Energetic Competition Effects on Thermodynamic Properties of

Article pubs.acs.org/JPCC

Energetic Competition Effects on Thermodynamic Properties of Association between β‑CD and Fc Group: A Potential of Mean Force Approach Gael̈ le Filippini, Florent Goujon, Christine Bonal,* and Patrice Malfreyt Clermont Université, Université Blaise Pascal, ICCF, UMR CNRS 6296, BP 10448, F-63000 Clermont-Ferrand, France S Supporting Information *

ABSTRACT: A host−guest system involving ferrocenemethanol (FcOH) and β-cyclodextrin (CD) in both homogeneous (free CD) and heterogeneous conditions (gold-confined CD) is studied by applying an integrated approach that combines energy and structure. Numerical experiments were used to calculate the potential of mean force between the host and guest at different separation distances. The thermodynamic properties of association are obtained by integrating the free-energy profile. In this study, we specially focus on the comparison of the association process between β-CD and FcOH in both isolated and water phases. We establish that the association process is enthalpy driven in all conditions (homogeneous and heterogeneous systems in both isolated and water phases). As a consequence, the driving forces involved in the complexation by β-CD are then essentially due to van der Waals interactions. As concerns the comparison between the isolated and water phases, the simulations have shown that the association constants in vacuum are significantly greater than the corresponding ones in solution. A significant difference appears in the enthalpy between the two conditions. From the analysis of the different energy contributions, we have found that the more favorable free energy in gas comes from the electrostatic contributions. The differences observed between the thermodynamic properties are also interpreted through an atomistic description. The ability of molecular dynamic simulations to enable a better understanding of the role of liquid water and hydrogen bonds on the complexation thermodynamics of β-CD is illustrated in this paper.

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of Fc derivatives for the β-CD was also used to modify the surface of thiol-derivatized CDs immobilized as self-assembled monolayers (SAMs) on solid surfaces. In fact, ferroceneterminated self-assembled monolayers are one of the most studied redox-active assemblies on metal surfaces to date due to their ease of preparation and the reversible electrochemistry of the ferrocenyl group.16 The inclusion mechanism results from the energetically favorable weak interactions.17 The penetration of the guest molecule into the cyclodextrin cavity and the dehydration of the organic guest are the most important contributions to the complexation thermodynamics of cyclodextrins. The other contributions to the thermodynamic complexation quantities come from the release of the water molecules originally included in the cyclodextrin cavity to bulk water and also the conformational changes of the cyclodextrin molecule upon complexation. The hydrogen-bonding interactions are also of fundamental importance contributing to the stabilization of cyclodextrin complexes with guest molecules. As a consequence, the molecular association results from the simultaneous cooperation of all these interactions. However, in spite of the great number of investigations made on the complexation thermodynamics of CDs, few attempts have been made to estimate the thermodynamic consequence of contributions to

INTRODUCTION β-Cyclodextrins (β-CDs) are water-soluble cyclic oligosaccharides consisting of seven glucose units connected via α-1,4glycosidic linkages and possessing a hydrophobic cavity. β-CD is a prototype host for inclusion compounds of neutral and hydrophobic organic guests of biological interest.1,2 In fact, many of the potential applications of host−guest systems require immobilization of either the host molecule or the guest molecule. CDs can be tethered to surfaces such as gold forming densely packed self-assembled monolayers (SAMs).3 The molecular recognition ability of SAMs of host molecules on surfaces offers a selective attachment and an accurate, but reversible, positioning of molecules.4 It is also a promising method to obtain relatively simple structures, which are difficult to prepare by other techniques.4 Thus, they have attracted considerable attention for their expected applications to analyte-sensitive sensors and reactive selective catalysts3 or to modify the surface of CD capped nanoparticles.5−9 A fundamental understanding of the guest-binding abilities of these immobilized β-CDs on the surface is required in order to design materials with predictable properties. A promising candidate in guest recognition in water is the ferrocenemethanol (FcOH). FcOH is a small-size molecule that forms stable 1:1 complexes with β-CDs10 via noncovalent bonds. The formation of these host−guest complexes has been widely reported and used to elaborate mediators and molecular sensors11,12 and to assist organic reactions such as asymmetric inductions13,14 or condensation reactions.15 The strong affinity © 2012 American Chemical Society

