J. Phys. Chem. 1994, 98, 11193-11203
11193
Solvation Thermodynamics of Simple Crown Ethers by the XRISM Method Yuk Lung Ha and Amp K. Chakraborty' Department of Chemical Engineering, University of Califomia at Berkeley, Berkeley, California 94720 Received: May 19, 1994; In Final Form: July 29, 1994@
In this work, the solvation thermodynamics of the D3d and C, symmetry conformations of 18-crown-6 are investigated by way of extended reference interaction site model (XRISM) calculations. A broad range of solvent conditions are explored; viz., water, carbon tetrachloride, and acetonitrile at 25 "C and 1 a m . We find that the relative free energies of solvation between the D3d and C, conformers display a strong dependence on solvent type with the D3d structure becoming increasingly favored as solvent polarity increases. Our study of acetonitrile shows that electrostatic effects alone (with no hydrogen bonding) are sufficient to stabilize the D3d conformer in solution. In addition to energetics, the structuring of the solvent in the vicinity of the solute is examined. We also consider the solvation of dibenzo-18-crown-6. Our results show that the attachment of lateral groups to the crown perturbs the solvent structure in largely a local manner.
I. Introduction Solvent-mediated effects upon reaction rates as well as chemical and conformational equilibria are well appreciated.'-lo The latter issue is especially relevant for biological molecules (i.e., proteins) whose function is highly structure dependent."^'* Crown ethers (macrocyclic polyethers), which may be considered to be the simplest abiotic analogues of enzymes, demonstrate a similar structure dependent activity that is strongly influenced by the solvent environment.13-18 A deep understanding of how crown ethers are solvated in different environments is therefore crucial for elucidating the remarkable specificity of binding exhibited by these molecules. Crown ethers have been at the center of immense scientific and technological i n t e r e ~ t ' ~during - ~ ~ the past several decades since their discovery by P e d e r ~ e in n ~1967. ~ ~ ~This ~ has been motivated by the fascinating features of these macromolecules which mimic, at the simplest level, the action of true enzymatic systems. Specifically, crown ethers can selectively complex ionic and neutral specie^,*^-^^ can serve as active carrier^,^'-^^ and last, can catalyze reactions on bound substrate^.^^,^^ Therefore, a thorough understanding of these simple systems may offer corresponding insight into more complicated biological systems and our ability to emulate in practical applications the efficiency demonstrated by nature. The most elementary crown ethers with this potential have been the much studied 18-crown-6 macrocycle (1,4,7,10,13,16-hexaoxacyclooctadecane) and its derivatives. In a manner reminiscent of true enzymes, the ability of 18crown-6 to bind a substrate species is dependent upon the conformation that it adopts.14 Specifically, the D3d symmetry structure of 18-crown-6 (Figure la) is the optimal one for substrate inclusion due to the cavity formed by the ring of ether sites. In contrast, the low-energy structure in vacuum exhibits a C, symmetry (Figure lb) which is not optimal for cation complexation. The relative stabilities of these conformations are dependent upon solvent polarity, with tP. D3d structure becoming increasingly more stable for solvents with higher polarity. Our previous on 18-crown-6 clearly demonstrate that, in a polar and hydrogen bonding environment such as water, the crown is preorganized for complexation. In contrast, in an apolar environment such as carbon tetrachloride,
* To whom all correspondence should be addressed. @
Abstract published in Advance ACS Abstracts, September 1, 1994.
