Determination of the Enthalpy of Solute−Solvent Interaction from the

9280

J. Phys. Chem. B 2006, 110, 9280-9285

Determination of the Enthalpy of Solute-Solvent Interaction from the Enthalpy of Solution: Aqueous Solutions of Erythritol and L-Threitol A. J. Lopes Jesus, Luciana I. N. Tome´ , M. Ermelinda S. Euse´ bio,* and J. S. Redinha Department of Chemistry, UniVersity of Coimbra, 3004-535, Coimbra, Portugal ReceiVed: October 25, 2005; In Final Form: March 8, 2006

In this work the enthalpy of the solute-solvent interaction of erythritol and L-threitol in aqueous solution was determined from the values obtained for the enthalpy of solvation. The values for this property were calculated from those determined for the enthalpies of solution and sublimation. To determine the values of the enthalpy of solute-solvent interaction, the solvation process is considered as taking place in three steps: opening a cavity in the solvent to hold the solute molecule, changing the solute conformation when it passes from the gas phase into solution, and interaction between the solute and the solvent molecules. The cavity enthalpy was calculated by the scaled particle theory and the conformational enthalpy change was estimated from the value of this function in the gas phase and in solution. Both terms were determined by DFT calculations. The solvent effect on the solute conformation in solution was estimated using the CPCM solvation model. The importance of the cavity and conformational terms in the interpretation of the enthalpy of solvation is noted. While the cavity term has been used by some authors, the conformational term is considered for the first time. The structural features in aqueous solution of erythritol and L-threitol are discussed.

1. Introduction The hydration of erythritol and L-threitol, two diastereomers of 1,2,3,4-butanetetrol, is discussed in this paper. The first is a meso form while the second is optically active. These two molecules are alditols, an important group of compounds. Those with between 2 and 5 carbon atoms are widely found in nature, and a few with a higher number of carbon atoms are also naturally occurring, while some long chain ones are obtained synthetically.1 Erythritol is being increasingly used in the food industry as an alternative sweetening agent to sugar. Its advantage is a lower caloric content. In fact, most ingested erythritol is excreted without being metabolized.2 It is also widely used in the pharmaceutical industry as an excipient, and current research on its interaction with medicinal compounds is emphasizing the role it can play in pharmaceutical manufacturing.3-6 Both diastereomers are also known to act as cryoprotectant agents in animal and plant tissues.7-9 From the structural point of view, each of the two tetritol isomers is a system capable of providing valuable data on the aqueous solution of polyhydroxylated compounds. The number of hydroxyl groups is large enough to simulate a variety of structures exhibited by polyfunctional solutes, but of a size that allows them to be computationally studied at a high level of theory. The molecule with the maximum number of hydroxyl groups studied until now by high level electronic structure methods is glycerol.10-12 Hence, the contribution that the system under study can give to the knowledge of the hydration of polyfunctional compounds is particularly relevant. Despite the importance of these two compounds, only one work dedicated to their structure in solution using molecular-dynamics has been published in the literature.13 Another aim of this paper is concerned with the refinement of the method to deduce the enthalpy due to the solute-solvent * To whom all correspondence should be addressed. [email protected].

interaction from the enthalpy of solvation. This is a question of utmost importance for the thermodynamic study of solutions. For the first time, allowance is made for the variation of the conformation of the solute in the solvation process. 2. Solvation-Related Thermodynamic Properties The standard enthalpy of solution, ∆solH°, corresponds to the limiting value determined for the enthalpy of the following process

A (crystal, p ) 1 bar) f A (ideal solution, CA,sol ) 1 M) (1) A stands for solute. It will not be possible to get much information on the structure of the solutions from ∆solH° when the solute is in the solid (or liquid) state, considering the intermolecular forces present in such states. Contrary to the enthalpy of solution, the enthalpy of solvation, enthalpy change corresponding to the transfer of the solute from the gas state to the solution, is a thermodynamic property more directly related to the structure of the solution. Adopting the definition proposed by Ben-Naim,14 the standard value of the thermodynamic property of solvation corresponds to the following process

A (ideal gas, CA,gas ) 1 M) f A (ideal solution, CA,sol ) 1 M) (2) The standard enthalpy of solvation, ∆solvH°, can be determined from the thermodynamic cycle involving this quantity, the enthalpy of solution, and the enthalpy of sublimation. The last two may be determined by calorimetry. The standard enthalpy of sublimation, ∆subH°, corresponds to the enthalpy of the process

A (crystal, p ) 1 bar) f A (ideal gas, p ) 1 bar)

10.1021/jp0561221 CCC: $33.50 © 2006 American Chemical Society Published on Web 04/14/2006

(3)

Enthalpy of Solute-Solvent Interaction

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9281

thus, the expression deduced for the calculation of ∆solvH° is15

∆solvH° ) ∆solH° - ∆subH° + RT(1 - RT)