Received: June 13, 2012 Revised: August 27, 2012 Published: September 25, 2012 22350

dx.doi.org/10.1021/jp3057724 | J. Phys. Chem. C 2012, 116, 22350−22358

The Journal of Physical Chemistry C

Article

Figure 1. Structures of minimal energy of complexes between ferrocenemethanol and (a and b) free CD and (c) surface-confined CD in water. Labels 1 and 2 refer to structures that correspond to the minima of the PMF profile of Figure 2.

results of the potential of mean force (PMF) between β-CD and FcOH at different separation distances and discuss the thermodynamic properties deduced from the PMF profiles. To address the driving forces of cyclodextrin complexation, structural and energetic properties obtained from MD simulations are investigated. Finally, the association process of FcOH into β-CD is compared as a function of the various environments. In the last section we draw the main conclusions from this work.

the complexation thermodynamics of cyclodextrins. Furthermore, the knowledge of the role of liquid water is still limited. Computer simulations have shown to be highly successful in capturing both the structural and energetical properties of SAMs.18−21 More recently, our group has demonstrated that an approach that combines a molecular description and a thermodynamic characterization is powerful to explain why the association process of supramolecular assemblies is different between homogeneous and heterogeneous conditions in water.22 For this purpose, the thermodynamic properties of association in aqueous solution of the CD-FcOH system were determined from numerical experiments. The differences observed between the thermodynamic properties as a function of the two environments (free or grafted CD in water) were interpreted through an atomistic description. Interestingly, we showed a significant difference in the enthalpy of association with a larger negative change for the surface-confined CD. We also found that the most favorable ΔrH0 is associated with the largest number of inserted atoms. In fact, a conformational change of the β-CD can occur with the grafting. The wider opening of the cavity allows a deeper insertion of FcOH. Molecular dynamics (MD) simulations provided information regarding the hydration and highlighted the fact that solvation effect contributes to the overall thermodynamic complexation quantities in water. In this study, we specially focus on the comparison of the association process of the CD-FcOH system (Figure 1) in both isolated and water phases. For this purpose, numerical experiments are used to calculate the potential of mean force (PMF) between β-CD and FcOH at different separation distances. The thermodynamic properties of association in the gas phase are determined and compared to that obtained in aqueous solution in both homogeneous (free CD) and heterogeneous (surface-confined CD) conditions. A thorough analysis of the extent of each contribution to the stabilization of the complex in both gas and water phases sheds new light on the role of liquid water. The water molecules distributed around β-CD as well as inside the cavity exhibit a large number of hydrogen bonds: the hydrogen bonding in the system is also of central interest in this work to explain the stabilization of CD complexes. So, we also focused our attention on the contribution of hydrogen bonding in both gas and water phases. The outline of this work is as follows. In the section concerning the experimental methods, we give the details of the computational procedures. In the next section, we present the

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EXPERIMENTAL SECTION Molecular Systems. The free-CD system is composed by one β-CD and one FcOH. FcOH is used in this work because ferrocene has no solubility in water. The grafted CD system consists of one per-6-thio-β-cyclodextrin immobilized on a fivelayer Au(111) surface through the seven sulfur atoms. The Au atoms of the surface involved in the grafting are selected with an angle between the carbon, sulfur, and gold atoms that is the closest to the equilibrium angle value defined in the forcefield. The gold surface is composed of five 13 × 16 hexagonal layers representing a fcc lattice, so that the dimensions of the simulation box along the x and y axis are 37.4 and 39.9 Å, respectively. Since the system is nonperiodic along the direction normal to the surface (z axis), the simulation cell is closed by an additional gold layer. The separation distance between the two surfaces is fixed to 50 Å. The aqueous phase is modeled by adding 3000 water molecules to the free-CD system. The space between the two gold surfaces is filled by 2000 water molecules in the grafted-CD system to reach the correct bulk-water density. In this last case, the simulation box is then elongated along the z-direction with empty spaces, up to 280 Å, in order to apply a three-dimensional scheme for the calculation of the electrostatic interactions.18,23 Interaction Model. The intramolecular and intermolecular interactions are described by the CHARMM forcefield.24−26 The Au parameters are taken from the work of Ayappa and coworkers.27 The ferrocene part is modeled by the parameters described by de Hatten et al.26 The water molecules are represented by the TIP4P/2005 model.28 The partial charges of the per-6-thio-β-cyclodextrin are calculated from the density functional theory (DFT)29,30 with the B3LYP functional31,32 with effective core potential (SD-DALL) Gaussian basis using the Gaussian 03 package33 and the CHELPG34 procedure as a grid-based method. The repulsion−dispersion interactions are described using the Lennard-Jones (LJ) potential. The LJ potential parameters between unlike atoms are calculated with 22351