0022-365419412098-11193$04.50/0
complexation requires a reorganization of the crown from a C, to a D3d symmetry structure. Other studies have examined via fully atomistic stimulations the behavior of 18-crown-6 in s o l ~ t i o n . ~The ~ - ~authors ~ note that the vast span of configuration space was not exhaustively sampled even for extremely long simulation times. Consequently, the question of adequate sampling will become more severe as larger systems are investigated. Less computationally intensive schemes must be considered if we hope to address fully the characteristics of large 18-crown-6 derivatives in solution. To this end, we propose to treat the solvating fluid around the 18-crown-6macromolecule with a continuum instead of discrete representation. Specifically, we shall use the reference interaction site model (RISM) approach pioneered by Chandler and c o - w ~ r k e r s . ~The ~ - ~computational ~ expense of incorporating solvent effects can be greatly mitigated by such a treatment without sacrificing much in terms of accuracy. In this paper, we will examine the relative stabilities of the D3d and Ci conformations of 18-crown-6 in solvents of differing polarity via the XRISM integral equation approach. 1,39-42,46-53 Specifically, we study the following solvents: water, carbon tetrachloride, and acetonitrile. In the last instance, we scale the partial charges of the model potential to span the range from a purely apolar to a strongly polar solvent. Acetonitrile is of interest here due to the fact that it is often used in organic reactions as a highly polar, aprotic medium while water and carbon tetrachloride exemplify, respectively, archetypical protic polar and apolar solvents. In addition to 18-crown-6, we also briefly discuss the solvation of dibenzo-18-crownd in the same solvents and examine the effects that adding such lateral groups onto the principal crown ring has upon solvation thermodynamics and solvent structure. This last study also demonstrates how larger macrocycles can be studied in a computationally tractable manner using the XRISM integral equation approach. This paper is organized as follows: In section 11, we describe previous studies that have addressed related issues. In section 111, we present the computational method that we adopt to investigate the problem at hand. In section IV, we discuss our results pertaining to the free energy of solvation and the structuring of solvent molecules in the vicinity of the solute. Finally, we conclude with a brief summary of our findings in section V. 0 1994 American Chemical Society
Ha and Chakraborty
11194 J. Phys. Chem., Vol. 98, No. 43, 1994
C
Figure 1. (a) D3d conformation of 18-crown-6. (b) Ci conformation of 18-crown-6. (c) Dibenzo-18-crown-6. First three ether sites of each configuration have been labeled.
11. Background The issue of solvent effects on conformational equilibria can be addressed using various theoretical methods which vary in their level of atomistic detail and, concomitantly, computational cost. On one extreme are continuum theories such as the primitive model and the reaction field method. In these approaches, the structure of the solvating medium is completely discarded in favor of a macroscopic dielectric that describes the polarizable environment. Consequently, significant aspects of short-range steric as well as specific interactions between the solute and surrounding solvent molecules are neglected. At the other extreme are molecular simulations, both Monte Carlo and molecular dynamics, where the solvent molecules are represented explicitly. Molecular simulations for solutions are hindered by several considerations. First, one is often limited to either very dilute or very concentrated solutions. Moderate concentrations are difficult to achieve simply because of the prohibitive number of solvent molecules required to reach such a regime. Second, free energies are computationally demanding
quantities to obtain since they are statistical rather than mechanical averages. Intermediate between these two approaches are integral equations. To our knowledge, integral equation approaches have not previously been applied to the study of the conformational statistics of crown ethers. Molecular mechanics ~ t u d i e s ' ~at, zero ~ ~ , temperature ~~ have addressed the relative stabilities of the D3d and Ci conformations of 18-crown-6 in vacuum. The study by Wipff et al.14 finds the D3d structure to be 1.1 kcal mol-' higher in energy than the Ci. By repeating their calculations with no electrostatic charges, corresponding to a medium with an infinite dielectric constant, they show that the D3d structure eventually becomes 3.4 kcal mol-' more stable than Ci. More realistic considerations of solvent effects have been achieved in Monte Carlo simulations conducted by Ranghino et al.13 and by Ha and Chakraborty.'* In the former study, Ranghino et al. find the potential energy of solvation is 23 kcal mol-' lower for the D3d than the Ci structure in aqueous solution. Ha and Chakraborty find that the crown adopts Ci and D3d symmetry-like conformations when placed in apolar and polar environments of carbon tetrachloride and water, respectively. Nevertheless, they have reported significant fluctuations about these symmetric structures. Although the results of these molecular mechanics and Monte Carlo simulations provide valuable insight into the behavior of the 18-crown-6 macrocycle, they do not address the issue of free energy for the intraconversion between these two important crown conformations. This was calculated by Sun and Kollman36,37through free energy perturbation where the molecular dynamics trajectories consisted of the forward and backward transformations of the crown between the ci and D3d conformers. They determine that in aqueous solution the D3d conformer is stabilized relative to Ci by a solvation