TABLE 1: Enthalpy of Solution of Erythritol and L-threitol in Water at 298.15 K erythritol

(4)

where R is the thermal expansion of the solvent. The last term of the right-hand side member of the eq 4 accounts for the difference between the reference state taken for gas in eq 2 and eq 3. The standard enthalpy of solvation has been widely used in the study of molecular interactions in solution. Although referred to as a state free from intermolecular forces, solvation thermodynamic functions include contributions other than the solutesolvent interactions. One of these terms is related to the difference of the solute conformation in gaseous state and in solution. The intermolecular forces established with the solvent molecules can drastically change the conformation of the solute as it is transferred from the gas phase to the solvent. An allowance for the solute conformational variation, ∆confH°, must be made. This corresponds to the enthalpy of the following hypothetical transformation

A (ideal gas, CA ) 1 M, gas conf.) f A (ideal gas, CA ) 1 M, sol. conf.) (5) Another correction must be made due to the perturbation of the structure of the solvent on adding the solute molecule. In effect, intermolecular bonds are broken in the solvent as the solute molecule is introduced, making a positive contribution to the enthalpy of solvation. To calculate this term, the solvation of a solute is held to take place in two steps: first, a cavity with adequate size to hold the solute molecule is opened in the solvent, ∆cavH°, and then solute-solvent interactions are set up, ∆intH°. Considering those steps referred above, the following expression represents the enthalpy of solute-solvent interaction

∆intH° ) ∆solH° - ∆subH° - ∆confH° - ∆cavH° + RT(1 - RT) (6) The decomposition of solvation into cavity and molecular attraction terms is a classical procedure with roots in the 1930s.16,17 It became a popular interpretation of solvation as theories to calculate the cavity term were being developed, particularly after Pierotti successfully applied the scaled particle theory (SPT) to nonelectrolyte solutions including aqueous solutions.18-20 The role of the cavity term in interpreting the enthalpy of solvation has been emphasized, especially when results obtained for different solvents are compared.21,22 Conversely, conformational enthalpy has been ignored in the interpretation of ∆solvH°. However, as this research will show, systems involving solutions with flexible molecules, as most organic compounds do, give rise to molecular conformation changes that can on no account be neglected. In this work ∆solH° was determined by solution calorimetry. Data for ∆subH° were published by the authors,23 while the remaining terms of the second member of eq 6 were calculated. The cavity term was determined by the scaled particle theory and the enthalpy of conformational change was estimated from the DFT theoretical calculations performed in the isolated molecules and in aqueous solution using the CPCM solvation model. 3. Quantities Required for the Calculation of the Enthalpy of Interaction 3.1. Enthalpy of Solution. Erythritol from Fluka with specified purity greater than 99% and L-threitol from Aldrich

L-threitol

m mol kg-1

∆solH kJ mol-1

m mol kg-1

∆solH kJ mol-1

0.1059 0.1191 0.1302 0.1472 0.1546 0.1724 0.2130 0.2709 0.3382 0.3800 0.5168 0.5583 0.5897 0.6396 0.8386

23.890 23.968 23.926 24.107 23.955 24.012 24.056 24.194 24.130 24.143 24.113 24.189 24.137 24.266 24.332

0.0549 0.1221 0.1682 0.2081 0.2311 0.2961 0.3258 0.3777 0.4648 0.4874

19.280 19.304 19.186 19.205 19.225 19.190 19.280 19.226 19.285 19.213

Chemical Company, labeled as 99% pure, were the substances used in this research. The original substances were dried under vacuum at 353 K for erythritol and at 303 K for L-threitol. Purity of the dried compounds was determined by GC-MS, giving 99.9 mole percent for erythritol and 99.8 mole percent for L-threitol. To avoid uptake of water from the atmosphere, the compounds were handled under nitrogen atmosphere. Bidistilled water was used in the preparation of the solutions. Heat of solution measurements were carried out with a Calvet type Setaram C80 heat flux calorimeter consisting of the calorimeter block for the working and reference cells. The generated signal is amplified and supplied to a data acquisition system. Stainless steel standard reversal mixing vessels supplied by the manufacturer were used as working and reference cells. The experiments were performed at 298.15 K. The concentration of the solutions ranged between 0.1 and 0.8 mol kg-1 for erythritol and 0.05 to 0.5 mol kg-1 for L-threitol. The calorimeter calibration constant was determined from the results obtained for the dissolution of standard potassium chloride24-26 treated according to the recommendation for the purification of this standard substance.27 The performance of the calorimetric data was ascertained by measuring the enthalpy of solution of sodium chloride (Riedel de Haen, > 99.8 mole percent, dried under reduced pressure at 333 K for a few days28) in water at 298.15 K. The mean value obtained for eleven independent determinations covering the concentration range from 0.1 to 0.5 mol kg-1 was ∆solH° ) (4.26 ( 0.05) kJ mol-1. This figure is in good agreement with the value published in the literature, ∆solH° ) 4.2 kJ mol-1.29 The values of ∆solH obtained for erythritol and L-threitol are presented in Table 1. A slight increase of ∆solH with increasing concentration was observed for erythritol. The values obtained for this property fit the following equation