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Lorentz−Berthelot mixing rules. The electrostatic interactions are calculated with Coulombic potential for isolated systems and with the three-dimensional smooth particle mesh Ewald (SPME) method35 in aqueous phase. PMF. PMF36 W(r12) represents the interaction between two particles 1 and 2 kept at a fixed distance r12 from each other when the N − 2 particles are averaged over all the configurations. The expression of the PMF in the constantNpT ensemble is given by W (r12) = − kBT ln g (r12) = − kBT ⎡ ∫ dV exp( − βpV ) ∫ ∫ d r ...d r d p ...d p exp(− β /(r N , p N )) ⎤ 3 N 3 N ⎥ × ln⎢ ⎢⎣ ∫ dV exp( − βpV ) ∫ ∫ d r1...d rN d p ...d p exp(− β /(r N , p N )) ⎥⎦ 1 N +C

(1)

Figure 3. Free-energy profiles obtained for the inclusion complexes between FcOH and β-CD in homogeneous (black line) and heterogeneous (red line) systems. The dotted lines refer to the PMFs obtained in the gaseous phase whereas the solid lines are the PMFs for aqueous solution.22 Labels 1 and 2 refer to the structures given in Figure 1.

where g(r12) is the correlation function which represents the probability of finding the particles 1 and 2 at the separation distance r12 with respect to the probability resulting from a random distribution at the same density. C is a constant. / (rN, pN) is the total Hamiltonian corresponding to the sum of the kinetic energy and the potential energy U(rN). dr3...drNdp3...dpN and dr1dr2dp1dp2 correspond to the unconstrained and constrained phase spaces, respectively. By consideration that the sampling of phase space for the unconstrained degrees of freedom is not affected by the constrained ones, we can assume that the total phase space is the sum of the constrained and unconstrained phase spaces.37 Consequently, we can write the potential of mean force as a function of the free energy for the constrained phase space G(r12). W (r12) = −G(r12) + C

contribution of the PMF at the separation distance d(λ). It was chosen conventionally to set the free energy at zero for the maximal separation of the two molecules and consequently W(d(0)) = 0. The PMF profile is established by summing all the local contributions from this reference point. In the FEP formalism,43,44 W(d(λi)) is expressed as i−1

i−1

WFEP(d(λi)) = − ∑ ΔG(λj) = − ∑ −kBT j=0

(2)

j=0

⎡ U (r , λ ± Δλ) − U (r N , λ ) ⎤ j j ⎥ ln exp⎢ − ⎢⎣ ⎥⎦ kBT N

The PMF profile W(r) is then obtained by summing all the local contributions at each separation distance from a reference point. This PMF profile provides a measure of the difference in free energy along a reaction coordinate. In our case, to study the association process between the host and guest molecules, the considered reaction coordinate is the distance dFcOH−CD between the centers of mass of β-CD and FcOH (Figure 3). In

λj

(3)

where U(r ,λ) is the potential energy corresponding to state λ and depending only on the atomic coordinate set rN. kB is the Boltzmann constant, T is the absolute temperature and ⟨ ⟩ denotes an ensemble average reflecting state λ. The PMF profile is calculated in both forward (+Δλ) and backward (−Δλ) directions. The TI method43,44 expresses W(r(λ)) as the following integral N

WTI(d(λ)) = −

∫0

∂U (r N , λ) ∂λ

λ

dλ (4)

λ

The derivative of U(r ,λ) with respect to λ is calculated using a central finite difference technique between U(rN,λ+δλ) and U(rN,λ−δλ). N

Figure 2. Scheme of the reaction coordinate chosen for the PMF calculation.