free energy of -6.5 f 0.4 kcal mol-'. The overall stability is reduced to -4.5 kcal mol-' once the intramolecular energy difference of the two structures, 1.98 kcal mol-', is taken into account. In our current study, we first consider the same system as that examined by Sun and Kollman by way of XRISM integral equation theory. In contrast to the large computational expense of free energy perturbation simulations, integral equation approaches are considerably less expensive because the free energy coupling can be performed analytically. This results in a closed form expression for the free energy of s o l ~ a t i o n ? , ~ ~ - ~ ~ Using the extended RISM approach, we investigate the D3d and Ci conformations of 18-crown-6 in water, carbon tetrachloride, and acetonitrile. Acetonitrile is extremely polar, but unlike water, it is an aprotic solvent that is incapable of forming hydrogen bonds. Our study in acetonitrile solutions will reveal whether hydrogen bonding interactions are a prerequisite for stabilizing the D3d conformer in solution. In addition, we briefly consider the behavior of dibenzo-18-crown-6 in these same solvents. 111. Method II1.A. XRISM Theory. The RISM integral equation of Chandler and A n d e r ~ o n ~is~ -a~ direct ~ extension of the Omstein-Zemike equation for atomic fluids to molecular systems. As such, it relates the site-site direct correlation functions cav(r) to the site-site total correlation functions hur(r). This is compactly denoted in matrix notation as h = w*c*w
+ w*c*gh
(1)
where * denotes a convolution, w the matrix of intramolecular correlation functions, and e the diagonal number density matrix. For a rigid molecule characterized by internal site,-sitey
XRISM of Simple Crown Ethers
J. Phys. Chem., Vol. 98, No. 43, 1994 11195
separation distances of Lay, w defines the geometry of the molecule with W a y = d(r - Lay)/4~tLa,2. The original formulation of the RISM theory approximated the fluid molecules as hard-sphere assemblies. Appealing to physical considerations, Percus-Yevick type closures were used for the intermolecular correlation functions:
where day is the distance of closest approach for the two sites. For polar systems, the necessary closure to the XRISM equation was introducted by Rossky et a1.48-53via a direct generalization of the atomic hypernetted chain approximation to the intermolecular site-site correlations:
where /3 = l/kT, and @ay is the site-site pair potential which we here assume to consist of a long-range Coulombic contribution in addition to a short-range Lennard-Jones 6- 12 component: (4)
-
For a solute at infinite dilution with 0, eq 1 can be decomposed explicitly in terms of the solvent-solvent ( Y V ) , solute-solvent @v), and solute-solute @p) submatrixes:
This set of euations can be solved sequentially to characterize the thermodynamic behavior of the solute-solvent mixture. The solute-solvent pair correlations, gpv(r-) = hpv(r) 1, provide structural information regarding the organization of the solvent about the solute. In turn, such important quantities as the potential and free energies of solvation, Uso1and Asol, can be expressed in terms of the correlation function^^,^^ as
+
a=ly=l
where np and nv are the number of sites present on the solute and solvent, respectively. 1II.B. Description of System. We first consider the Solvation characteristics of the D3d and cjsymmetry conformations of 18-crown-6 in various solvents. These two solute conformations of the crown are illustrated in Figure 1a.b with the various interaction sites appropriately labeled. We note that the structures were obtained from crystallographic data59$60 and that there is only one equivalent ether site (01) on the D3d symmetry structure and three distinct sites (01, 0 4 , and 0 7 ) on the low-symmetry Ci structure. Rossky's modified TIP3P model of water,6l Robertus' model for a united CC4,3 and Jorgensen's three-site model of acetonitrile6* are utilized in
TABLE 1: Potential Parameters and Solvent Densities 4i
i
le1
water 0.033 34 H 0.000 087 4 0 0.4 0 580 525 -0.8 carbon tetrachloride 0.006 303 CC4 1 360 650 63516 0 acetonitrile 0.011 4 6 934 2 396 0.15 CH3 C 3 357 1420 0.28 N 784 730 -0.43 benzene C 1122 560 -0.115 H 4.841 24.1 0.115
representing the three solvents that we consider. Previous molecular mechanics studies performed on the crown by Wipff et al.14 provide the remaining values necessary to complete the description of the system. The number density of the three solvents at standard conditions (25 "C, 1 atm) along with the potential parameters of their various interaction sites are listed in Table 1. The cross interactions are described by the geometric mean; A~ = 1/A,p,,cij= Interest in laterally substituted 18-crown-6 stems from the fact that the properties of the parent molecule can be greatly modified by the attached groups. For example, the complexation strengths and transport rates of dibenzo-18-crown-6 are quite distinct from that of 1 8 - c r o ~ n - 6 Therefore, . ~ ~ ~ ~ we seek to examine how the introduction of lateral groups onto 18crown-6 affects the interaction of the solvent molecules with the prinicipal structure. Attaching two benzyl groups onto the main ring of the D3d symmetric 18-crown-6 results in the dibenzo-18-crown-6 structure as shown in Figure IC. In our study, the interaction parameters for sites on the main ring are unchanged from their values for the 18-crown-6 molecule. The parameters for sites on the lateral groups are derived from the work of Jorgensen and Severance65and are listed in Table 1. This model for dibenzo-18-crown-6 is not meant to be truly representative of the real system. We choose this simple representation because our primary motivation is to delineate the influence of lateral groups upon the solvent structure. Notice that there are now two nonequivalent either sites (01 and 0 7 ) present on the crown.
