the four lactose species, as indicated in Table S13. 4.5.1.2. CH modes. For sucrose and their complexes,34 the CeH stretching modes are assigned between 3094 and 2830 cm1 while for the lactose species those vibration modes are predicted between 3086 and 2881 cm1, as shown in Table S13. Note that for the dimer these modes are predicted at higher wavenumbers than in the other species. For this reason, those modes are associated with bands observed in those region. Here, the Raman bands between 3116 and 3011 cm1, assigned to these stretching modes justify clearly the presence of the dimer in an aqueous lactose solution, as can be seen in Table S13. Moreover, the symmetric stretching modes of this species support the intense band at 2977 cm1 in the Raman spectrum. The rocking modes for the lactose species are predicted in the 1464e1210 cm1 region, hence, the shoulder and bands observed in the HATR and Raman spectra between 1469 and 1212 cm1 are assigned to those modes, as observed in Table S13. 4.5.1.3. CH2 modes. The antisymmetric symmetric stretching modes for a- and b-lactose and a-lactose monohydrate are predicted as totally pure modes (Fig. S8 and Tables S14eS16) and, they are clearly identified as well in the IR spectrum in the solid phase (Fig. 3) as in the Raman spectrum of an aqueous saturated solution (Fig. 4). In the dihydrate, those modes are predicted between 2983 and 2909 cm1 while in the dimer between 3116 and 2988 cm1. Thus, those stretching modes for all the lactose species are assigned to the HATR and Raman bands between 3115 and 2898 cm1. Note that the latter band due to their intensity in the Raman spectrum is clearly attributed to a symmetric mode of the dihydrate. This way, the band at 2898 cm1 justifies the presence of this form in an aqueous solution of lactose. In the lactose species the SQM calculations have predicted the scissoring modes between 1471 and 1444 cm1 and, for this reason, they are assigned in this region. Gafour et al.16 have previously assigned these modes to the bands at 1457 and 1367 cm1. On the other hand, the wagging, rocking and twisting modes for the species of lactose are assigned, in accordance to similar compounds16,34,48e52 and as predicted by SQM calculation.
4.5.1.4. Skeletal modes. In the previous assignment16 of lactose in solid phase the CeO stretching modes were observed at 1120, 1095 and 1032 cm1 while, in this work, we observed that the bands attributed to these modes for all the lactose species changes with the hydration, as also was observed in species of sucrose in an aqueous solution.34,40 In this case, the HATR and Raman bands between 1184 and 807 cm1 are assigned to these stretching modes. On the other hand, the Raman bands of medium intensities at 928, 900 and 876 cm1 are assigned to CeC stretching modes of the dimeric species while the weak bands in the same spectrum at 800 and 793 cm1 are assigned to ring deformations of the same species. Thus, these two sets of bands also support the presence of the dimeric species in an aqueous solution of lactose. The very strong HATR bands at 1031 and 538 cm1 and the Raman bands at 1184, 552 and 483 cm1 justify the presence of a- and b-lactose in an aqueous solution while the weak band at 1639 cm1 supports the presence of the dihydrate in an aqueous solution of lactose. Other bands that also justify the presence of a- and b-lactose in an aqueous solution are those shoulders observed in both HATR and Raman spectra at 677 and 686 cm1, respectively which are assigned to the CCO deformation modes. Tables S14, S15 and S16 show clearly that for the remains skeletal modes the SQM calculations predict strong coupling among them. 4.6. Force field The force constants, expressed in terms of simple valence internal coordinates, for the three lactose species in aqueous solution at the B3LYP/6-31G* theory level were calculated from the corresponding scaled force fields employing the SQM methodology26 with the Molvib program.37 Table 2 shows that in general, for aand b-lactose the f(nCH2) f(nCeC)R5,R6, f(dHeCeH) force constants values are approximately the same in the gas phase while for the other ones some differences related to the position of the OH groups is expected because it is the structural difference between both species. In aqueous solution is notable the decreasing in the f(nOeH), f(nCeO)C, (nCeO)H, f(dCeOeC) and f(dCeOeH) constants values due to the H bond formation as a consequence of the hydration. Here, a very important result is related to the change that experiment the f(dCeOeC) force constant of a-lactose in the gas phase because in solution the value decrease while for b-lactose the value remains
Table 2 Comparison of scaled internal force constants for lactose with those corresponding to sucrose B3LYP/6-31G* Force constant
f(nOeH)HOH f(nOeH) f(nCH2) f(nCeH) f(nCeO)C (nCeO)H f(nCeC)R5,R6 f(nCeC)R6 f(dCeOeC) f(dCeOeH) f(dHeCeH)
a-Lactose
b-Lactose
a-Lactose
anhydrousa
anhydrousa
monoydrated
Sucrose anhydrousb
Gas
PCM
Gas
PCM
Gas
PCM
Gas
PCM
7.118 4.731 4.642 4.669 5.015 3.908 3.972 1.875 0.739 0.816
7.030 4.803 4.732 4.513 4.995 3.907 3.969 1.861 0.729 0.796
7.103 4.727 4.593 4.675 5.112 3.909 3.924 1.890 0.744 0.816
7.017 4.803 4.705 4.516 5.052 3.857 3.943 1.890 0.741 0.798
6.957 7.004 4.818 4.646 4.652 3.819 3.914 4.019 1.918 0.826 0.812
7.262 6.914 4.799 4.734 4.502 4.982 3.870 3.991 1.982 0.693 0.800
7.186 4.767 4.723 4.460 4.976 3.868 3.965 1.728 0.733 0.803
7.062 4.812 4.728 4.266 4.895 3.855 3.965 1.299 0.741 0.796
Units are mdyn Å1 for stretching and mdyn Å rad2 for angle deformations. R5 and R6, Rings glucofuran and glucopyran in sucrose, respectively. R5 and R6, Rings galactose and glucose in lactose, respectively. a This work. b From Ref. 34.