∂U (r N , λ) ∂λ

solution, the PMF includes solvent effects in addition to interactions between the molecules of the complex. The PMF is calculated using both free energy perturbation (FEP)38,39 and thermodynamic integration (TI)38−43 methods. The coupling parameter λ is introduced to make the separation distance dependent on λ as d(λ) = (1 − λ)d(0) + λd(1), where d(0) and d(1) are the largest and smallest separation distances, respectively. The total pathway between d(0) and d(1) is partitioned into Nw windows corresponding to Nw separation distance values. The quantity W(d(λ)) corresponds to the local

λ ,C N

=

(U (r , λ + δλ) − U (r N , λ − δλ) 2δλ

(5)

λ

The derivative is also evaluated in the forward direction (F) ∂U (r N , λ) ∂λ

= λ ,F

(U (r N , λ + δλ) − U (r N , λ) δλ

λ

(6) 22352



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interaction) to the central maximum. Thermodynamic properties were averaged over these two reaction pathways. Simulation Details. MD simulations were performed in the constant-NVE statistical ensemble for isolated systems and in the constant-NpT ensemble using Hoover thermostat and barostat for systems in aqueous phase. The relaxation times for thermostat and barostat were 1 and 5 ps, respectively. The equations of motion were integrated using the Verlet leapfrog algorithm scheme at T = 298 K and p = 1 atm with a time step equal to 2 fs. The C−H and O−H covalent bonds were kept of fixed length by using the SHAKE algorithm.49 The cutoff radius for the LJ interactions and for the real part of the electrostatic interactions was chosen to 16 Å. The convergence parameter for the SPME summation was fixed to 0.1960 Å−1. The reciprocal space for the SPME method was developed on a number of k-vectors equal to 8, 8, and 64, along the x-, y-, and z-direction, respectively. With these parameters the calculation of the electrostatic interactions satisfies a relative error of 10−6. Simulations were performed using the parallel version of the modified DL_POLY_MD package50 using up to 12 processors at a time. Each separation distance between host and guest molecules corresponds to one simulation. The distance between the molecules was constrained with the SHAKE algorithm. One simulation was performed every 0.05 Å, and each typical simulation run of the system consisted of an equilibrium period of 200 ps and a production phase of 400 ps. For example, in the free-CD system in aqueous phase, the total simulation time to obtain the PMF curve is 163 ns which would represent 6.2 CPU years on a single processor. This shows the computational effort to calculate this property.

and in the backward direction (B) considering the difference U(rN,λ)−U(rN,λ−δλ). The finite difference thermodynamic integration (FDTI) method uses the perturbation formalism to calculate the derivative of the potential energy with respect to λ as ∂U (r N , λ) ∂λ

kT ΔG(λ) ∂G(λ) ≃ =− B δλ ∂λ 2δλ

= λ ,C

⎡ U (r N , λ + δλ) − U (r N , λ − δλ) ⎤ ln exp⎢− ⎥ kBT ⎣ ⎦

(7)

Simulations in the forward (+δλ) and backward (−δλ) directions give an estimate of the statistical incertainty for the TI and FDTI approaches. The integration over λ for both techniques is carried out by a trapezoidal algorithm. A comparison between FEP and TI calculations is given in Figures S1 and S2 of the Supporting Information. Thermodynamic Properties. The thermodynamic quantities are obtained by integrating the PMF profile along the separation distance between β-CD and FcOH44−46 considering a cylindrical approach.47,48 Indeed, when the FcOH enters into the β-CD cavity, the accessible volume for FcOH is restrained to a small cylinder defined by the area accessible for its in-plane movement (perpendicular to the β-CD axis). The mean radius of that cylinder rcyl was evaluated from the trajectory of the center of mass of the FcOH at each separation distance. The association constant K is given by K=

⎞

⎛

∫ dh πrcyl2NA exp⎜⎝− Wk (Th) ⎟⎠

■

(8)