G.
IV. Results and Discussion We now present the results of our XRISM calculations. Firstly, we briefly discuss our results for the pure solvents. Next, we turn to the solvation thermodynamics of the crown ethers at infinite dilution. For a solute at infinite dilution, the hierarchy of eqs 5a, 5b, and 5c must be solved sequentially with the first describing the behavior of the pure solvent; the second, the coupling between the solute and solvent; and the last, the solute-solute correlations. Only the first two equations are required to characterize solvation thermodynamics at infinite dilution, but the last equation has been included for completeness. While the structure of the pure solvent, h,,, is a necessary input into the second equation, one could imagine using structures obtained from experimental data of real systems or from large scale molecular simulations. In our present study, we choose to address the entire system via the XRISM integral approach rather than through some semiempirical scheme. Thus, as a requisite starting point, we first describe our XRISM results for the pure solvents. The modified TIP3P water system has been well characterized in previous XRISM calculations and compared to molecular simulations.61 We merely note that the important features of
11196 J. Phys. Chem., Vol. 98, No. 43, 1994
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Figure 2. (a) C-C radial distribution function of acetonitrile at zero and full charge. (b) N-N radial distribution function. (c) CH3-CH3 radial distribution function of acetonitrile at zero and full charge. (d) CHs-N radial distribution function. (e) CH3-C radial distribution function of acetonitrile at zero and full charge. (f) C-N radial distribution function.
the radial distribution functions are in qualitative agreement with simulation results; the one exception is that XRISM predicts too much structure in the hydrogen bonding of the liquid as illustrated by the 0-H pair distribution function. This is due to the small repulsive cores placed on the hydrogen atoms in the modified TiP3P model for water. These repulsive cores are necessary to prevent catastrophic divergences in the solution of the XRISM equations. As the repulsive core is decreased, the first peak in go+ sharpens and shifts to smaller dist a n c e ~ . ~Notwithstanding ~ . ~ ~ ~ ~ ~ this discrepancy, the 0-H
coordination number is quite consistent with simulation, thus indicating that the discrepancy is in the shape of go-^ and not in the overall coordination of the system. The solvent structure of carbon tetrachloride is well characterized as that of a simple atomic fluid.67 Acetonitrile has been previously examined by Hsu and Chandler via RISM calculations.68 In their calculations, however, acetonitrile was modeled as a six-site hard-sphere fluid without incorporating electrostatic effects. This seems unreasonable given the high polarity of the molecule (dipole moment
XRISM of Simple Crown Ethers 1.2
J. Phys. Chem., Vol. 98, No. 43, 1994 11197
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TABLE 2: Relative Total Free Energies of Solvation AAtot for 18-Crown-6 in Acetonitrile as a Function of Solvent Polarity, 8 (Units in kcal mol-')
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Figure 5. Radial distribution function of CCL about the various 18crown-6 ether sites.
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Figure 3. (a) Radial distribution function of water H about the various 18-crown-6 ether sites. (b) Same as (a) but for water 0.