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constant in both media. Hence, these difference observed in the values are probably related in part to the different proportions of both species in the equilibrium and to the structural difference between both species. The variations observed in the f(nOeH), f(nCeO)H and f(dCeOeH) force constants can be justified by the hydration due to the H bonds formation between the OH groups of lactose and the water molecules of the solvent while the differences between the force constants of lactose and sucrose could be attributed to the lower solvation energy of lactose. This way, the f(dCeOeC) force constant of sucrose has a lower value in solution than in all the lactose species. 5. Conclusions In this work, the a-lactose monohydrate was completely characterized in saturated aqueous solution and, in aqueous solutions of different molar concentrations by using infrared, HATR and Raman spectroscopies. The theoretical structures of a and b-lactose, of alactose monohydrate and dihydrate and of the dimeric form in gas and aqueous solution phases were determined by the hybrid B3LYP/6-31G* method. The solvation energies for all the species in aqueous solution were predicted at the same level of theory. The complete assignments of all the studied lactose species were performed by using the hybrid B3LYP/6-31G* method. Here, the IR bands between 3116 and 3011 cm1 and the five Raman bands between 928 and 793 cm1 evidence clearly the presence of the dimeric form in an aqueous lactose solution while the very strong band in the Raman spectrum at 2898 cm1 and the weak Raman band at 1639 cm1 support the presence of the dihydrate in an aqueous solution of lactose. The very strong HATR bands at 1031 and 538 cm1 and the Raman bands at 1184, 552 and 483 cm1 justify the presence of a- and b-lactose in an aqueous lactose solution. Thus, the presence of these species is proposed by means of theoretical calculations and vibrational spectroscopy. The frontier orbitals suggest that b-lactose anhydrous is slight less reactive in solution than a-lactose anhydrous, hence, this difference probably explains the different proportions of each form in aqueous solution.
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.
Acknowledgements This work was subsidized with grants from CIUNT (Consejo de n). The authors Investigaciones, Universidad Nacional de Tucuma thank Prof. Tom Sundius for his permission to use MOLVIB. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carres.2015.01.019.
39. 40. 41. 42. 43. 44. 45. 46. 47. 48.
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Spectroscopic and structural studies on lactose species in aqueous solution combining the HATR and Raman spectra with SCRF calculations rquez a, Alicia Beatriz Brizuela b, Lilian Davies c, María Jimena Ma n a, * Silvia Antonia Branda a nica, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucuma n, Ayacucho Catedra de Química General, Instituto de Química Inorga n, Tucuma n, Argentina 471, 4000 San Miguel de Tucuma b n, San Lorenzo Catedra de Bromatología, Instituto de Bioquímica Aplicada, Facultad de Bioquímica, Química y Farmacia, Universidad Nacional de Tucuma n, Tucuma n, Argentina 456, 4000 San Miguel de Tucuma c Instituto de Investigaciones para la Industria Química (INIQUI, CONICET), Universidad Nacional de Salta, Av. Bolivia 5150, 4400 Salta, Argentina
a r t i c l e i n f o
a b s t r a c t
Article history: Received 26 September 2014 Received in revised form 23 January 2015 Accepted 26 January 2015 Available online 31 January 2015
In this work, the a and b isomers, the a-lactose monohydrate and dihydrate and the dimeric species of lactose were studied from the spectroscopic point of view in gas and aqueous solution phases combining the infrared, Horizontal Attenuated Total Reflectance (HATR) and Raman spectra with the density functional theory (DFT) calculations. Aqueous saturated solutions of a-lactose monohydrate and solutions at different molar concentrations of a-lactose monohydrate in water were completely characterized by infrared, HATR and Raman spectroscopies. For all the species in solution, the solvent effects were studied using the solvation polarizable continuum (PCM) and solvation (SM) models and, then, their corresponding solvation energies were predicted. The vibrational spectra of those species in aqueous solution were completely assigned by employing the Scaled Quantum Mechanics Force Field (SQMFF) methodology and the self-consistent reaction field (SCRF) calculations. The stabilities of all those species were studied by using the natural bond orbital (NBO), and atoms in molecules (AIM) calculations. © 2015 Elsevier Ltd. All rights reserved.
Keywords: Lactose Vibrational spectra Molecular structure Force field DFT calculations
1. Introduction The milk sugar is well-known as lactose whose chemical name is 4-O-b-D-Galactopyranosyl-a-D-glucopyranose.1e11 Different studies show that structurally in an aqueous solution of this disaccharide their two, a and b isomers, are present in a continuous and a reversible equilibrium called mutarotation.3,6,9 Both isomers have different solubilities in water and only differ in the orientation of the OH group at the position C1 in the glucose unit and, the proportion of each form is determined by the temperature.9 Hence, the studies of the physical chemistry properties of diverse systems of lactose in water or in different solvents are of pharmaceutical and industrial interest to know the involved solute-solvent and solutesolute interactions and the type of system formed.3e5,7,8,10e12 In particular, the inter-conversion of lactose solutions and the crystallization process are important characteristics in the fabrication of
* Corresponding author. Tel.: þ54 381 4247752; fax: þ54 381 4248169. n). E-mail address: [email protected] (S.A. Branda http://dx.doi.org/10.1016/j.carres.2015.01.019 0008-6215/© 2015 Elsevier Ltd. All rights reserved.