∆solH ) (23.93 ( 0.07) + (0.5 ( 0.2)m

(7)

No significant trend for the dependency of ∆solH on the concentration was shown for L-threitol. Thus, the value taken for standard enthalpy is just the mean of the experimental results. The values of ∆solH° for both compounds are presented in Table 5. 3.2. Enthalpy of Solvation. The values obtained for ∆solvH° calculated by eq 4 are given in Table 5. The quantities needed for their calculation are also inserted in this table. The value taken for the expansibility coefficient of water is R ) 0.257 × 10-3 K-1.

9282 J. Phys. Chem. B, Vol. 110, No. 18, 2006

Lopes Jesus et al.

TABLE 2: Calculated (B3LYP/6-311++G**) Enthalpy, Gibbs Energy, and Boltzmann Population of Erythritol Conformers in Gas State and in Aqueous Solution (CPCM) at 298.15 Ka

a

conformer

label

Hi,gas Hartree

Gi,gas Hartree

pi,gas (%)

∆Gi,solv kJ mol-1

Gi,sol Hartree

pi,sol (%)

E1 E2 E3 E4 E5 E6 E7 E8 E9 E10 E11 E12 E13 E14 E15 E16 E17 E18 E19 E20 E21 E22 E23 E24 E25 E26 E27 E28 E29 E30 E31 E32 E33 E34 E35

G′TG1 GTG1 GG′G′1 G′TG2 GG′G′2 GTG′1 GTG2 GGG1 TTG′1 G′TT1 TTG′2 GGG2 G′TT2 GGG3 GG′G1 GGT1 TTG′3 G′TT3 GG′G2 TGG1 G′TT4 TGG2 TGG3 GG′G3 TGG4 TGG5 TTT1 TTT2 G′GT1 TTT3 TTT4 TTT5 G′GG1 G′GG2 G′GG3

-459.309248 -459.310832 -459.310218 -459.309915 -459.311532 -459.311139 -459.308816 -459.311531 -459.309923 -459.309508 -459.310132 -459.308770 -459.309930 -459.312278 -459.311270 -459.308585 -459.307949 -459.309335 -459.310273 -459.309189 -459.310815 -459.312925 -459.309125 -459.310739 -459.312317 -459.312457 -459.308180 -459.306750 -459.308211 -459.309448 -459.309359 -459.309559 -459.307694 -459.308516 -459.309958

-459.356780 -459.357046 -459.355503 -459.355144 -459.356799 -459.356453 -459.354417 -459.356334 -459.355390 -459.354732 -459.355725 -459.353637 -459.355678 -459.357102 -459.355996 -459.354311 -459.353461 -459.354605 -459.355087 -459.353242 -459.356045 -459.356737 -459.353177 -459.355581 -459.356140 -459.356234 -459.352496 -459.351852 -459.353389 -459.354121 -459.353610 -459.353372 -459.351515 -459.352441 -459.353510

8.7 11.6 2.3 1.5 8.9 6.2 0.7 5.4 2.0 1.0 2.9 0.3 2.7 12.3 3.8 0.6 0.3 0.9 1.5 0.2 4.0 8.4 0.2 2.5 4.4 4.9 0.1 0.0 0.2 0.5 0.3 0.2 0.0 0.1 0.3

-76.20 -72.89 -76.21 -75.74 -70.46 -71.28 -76.37 -70.53 -72.53 -74.10 -71.49 -76.96 -71.55 -67.65 -70.32 -74.05 -76.04 -72.99 -71.71 -75.90 -68.46 -66.53 -74.96 -68.45 -66.44 -66.14 -75.24 -76.25 -71.41 -68.71 -68.64 -67.33 -67.99 -65.40 -60.16

-459.385805 -459.384810 -459.384529 -459.383992 -459.383636 -459.383603 -459.383505 -459.383198 -459.383014 -459.382957 -459.382956 -459.382950 -459.382932 -459.382871 -459.382781 -459.382516 -459.382422 -459.382404 -459.382400 -459.382152 -459.382121 -459.382076 -459.381729 -459.381654 -459.381445 -459.381424 -459.381154 -459.380894 -459.380590 -459.380291 -459.379753 -459.379016 -459.377410 -459.377351 -459.376423

37.4 13.0 9.7 5.5 3.8 3.6 3.3 2.4 1.9 1.8 1.8 1.8 1.8 1.7 1.5 1.1 1.0 1.0 1.0 0.8 0.8 0.7 0.5 0.5 0.4 0.4 0.3 0.2 0.1 0.1 0.1 0.0 0.0 0.0 0.0

Values of Hi,gas, Gi,gas and pi,gas were taken from ref 30.

3.3. Enthalpy of Conformational Change. The variation of the solute conformational enthalpy corresponding to the transfer from the gas to the solution is given by the difference between the enthalpies of the molecular conformation in solution g (Hsol conf) and in the gas phase (Hconf): g ∆H°conf ) Hsol conf - Hconf

(8)

The two quantities of the right-hand side of eq 8 were estimated by computational methods and a description of their calculation method is given below. In a previous work the authors calculated the electronic energy, enthalpy, and Gibbs energy of the most stable conformers of erythritol and L-threitol in gas phase30 at the B3LYP/6-311++G** level of theory. Thirty-five conformers of erythritol and eighteen of L-threitol, within a range of about 26 and 17 kJ mol-1, respectively, above the lowest energy conformers, were characterized. The relative weight of each conformer in the structure of the isomers (pi,gas) was calculated using the Boltzmann distribution, based on Gibbs energy at 298.15 K, taking into account the degeneracy degree of each conformer. The conformational enthalpy for each isomer was determined from the values obtained for the respective conformers by the expression (see ref 30 for details)

Hgconf )

∑ Hi,gaspi,gas

(9)

An expression identical to eq 9 holds for the calculation of the conformational Gibbs energy of the isomers.

The Gibbs energy, enthalpy and relative weight for the conformers of erythritol and L-threitol in the gas phase are presented in Tables 2 and 3, respectively. In these tables, the conformers are labeled with three capital letters, defining the orientation of the dihedrals: O1-C1-C2-O2, C1-C2-C3-C4 and O3-C3-C4-O4, respectively (see Figure 1 for atom numbering). The letters used are G, G′, and T, representing dihedrals of 60° (gauche clockwise), -60° (gauche anticlockwise), and 180° (trans), respectively, within a tolerance of ( 30°. Conformers with the same backbone but different energies owing to OH orientation are discriminated by a number at the end of the backbone designation. The conformers of each isomer are ordered by the increase of the Gibbs energy in solution, which is determined next. The values of Hgconf for the two compounds calculated by eq 9 are given in Table 4. The conformational enthalpy of the isomers in solution (Hsol conf) was determined from the values of the enthalpies of the conformers given in Tables 2 and 3, using an expression identical to eq 9, but now considering the relative weights (pi,sol) of the conformers in solution:

Hsol conf )

∑ Hi,gaspi,sol

(10)

pi,sol was determined from the Boltzmann distribution of the Gibbs energy of the conformers in aqueous solution. The values obtained for Hsol conf are also presented in Table 4. The Gibbs energy of the conformers in water (Gi,sol) was determined by single point calculations at the B3LYP/6-311++G**31-33 level of theory using the conductor-

Enthalpy of Solute-Solvent Interaction

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9283

TABLE 3: Calculated (B3LYP/6-311++G**) Enthalpy, Gibbs Energy, and Boltzmann Population of L-Threitol Conformers in Gas State and in Aqueous Solution (CPCM) at 298.15 Ka

a

conformer

label

Hi,gas Hartree

Gi,gas Hartree

pi,gas (%)

∆Gi,solv kJ mol-1

Gi,sol Hartree

pi,sol (%)

T1 T2 T3 T4 T5 T6 T7 T8 T9 T10 T11 T12 T13 T14 T15 T16 T17 T18

GG′G′1 G′TG′1 G′TG1 G′TG2 GTT1 G′TG3 TG′T1 TG′T2 GGG1 GGG2 GTT2 GTG1 GTT3 GTG2 GTT4 GTG3 GTG4 TGT1

-459.312045 -459.312611 -459.312319 -459.314076 -459.309418 -459.312554 -459.309796 -459.309588 -459.312966 -459.311162 -459.308228 -459.308792 -459.310228 -459.316427 -459.308619 -459.316638 -459.307656 -459.307270

-459.357656 -459.357764 -459.357398 -459.358527 -459.355112 -459.357233 -459.354240 -459.354183 -459.356780 -459.355156 -459.353196 -459.353339 -459.354918 -459.359119 -459.354752 -459.359090 -459.352817 -459.351533

6.2 7.0 4.7 15.7 0.4 4.0 0.2 0.2 2.5 0.4 0.1 0.1 0.3 29.4 0.3 28.5 0.0 0.0

-73.17 -71.49 -70.09 -66.27 -74.71 -67.56 -73.86 -72.66 -65.41 -69.30 -74.03 -72.56 -67.91 -56.36 -67.52 -53.99 -68.69 -67.31

-459.385527 -459.384993 -459.384093 -459.383769 -459.383569 -459.382965 -459.382372 -459.381859 -459.381694 -459.381551 -459.381393 -459.380976 -459.380784 -459.380587 -459.380469 -459.379656 -459.378981 -459.377172

44.2 25.1 9.7 6.9 5.6 2.9 1.6 0.9 0.8 0.7 0.6 0.4 0.3 0.2 0.2 0.1 0.0 0.0

Values of Hi,gas, Gi,gas and pi,gas were taken from ref 30.

TABLE 4: Conformational Enthalpy of Erythritol and L-Threitol in Gas State and Aqueous Solution at 298.15 K compound

Hgconf/Hartree

Hsol conf/Hartree

erythritol

-459.311119 -459.315011

-459.309946 -459.312133

L-threitol

Figure 1. Some relevant molecular conformations of erythritol (A) and L-threitol (B) in the gas phase and in aqueous solution. Erythritol: G′TG is the preferred backbone conformation in solution (pi,sol ) 42.9 and pi,gas ) 10.2%); GG′G′ has significant and identical contributions in both phases (pi,sol ) 13.5 and pi,gas ) 11.2%); TGG is the most relevant backbone conformation in the gas phase but has an insignificant contribution in solution (pi,sol ) 2.8 and pi,gas ) 18.1%). L-Threitol: GG′G′ is the most stable backbone conformation in solution (pi,sol ) 44.2 and pi,gas ) 6.2%); G′TG has significant and identical contributions in both phases (pi,sol ) 19.5 and pi,gas ) 24.4%); GTG is the favored backbone conformation in the gas but almost inexistent in solution (pi,sol ) 0.7 and pi,gas ) 58.0%). Atom numbering scheme is shown in the G′TG backbone conformation of erythritol.

like polarizable continuum model (CPCM).34-36 According to this model, the solute molecule is placed in a cavity surrounded

by a solvent considered as continuum medium of a certain dielectric constant. The charge distribution of the solute polarizes the dielectric continuum which creates an electrostatic field that in turn polarizes the solute. The electrostatic terms of the Gibbs energy are determined. To these were added nonelectrostatic terms, which include the dispersion and repulsion energies that were obtained using Floris and Tomasi’s procedure,37,38 with the parameters proposed by Caillet and Claverie39 and the cavity term calculated from the expression deduced by Pierotti from SPT.20 Attempts to perform full geometry optimization in solution face difficulties of convergence for some conformers. The same problem has been reported by other authors.12 For the conformers we were able to optimize, it was found that the resulting structures did not differ significantly from those in the gas state. This finding supports the approximation of using single point calculation for the estimation of the Gibbs energy in solution. In this work, the dielectric constant of water at 298.15 K ( ) 78.4) was used to simulate the aqueous environment. The cavity was built according to the United Atom Topological model. In this model, the van der Waals surface was built by putting a sphere at each atom, except for hydrogen atoms which were enclosed in the sphere of the atom to which they were bonded. The number of surface elements (tesserae) for each sphere was 60, and an area of 0.4 Å2 was set for each tessera. Tight SCF convergence criteria were used in all single-point calculations. All calculations were performed using the Gaussian 98 program package.40 The values obtained for Gi,sol and for the respective pi,sol are shown in Tables 2 and 3. These tables contain the data required to calculate the conformational Gibbs energy and enthalpy of erythritol and L-threitol in the gas phase and in solution by applying eqs 9 and 10 to the set of results obtained for each isomer in both phases. The results obtained for the enthalpy and Gibbs energy are given in Tables 5 and 6, respectively.

9284 J. Phys. Chem. B, Vol. 110, No. 18, 2006

Lopes Jesus et al.

TABLE 5: Enthalpies of Solute-Solvent Interaction in Aqueous Solutions of Erythritol and L-Threitol and the Terms Required for Their Calculation at T ) 298.15 Ka solute

∆solH°

∆subH°b

∆solvH°

erythritol 23.93 ( 0.07 140 ( 1 -114 ( 1 L-threitol 19.28 ( 0.08 123 ( 1 -101 ( 1 a

∆confH° ∆cavH° ∆intH° 3.1 7.6

9.1 9.1

-126 -118

Results are in kJ mol-1. b Taken from ref 23.

TABLE 6: Gibbs Energies of Solute-Solvent Interaction in Aqueous Solutions of Erythritol and L-Threitol and the Terms Required for Their Calculation at T ) 298.15 Ka′ solute

∆solvG°

∆confG°

∆cavG°

∆intG°

erythritol L-threitol

-73.9 -68.8

0.5 3.0

68.5 68.5

-143 -140

a

Results are in kJ mol-1.

The values estimated for the enthalpy accompanying the change of the molecular conformation as the solute is transferred from the gas phase to solution are ca. 3 kJ mol-1 for erythritol and ca. 8 kJ mol-1 for L-threitol. 3.4. Enthalpy of Cavity Creation. As stated above, SPT was used to calculate the thermodynamic functions corresponding to the formation of a cavity into the solvent to introduce the solute molecule. SPT is a statistical mechanics theory developed by Reiss et al.41,42 for hard sphere liquids. It allows the calculation of the work required to create an exclusion volume in this oversimplified liquid model. The introduction of solvent molecular parameters into the expressions deduced to calculate the cavity contribution makes SPT valid for real liquids. Since the pioneering work of Pierotti, this theory has been widely used in the interpretation of solvation data.21,22,43-46 The expression used to calculate ∆cavH° was that proposed by Pierotti.18-20 The following are the values taken for the solvent parameters: 0.275 nm for molecular diameter, 18.07 cm3 mol-1 for the molar volume, and 0.257 × 10-3 K-1 for the expansibility coefficient. The value of the solute molecular diameter was taken from the CPCM Gaussian output. The value obtained for ∆cavH° can be found in Table 5, which also contains the results determined for ∆intH°, and the values of the terms of eq 6. 4. Discussion From the values given in Table 5, the difference between ∆solvH° and ∆intH° is 12 kJ mol-1 and 17 kJ mol-1 for erythritol and L-threitol, respectively. Such differences mean that solutesolvent interactions would be underestimated if they were incorrectly evaluated by the first property instead of being evaluated by the second. As a rule, a smaller value of ∆intH° relative to ∆solvH° will be obtained, bearing in mind the positive contributions given by the conformational and the cavity terms. Both terms give significant contributions to the solvation enthalpy. For the systems we are dealing with, the cavity does not affect their relative hydration values since the compounds are isomers. However, even in such cases it is required to estimate the enthalpy of solute-solvent interaction. Neglecting these terms, even conclusions about the relative hydration of solutes taken on the grounds of ∆solvH° can be incorrect. For the systems we are dealing with, the values found for ∆solvH° would indicate stronger hydration forces in erythritol than in L-threitol solutions. However, this difference is not so evident when ∆intH° is considered. Conclusions on solvation based on ∆solvH° are still less valid when the systems being compared involve different solvents.21,22

The knowledge of the Gibbs energy of the conformers in the gas phase and in solution allows the solvation Gibbs energy to be calculated for each conformer and for the isomers

∆solvGi ) Gi,sol - Gi,gas ∆solvG° )

∑ pi,solGi,sol - ∑ pi,gasGi,gas

(11) (12)

The values of the hydration Gibbs energy are highly dependent on the conformation, with differences of up to 17 kJ mol-1 and 21 kJ mol-1 found between the conformers for erythritol and L-threitol, respectively. From the values of the Gibbs energy of solvation, used to study the contribution of the conformational enthalpy, it is of interest to determine the Gibbs energy of solute-solvent interactions. The terms corresponding to the conformation change and cavity formation were calculated by the methods described above for the enthalpy. The values for ∆intG° and those required for its calculation using eq 13 are presented in Table 6.

∆intG° ) ∆solvG° - ∆confG° - ∆cavG°

(13)

As was observed for the enthalpy, ∆solvG° would indicate a stronger solute-solvent interaction in erythritol than in L-threitol, while ∆intG° indicates only a small difference between the two solutes. From the values obtained for the Gibbs energy and enthalpy of solute-solvent interaction, 87 and 104 J K-1 mol-1 are the entropy values corresponding to these interactions for erythritol and L-threitol, respectively. Let us interpret the thermodynamic data in molecular terms. The main contribution to the hydration of erythritol and L-threitol arises from the hydroxyl groups. Indeed, the results obtained for the hydration of several compounds of the same type as those under study leads to values of the enthalpy of interaction between CH2 and OH groups and water of -6 and -25 kJ mol-1, respectively.21 Therefore, the hydration of the tetritols in this study depends principally upon the OH groups. The directional character of hydrogen bonds renders hydration dependent not only on the number of the OH groups but also on their orientation. The conformational distribution of the two diastereomers in gas and solution at 298.15 K is given in Tables 2 and 3. Figure 1 shows some of the most important conformations in both phases. Erythritol presents a considerable number of conformations in solution, which provide the main contributions to the Gibbs energy and enthalpy of hydration. The fifteen most abundant conformations make up 91% of the solution structure. Each of the remaining twenty conformations has a relative weight less than 1.5%. The interaction with the solvent gives rise to changes in the conformational equilibrium in solution relative to that in the gas phase. The preferred structures in solution exhibit a distended hydrocarbon chain with all the hydroxyl groups more exposed in order to fulfill their hydration spheres (Figure 1). G′TG, GTG, and GG′G′, the three most stable backbone conformations in solution, make up ca.73% of the whole population at 298.15 K. In contrast, bent backbone structures capable of having strong hydrogen bonds between the terminal hydroxyl groups, as in the case of the TGG conformations, are very unfavorable in solution (pi,sol ) 2.8%), despite being present in the gas phase in significant amounts (pi,sol ) 18.1%). It is worth nothing that some backbone conformations of erythritol give significant and identical contributions in both solution and in the gas phase. For example the GG′G′ backbone conformations have pi,sol ) 13.5% and pi,gas ) 11.2%.

Enthalpy of Solute-Solvent Interaction L-Threitol has a simpler conformational distribution in aqueous solution than erythritol, since the five most stable conformations in solution represent ca. 92% of the whole population. The two most stable backbone conformations in solution, GG′G′ and G′TG′, with pi,sol ) 44.2 and 25.1%, respectively, have weights of 6.2 and 7.0% in the gas state. However, the G′TG backbone conformations have similar populations in the gas (pi,gas ) 24.4%) and solution phases (pi,sol ) 19.5%). Apparently, apart from its significant contribution to the gas behavior, this structure is well adapted for interaction with water. The two most stable conformations in the gas phase (GTG2 and GTG3) represent a type of structure almost nonexistent in solution. As can be seen in Figure 1, all the OH groups are involved in a cyclic system of intramolecular hydrogen bonds, which make these two conformations quite stable in the gas phase but very unfavorable for interactions with water.

5. Conclusions A stepwise solvation model consisting of variation of the solute conformation from gas to solution phases, cavity formation within the solvent to incorporate the solute followed by switching on of solute-solvent forces provides a way to determine correct values for a thermodynamic quantity to measure the solute-solvent interactions from the enthalpy of solvation. In this work, this methodology has been applied to the determination of the enthalpy of hydration of erythritol and L-threitol. The importance of the conformational variation in the solvation process has been proved, even in compounds with structures as similar as those of isomers. This term has been ignored so far. The combination of the DFT method with the CPCM solvation model enabled the calculation of the equilibrium distribution of the most relevant conformations in the gas and solution phases as well as the estimation of the conformational enthalpy change on solvation. In both diastereomers, the conformations with stronger hydrogen bonds are the preferred structures in the gas phase, but give a weak contribution to the structure in solution. In contrast, structures with only weak internal hydrogen bonds (involving only vicinal OH groups) are favored in solution. The thermodynamic quantity involved in the enthalpy of the solute-solvent interaction gives an important insight into the complexity of the tetritols aqueous solutions. The value obtained for the enthalpy of the solute-solvent interaction of erythritol is significantly lower than that of L-threitol. Acknowledgment. The authors whish to dedicate this work to the memory of Prof. M. Luı´sa P. Leita˜o, head of the Molecular Thermodynamics research group, for her contribution to the development of Solution Thermodynamics. A.J.L.J and L.I.N.T. acknowledge Fundac¸ a˜o para a Cieˆncia e a Tecnologia (FCT), Lisbon, for financial support, grants SFRH/BD/9110/ 2002 and SFRH/BD/12373/2003, respectively. References and Notes (1) Lindsat, R. I.; Ko¨ll, P.; Mckinley-Mckee, J. S. Biochem. J. 1998, 330, 479. (2) Munro, I. C.; Bernt, W. O.; Borzelleca, J. F.; Flamm, G.; Lynch, B. S.; Kennepohl, E.; Bar, E. A.; Modderman, J. Food Chem. Toxicol. 1998, 36, 1139. (3) Traini, D.; Young, P. M.; Jones, M.; Edge, S.; Price, R. Eur. J. Pharm. Sci. 2006, 27, 243.

J. Phys. Chem. B, Vol. 110, No. 18, 2006 9285 (4) Zhou, L. M.; Sirithunyalug, J.; Yonemochi, E.; Oguchi, T.; Yamamoto, K. J. Therm. Anal. Calorim. 2000, 59, 951. (5) Ohmori, S.; Ohno, Y.; Makino, T.; Kashihara, T. Int. J. Pharm. 2004, 278, 447. (6) Michaud, J.; Haest, G. Pharmaceutical Technology Europe, Oct 1, Erythritol: A New Multipurpose Excipient, 2003. (7) Turner, S.; Senaratna, T.; Touchell, D.; Bunn, E.; Dixon, K.; Tan, B. Plant Sci. 2001, 160, 489. (8) Storey, K. B.; Storey, J. M. Annu. ReV. Ecol. Syst. 1996, 27, 365. (9) Wowk, B.; Darwin, M.; Harris, S.; Russell, S.; Rasch, C. M. Cryobiology 1999, 39, 215. (10) Chelli, R.; Gervasio, F. L.; Gellini, C.; Procacci, P.; Cardini, G.; Schettino, V. J. Phys. Chem. A 2000, 104, 11220. (11) Chelli, R.; Gervasio, F. L.; Gellini, C.; Procacci, P.; Cardini, G.; Schettino, V. J. Phys. Chem. A 2000, 104, 5351. (12) Callam, C. S.; Singer, S. J.; Lowary, T. L.; Hadad, C. M. J. Am. Chem. Soc. 2001, 123, 11743. (13) Howard, E.; Grigera, J. R. J. Chem. Soc.-Faraday Trans. 1992, 88, 437. (14) Ben-Naim, A. J. Phys. Chem. 1978, 82, 792. (15) Ben-Naim, A.; Marcus, Y. J. Chem. Phys. 1984, 81, 2016. (16) Uhlig, H. H. J. Phys. Chem. 1937, 41, 1215. (17) Eley, D. D. Trans. Faraday Soc. 1939, 35, 1281. (18) Pierotti, R. A. J. Phys. Chem. 1963, 67, 1840. (19) Pierotti, R. A. J. Phys. Chem. 1965, 69, 281. (20) Pierotti, R. A. Chem. ReV. 1976, 76, 717. (21) Costa, F. S.; Euse´bio, M. E.; Redinha, J. S.; Leita˜o, M. L. P. J. Chem. Thermodyn. 2000, 32, 311. (22) Jesus, A. J. L.; Euse´bio, M. E.; Redinha, J. S.; Leita˜o, M. L. P. Thermochim. Acta 2000, 344, 3. (23) Jesus, A. J. L.; Tome´, L. I. N.; Redinha, J. S.; Euse´bio, M. E. J. Phys. Chem. B 2005. (24) Kilday, M. V. J. Res. Nat. Bur. Stand. 1980, 85, 449. (25) Kilday, M. V. J. Res. Nat. Bur. Stand. 1980, 85, 467. (26) Sabbah, R.; An, X. W.; Chickos, J. S.; Leitao, M. L. P.; Roux, M. V.; Torres, L. A. Thermochim. Acta 1999, 331, 93. (27) Goffredi, F.; Goffredi, M.; Liveri, V. T. J. Solution Chem. 1995, 24, 813. (28) Nowicka, B.; Osinska, S. T.; Della Gatta, G. J. Chem. Thermodyn. 1997, 29, 1017. (29) Archer, D. G.; Kirklin, D. R. Thermochim. Acta 2000, 347, 21. (30) Jesus, A. J. L.; Tome´, L. I. N.; Rosado, M. T. S.; Leita˜o, M. L. P.; Redinha, J. S. Carbohydr. Res. 2005, 340, 283. (31) Becke, A. D. J. Chem. Phys. 1993, 98, 5648. (32) Becke, A. D. Phys. ReV. A 1988, 38, 3098. (33) Lee, C. T.; Yang, W. T.; Parr, R. G. Phys. ReV. B 1988, 37, 785. (34) Klamt, A.; Schuurmann, G. J. Chem. Soc.-Perkin Trans. 2 1993, 799. (35) Barone, V.; Cossi, M. J. Phys. Chem. A 1998, 102, 1995. (36) Cossi, M.; Rega, N.; Scalmani, G.; Barone, V. J. Comput. Chem. 2003, 24, 669. (37) Floris, F.; Tomasi, J. J. Comput. Chem. 1989, 10, 616. (38) Floris, F. M.; Tomasi, J.; Ahuir, J. L. P. J. Comput. Chem. 1991, 12, 784. (39) Caillet, J.; Claverie, P.; Pullman, B. Acta Crystallogr. Sect. B-Struct. Commun. 1978, 34, 3266. (40) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Zakrzewski, V. G.; J. A. Montgomery, J.; Stratmann, R. E.; Burant, J. C.; Dapprich, S.; Millam, J. M.; Daniels, A. D.; Kudin, K. N.; Strain, M. C.; Farkas, O.; Tomasi, J.; Barone, V.; Cossi, M.; Cammi, R.; Mennucci, B.; Pomelli, C.; Adamo, C.; Clifford, S.; Ochterski, J.; Petersson, G. A.; Ayala, P. Y.; Cui, Q.; Morokuma, K.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Cioslowski, J.; Ortiz, J. V.; Baboul, A. G.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Gomperts, R.; Martin, R. L.; Fox, D. J.; Keith, T.; AlLaham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Andres, J. L.; Gonzalez, C.; Head-Gordon, M.; Replogle, E. S.; Pople, J. A. Gaussian 98; A.9 ed.; Gaussian, Inc: Pittsburgh, PA, 1998. (41) Reiss, H.; Casberg, R. V. J. Chem. Phys. 1974, 61, 1107. (42) Reiss, H.; Frisch, H. L.; Lebowitz, J. L. J. Chem. Phys. 1959, 31, 369. (43) Bernazzani, L.; Carosi, M. R.; Ceccanti, N.; Conti, G.; Gianni, P.; Mollica, V.; Tine, M. R.; Lepori, L.; Matteoli, E. Phys. Chem. Chem. Phys. 2000, 2, 4829. (44) Matteoli, E.; Lepori, L.; Spanedda, A. Fluid Phase Equilib. 2003, 212, 41. (45) Graziano, G.; Lee, B. J. Phys. Chem. B 2001, 105, 10367. (46) Pais, A.; Sousa, A.; Euse´bio, M. E.; Redinha, J. S. Phys. Chem. Chem. Phys. 2001, 3, 4001.