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of 3.92 D). Nevertheless, Hsu and Chandler obtained good agreement with the structure factors derived from X-ray and neutron diffraction experiments. In attempting to further elucidate the behavior of acetonitrile, Jorgensen and Briggs6* developed an accurate three-site model for this molecule which included partial charges; good thermodynamic and structural results were obtained in their Monte Carlo simulations. They discovered that although the intermolecular structure exhibits significant changes with the removal of electrostatic effects, the
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structure factors manifest little sensitivity to these variations, thus explaining the remarkable agreement obtained by Hsu and Chandler for their charge neutral model for acetonitrile. We have conducted XFUSM calculations on acetonitrile with the model developed by Jorgensen and Briggs and briefly compare our results to those obtained by Monte Carlo simulations (Figures 3-8 of ref 62). Figure 2a-f shows the various site-site pair correlations at full and zero charge of acetonitrile as determined from the solution of the XRISM equations. The number of peaks as well as the locations of the maxima and minima of the radial distribution functions compare very well with simulation. The XRISM results are able to capture subtle features of the solvent structure which are manifested as shoulders in some of the peaks as in the case of gN-N at approximately 5.57 A (Figure 2b). Furthermore, the XRISM approach accurately reproduces the effects of electrostatic interactions in the system. This is seen most clearly in gCH3-N of Figure 2d where the introduction of Coulombic interactions induces a strong ordering of the first peak attributable to the head-to-tail alignment of the dipoles.62 In contrast to the Monte Carlo simulations where some of the shoulders in the distributions are smeared out, they persist or are perhaps more
Ha and Chakraborty
11198 J. Phys. Chem., Vol. 98, No. 43, 1994
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pronounced in the XRISM results. For Instance, gCH3-CH3 (Figure 2c at full charge) possesses a definite dip at approximately 5 8, which is absent from the Monte Carlo Simulations. Instead, Figure 5 of ref 62 shows a single peak in this region. Finally, the solvent coordination (eq 8) of the various acetonitrile sites that we calculate compare quite favorably with simulation. Whereas simulation predicts 2.8 CH3 and 1.6 C nearest neighbors within 4 8, of the N site in acetonitrile, XRISM predicts values of 2.8 and 1.7. At 5.1 A, simulation gives 5.7 CH3 and 5.7 C coordinating sites about N while our XRISM results give 5.8 and 5.7. Now that we have characterized the solvents, we turn to examine the solvation of the two conformers of 18-crown-6 in solution, beginning with water. Figure 3a,b shows the pair distribution functions for the hydrogen and oxygen atoms of water about the various ether sites (as labeled in Figure la,b of the crown configurations); Figure 4 shows the corresponding running coordination numbers. The running coordination number Npv(4= e v K 4 n J Z dJ g p v V >
00
(8)
gives the number of molecular sites Y about the central site ,D as a function of distance. Figures 3a and 4 indicate that hydrogen bonding is optimal for the D3d conformer. In comparison, the first 0-H peaks for all three ether sites of the Ci conformer are depressed with a fewer number of H neighbors.
Figure 7. (a) Radial distribution function of acetonitrile solvent sites at zero charge about 0 1 of C, 18-crown-6. (b) Same as (a) but at full solvent charge. In a previous Monte Carlo study by Ranghino et al.,I3 the authors find the D3d conformer to be better incorporated than C, into the hydrogen-bonding network of the water with bridging water molecules spanning the various ether sites. In our calculations, this is manifested in the radial distribution functions by the large and prominent first peaks not only for go-H but also for go-0 of the D3d conformer. On the other hand, the less structured go-0's for the C, conformer indicate less effective coordination by the water molecules. From the correlation functions, the potential energy of solvation (as determined from eq 6) for the D3d conformer is found to be 13.04 kcal mol-' lower than that for the C, structure. Further, the difference in the free energies of solvation (eq 7) between the two is -6.85 kcal mol-' which compares well with the value of -6.5 kcal mol-' determined by Sun and K ~ l l m a nvia ~ ~the computationally much more demanding free energy perturbation calculations. From the potential and free energies of solvation, the relative entropy change of the system is 6.19 kcal mol-' higher for the C, than the D3d conformer. Hence, this again points to the fact that when the D3d conformer is solvated by water, the solvent structure is much more ordered than that for solvating the Cj structure. The internal energy difference between the D3d and Ciconfigurations of 18-crown-6 must be taken into account when determining the total free energy difference between the two conformers in solution. We have applied the potential force field14 to the two crystallographic structure^^^^^^ of the crown, and we obtain a value of A~nva(D3d-cj)= 2.93 kcal mol-'. This value is somewhat larger than the value of 1.1 kcal mol-'
XRISM of Simple Crown Ethers
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Figure 8. (a) Radial distribution function of acetonitrile solvent sites at zero charge about 0 4 of Ci 18-crown-6. (b) Same as (a) but at full solvent charge.