compressible lactose in hard tablets.10,11 On the other hand, the presence of lactose in protein complexes such as lectins, is of importance in diverse biological processes because they provide tools for deciphering the biological information stored in the sugar code, as reported by Mikeska et al.13 In this context, a technique easy and common to identify and quantify the different systems containing lactose is the vibrational spectroscopy, as reported in the literature.14e16 So far, a vibrational study of lactose was reported by Gafour et al.16 but, the vibrational spectra and the completed assignments for the different forms of lactose in aqueous media were not reported. Hence, the goals of this paper are the structural and vibrational studies of the different species of lactose in gas and aqueous solution phases in order to know their structural and vibrational properties and to perform the complete assignments of their vibrational spectra. For these purposes, aqueous saturated solutions of a-lactose monohydrate and solutions at different molar concentrations of lactose in water were completely characterized by infrared, HATR and Raman spectroscopies. Simultaneously, the theoretical initial structures of a and b-lactose and of a-lactose monohydrate and dihydrate and the dimeric species were
rquez et al. / Carbohydrate Research 407 (2015) 34e41 M.J. Ma
35
modelled according to the experimental structures reported by Fries et al.1 and Smith et al.2 for a-lactose monohydrated. All the structures were optimized in both media by using the hybrid B3LYP/6-31G* method17,18 while the solvent effects were studied by using the SCRF method with the PCM and SM models.19e21 The nature and topological properties of the b-1,4 glycosidic bonds were studied by using the NBO22,23 calculations and the AIM theory.24,25 Furthermore, the harmonic frequencies of the three species of lactose were also calculated and the vibrational spectra were completely assigned by combining the normal coordinate analysis with the SQMFF methodology.26 2. Experimental methods A pure commercial sample of a-lactose monohydrate was used. Due to the low solubility of lactose in water (18.9049 g at 25 C), as reported by Palani et al.4 only was possible to prepare solutions at molar concentrations 0.5 and 0.1 M of lactose in water. Both solutions were characterized by HATR and Raman spectroscopies. In addition, the FTIR spectrum in the region of 4000e400 cm1 was recorded by putting one drop of a water saturated solution of lactose between KRS5 windows. All spectra were recorded with a resolution of 4 cm1 and 100 scans. HATR spectra of those two solutions of lactose were also performed by a cell with a top plate fitted with a ZnS crystal using pure water as a background. Liquid samples for Raman measurements with saturated solution of lactose and solutions of lactose 0.5 and 0.1 M in water were performed with a 10 mm path length glass cuvette, the sample holder has a reflective recess that increases the intensity of the spectra. FTIR GX1 Perkin Elmer spectrometer, equipped with Raman accessory was used for all measurements. Raman has an Nd-YAG* laser (excitation line of 1064 nm, 1900 mW of laser power) and an InGaAs detector cooled at liquid nitrogen temperature. The FTRaman spectra were recorded in the 3500e100 cm1 region. 3. Computational details The theoretical initial structures of a and b-lactose, of a-lactose monohydrate and dihydrate and of the dimeric form were modelled according to the experimental structures reported by Fries et al.1 and Smith et al.2 for a-lactose monohydrated with the GaussView program.27 The structures in gas and aqueous solution phases were optimized by using the hybrid B3LYP/6-31G* level of theory15,16 employing the Gaussian 09 program.28 Fig. 1 shows the structures of a and b-lactose together with the labelling of the atoms while the corresponding to a-lactose monohydrate is given in Fig. 2 together with a comparison with the experimental structure determinate by X-ray diffraction by Fries et al.1 These three structures in aqueous solution were optimized by means of the SCRF method,19,20 as implemented in the PCM model using the Gaussian 09 program package.28 Here, the solvation energies for the different species in solution were calculated with the solvation SM model21 and the obtained values were corrected by the total non electrostatic terms due to the cavitation, dispersion and repulsion energies, as reported for diverse molecules in aqueous solution.29e34 In addition, the total energy calculated for lactose monohydrate by using the 6-31G* basis set was corrected for Basis Set Superposition Error (BSSE) by the standard BoyseBernardi counterpoise method.35 The molecular electrostatic potentials and the atomic charges derived from MerzeKollman (MK)36 were computed for all the species in both media by using the 6-31G* basis set while, the NBO 3.1 program,23 was used to calculate the natural atomic charges (NPA), the bond orders expressed as Wiberg indexes and, the stabilization energies. The topological properties were calculated by using the AIM2000 program.25 On the other hand, the force fields
Fig. 1. Theoretical structures of a-Lactose and b-Lactose anhydrous and atoms numbering corresponding. The circle indicates the difference between both structures.
and their corresponding frequencies were also calculated using the same level approximation in order to perform the complete vibrational assignments. For these purposes, the natural internal coordinates for both anhydrous and monohydrated species were defined like those reported for sucrose,34 the same are summarized in Tables S1, S2 and S3 (Supplementary data), respectively. Afterwards, the resultant force fields expressed in Cartesian coordinates were transformed to natural internal coordinates by means of the Molvib program.37 In general; the completed assignments of the three species were performed considering the potential energy distribution (PED) components 10% while for those strongly coupled modes the PED contributions of 8 and 9% were also considered. Furthermore, two additional species of lactose, the alactose dimer and a-lactose di-hydrate, were also considered only in the vibrational analysis because there are bands in the infrared and Raman spectra not attributed to a and b-lactose and to alactose monohydrate. The vibrational assignment for the dihydrate (Fig. S1a) was performed taking into account the SQM methodology and the internal coordinates for the monohydrate presented in Table S2 and the nine additional coordinates summarized in Table S3. For the dimeric species (Fig. S1b), the complete assignment was performed by using the GaussView program.27
4. Results and discussion 4.1. Geometry optimization Table S4 shows the total energies and dipole moment values for the optimized a and b-lactose and a-lactose monohydrate
36
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Fig. 2. Experimental (upper) and theoretical (bottom) structures and atoms numbering for a-Lactose monohydrate. In both structures the water molecules are indicated with a ‘w’ letter.