B

where h is the height of the cylinder defined by the FcOH movement. NA is the Avogadro number. The thermodynamic properties of binding are calculated using the following expressions Δr G 0 = −kBT ln K =−kBT ln

(9)

⎞

⎛

∫ dh πrcyl2NA exp⎜⎝− Wk (Th) ⎟⎠

(10)

B

Δr H 0 = kBT 2

=

d ln K dT

(11)

(

W (h) 2 W (h)exp − k T ∫ dh rcyl B

(

2 exp ∫ dh rcyl

W (h) − kT B

)

)

(12)

T Δr S 0 = Δr H 0 − Δr G 0

=

(13)

(

W (h) 2 W (h) exp − k T ∫ dh rcyl B

∫ dh

2 rcyl

(

exp

⎛ W (h) ⎞ exp⎜ − ⎟ ⎝ kBT ⎠

RESULTS AND DISCUSSIONS The free energy profiles characterizing the association process of ferrocenemethanol into β-CD in various environments are shown in Figure 2. These PMF curves are calculated with the TI method. Indeed, some drawbacks have been evidenced using FEP method (see Figures S1 and S2 in the Supporting Information for a comparison between FEP and TI calculations). The convergence of the PMF using TI method is checked in Figure S3 in the Supporting Information. The analysis of these PMFs sheds more light on four points. First, the PMF curves have similar shapes in both gas phase and aqueous solution22 for a given environment (free or grafted CD). Thus, for free CDs the profiles present two local minima separated by a barrier. We only focus on the first minimum since the second minimum may never occur for per-6-thio-βCD SAMs because of the grafting points.22 As concerns the surface-confined CDs, the PMF curves show only one deeper free energy minimum. Additional unconstrained MD simulations for each most stable structure for both free and surfaceconfined CD in water are performed. They are in perfect agreement with the constrained simulations. Structural and energetic details obtained from these simulations are given in the Supporting Information (see pages S7−S10). Second, the PMFs calculated in the gas phase show deeper minima than in aqueous solutions. Actually, in the case of the free CD, the free energy minimum is lowered by 25% in the isolated phase whereas for grafted CD in gas, and we observe a decrease of 48% of the well depth. Third, the positions of the free energy minima for the grafted CD are shifted within the cavity with a similar magnitude (∼2 Å) for the gas and water phases. Fourth, the approach of FcOH at larger separation distances is significantly different between the isolated and water phases.

W (h) − kT B

)

) + k T ln ∫ dh πr B

2 cylNA

(14)

For the surface-confined β-CD, the PMF was integrated from the largest separation distance for which the PMF is considered to be zero to that for which the repulsion is maximum. As concerns free β-CD, the integration was calculated from each side of the PMF curve (where FcOH and β-CD have no 22353



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confined CD involves the calculation of a new contribution (FcOH−surface) with a profile which is similar in both gaseous and aqueous phases. The different contributions are represented in Figure 4 along the reaction pathway for both the free CD and grafted CD. This decomposition into specific contributions is relevant to conclude on the following points: (i) the FcOH−CD contributions are significantly smaller in water than in the gas phase; (ii) the major contribution to the total free energy profiles in water comes from the FcOH−H2O free energy contributions; (iii) the more favorable association between FcOH and surface confined-CD in water finds its origin in the more negative FcOH−H 2O free energy contribution compared to that with free CD in aqueous solution.22 We propose here to explain the differences in the FcOH− CD free energy profiles in water and isolated phases. To do so, we report in Figure 5 the LJ and electrostatic parts of the FcOH−CD energy contributions at different separation distances between FcOH and CD. First, the LJ interactions are similar in water and gas phases for a given environment (see parts a and b of Figure 5). Parts c and d of Figure 5 show the percentage of insertion into the CD cavity. There is a strong correlation between the van der Waals interactions and the number of inserted atoms. The insertion is found to be similar between the water and gas phases for a given environment (free or grafted CD) in line with the LJ contributions. Consequently, the more favorable free energy in gas comes from the electrostatic part. Actually, the FcOH−CD electrostatic energy is always more negative in gas than in water. The different approach of FcOH toward CD in gas also finds its origin in the electrostatic interactions as shown in parts a and b of Figure 5 at the largest separation distances. As the electrostatic part of the FcOH−CD energy contributions are highly dependent on the host−guest hydrogen bonds, we now investigate the number of hydrogen bonds along the host guest separation distances in both gas and aqueous phases. The number of hydrogen bonds and the electrostatic part of the FcOH−CD energy contributions have been reported in Figure 6 as a function of the separation distance. We observe a correlation between the number of hydrogen bonds and the FcOH−CD electrostatic energy. It means that a favorable negative electrostatic energy occurs when an hydrogen bond is formed between FcOH and CD in both gas and water phases. At the Gibbs free energy minimum corresponding to a strong insertion of FcOH, we do not observe any hydrogen bond

Isolated FcOH starts to interact with CD at larger separation distances. All the points discussed here will be interpreted through the analysis of the free energy and energy contributions. By integrating the free energy profiles in the gas phase, we obtain the association constants and the enthalpies of binding (see Table S7 in the Supporting Information for completeness). All the thermodynamic properties are gathered in Table 1. For Table 1. Thermodynamic Parameters (kJ mol−1) Characterizing the Complexation of FcOH by the β-CDs in Both the Gas and Water Phases for Free CD and SurfaceConfined CD Systems water (simulations)

isolated free CD log K ΔrG0 ΔrH0 TΔrS0

4.5 −26 −34 −8

grafted CD 8.4 −38 −48 −10

free CD 3.4a −20a −29a −9a

grafted CD 5.1a −29a −39a −10a

water (experiments) free CD 3.6b/4.0c −21b/−23c −26c −3c

grafted CD 4.9d −28d

a

Taken from ref 22. bTaken from ref 51. cTaken from ref 52. dTaken from ref 53.

comparison, the experimental and theoretical thermodynamic values in aqueous solution22 are also included in Table 1. In all cases, we can notice that the association process is enthalpically favored (ΔrH0 < 0) and entropically unfavored (ΔrS0 < 0). Clearly, the association process is then essentially enthalpy driven. However, the association constants in vacuum are significantly greater than the corresponding association constants in solution. This agrees with the deeper free-energy minima calculated in the gas phase. In fact, the difference between the association in gas and water phases comes from the enthalpy contributions whereas the entropy contributions do not depend on the environment. As an illustration, the remarkably negative enthalpy of binding (−48 kJ mol−1) upon complexation of FcOH with surface-confined CD in vacuum indicates an affinity much higher than in aqueous solution. Now, we focus on the partitioning of the free energy profile to extract the driving forces of CD complexation. In water, entering FcOH into the free β-CD is modeled along the reaction pathway by the FcOH−CD and FcOH−H2O freeenergy contributions. The inclusion of FcOH into the surface-

Figure 4. Partitioning of the PMF into the FcOH−CD, FcOH−H2O, and FcOH−surface free-energy contributions (a) for the association between FcOH and the free β-CD in gaseous (dotted line) and aqueous (solid line) phases and (b) for the association between FcOH and the surfaceconfined CD in gaseous (dotted line) and aqueous (solid line) phases. 22354



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Figure 5. Some LJ and electrostatic energy contributions between the ferrocene group and (a) free β-CD and (b) surface-confined CD. Percentage of inserted molecules into (c) the free CD cavity and (d) the surface-confined CD cavity.

between FcOH and CD, the electrostatic energy is less favorable but it is compensated by the LJ energy contribution (Figure 5). In water, parts c and d of Figure 6 show no hydrogen bond between FcOH and CD with a small FcOH− CD electrostatic energy contribution. Nevertheless, FcOH establishes an hydrogen bond with water molecules. The hydration of FcOH is constant along the reaction pathway as shown in parts c and d of Figure 6. The different approach of FcOH in gas is explained by the favorable hydrogen bond between FcOH and CD that does not occur in water due to the competition of water molecules to form hydrogen bonds (see snapshots in Figure 7). It means that the difference in the PMF curves at larger separation distances between the gas and water phases is essentially due to the formation of hydrogen bonds between the host and guest. As indicated above, the PMF calculations show that the differences between association in gas and water phases are essentially due to the enthalpy change since the entropic contributions are rather similar. In fact, the entropy change in the inclusion thermodynamics mainly results from two different contributions: a favorable term due to the total desolvation of the cavity and an unfavorable term associated with the insertion of atoms into the cavity (that implies a loss of conformational flexibility). In these molecular recognition processes, our results seems to indicate that the contributions related to the desolvation do not contribute significantly to the complexation thermodynamics. This observation is also perfectly consistent

with our previous results obtained for these systems in aqueous solution.22 Let us remember that the change in entropy in water is almost similar for the complexation of FcOH in both homogeneous and heterogeneous systems (Table 1), whereas our simulations have shown a larger desolvation for the heterogeneous system than for free CD in water. The association process is more enthalpically favored in the gas phase than in water. This is explained by a more favorable electrostatic part of the FcOH−CD energy contribution and an unfavorable desolvation enthalpy contribution that does not occur in the gas phase. The difference in the enthalpy change between the free and grafted CDs is 14 and 10 kJ mol−1 in the isolated and water phases, respectively. The association for grafted CD in water leads to a deeper insertion accompanied by a larger desolvation.22 The association in the gas phase predicts an overestimated enthalpy difference between the free and grafted CDs because of the unfavorable enthalpy term due to the desolvation that is not considered in the gas phase. It underlines the importance of the compensation effects due to the solvent and hydrogen bonds on the thermodynamic properties of systems interacting through weak interactions.

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CONCLUSION

Throughout this paper, we report computational investigations of supramolecular assemblies of both free β-CD and surfaceconfined CD with ferrocenemethanol in the gaseous phase organized by weak forces. The PMF between β-CD and FcOH 22355



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Figure 6. Correlation between the number of the host−guest hydrogen bonds and the calculated electrostatic part of the FcOH−CD energy contributions along the host−guest separation distances (a) in the free CD in vacuum, (b) in the grafted CD in vacuum, (c) in the free CD in water, and (d) in the grafted CD in water. For the definition of hydrogen bonds we used the geometrical criteria described in refs 54−56.

Figure 7. Scheme of the approach of FcOH toward the surface-confined β-CDs (a) in the gas phase and (b) in aqueous solution. The hydrogen bond observed in the gas phase is represented in green.

is calculated, and the thermodynamic properties of association in the gas phase are determined. We have compared the results with those obtained in water. The comparison is very interesting to highlight the multiple effects of the solvent and the contribution of hydrogen bonding in both isolated and water phases to the thermodynamic properties. The association process is essentially enthalpy driven in all conditions. The major contribution to the enthalpy of association comes from the van der Waals interaction associated with the inclusion of the guest molecule into the β-CD cavity in both homogeneous and heterogeneous phases. The simulations show that the FcOH−CD association is more favorable in gas than in water, whatever the environment (free or grafted CD). The origin is essentially enthalpic for however a

quasi-identical insertion. From the analysis of the different energy contributions, it has been shown more favorable electrostatic energy contributions in gas than in water due to the formation of hydrogen bond between FcOH and CD. In water, FcOH forms hydrogen bonds with water molecules that change the approach of the guest along the reaction pathway. The PMF calculations have been shown to reproduce very accurately the thermodynamic properties of binding in water. The free-energy curves calculated in the gas phase show that it remains very difficult to interpret and rationalize experiments for only considering the energy between the host and guest and that additional factors such as hydrogen bonds, compensation effects with water can significantly modify the association process. These factors are difficult to access experimentally. 22356



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Thus, the molecular simulations combined with a PMF calculation represent an interesting and powerful alternative to interpret the association process and the underlying microscopic effects.

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ASSOCIATED CONTENT

S Supporting Information *

The reversibility, the correlation of the different contributions, the convergence of the PMF calculations, the structural and energetic properties of minima, and the calculation of the thermodynamic properties as a function of the integration volume. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS This work was supported by a Contrat d’Objectifs Partagés of the CNRS, the Université Blaise Pascal, and the Conseil Régional d’Auvergne.

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REFERENCES

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Energetic Competition Effects on Thermodynamic Properties of

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