Figure 9. (a) Radial distribution function of acetomtrile solvent sites at zero charge about 0 7 of C, 18-crown-6. (b) Same as (a) but at full solvent charge.
reported by Wipff et al.14 since we do not perform any sort of energy minimization upon the crystal structures. Accounting for the internal strain difference of these two crown configurations, the total free energy difference between them in aqueous solution is found to be 3.92 kcal mol-' lower for the D3d conformer. Figure 5 shows the radial distribution functions for the carbon tetrachloride molecules about the different ether sites of the two crown configurations. Although the distributions are quite distinct, they do not result in a very large difference in the potential and free energies of solvation for the two macrocycle symmetries. This is because there are only weak solute-solvent interactions for cc4. Specifically, we find that hASo1(D3d-Cj) = 0.03 kcal mol-' and huo1(D3d-Cj) = -0.78 kcal mol-'. Thus, the total free energy difference, hAtot(D3d-Ci) = 2.96 kcal mol-', is dominated primarily by the internal strain difference between the D3d and C, symmetry structures rather than through any solvent mediated differences. Having considered systems that have been studied previously using computationally more demanding methods, we now turn to the solvation of 18-crown-6 in acetonitrile. We examine this system for two reasons. First, crown ethers solvated in acetonitrile are used in practical situations. Second, we wish to address a question that has not been considered in detail heretofore, viz., how are various crown ether conformers solvated in polar solvents that are aprotic and hence cannot form hydrogen bonds. Table 2 shows the relative total free energies which consist of the internal strain difference between the Ci
and D3d conformers as well as the free energies of solvation for the two crown conformers as a function of solvent polarity. We vary the solvent polarity by changing the magnitude of the partial charges at the various sites of our model for acetonitrile; specifically, at 5 = 0, the partial charges of the solvent model have been set to zero while, at 5 = 1, the partial charges are fully turned on, thus mimicking true acetonitrile. At 6 = 0, the solvent is purely apolar and as 6 increases, the solvent acquires greater polar character. Intermediate states are characterized by correspondingly scaling the charges of the solvent model by lI4, '12, and 3t4. Performing calculations for various values of 5 enables us to isolate and examine the effects of solvent polarity systematically. As expected, for both the C, and D3d conformers the total free energy decreases as solvent polarity increases. However, the incremental stabilization of the D3d structure is much more dramatic than that for C,. As a result, although the C, structure is initially more stable than D3d at 5 = 0, this is eventually reversed at 5 = 1 with the D3d conformer being more stable. These results show unequivocally that electrostatic effects alone can cause the D3d structure to be more stable in polar solvents. In other words, hydrogen-bonding interactions (e.g., in water) are not a prerequisite for stabilizing the D3d conformer in solution. Table 3 shows the relative potential energies of solvation of the two crown conformers and of their methylene and ether sites. As with the free energy, the rate of stabilization with solvent polarity is greater for the D3d than the c, structure. The contributions of the individual ether and methylene groups clearly
11200 J. Phys. Chem., Vol. 98, No. 43, 1994
Ha and Chakraborty 10 0
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6.0
6.0
4.0
2.0
0.0
3
2
100
1
-z
1
5
6 r [angstroms] l
- Ci
6.0
4 r [angstroms]
(01-CH3) Ci (01-C) ..... Ci (01-N)
10.0
8.0 -
fullcharge
- Ci
(07-CH3) Ci ( 0 7 4 )
fullcharge
..... Ci (07-N)
-i
4.0 -
6.0 -
4.0
-
2.0
-
0.0 r [angstroms]
Figure 10. (a) Running coordination number of acetonitrile solvent sites at full charge about 0 1 of D3d 18-crown-6. (b) Same as (a) but about 0 1 of Ci18-crown-6. (c) Same as (a) but about 0 4 of Ci 18-crown-6. (d) Same as (a) but about 0 7 of Ci18-crown-6.
indicate that this behavior does not follow some simple scaling with solvent polarity but is instead dependent upon the structure of acetonitrile in a complicated way. Figure 6a,b shows the radial distribution functions (gO-CH3, go-c, and go-N) of the acetonitrile sites at both zero and full charge about the ether sites of the D3d crown conformer. Figures 7a,b 8a,b and 9a,b show the corresponding distributions for the three distinct (01, 04, and 07) ether sites of Ci. These radial distribution functions provide insight as to why the ether sites in the D3d conformer are so well solvated at the expense of the methylene sites while, in comparison, no such marked difference is observed for the Ci structure (Table 3). The most striking feature in Figure 6b is the large peak in go-CH3. This is due to more than just the favorable electrostatic interactions between acetonitrile and the D3d crown ether sites since the corresponding pair distribution functions about the 0 1 , 0 4 , and 0 7 ether sites of the Cj crown (Figures 7b, 8b, and 9b) do not display such strong analogous structuring. In those instances, the effects of solvent polarity on the organization of acetonitrile about the solute are much more modest, the implication being that the asymmetry of the Ci conformer prevents efficient solvent packing. In contrast, the open cavity of the D3d conformer allows for close approach of the CH3 group of acetonitrile towards either surface of the 18-crown-6 macrocycle. This accounts for the very favorable solvation of the D3d ether sites in comparison to the Ci configuration. In Figure 6a,b, the radial distribution function, go-c, is not very much affected by the introduction of charges. This implies
that the central carbon atom of the solvent structures around the ether sites in the same way at both zero and full charge. Since the other sites of acetonitrile (CH3 and N) are connected to this carbon atom, the augmentation of the gO-CH3 peak at -3.4 A along with the displacement of the go-N peak from -3.3 to -4.4 A are indicative of significant rotational reordering of the acetonitrile molecules about the D3d crown oxygens as electrostatic interactions are introduced; this does not occur with the Ci conformer. This is perhaps more clearly noted in Figure 10a which shows the corresponding running coordination numbers of solvent sites at full charge about the D3d crown oxygens. For comparison, the analogous curves for the Ci case are shown in Figure lob-d. Any disparity between the three curves in each figure indicates a deviation from a rotationally isotropic distribution. Thus, we see evidence for strong orientational ordering of acetonitrile about the D3d conformer that is much more prominent and long-ranged than that for the Ci conformer. Crystallographic studies of the 2: 1 acetonitrile- 18-crown-6 c o m p l e ~ show ~ ~ * that ~ ~ the two acetonitrile molecules are anchored by their CH3 groups on either face of the D3d crown macrocycle. We compare this to the coordination behavior in solution where the first peak of go-CH3 in Figure 6b extends to 4.3 A, corresponding to 2.7 CH3 neighbors (Figure loa) in the first solvation shell of the D3d ether sites. To estimate how many of these neighbors are actually in the cavity of the D3d crown structure, we also calculate the coordination number from the center-of-mass of the D3d conformer. We find 1.8 CH3 sites
XRISM of Simple Crown Ethers
J. Phys. Chem., Vol. 98, No. 43, 1994 11201
a lo!
08.I
?5
-
6
06 -
-
m
04
J
18-crown-6 (01-H) dibenzo (01-H) dibenzo (07-H)
-
I
I 05 -
- dibenzo (01-CH3) __ . dibenzo
zero charge
(01-C)
dibenzo (01-N)
02 -
I
00
I.
I
J , , ,
0
1I
5
10
15
r [angstroms] 1.5 r 1.5
1.0 -
-c
8
I
0.5 -
o_ m
1
-
~' 0.5
dibenzo (01-CH3) dibenzo (01-C) dibenzo (01-N)
I'
-
full charge
,
I
I
0.0 0
0.0
-
I
,
,
,
,
,
,
5
0
,
,
,
5
10
15
r [angstroms]
.
,
,
,
15
10 r(0-CCl4) [angstroms]
Figure 12. Radial distribution function of CC4 about the various ether sites of D3d 18-crown-6 and of dibenzo-18-crown-6. TABLE 4: Relative Entropies of Solvation TAPo1for 18-Crown-6 in Acetonitrile as a Function of Solvent Polarity, 6 (Unitsin kcal mol-')
5 0
'14
'I2
314
D3d
0.00
-0.77
-3.18
Ci
0.71
-2.24 0.20
0.50
1,
0.27
1 -3.35
0.83
in the first solvation shell at 3.8 A. From this information and that depicted in Figures 6b and loa, the following description emerges, For the 18-crown-6 D3d conformer, as the solvent polarity of acetonitrile increases, the moelcules near the surface of the crown begin to interact strongly with the ether sites, inducing the solvent to order rotationally in a manner such that the CH3 groups enter the crown cavity and the N groups are pushed away. This gives rise to the large peak in the radial distribution function, go-cHS. The 1.8 coordination number is consistent with the crystallogrpahic picture of two acetonitrile molecules binding with both surfaces of the crown. The remaining solvent molecules, 2.7 - 1.8 = 0.9 CH3, in the first coordination shell of the ether sites are due to acetonitrile molecules outside of the crown cavity. Table 4 shows the relative entropies of solvation for the two crown configurations as the site charges in acetonitrile are varied. The solvation of the Ci conformer leads to a gain in entropy which does not change much with solvent polarity. In contrast, the solvation of the D3d configuration is accompanied
Figure 13. (a) Radial distribution function of acetonitrile solvent sites at zero charge about 0 1 of dibenzo-18-crown-6. (b) Same as (a) but at full solvent charge.
by a loss of system entropy which exhibits a significant dependence upon the solvent polarity. This implies that in contrast to the C, structure, the high-symmetry D3d conformer has a structure making effect on the solvent. It is also interesting to note that the entropy of solvation for the Ci configuration does not vary monotonically with solvent polarity. This arises from competing effects. At 6 = 0, the 18-crown-6 solute merely disrupts the packing of acetonitrile. At 6 = '/z, the electrostatic interactions between the 18-crown-6 solute and the surrounding solvent molecules induce sufficient local order to compensate for the disruption in solvent packing caused by the low symmetry of the Ci crown. Thus, the solvation entropy decreases. At 6 = 1, however, the pure solvent (before 18crown-6 is introduced) is highly structured due to the strong dipole alignment of the acetonitrile molecules discussed earlier in Figure 2a-f. The additional order arising from the solutesolvent interactions is no longer able to compensate adequately for the disorder that the C, configuration causes in the solvent structure. This is so because the solvent-solvent electrostatic interactions scale quadratically with 6while the solute-solvent interactions scale linearly. Thus, the solvation entropy increases. The influence of introducing lateral groups to the D3d conformer on solvent structuring is now examined. Figure 11 shows the radial distribution functions of the hydrogen atoms in water about the ether sites of the dibenzo-18-crown-6 structure; Figure 12 shows that for carbon tetrachloride about the same sites. For reference, the distribution functions corresponding to the D3d conformer of 18-crown-6 have also been
Ha and Chakraborty
11202 J. Phys. Chem., Vol. 98, No. 43, 1994
l
a
!
I
05 -
- dibenzo _ _ _ dibenzo
(07-CH3) (074) dibenzo (07-N)
1.
00
,
zero charge
1
,
I
0.5
0.0
1,
I
- D3d
(CH2-CH3) D3d (CHP-C) D3d (CHP-N)
'
I
I
.
,
,
1.5
I
1
b
I I
I
0.5
I
I
' -
dibenzo (07-CH3) dibenzo ( 0 7 4 ) dibenzo (07-N)
full charge
I
0.5
1
- dibenzo
(CH2-CH3)
full charge
_ _ _ dibenzo (CH2.C)
dibenzo (CH2-N)
1 ,
0
1.0
I
A
I
1
00
I 15
10
r [angstroms]
r [angstroms] 1.5
,
5
0
fullcharge
5
10
I 15
'
0.0 0
r (angstroms]
Figure 14. (a) