Solubility of simvastatin: A theoretical and experimental study

Journal of Molecular Structure 995 (2011) 41–50

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Solubility of simvastatin: A theoretical and experimental study Juan M. Aceves-Hernández a,⇑, Jaime Hinojosa-Torres b, Inés Nicolás-Vázquez a, Rene Miranda Ruvalcaba a, Rosa María Lima García c a

Sección de Fisicoquímica, Inorgánica y Química Orgánica, Departamento de Ciencias Químicas, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Av. 1 de Mayo s/n, Cuautitlán Izcalli, Estado de México, Mexico b Centro de Asimilación Tecnológica, Facultad de Estudios Superiores Cuautitlán, Universidad Nacional Autónoma de México, Av. 1 de Mayo s/n, Cuautitlán Izcalli, Estado de México, Mexico c CFATA, UNAM, Juriquilla, Santiago de Querétaro, Mexico

a r t i c l e

i n f o

Article history: Received 19 January 2011 Received in revised form 17 March 2011 Accepted 18 March 2011 Available online 5 April 2011 Keywords: Simvastatin Solubility Alcohols Enthalpy Density functional theory Theoretical calculations

a b s t r a c t Solubility experimental data from Simvastatin in a family of alcohols were obtained at different temperatures. Simvastatin was characterized by using thermal analysis and X-ray diffraction. From the experimental solubility data an anomalous behavior was observed, since an increase the number of alcohol carbon atoms shows an increase in solubility only for the three first alcohols, ethanol, 1-propanol and 1-butanol. A decrease in solubility was obtained for 1-pentanol, 1-hexanol and 1-octanol. Van’tHoff equation was used to obtain the theoretical solubility value and the ideal activity coefficient. Experimental error was very low and does not affect the plots and equations used. No polymorphic phenomenon was found from the Simvastatin characterization. Theoretical calculations were carried out in order to corroborate the experimental solubility data. Trends and results are similar in both cases. The geometry optimizations of Simvastatin was carried out using density functional theory with Becke’s three parameter hybrid method and correlation functional of Lee, Yang and Parr (B3LYP) with 6-311++G⁄⁄ basis set. The solvent effect was treated using a continuum model as modeled in water, methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol and 1-octanol. Moreover, dielectric constant, dipolar moment and solubility in the solvents were obtained for explaining the former behavior. Ó 2011 Elsevier B.V. All rights reserved.

1. Introduction Experimental characterization and theoretical examination of liquid solutions is one of the most difficult tasks of Physical-chemistry area (1), due to the fact that there are a variety of forces and several interactions between the solvent and the solute are involved. Therefore, efforts are made in explaining the empirical behaviour of well defined compounds; however, there is the need to examine theoretical models for explaining the thermodynamic behaviour of these interactions. Drug solubility is one of the most important physicochemical properties, which is useful in great number of several important applications in the pharmaceutical, chemical, biotechnological and food industries. Solubility data for process design of Active Pharmaceutical Ingredients (APIs) are needed. Drug solubility data using different solvents are scarce in the literature [1–5]. However, there is the need of solubility data of solvent–solvate system to be investigated, especially for novel and non-common drugs. ⇑ Corresponding author. Tel.: +52 55 56231999x39431. E-mail address: [email protected] (J.M. Aceves-Hernández). 0022-2860/$ - see front matter Ó 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.molstruc.2011.03.048

It is relevant for low solubility compounds that extended solubility data, in both aqueous and organic common solvents, are needed, in order to select pre-formulation strategies for toxicological, kinetics and pharmaco-dynamics (PK/PD) studies [3]. With limited amounts of novel APIs, the challenges in crystallization and optimization have grown significantly in the last years. Therefore, prediction of solubility based on limited experimental data is getting more attention and importance [6]. In the present work, Simvastatin (SVS), solubility in a family of alcohols was experimentally determined, also it is characterized with several techniques, and the melting temperature, enthalpy of fusion and differential molar heat capacities at the melting point were measured in order to understand its behavior. These data were used for calculating the solubility of SVS in order to estimate its infinite dilution activity coefficient in the corresponding alcohols. However, accurate differential heat capacity data should be used for obtaining real consistent activity coefficients. In the other hand, theoretical calculations were carried out, all quantum calculations by using the B3LYP of density functional theory (DFT) were obtained. Geometry optimization was performed at the B3LYP/ 6-311++G(d,p) level in gas phase.

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1.1. Chemical details Simvastatin belongs to the statins family and it is a powerful lipid decreasing drug compound [7]. Its chemical structure is presented in Fig. 1. It is inhibitor of the (3,5)-hydroxy-3-methylglutaryl coenzyme A (HMGr-CoA) reductase, this enzyme catalyzes the conversion of HMa–CoA to an intermediate in an early rate-limiting step in the cholesterol biosynthesis in human body. Depletion of intracellular cholesterol results in compensatory increase in cholesterol up-take by means of low density lipoprotein (LDL) receptors and the consequent decrease in plasma cholesterol. It is used for control of hyper-cholesterolaemia due to their well proven efficacy and safety behavior [8–12]. Simvastatin is obtained from a process where lovastatin is used as raw material. Lovastatin is a natural product, a secondary metabolite, derived from fermentation of Aspergillus terreus [11]. Following lovastatin isolation, the compound is purified by a set of crystallization steps prior to milling the final product and drug formulation [13]. There are very few reports of statins solubility in organic solvents [14], in one of them it is reported a method using laser monitoring observation technique to determine lovastatin solubility in acetone, ethyl acetate, butyl acetate, ethanol and methanol at different temperatures. In our work, temperature dependence of simvastatin (SVS) solubility is obtained by the thermodynamic relationship [15],

ln X 2 ¼ ln X 2;Ideal  ln c2

temperature dependence of equilibrium solubility X2 in Eq. (1) it is necessary to know the variation of ln c1 2 with temperature. It is common to assume that in a narrow temperature range, the activity coefficient follows van’t Hoff equation or the so-called regular solution approach [15]. 

 DHfus ðTmÞ DCp  ð1  ln TmÞ RTm R   DCpTm DHfus ðTmÞ 1 DCp þ  þ ln T R R T R

Substituting (4) and (2) into (1) and rearranging

ln X 2 ¼

 DHfus ðTmÞ DCp  ½1 þ ln Tm  A RTm R   DCpAm DHfus ðTmÞ 1 DCp þ  B þ ln T R R T R

ð2Þ

ð5Þ

b þ c ln T T

ð6Þ

where

O

O O CH 3 O H

Fig. 1. Chemical structure of Simvastatin.



ln X 2 ¼ a þ

OH

CH 3

ð4Þ

Then

where X2, c2, Tm, DHfus (Tm), DCp, R and T, represent solubility mole fraction of solute (component 2), activity coefficient, melting temperature of 2, differential molar heat capacity of pure 2, (difference between molar heat capacity of the solid and the liquid at their melting temperatures), gas constant and temperature respectively. In low solubility drugs such as statins; the equilibrium mole fraction or solubility of statins in alcohols is very low (102 for SVS at room temperature), it is assumed that the last term in Eq. (1) is ln c1 2 , the activity coefficient at infinite dilution. The influence of the solvent on the solute solubility is represented by the activity coefficient ln c1 2 , which is originated by the solvent–solute molecules interactions while ln X ideal is temperature 2 dependent and is determined from pure solute properties, such as Tm, DHmel(Tm) and DCp. In order to find accurately the

CH 3

DH 1 DS1 B  ¼Aþ T RT R

ln c1 2 ¼

ð1Þ



ð3Þ

where H2E;1 , S2E;1 , DH1 and DS1 are the limiting partial excess enthalpy, partial excess entropy, enthalpy of mixing and mixing entropy, respectively. In system where solubility increases with temperature (endothermic dissolution), the activity coefficient decrease with increasing temperature, therefore, a plot of ln c1 2 vs 1/T must yield a straight line with a slope equal to DH1/R, the opposite is obtained from a exothermic dissolution process. Besides, positive intercept (DS1/R) would be obtained from an entropically driven dissolution process. When DH1 and DS1 are unknown, Eq. (3) could be given with empirical constants, A, B, in the canonical equation form.

Ln X2,id = ideal solubility of solute (drug, 2) and defined as follows.

ln X 2;Ideal ¼



HE;1 SE;1 DH1 DS1 2  2 ¼  RT R RT R

ln c1 2 ¼

CH 3

a¼

  DHfus ðTmÞ DCp  ½1 þ ln Tm  A RTm R 

b¼

c¼

 DCpTm DHfus ðTmÞ  B R R

DCp R

ð7Þ

ð8Þ

ð9Þ

Eq. (6) is known as Apelblat equation [2] and is frequently used to obtain solubility data. The a, b and c values can be obtained by regression process of the Eq. (6) against experimental values and usually good fit is obtained [14,16–18]. However, activity coefficient ln c1 2 values can not be easily extracted from the a, b and c constants in Eq. (6), due to the fact that differential heat capacity DCp is not easily available experimentally or through the best fit values of C = DCp/R. It is worth to mention that for the very same solute (identical crystalline properties) the value of the fitted parameter ‘‘c’’, should remain identical regardless of the solvent since ‘‘c’’ is a pure solute property. Literature data show that c = DCp/R for a solute dissolved in different solvents, not only changes, but varies commonly as much a 50% and in extreme cases up to 300%. This fact dramatically indicates inconsistencies in the fitted values of the constants a, b and c, and therefore is it hardly difficult to obtain good activity coefficients from solubility data, as can be probed in the present work. Since DCp values are not readily available for most compounds, two assumptions could be made in respect to the differential specific molar heat capacity at constant pressure [19]. (1) DCp is assumed negligible and can be considered equal to zero, thus Eq. (1) becomes

J.M. Aceves-Hernández et al. / Journal of Molecular Structure 995 (2011) 41–50

  DHfus ðTmÞ Tm  T ln X 2 ¼  ln c1 2 R TmT

ð10Þ

(1) DCp may be approximately influenced by the entropy of fusion, DS thus, the equilibrium solubility is a follows.

ln X 2 ¼

DHfus ðTmÞ RTm

ln Tm

T

 ln c1 2

ð11Þ

The ideal solubility X id 2 for either case would simply be the first term in each equation. In [19] the authors used the above assumption with homologous series of n-alkylparaminobenzoates and concluded that the second assumption was more exact and valid for these compounds. These results suggested that the contribution of heat capacity to the predicted ideal solubility is not negligible in these substances. In this paper, melting temperature, heat of fusion and differential molar heat capacity of SMV via differential scanning calorimetry (DSC) were measured. From the data, the ideal solubility of SVS was calculated and the validity of the assumption made in Eqs. (10) and (11) was examined. Additionally, we measure the equilibrium solubility of SVS in different alcohols and determine the activity coefficient at infinite dilution ln c1 1 , subtracting the measured solubility from the ideal solubility, thus Ideal ln c1  ln X Exp 2 ¼ ln X 2 2

ð12Þ

X Exp 2

where is the measured equilibrium solubility of SVS in the corresponding solvent. Finally, we examine if infinite dilution activity coefficient, ln c1 2 , follows van’t Hoff like behavior and whether it can be represented by Eqs. (1) and (2); (10) and (2) and/or (11) and (2). The experimental error of 30 measurements of the same system and same temperature, was 1.3% and it is negligible. It is considered that not affect the average value used for the determination of SVS solubility, it is not considered in the calculations and plots of SVS solubility (experimental and theoretical).

43

atmospheric pressure, in all cases excess of solid SVS was confirmed. The vials were then loaded into thermostat-temperature controlled autosampler of the spectrophotometer and the temperature was lowered to the desired value at a cooling rate of 0.5 °C/h. Upon reaching the desired temperature, the mixture was allowed to equilibrate for 24 h. Afterwards the solution was analyzed via the reversed phase method to obtain the equilibrium concentration and to ensure SVS was stable in the corresponding solvent. Each vial was sampled and analyzed in triplicate. The method was validated by comparing the results with literature values for equilibrium solubility of SVS in ethanol, Concentration of SVS was calculated based on a calibration curve and the value was used to calculate the equilibrium solubility mole fraction X2 as follows

X2 ¼

m2 m1 þ m2

ð13Þ

where m1 and m2 are the solvent mole value and solute mole value, respectively. 3.2. Thermal analysis Approximately 6 mg of simvastatin powder were loaded in a hermetic DSC pan. For each DSC measurement, new DSC pan was used as blank reference. The samples were scanned from 25 to 250 °C at a heating rate of 2 and 20 °C/min. The heat of fusion melting temperature and differential specific heat were determined from the DSC data with thermal analysis software. 3.3. X-ray diffraction Diffractometer model Krystalloflex 5000 made by Philips, with a Cu Target, Ka radiation with 1.504 nm wavelength and Nickel filter was used to obtain the diffraction patterns by the powder method, in the 2h range of 5–40°.

2. Experimental

3.4. Theoretical calculations

2.1. Materials

The hardware and the software from the Kalam–Balam Supercomputer were used for obtaining the theoretical calculations and the optimized structures of simvastatin and the family of alcohols used as solvents. the KanBalam Supercomputer uses a HP Cluster Platform 4000, with HP Alpha Server SC45 and SGI Altix 350.

The compound simvastatin as powder was donated by CINDETEC, S.A. de C.V. (Mexico), with a purity of 99.5 wt.%. Analytical grade solvents (99.5 wt.% purity) ethanol, 1-propanol, 1-butanol, 1-hexanol, 1-pentanol and 1-octanol were obtained from Aldrich, the purity of the alcohols was confirmed by gas chromatography to be more than 99%.

4. Results and discussion

2.2. Equipment

4.1. Calorimetric data

Digital analytical balance made by Mettler model AE160, sensitivity 0.01 mg for weighting the SVS was used. For thermal analyses a TA Instruments model 2060 Differential scanning calorimeter, DSC, and a TGA model 2010 were used. Spectrophotometer made by Thermo Scientific UV–Vis model Genesys UV, at 215 nm was used to obtain the calibration curve and for determining the equilibrium concentrations of SVS upon sampling and analysis.

The melting temperature and fusion enthalpy of simvastatin were measured by DSC with values of 410.92 ± 0.5 K and 24,464 J/mol, respectively. The differential molar heat capacity DCp was measured by DSC to be 268.61 J/mol K.

3. Experimental methods 3.1. Solubility determination Analytical method with approach to equilibrium from oversaturation strategies [20], was used for determining saturation solubility. For solubility measurements with each solvent, about 100 mg of simvastatin was added to 5 mL vials, containing 5 mL of the corresponding solvent. The system was shaked mechanically at 55 °C for 12 h, evaporation was avoided by reflux equipment at

4.2. Theoretical solubility Ideal solubility ln X id 2 of SVS from the values of DHfus, Tm and DCp the ideal solubility of SVS can be determined. It is interesting to examine the accuracy of the approximate values obtained, since the solvent–solute systems are in equilibrium at constant pressure. Ideal solubility values were obtained from Eq. (10). The theoretical ideal solubility values are presented in Fig. 2 and compared with the experimental values and the correlated solubility are in Table 1. Then, Fig. 2 shows that both assumptions: I (DCp = 0) and II (DCp = DSfus) under-estimate the theoretical ideal solubility of SVS. These facts are consistent whit other reports in different compounds [19,21] suggesting that DCp has a significant

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55 50

Solubility Mole Fraction *10

-3

45 40 35 30 25 20 15 10 5 0 280,00

285,00

290,00

295,00

300,00

305,00

310,00

315,00

T/K Ethanol

Propanol

Butanol

Octanol

Hexanol

Pentanol

Theoretical

Fig. 2. Theoretical ideal solubility of SVS with measured Cp and those calculated from assumption I, DCp = 0 and assumption II, DCp = Ds and experimental equilibrium solubility of SMV in different alcohols and temperatures.

Table 1 Experimental solubility (mole fraction) of Simvastatin in different alcohols and different temperatures. X2

Temperature (K)

Temperature (°C)

Molality (m/kg)

Ln Molality

(1/T)  103

Ethanol 2.06E02 2.51E02 4.08E02 5.43E02 6.26E02

286.15 291.1 301.15 307.15 310.55

13.00 17.95 28.00 34.00 37.40

0.448 0.546 0.890 1.19 1.37

0.80296 0.60514 0.11653 0.17395 0.31481

3.4947 3.4352 3.3206 3.2557 3.2201

1-Propanol 4.21E02 4.88E02 7.19E02 7.59E02 8.44E02

286.15 291.10 304.55 307.15 310.55

13.00 17.95 31.40 34.00 37.40

0.7017 0.8133 1.1983 1.265 1.407

0.35429 0.20661 0.18093 0.23507 0.34121

3.4947 3.4352 3.2835 3.2557 3.2201

1-Butanol 4.60E02 5.26E02 7.02E02 7.86E02 8.09E02

285.70 290.65 301.20 305.20 308.70

12.55 17.50 28.05 32.05 35.55

0.6389 0.7305 0.9750 1.0917 1.236

0.44801 0.31471 0.02532 0.08773 0.21196

3.5002 3.4406 3.3201 3.2765 3.2394

1-Pentanol 3.12E02 4.04E02 5.71E02 6.40E02 7.38E02

289.15 295.50 304.55 307.15 310.55

16.00 22.35 31.40 34.00 37.40

0.37143 0.48095 0.67976 0.76190 0.87857

0.99039 0.73199 0.386012 0.271935 0.129459

3.4584 3.3841 3.2835 3.2557 3.2201

1-Hexanol 3.63E02 4.55E02 5.65E02 7.68E02

293.85 298.95 303.90 312.00

20.70 25.80 30.75 38.85

0.37812 0.47395 0.58854 0.80000

0.97253 0.74663 0.53011 0.22314

3.4031 3.3450 3.2906 3.2051

1-Octanol 2.55E02 3.13E02 4.67E02 5.15E02 6.19E02

285.70 290.65 301.20 305.20 308.70

12.55 17.50 28.05 32.05 35.55

0.23702 0.29111 0.43506 0.48002 0.57759

1.44346 1.23405 0.83228 0.73393 0.54888

3.5002 3.4406 3.3201 3.2765 3.2394

contribution to the ideal solubility of SVS, mainly at temperatures far from the solute melting temperature. It is worth to mention

that the theoretical ideal solubility of SVS under assumption I is actually lower than that experimentally obtained equilibrium mole

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fraction dissolved for each solvent studied. For all case, solubility of SVS increases with temperature, indicating that the dissolution process is endothermic. Additionally, SVS solubility increases with increasing alkyl chain length (from ethanol to 1-butanol) and then decreases as carbon number increases, this fact can be explained by the possible solute–solvent interaction. 4.3. Simvastatin activity coefficient ln c1 2 The SVS activity coefficient at infinite dilution ln c1 2 in different alcohols can be obtained from Eqs. (1), (2), and (12) using the experimentally values Tm, DHfus(Tm), DCp and equilibrium solubil1 ity X Exp 2 . The plots of ln c2 versus 1/T are presented in Fig. 3. The SVS coefficient values ln c1 2 follows van’t Hoff’s relation Eq. (4), for all alcohols used. 1 2

ln c ¼ A þ B=T

ð14Þ

where A and B could be identified as DS°/R and DH°/R, respectively. A simple linear relationship between ln c1 2 and 1/T is observed confirming that DH° is constant over the temperature range considered. The quality of the fit is very good and it is confirmed from the regression coefficient R2 > 0.995 (Table 2) since the slope of ln c1 2 vs 1/T plots is positive for all alcohols studied, DH1 > 0 is consistent with the endothermic dissolution. From examining the effect of assumptions I and II on the activity coefficient ln c1 2 by using Eqs. (10) and (12), the resulting activity coefficient of SVS in various alcohols are displayed in Fig. 4. Now, the slope of the straight lines was a negative value, indicating that the solubility decreases with temperature. This fact contradicts the real experimental data, Fig. 5, therefore the assumption I DCp = 0 is inconsistent with solubility data and is not applicable for the equilibrium data for SVS in alcohols. In examining assumption II, DCp = DS and Eq. (11) it is found than van’t Hoff plot of ln c1 2 vs 1/T shows a linear behavior with scattered correlation. Similar to the previous case, DCp = DS assumption again indicates that activity coefficients are not consistent with solubility data, Fig. 6, and is not applicable in correlating temperature dependant equilibrium data of SVS in alcohols.

Table 2 Equations corresponding to the plot Ln molality vs 1/T, for each alcohol dissolving simvastatin. Alcohol

Equation

Correlation coefficient, R2

Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol

y = 4133.2x + 11.315 y = 2529.8x + 6.1862 y = 2275.1x + 5.1922 y = 3594.3x + 9.0874 y = 3816.4x + 9.6571 y = 3314.4x + 7.7521

0.9986 0.9996 0.9932 0.999 0.9994 0996

4.4. Temperature dependence of simvastatin solubility in different alcohols Simvastatin solubility in several alcohols were measured at different temperatures, however there is not a normal behavior as the number of carbons increase in the alcohols, since the solubility is the lower for ethanol and the highest values is not for the 1-octanol, but for the 1-butanol. Therefore, a possible explanation for this anomalous behavior is the folding of the longer compound such as 1-octanol. Theoretical studies are needed and were carried out for supporting the corresponding explanation. 4.5. X-ray diffraction measurements X-ray diffraction pattern from simvastatin sample shows that is a solid with an orthorhombic crystalline system, as reported in the literature [22]. From the results obtained with the thermal analysis and presented in Fig. 7 it is possible to observe that SVS is a crystalline solid where no polymorphic phenomenon is present. The peak sharpness of the fusion process indicates that there is not solid polymorphic transition and that enthalpy fusion value is low. From the Fig. 8 it is possible to observe that SVS is stable until 170 °C, with weight loss of 0.15% at 120.1 °C due to absorbed water, and with a weight loss of 13.5% at 250.9 °C, probably due to the sublimation or decomposition of the compound studied.

Fig. 3. Values of experimental equilibrium solubility of SVS in different alcohols and temperatures.

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5. Theoretical calculations 5.1. Introduction Dipole moment represents a direct measure of electron distribution in a molecule of known geometry. It is a physical constant which can be obtained by experimental and theoretical methods. A number of excellent texts, monographs, and reviews devoted to dipole moments are available and contain a detailed discussion of the corresponding theory [23–28]. Although most of these references are not recent, they have served as an excellent source of information and a starting point for any work of this type. It seems worthwhile to point out here that prior to the development and widespread applications of modern spectroscopic techniques, dipole moments represent one of the most important sources of structural information about organic molecules and solvents. Examples of the various practical applications of dipole moments include, but are not limited to: differentiation between isomers (cis and trans, o, m, and p, tautomers, etc.), conformational analysis, studies of molecular geometry, supporting evidence for resonance hybrids, information about the polar character of molecules (important for solubility in different solvents and permeability through membranes), information about electrical effects of

Table 3 Equations corresponding to the plots in Fig. 5. Alcohol

Equation

Correlation coefficient, R2

Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol

y = 0.0101x + 3.3111 y = 0.0198x + 6.3632 y = 0.0229x + 7.3889 y = 0.0171x + 5.6679 y = 0.0261x + 8.5658 y = 0.0256x + 8.4356

0.9937 0.9771 0.9836 0.9897 0.9963 0.9889

substitutes (inductive, resonance), studies of hydrogen bonding and electron donor–acceptor interactions (e.g., charge transfer complexes) [29]. 5.2. Computational details The geometry optimizations of Simvastatin was carried out using density functional theory, Fig. 9, with Becke’s three parameter hybrid method and correlation functional of Lee, Yang and Parr (B3LYP) [30–31] with 6-311++G⁄⁄ basis set [32]. Local minima were identified by the absence of imaginary frequencies. PCM [33,34] was used for evaluating the bulk solvent effects, in which

Fig. 4. Van’t Hoff equation representation of experimental Simvastatin solubility in different alcohols, the equation from each plot is given in Table 2.

Fig. 5. Activity coefficient as temperature function at infinite dilution using different alcohols for dissolving simvastatin and the assumption 1, DCp = 0.

J.M. Aceves-Hernández et al. / Journal of Molecular Structure 995 (2011) 41–50

47

Fig. 6. Simvastatin X-ray diffraction pattern at room temperature, using Cu Ka radiation of 1.504 Å, using the powder method.

Fig. 7. Simvastatin differential scanning calorimetry, DSC, with a melting point of 137.9 °C, and a melting enthalpy of 25.055 kJ/mol.

the problem is divided into a solute part (simvastatin) lying inside a cavity and a solvent part (in our case, water, methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol and 1-octanol, respectively) represented as a structure-less material, characterized by its dielectric constant as well as other parameters [35]. All calculations were performed using Gaussian 09 [36]. 5.3. Results and discussion To see how the solvency will affect the geometry, the geometry optimization of simvastatin was performed using the PCM at B3LYP/6-311++G(d,p) level. As shown in Table CD1-CD3, solvation

process only slightly changed the molecule in the space, re-optimized geometry parameters in the dielectric continuum corresponding to the different solvent-simvastatin solutions (e = 78.355, 32.613, 24.852, 20.524, 17.332, 15.130, 12.510 and 9.863, respectively) leads to small changes by no more than 0.007 Å in bond lengths and 0.5° in dihedral angles, which means that introduction of a solvent reaction field has slight effect on the geometry of simvastatin structure (see Table 3). The charge distributions of dipolar compounds are often altered significantly in the presence of a solvent reaction field. The Natural population analysis of the type of atomic net charge was utilized for studying the change tendencies of one structure to another,

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Fig. 8. Simvastatin thermo-gravimetric analysis, TGA, with a weight loss of 13.5% at 250.9 °C, probably due to the sublimation/decomposition of the compound studied.

Fig. 9. (a) Optimized structure of the simvastatin molecules, with B3LYP/63111++G(d,p) level. (b) Ground-state dipole moment in gas phase.

of the atoms for the discussed molecule. The difference on charge distributions is in accord with the changes in dipole moments. As expected, the charge distributions are slightly influenced by a dielectric medium. Small changes are predicted with the increasing value of the dielectric constant of each atom (O1, O2, O3, O4, O5, C11, C23 and C25). The oxygen atoms (O1, O3, O4 and O5) showed little net charge in gas phase, but an increase of the negative charge was observed when the solvent was water. However, in other solvents the charge of these atoms is decreasing. The carbon atom C23, within the simvastatin molecule becomes more positive when changing water by 1-octanol as solvent. Moreover, carbon atoms C11 and C25 increase their positive charge, when changing the gas phase by water, but their charge decrease when changing methanol by 1-octanol. The quantum-chemical calculations predict a large positive charge on the O23 atom in 1-octanol solvent and larger negative charges on O4 atom. The charge distributions on these atoms were different in different solvents as would be expected. Theoretical values of solvent energies (ES) and ground-state dipole moments of simvastatin in vacuum and in solutions obtained by B3LYP/6-311++G(d,p) are listed in Tables 5 and 6. Lower values of the solvent dielectric constant (e) yield low total molecular energies values as well, Fig. 10. Solvent properties such as dipole moment change the value of the charge delocalized in the molecules, therefore, solvent energies show correlation with the dielectric constant or dipole moment. Ground-state dipole moment is an important factor in measuring solvent effect on the molecule under study, a large ground-state dipole moment gives rise to a strong solvent polarity effects [37]. The dipole moments of simvastatin varies just from 5.854 D to 6.016 D when the values change from the e = 9.863 to e = 78.355, which also demonstrate that the solvent effects on simvastatin are important. 6. Conclusions

considering the dissolvent. Natural population analyses of atomic charges both in gas phase and in solutions have been examined. The results are shown in Table 4, which contains some charge data

Ideal solubility values are rather high that the experimental values, but thermodynamic consideration allows us to present a

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J.M. Aceves-Hernández et al. / Journal of Molecular Structure 995 (2011) 41–50 Table 4 Atomic net charges of atoms in the skeleton of simvastatin molecule at level B3LYP/6-311++G(d,p). Charge values in electrons (e). Atom

Gas phase

water

Methanol

Ethanol

1-Propanol

1-Butanol

1-Pentanol

1-Hexanol

1-Octanol

Charge O1 O3 O3 O4 O5 C11 C23 C25

0.629 0.764 0.570 0.571 0.735 0.745 0.130 0.817

0.672 0.5S6 0.590 0.660 0.799 0.859 0.118 0.851

0.671 0.585 0.590 0.658 0.797 0.858 0.119 0.850

0.670 0.585 0.589 0.656 0.796 0.858 0.119 0.850

0.670 0.585 0.589 0.655 0.795 0.858 0.119 0.849

0.669 0.585 0.588 0.654 0.794 0.857 0.119 0.849

0.669 0.585 0.588 0.653 0.793 0.857 0.119 0.848

0.668 0.584 0.587 0.651 0.790 0.857 0.119 0.847

0.667 0.584 0.587 0.648 0.788 0.856 0.120 0.846

Table 5 Free energies, G, (in kcal/mol) for simvastatin molecule in different solvents, at level B3LYP/6-311++G(d,p). Solvent

DG

e

Gas phase Water Methanol Ethanol 1-Propanol 1-Butanol 1-Pentanol 1-Hexanol 1-Octanol

848035.3728 848081.6596 848080.1123 848079.3024 848078.5971 848077.8589 848077.1787 848076.0788 848074.4247

0.000 78.355 32.613 24.852 20.524 17.332 15.130 12.510 9.863

equation where it is possible to assign values to the free energy parameter, DG, to entropy change DS, and the Cp. It is worth to mention that SVS solubility data are important for formulation of controlled delivery systems, therefore new studies are needed with other compounds used in pharmacy. Solubility of SVS was determined at different temperatures in several alcohols; however, abnormal tendency was found between those values, the solubility increase with the number of carbons from ethanol to 1-butanol, but a decrease was observed from 1-pentanol to 1-octanol. It is possible that the folding of alcohol molecules with more carbons than that of the 1-butanol is occurring. The molecular geometry of simvastatin in gas phase and solutions have been investigated by using DFT approach at B3LYP/6-311++G(d,p) level, while the

Table 6 Dipole moment of simvastatin molecule at level B3LYP/6-311++G(d,p). In Debye (D). Gas phase

Water

Dipole moment (D) 3.861 6.016

Methanol

Ethanol

1-Propanol

1-Butanol

1-Pentanol

1-Hexanol

1-Octanol

5.915

5.864

5.821

5.777

5.738

5.675

5.584

Fig. 10. Dielectric constant e, from water, methanol, ethanol, 1-propanol, 1-butanol, 1-pentanol, 1-hexanol and 1-octanol vs Gibbs free energy in kcal mol1.

50

J.M. Aceves-Hernández et al. / Journal of Molecular Structure 995 (2011) 41–50

solvents values were obtained with the PCM method. We conclude that the solvent effects on the molecular structure of simvastatin are not obvious. The computed results show than maximum change in charge occurs at carbonyl oxygen O4, increasing when changing from gas phase to aqueous solution just by 0.077e, while changing from gas phase to 1-octanol solution only by 0.065e. It is concluded that the explanation of the anomalous behavior in the experimental solubility values could be explained by the theoretical calculations. The dipole moments of simvastatin varies just from 5.854 D to 6.016 D when the values change from the e = 9.863 to e = 78.355, which also demonstrate that the solvent effects on simvastatin are important. Acknowledgements The authors thank CINDETEC, S.A. de C.V. (Mexico) for the Simvastatin drug. Thanks are due to Manuel Aguilar (Instituto de Física, UNAM) for the support in the experimental work. The access to the KanBalam supercomputer at DGSCA-UNAM is strongly appreciated by the authors and I. Nicolás acknowledges financial support from DGAPA-UNAM under Projects PAPIME: PE201905. Appendix A. Supplementary material Supplementary data associated with this article can be found, in the online version, at doi:10.1016/j.molstruc.2011.03.048. References [1] [2] [3] [4] [5] [6] [7] [8] [9] [10]

E. Manzurola, A. Apelblat, J. Chem. Thermodyn. 34 (7) (2002) 1127–1136. A. Apelblat, E. Manzurola, J. Chem. Thermodyn. 31 (1999) 85–91. F. Tiziana, F. Montanes, A. Olano, E. Ibanez, J. AIChE 53 (2007) 2411–2418. M. Mirmehrabia, S. Rohani, K.S.K. Murthy, B. Radatusb, Int. J. Pharm. 282 (2004) 73–85. Z. Huang, G.B. Sun, Y.C. Chiew, S. Kawi, Powder Technol. 160 (2005) 127–134. M.A. Herrador, A.G. Gonzalez, Int. J. Pharm. 156 (1997) 239–244. E.S. Istvan, J. Deisenhofer, Science 292 (2001) 1160–1164. W. Palinski, Nat. Med. 6 (2000) 1311–1312. W.A. Greenberg, A. Varvak, S.R. Hanson, K. Wong, H. Huang, P. Chen, M.J. Burk, PNAS 101 (2004) 5788–5793. S. Javernik, S. Kreft, B. Strukelj, F. Vrecer, Croat. Chem. Acta 76 (2003) 263–268.

[11] A. Sutherland, K.K. Auclair, J.C. Vederas, Curr. Opin. Drug Discov. Dev. 4 (2003) 229–236. [12] M. Shachter, Fundam. Clin. Pharmacol. 19 (2004) 117–125. [13] J.P. Elder, Thermochim. Acta 134 (1988) 41–45. [14] H. Sun, J. Gong, J.K. Wang, J. Chem. Eng. Data 50 (2005) 1389–1391. [15] J.M. Prausnitz, R.N. Lichtenthaler, E. Gomes de Azevedo, Molecular Thermodynamics of Fluid-phase Equilibria, second ed., Prentice-Hall, Englewood Cliffs, NJ, 1986. [16] Q. Jiang, G.-H. Gao, Y.-X. Yu, Y. Qin, J. Chem. Eng. Data 45 (2000) 292–294. [17] S. Wang, J.K. Wang, Q.X. Yin, Ind. Eng. Chem. Res. 44 (2005) 3783–3787. [18] B.S. Liu, J.B. Gong, J.K. Wang, C.Y. Jia, J. Chem. Eng. Data 50 (2005) 1684–1686. [19] S.H. Neau, G.L. Flynn, Pharm. Res. 11 (1990) 1157–1162. [20] J. Alsenz, E. Meister, E. Haenel, J. Pharm. Sci. 96 (2007) 1748–1762. [21] S. Gracin, T. Brinck, A. Rusmuson, Ind. Eng. Chem. Res. 41 (2002) 5114–5124. [22] J. Cejka, B. Kratovich, I. Cisarova, A. Jegorov, Acta Crystallogr. Sect. C. c59 (2003) 428–430. [23] R.J.W. Le Fevre, Dipole Moments, Methuen, London, 1953. [24] J.W. Smith, Electric Dipole Moments, Butterworth, London, 1955. [25] V.I. Minkin, O.A. Osipov, Y.A. Zhdanov, Dipole Moments in Organic Chemistry, Plenum Press, New York, 1970. [26] G.J. Moody, J.D.R. Thomas, Dipole Moments in Inorganic Chemistry, E. Arnold, London, 1971. [27] W. Liptay, in: E.C. Lim (Ed.), Excited States, vol. 1, Academic Press, New York, 1974, p. 129. [28] O. Exner, Dipole Moments in Organic Chemistry, G. Thieme Verlag, Stuttgart, 1975. [29] B. Siddlingeshwar, S.M. Hanagodimath, E.M. Kirilova, G.K. Kirilov, J. Quantitative Spectrosc. Radiat. Transfer (2010). [30] A.D. Becke, Phys. Rev. A 38 (1988) 3098. [31] C. Lee, W. Yang, R.G. Parr, Phys. Rev. B 37 (1988) 785. [32] M.O. Andersson, P. Uvdal, J. Phys. Chem. A 109 (2005) 2937. [33] M.A. Aguilar, F.J. Olivares, J. Tomasi, J. Chem. Phys. 98 (1993) 7375. [34] M. Cossi, V. Barone, R. Cammi, J. Tomasi, Chem. Phys. Lett. 255 (1996) 327. [35] J. Preat, D. Jacquemin, V. walthelet, J.M. Andre, E.A. Perpete, J. Phys. Chem. A 110 (2006) 8144. [36] Gaussian 09, Revision A.02, M. J. Frisch, G. W. Trucks, H. B. Schlegel, G. E. Scuseria, M. A. Robb, J. R. Cheeseman, G. Scalmani, V. Barone, B. Mennucci, G. A. Petersson, H. Nakatsuji, M. Caricato, X. Li, H. P. Hratchian, A. F. Izmaylov, J. Bloino, G. Zheng, J. L. Sonnenberg, M. Hada, M. Ehara, K. Toyota, R. Fukuda, J. Hasegawa, M. Ishida, T. Nakajima, Y. Honda, O. Kitao, H. Nakai, T. Vreven, J. A. Montgomery, Jr., J. E. Peralta, F. Ogliaro, M. Bearpark, J. J. Heyd, E. Brothers, K. N. Kudin, V. N. Staroverov, R. Kobayashi, J. Normand, K. Raghavachari, A. Rendell, J. C. Burant, S. S. Iyengar, J. Tomasi, M. Cossi, N. Rega, J. M. Millam, M. Klene, J. E. Knox, J. B. Cross, V. Bakken, C. Adamo, J. Jaramillo, R. Gomperts, R. E. Stratmann, O. Yazyev, A. J. Austin, R. Cammi, C. Pomelli, J. W. Ochterski, R. L. Martin, K. Morokuma, V. G. Zakrzewski, G. A. Voth, P. Salvador, J. J. Dannenberg, S. Dapprich, A. D. Daniels, O. Farkas, J. B. Foresman, J. V. Ortiz, J. Cioslowski, and D. J. Fox, Gaussian, Inc., Wallingford CT, 2009. [37] A. Masternak, G. Wenska, J. Milecki, B. Skalski, S. Franzen, J. Phys. Chem. 109 (2005) 759.