structures in gas phase and in aqueous solutions by using the B3LYP/6-31G* method. The obtained values are compared with those reported for the species neutral, di-hydrate and pentahydrate of sucrose in the two media and at the same level of theory. Here, the more important results obtained are: (i) that the blactose structure in both media have higher energy values than the corresponding to a-lactose form confirming that both species are present in aqueous solution in an equilibrium, as reported by different authors,3,6,9 (ii) that the optimization of a-lactose monohydrate in the gas phase produce imaginary frequencies indicating this way that this form can to exit in solid phase or in aqueous solution and, (iii) that the a-lactose isomer in solution is more stable than b-lactose, showing thus that the proportions of each isomer in the equilibrium are different being higher the presence of a-isomer than b with a relative energy between them of 1.57 kJ/ mol. Hence, the population a/b-lactose ratio in solution is 65/35, a result similar to those reported in the literature from 62/38 to 58/42 between 0 C and 100 C.38 Another very important result is that despite sucrose has a different structure from lactose, as observed in Fig. S2, the energy values for a-Lactose anhydrous only in solution is similar to sucrose anhydrous, as can be seen in Table S4. This observation is justified because sucrose is hydrolysed in solution to glucose and fructose while lactose is hydrolysed to galactose and glucose. Moreover, in aqueous solution, glucose has two hydrates: penta-hydrate and di-hydrate, as sucrose while fructose has two hydrates: penta-hydrate and mono-hydrate. Thus, probably the rigidity of fructose compared to that of glucose and sucrose justify in these species the different hydrate formed in solution.39,40
Analysing the dipole moments, we observed that the values for the species of lactose in solution are slightly higher than in the gas phase, as expected because the species are hydrated in a solution but, the values are also different from sucrose species. Probably, in part the different solubilities between lactose and sucrose in water or the presence of both forms of lactose justify the latter observation. On the other hand, the dipole moment value for a-lactose monohydrate in solution is lower than in the gas phase indicating clearly that the role of water in the lactose molecule is different from sucrose. Evidently, the water mobility has influence on the properties of lactose in solution. Table 1 shows a comparison between the calculated geometrical parameters for the three forms derived from lactose with the corresponding experimental values reported by Fries et al.1 The comparisons between the experimental and theoretical values were expressed by means of the root mean of square deviations (rmsd) and the values are also presented in Table 1. Note that between the a and b-isomers few changes are observed in the bond length (between 0.009 and 0.028 Å) and angles (between 1.2 and 1.7 ), as expected because the only difference between both species is the position of an OH group while the higher difference are observed in the C4eC5eC6eO32 dihedral angles. For a-lactose monohydrate in solution the better correlations are obtained for the bond length in gas phase (0.010 Å) while the higher variations are observed in the dihedral angles (82.7e83.1 ) of this species probably due to the water mobility, as above mentioned. Besides, for the three species in solution practically the inter-glycosidic bond angle (C1eO7eC21) do not change, as observed by Desai et al.41 for sucrose octasulfate and by Brizuela et al. for sucrose,34 due to a limited conformational mobility as a consequence of the electrostatic repulsions. In general, for the a-lactose monohydrate in aqueous solution have observed the higher changes in the geometrical parameters, which are related to the sites in which occur the H bonds with the water molecules. For the species a and b-lactose similar correlations in the geometrical parameters are observed. Table S5 shows the molecular volumes and calculated solvation energies for all the forms derived from lactose in different media by using the B3LYP/6-31G* method. Here, the Moldraw program42 was used to calculate the volume variations. For the monohydrate, the higher volume variation in the solution is observed, indicating probably strong solutesolvent interactions, as reported for sucrose by Gupta and Singh.43 4.2. Molecular electrostatic potentials and atomic charges For the three species of lactose the molecular electrostatic potentials, the atomic derived from the ESPs (MK)36 and the natural atomic charges (NPA) and, the bond orders expressed as Wiberg indexes were calculated by using B3LYP/6-31G*Method. These parameters are of importance to analyse the electrostatic forces of packing of a solute hydrated among water molecules because they determine the compaction of the hydration layer, as reported by Birch.44 Tables S6 and S7 show the calculated molecular electrostatic potential and the two atomic charges studied for the three lactose species, respectively. The exhaustive analysis of the molecular electrostatic potential values reveals that (i) the higher values in all the species are observed on the O atoms and, particularly, the low values are observed on the O10 atoms belonging to the galactose rings of all the species and on the O34 atoms belonging to a OH group, (ii) the value corresponding to the O7 atom for b-lactose decrease in solution while the value corresponding to this atom for a-lactose monohydrate increase in that medium, (iii) a similar variation is observed in the O10 atoms belonging to the C5eO10eC1 angles of the galactose rings of the two species, a and b-lactose and a-lactose monohydrate, (iv) the
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37
Table 1 Comparison of calculated geometrical parameters for lactose with the corresponding experimental values B3LYP/6-31G*a Parameter
Expb
a-Lactose anhydrous
b-Lactose anhydrous
a-Lactose monohydrate
Gas
PCM
Gas
PCM
Gas
PCM
Bond lengths (Å) C1eO7 O10eC1 C1eC2 C2eC3 C3eC4 C4eC5 C5eO10 C4eO34 C2eO8 C3eO9 C5eC6 C6eO32 C21eO7 C20eC21 C20eO30 C19eO30 C19eC26 C22eC26 C21eC22 C19eO36 C26eO28 C22eO24 C20eC39 C39eO43 RMSD
1.380 1.436 1.526 1.537 1.532 1.538 1.423 1.434 1.415 1.420 1.520 1.420 1.437 1.541 1.431 1.419 1.527 1.530 1.534 1.406 1.412 1.423 1.528 1.422 0.012
1.396 1.433 1.526 1.536 1.532 1.535 1.442 1.434 1.424 1.425 1.517 1.428 1.441 1.539 1.438 1.420 1.527 1.529 1.536 1.410 1.424 1.426 1.524 1.427 0.010
1.381 1.436 1.526 1.537 1.532 1.538 1.424 1.434 1.415 1.420 1.520 1.419 1.436 1.542 1.420 1.428 1.530 1.531 1.533 1.386 1.413 1.420 1.530 1.419 0.011
1.396 1.433 1.535 1.540 1.535 1.533 1.440 1.435 1.424 1.423 1.517 1.428 1.439 1.540 1.432 1.427 1.527 1.528 1.535 1.401 1.424 1.425 1.524 1.427 0.009
1.380 1.443 1.525 1.536 1.531 1.538 1.432 1.433 1.415 1.420 1.529 1.414 1.440 1.534 1.426 1.436 1.531 1.533 1.537 1.388 1.413 1.426 1.521 1.438 0.010
1.396 1.433 1.534 1.540 1.536 1.533 1.440 1.436 1.424 1.423 1.517 1.428 1.441 1.539 1.435 1.429 1.528 1.528 1.535 1.401 1.425 1.426 1.426 1.525 0.028
1.389 1.427 1.517 1.523 1.533 1.536 1.448 1.429 1.425 1.433 1.514 1.419 1.437 1.525 1.425 1.443 1.531 1.516 1.533 1.387 1.429 1.434 1.514 1.430
(4) (3) (5) (4) (4) (4) (4) (4) (3) (4) (4) (5) (4) (5) (5) (4) (5) (5) (4) (4) (3) (4) (4) (5)
C1eO10eC5 C10eC5eC4 C5eC4eC3 C4eC3eC2 C3eC2eC1 C2eC1eO10 O7eC1eC2 O10eC1eO7 C1eO7eC21 O7eC21eC20 C21eC20eO30 C20eO30eC19 O30eC19eC26 C19eC26eC22 C26eC22eC21 C22eC21eC20 C5eC6eO32 C20eC39eO43 RMSD
114.5 111.2 109.4 111.9 109.9 108.2 109.2 108.0 118.2 105.1 111.0 114.8 108.8 110.5 110.0 111.2 107.3 112.9 1.7
113.5 110.0 109.4 111.5 110.1 108.6 108.8 107.7 117.7 105.7 110.6 115.0 109.1 111.3 110.6 111.3 108.2 112.5 1.3
114.6 111.2 109.5 111.8 109.9 108.3 109.2 108.0 118.3 105.6 110.6 114.6 107.5 110.4 111.1 110.4 107.3 113.2 1.7
113.1 109.7 110.3 111.6 110.3 109.4 108.6 107.7 117.8 105.9 110.2 113.7 108.4 110.6 111.5 110.7 108.1 112.5 1.2
115.7 111.0 109.8 111.5 110.0 108.4 109.1 108.0 118.6 106.1 109.3 113.0 107.1 110.8 111.1 109.2 112.8 110.5 1.7
113.2 109.9 110.5 111.6 110.1 109.2 108.7 107.7 117.7 105.8 110.6 114.8 108.3 111.1 110.7 111.2 108.3 112.5 1.3
112.2 109.0 108.9 110.9 110.9 111.2 107.7 107.0 117.1 107.0 107.9 114.1 109.7 110.9 110.3 111.1 110.3 111.2
(0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2) (0.2)
O10eC1eO7eC21 C2eC1eO7eC21 C1eO7eC21eC20 O10eC5eC6eO32 C4eC5eC6eO32 O30eC20eC39eO43 C21eC20eC39eO43 O30eC20eC21eO7 RMSD
90.4 151.9 157.0 65.4 171.9 70.7 167.0 172.5 82.8
89.4 152.8 151.6 65.5 172.9 64.8 173.7 172.2 82.9
90.2 152.0 156.5 65.1 172.2 68.3 169.6 172.7 82.8
88.8 152.6 151.6 65.9 172.8 64.7 174.0 172.6 82.9
87.0 155.1 153.7 65.8 171.7 70.0 168.3 176.7 82.7
89.5 152.1 152.8 65.0 173.7 64.2 174.2 172.2 83.1
92.6 146.2 143.0 59.4 (3) 178.7 (3) 63.2 (4) 177.6 (3)
a b
This work. From Ref. 1.
values corresponding to the O30 atoms belonging to the C19eO30eC20 angles of the glucose rings of a-lactose and its monohydrate increase in aqueous medium while the value of that atom in b-lactose decrease in solution, (v) in the monohydrate, the high molecular electrostatic potential value observed on the O36 atom in solution is justified by the hydration due to the H bonds with the water molecules, (vi) the molecular electrostatic potential value observed on the O46 atom belonging to the water molecule of the monohydrated species decrease in solution as a consequence of
the hydration and, finally (vi) the less negative molecular electrostatic potential values are observed, in the H35 atoms of the three species in agreeing with the lower values on the O34 atoms belonging to an O24eH35 groups. Fig. S3 shows the strong red colours on the O28, O36 and O43 atoms due to their high negative electrostatic potential values, being they nucleophilic sites, while the blue colours on the H17, H18, H33 and H35 atoms show the less negative electrostatic potential sites, which are electrophilic sites. Note the change in the colourations of the atoms for a-lactose
38
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monohydrate in solution as a consequence of the hydration, especially the strong blue colour on the water molecule, as can be seen in Fig. S4. In Table S7 can be observed the atomic MK and natural charges for the three species of lactose in gas and aqueous solution phases by using the 6-31G* basis set. The complete examination of both charges shows that in general the natural atomic charges for the three lactose species have higher values than the other ones and that for a-lactose the most negative MK values are localized on the O9, O24 and O43 atoms in gas phase increasing the O24 atom its value in solution while the other ones decrease the values in this medium. A similar relation is observed in b-lactose for the most negative MK values localized on the O9, O28 and O43 atoms while, for a-lactose monohydrate the higher MK value is localized on the O36 atom that significantly decrease in solution due to the formation of H bonds with water molecules. Note that the O36eH37 group is linked to the water molecule in this monohydrate compound. On the other hand, for a-lactose the most positive MK value is localized on the H35 atom in the gas phase decreasing its value in solution while on the C1 atom is observed a MK charge value of 0.610 in gas phase decreasing appreciably up to 0.573 in solution. A similar observation is found since b-lactose with a MK value on the C1 atom of 0.494 in gas phase. These sites in the galactose rings of a and b-lactose are strongly related to the hydration due to that two O atoms are linked to those C1 atoms. In the a-lactose monohydrate, the high positive MK charges are observed on the H37 and C1 atoms decreasing in both cases their value in the solution. Furthermore, from the three CeOeC inter-bonds for the three lactose species the high negative MK values are observed in the O30 atoms belonging to the glucose rings (C19eO30eC20), being higher the MK values in the monohydrate. In relation to the natural charges, different results are obtained for the three species of lactose. Thus, the results of the CeOeC inter-bonds of the three lactose species show the difference with the MK charges because the high negative natural charge values in the gas phase are observed on the O10 atoms corresponding to the galactose rings (C1eO10eC5) decreasing their value in aqueous solution. For a-lactose monohydrate the high negative charge values are observed on the O24 and O46 atoms while for both a and b-lactose the higher negative charge values are observed in the O24 atoms. In reference to the positive charges, for a and b-lactose the higher values are observed on the H25 atoms while for the monohydrate the higher values are observed in the H37 atoms, as expected because the water molecule of the monohydrate is linked to lactose through these atoms. In these latter cases the values decrease in solution due to the hydration. Thus, these studies on the molecular electrostatic potentials and the two atomic charges reveals different sites of formation of H bonds in alactose, b-lactose and a-lactose monohydrate. 4.3. NBO and AIM studies To investigate the charge transfers of the two galactose and glucose rings and its stabilization energies the most important delocalizations and the bond orders related to the different bonds for the three lactose species in both media were calculated by using of NBO calculations.23 Thus, the bond orders, expressed as Wiberg indexes and the energetic properties for a-lactose, b-lactose and alactose monohydrate can be observed in Tables S8 and S9, respectively. The total inspection of the bond orders shows that: (i) the bond orders for the three CeOeC inter-bonds in the three lactose species present the higher values having the O7 atom the higher values in the three species in gas phase, which decrease in solution, (ii) for the monohydrate, the values for the O10 and O30 atoms increase in solution, in relation on the values in gas phase while for a and b-Lactose anhydrous the values for the O30 atoms in the gas phase decreasing slightly in solution, (iii) in general in the three
species, the values for the O atoms decrease in solution probably due to the H bond formation in these regions, (iv) analysing the bond orders corresponding to the atoms involved in the OH groups, for a and b-lactose the O9 atoms have higher values while for alactose monohydrate the O28, O32 and O43 atoms have the same values in gas phase but notable change in solution toward lower values and, finally (v) the bond orders of the H atoms linked to C atoms in sp3 hybridation present the higher values, as expected because they are strongly bonded while, those H atoms belonging to OH groups have the lowest values, having the lower values in the gas phase the H25 atoms of a and b-lactose and the H37 atom of alactose monohydrate increasing slightly their values in the solution. Note that the lower bond order values for the O46 atoms corresponding to the water molecule of the monohydrate are justified due to the H bonds linked to a-lactose. Here, the results for the monohydrate are in accordance with those found by means of the molecular electrostatic potential and the MK charges while for aand b-lactose different results are obtained. Checking the main delocalization energies for the three lactose species presented in Table S9 in gas and aqueous solution phases, we observed that a-lactose in solution is more stable than in the gas phase and than b-lactose in solution but this latter species is more stable in gas phase because it has a total contribution of 640.51 kJ/ mol. Thus, the presence only in a-lactose of the LP(2) O36/s*C19eH38 charge transfers in the two media due to the lone pairs of the O36 atoms justify the difference between both species. On the other hand, the closer values in DETotal for a and b-lactose in solution support the equilibrium that exists between both species in solution. Note that the higher contributions of the stabilization energies to the total stabilization energy are observed in the monohydrated species, as indicated in Table S9, thus this species is the most stable form of lactose in both media. The topological properties for a-lactose, b-lactose and a-lactose monohydrate were calculated by using the AIM2000 program.24 This way, the analysis of the electron density distribution, r(r) in the bond critical points (BCPs), the values of the Laplacian, V2r(r), the eigenvalues (l1, l2, l3) of the Hessian matrix at these points matrix and, the l1/l3 ratio are calculated. Table S10 shows the values obtained in the two studied media for a-lactose and blactose species at the B3LYP/6-31G* level of theory while Table S11 summarizes the values for a-lactose monohydrate. The whole inspections of these parameters demonstrate the following points: (i) in all the cases the l1/l30 suggesting that the interactions are those called closed-shell interactions, which are typical of hydrogen bonds interactions (O/H),45 (ii) for a-lactose in both media is observed three H bonds interactions, which, in the gas phase are the O8/H41, O32/H25 and O34/H18 interactions while in solution two interactions are different (O8/H41, O10/H25 and O32/H25), (iii) for b-lactose is observed four H bonds interactions in both media, whose properties slightly increase in solution and finally, (iv) for the monohydrate in the gas phase are observing a total of seven H bonds interactions while only five are present in solution, whose properties have higher values in the solution, explaining this way the high stability of this species in both media, as revealed by the NBO study. Figs. S5, S6 and S7 show the details of the molecular model for a-lactose, b-lactose and alactose monohydrate, respectively in solution with the geometry of all their BCPs. 4.4. HOMOeLUMO studies It is known that lactose has particular physical chemistry properties, as compared with other sugars6 and, for this reason; it is broadly used in the industries, being the major application in the pharmaceutical industry. Here, the highest occupied molecular
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orbital (HOMO)-lowest unoccupied molecular orbital (LUMO) energy gaps46 for all the lactose forms in the different media were calculated by using the B3LYP/6-31G* method and the results are given in Table S12. The knowledge of these properties is important to understand the fact that lactose exists in two isomeric forms and their different behaviours and properties in both media. The inspection of the results show that b-lactose anhydrous has an energy gap of 7.2790 eV indicating that it is a species slight less reactive in solution than a-lactose anhydrous (7.1974 eV). This difference probably explains the different proportions of each form in aqueous solution while, a-lactose in solution is more reactive than in the gas phase (7.2682 eV) because in this medium it is in equilibrium with the b-lactose form. For the monohydrate, the values show the low reactivity in solution (7.0994 eV) than the other ones while in gas phase this species has a low reactivity (7.5294 eV). Thus, the reactivity orders according to the gap values in solution follow the tendency: a-lactose monohydrate>a-lactose>b-lactose. Comparing lactose with sucrose, the values for sucrose in the gas phase of 7.79878 eV and, in aqueous solution of 7.79797 eV show clearly that it is less reactive than lactose due to the di-hydrate and penta-hydrate formation in solution.34 This study demonstrates clearly that from the three lactose forms, the b-lactose species is chemically most stable and inert, in accordance with data reported in the literature.6,47 4.5. Vibrational analysis A comparison between the experimental infrared spectrum of
a-lactose monohydrate in solid phase and the HATR spectra in an aqueous saturated solution and in an aqueous solution at 0.5 M concentration can be seen in Fig. 3 while the experimental infrared spectrum of a-Lactose monohydrate in solid phase compared with the corresponding theoretical infrared spectra of a- and b-Lactose anhydrous, a-Lactose monohydrate and the dimer at B3LYP/6-31G* level of theory are presented in Fig. S8. The Raman spectra of a solution concentrated of the sample in water compared with the corresponding to aqueous solutions of 0.5 and 0.1 M concentrations are observed in Fig. 4. The optimized a- and b-lactose and a-lactose monohydrate and dihydrate structures have C1 symmetries, presenting the first two structures 129 normal vibration modes while the monohydrate has 138 normal vibration modes and the dihydrate 147 normal vibration modes, where all the vibration normal modes in the four species are active in both spectra. The observed and calculated SQM
Fig. 3. Experimental HATR spectrum of a-Lactose monohydrate in aqueous saturated solution (upper) compared with the corresponding to an aqueous solution at 0.5 M concentration (medium) and in the solid phase (bottom).
39
Fig. 4. Experimental Raman spectra of a-Lactose monohydrate in aqueous saturated solution (upper) and in aqueous solution at 0.5 (medium) and 0.1 M (bottom) concentrations.
wavenumbers for these four lactose species by using 6-31G* basis set together with the corresponding assignments are given in Table S13 while the PED contributions for the two anhydrous species of lactose and its monohydrate in aqueous solution are shown in Tables S14, S15 and S16, respectively. A rigorous comparison between the experimental Raman spectra of saturated solutions of a-lactose monohydrate in the water with that corresponding to sucrose in water at room temperature can be seen at different wavenumbers in Figs. S9 and S10. The vibrational assignment for a-lactose dihydrate was performed by using the calculated SQM26 wavenumbers and, for comparison they are included in Table S13. In the higher wavenumbers region (Figs.S8eS9), in the OH stretchings region, the spectrum of sucrose shows bands broad and intense with undefined bands assigned to CH2 and CH stretchings while in the Raman spectrum of lactose it is possible to observe bands with low intensities in the OH region and bands clearly defined in the CH2 and CH stretchings region. The numbers of OH groups are the same in both molecules but the total quantity of CeH bonds in lactose is ten while in sucrose is eight (Fig. S2). Note that the bands attributed to these vibration modes are clearly observed in the higher wavenumbers region for lactose while, on the contrary, these differences for sucrose in the water are evidently attributed to the high solubility of sucrose in this solvent, in relation to lactose, that favours the formation of both hydrates in the 4000e3000 cm1 region supporting, this way, the strong intensity observed in the IR spectrum of sucrose in aqueous solution. Another comparison between the theoretical infrared of a-lactose with that corresponding to the b-form in aqueous solution at B3LYP/6-31G* level of theory in two different regions are observed in Figs. S11 and S12. Here, as a consequence of the different positions of the OH groups in both spectra in the same region are observed bands but with diverse forms and intensities such as, those observed in the 3100e2900 and 1500e1400 cm1 regions. On the other hand, Figs. S13 and S14 show the comparisons between the theoretical infrared spectra of a-lactose and a-lactose monohydrate in aqueous solution at B3LYP/6-31G* level of theory. Here, the bands attributed to the vibration modes due to the water molecule are clearly evidenced in the two regions presented. Another interesting comparisons are the theoretical infrared spectra of a-lactose monohydrate and dihydrate in aqueous solution at the B3LYP/6-31G* level of theory, which are given in
40
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4000e3000 and 1800e0 cm1 regions in Figs. S15 and S16, respectively. At this point in the two regions, the dihydrate shows the bands more intense than the monohydrate with notable shifting of the bands toward lower wavenumbers, as expected because that form presents two water molecules. The complete vibrational analysis for all the lactose species were performed taking into account the assignment previous reported in solid phase,16 with the results of our calculations and by comparison with similar molecules.16,34,48e52 Later, a discussion related to the assignments of the most important groups is presented below. 4.5.1. Band assignments 4.5.1.1. OeH modes. For all the species of lactose, the OeH stretching modes are predicted as pure modes between 3645 and 3189 cm1 where the modes corresponding to the water molecules are predicted to higher wavenumbers than the other ones, as observed in Table S13, hence, these modes are associated with the observed HATR and Raman bands between 3588 and 3216 cm1. Note that in the IR spectrum of the dimer (Fig. S8) the bands related to these groups appear with lower intensities due to the H bond formation of these groups while in the other lactose forms those modes are observed more intense. The OH deformation modes in the forms studied of lactose those modes are assigned between 1464 and 1140 cm1 while the out-of-plane deformation modes (tOH or gOH) are predicted between 657 and 149 cm1, hence, those modes are assigned to the four lactose species, as indicated in Table S13. 4.5.1.2. CH modes. For sucrose and their complexes,34 the CeH stretching modes are assigned between 3094 and 2830 cm1 while for the lactose species those vibration modes are predicted between 3086 and 2881 cm1, as shown in Table S13. Note that for the dimer these modes are predicted at higher wavenumbers than in the other species. For this reason, those modes are associated with bands observed in those region. Here, the Raman bands between 3116 and 3011 cm1, assigned to these stretching modes justify clearly the presence of the dimer in an aqueous lactose solution, as can be seen in Table S13. Moreover, the symmetric stretching modes of this species support the intense band at 2977 cm1 in the Raman spectrum. The rocking modes for the lactose species are predicted in the 1464e1210 cm1 region, hence, the shoulder and bands observed in the HATR and Raman spectra between 1469 and 1212 cm1 are assigned to those modes, as observed in Table S13. 4.5.1.3. CH2 modes. The antisymmetric symmetric stretching modes for a- and b-lactose and a-lactose monohydrate are predicted as totally pure modes (Fig. S8 and Tables S14eS16) and, they are clearly identified as well in the IR spectrum in the solid phase (Fig. 3) as in the Raman spectrum of an aqueous saturated solution (Fig. 4). In the dihydrate, those modes are predicted between 2983 and 2909 cm1 while in the dimer between 3116 and 2988 cm1. Thus, those stretching modes for all the lactose species are assigned to the HATR and Raman bands between 3115 and 2898 cm1. Note that the latter band due to their intensity in the Raman spectrum is clearly attributed to a symmetric mode of the dihydrate. This way, the band at 2898 cm1 justifies the presence of this form in an aqueous solution of lactose. In the lactose species the SQM calculations have predicted the scissoring modes between 1471 and 1444 cm1 and, for this reason, they are assigned in this region. Gafour et al.16 have previously assigned these modes to the bands at 1457 and 1367 cm1. On the other hand, the wagging, rocking and twisting modes for the species of lactose are assigned, in accordance to similar compounds16,34,48e52 and as predicted by SQM calculation.
4.5.1.4. Skeletal modes. In the previous assignment16 of lactose in solid phase the CeO stretching modes were observed at 1120, 1095 and 1032 cm1 while, in this work, we observed that the bands attributed to these modes for all the lactose species changes with the hydration, as also was observed in species of sucrose in an aqueous solution.34,40 In this case, the HATR and Raman bands between 1184 and 807 cm1 are assigned to these stretching modes. On the other hand, the Raman bands of medium intensities at 928, 900 and 876 cm1 are assigned to CeC stretching modes of the dimeric species while the weak bands in the same spectrum at 800 and 793 cm1 are assigned to ring deformations of the same species. Thus, these two sets of bands also support the presence of the dimeric species in an aqueous solution of lactose. The very strong HATR bands at 1031 and 538 cm1 and the Raman bands at 1184, 552 and 483 cm1 justify the presence of a- and b-lactose in an aqueous solution while the weak band at 1639 cm1 supports the presence of the dihydrate in an aqueous solution of lactose. Other bands that also justify the presence of a- and b-lactose in an aqueous solution are those shoulders observed in both HATR and Raman spectra at 677 and 686 cm1, respectively which are assigned to the CCO deformation modes. Tables S14, S15 and S16 show clearly that for the remains skeletal modes the SQM calculations predict strong coupling among them. 4.6. Force field The force constants, expressed in terms of simple valence internal coordinates, for the three lactose species in aqueous solution at the B3LYP/6-31G* theory level were calculated from the corresponding scaled force fields employing the SQM methodology26 with the Molvib program.37 Table 2 shows that in general, for aand b-lactose the f(nCH2) f(nCeC)R5,R6, f(dHeCeH) force constants values are approximately the same in the gas phase while for the other ones some differences related to the position of the OH groups is expected because it is the structural difference between both species. In aqueous solution is notable the decreasing in the f(nOeH), f(nCeO)C, (nCeO)H, f(dCeOeC) and f(dCeOeH) constants values due to the H bond formation as a consequence of the hydration. Here, a very important result is related to the change that experiment the f(dCeOeC) force constant of a-lactose in the gas phase because in solution the value decrease while for b-lactose the value remains
Table 2 Comparison of scaled internal force constants for lactose with those corresponding to sucrose B3LYP/6-31G* Force constant
f(nOeH)HOH f(nOeH) f(nCH2) f(nCeH) f(nCeO)C (nCeO)H f(nCeC)R5,R6 f(nCeC)R6 f(dCeOeC) f(dCeOeH) f(dHeCeH)
a-Lactose
b-Lactose
a-Lactose
anhydrousa
anhydrousa
monoydrated
Sucrose anhydrousb
Gas
PCM
Gas
PCM
Gas
PCM
Gas
PCM
7.118 4.731 4.642 4.669 5.015 3.908 3.972 1.875 0.739 0.816
7.030 4.803 4.732 4.513 4.995 3.907 3.969 1.861 0.729 0.796
7.103 4.727 4.593 4.675 5.112 3.909 3.924 1.890 0.744 0.816
7.017 4.803 4.705 4.516 5.052 3.857 3.943 1.890 0.741 0.798
6.957 7.004 4.818 4.646 4.652 3.819 3.914 4.019 1.918 0.826 0.812
7.262 6.914 4.799 4.734 4.502 4.982 3.870 3.991 1.982 0.693 0.800
7.186 4.767 4.723 4.460 4.976 3.868 3.965 1.728 0.733 0.803
7.062 4.812 4.728 4.266 4.895 3.855 3.965 1.299 0.741 0.796
Units are mdyn Å1 for stretching and mdyn Å rad2 for angle deformations. R5 and R6, Rings glucofuran and glucopyran in sucrose, respectively. R5 and R6, Rings galactose and glucose in lactose, respectively. a This work. b From Ref. 34.
rquez et al. / Carbohydrate Research 407 (2015) 34e41 M.J. Ma
constant in both media. Hence, these difference observed in the values are probably related in part to the different proportions of both species in the equilibrium and to the structural difference between both species. The variations observed in the f(nOeH), f(nCeO)H and f(dCeOeH) force constants can be justified by the hydration due to the H bonds formation between the OH groups of lactose and the water molecules of the solvent while the differences between the force constants of lactose and sucrose could be attributed to the lower solvation energy of lactose. This way, the f(dCeOeC) force constant of sucrose has a lower value in solution than in all the lactose species. 5. Conclusions In this work, the a-lactose monohydrate was completely characterized in saturated aqueous solution and, in aqueous solutions of different molar concentrations by using infrared, HATR and Raman spectroscopies. The theoretical structures of a and b-lactose, of alactose monohydrate and dihydrate and of the dimeric form in gas and aqueous solution phases were determined by the hybrid B3LYP/6-31G* method. The solvation energies for all the species in aqueous solution were predicted at the same level of theory. The complete assignments of all the studied lactose species were performed by using the hybrid B3LYP/6-31G* method. Here, the IR bands between 3116 and 3011 cm1 and the five Raman bands between 928 and 793 cm1 evidence clearly the presence of the dimeric form in an aqueous lactose solution while the very strong band in the Raman spectrum at 2898 cm1 and the weak Raman band at 1639 cm1 support the presence of the dihydrate in an aqueous solution of lactose. The very strong HATR bands at 1031 and 538 cm1 and the Raman bands at 1184, 552 and 483 cm1 justify the presence of a- and b-lactose in an aqueous lactose solution. Thus, the presence of these species is proposed by means of theoretical calculations and vibrational spectroscopy. The frontier orbitals suggest that b-lactose anhydrous is slight less reactive in solution than a-lactose anhydrous, hence, this difference probably explains the different proportions of each form in aqueous solution.
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.
Acknowledgements This work was subsidized with grants from CIUNT (Consejo de n). The authors Investigaciones, Universidad Nacional de Tucuma thank Prof. Tom Sundius for his permission to use MOLVIB. Supplementary data Supplementary data related to this article can be found at http:// dx.doi.org/10.1016/j.carres.2015.01.019.
39. 40. 41. 42. 43. 44. 45. 46. 47. 48.
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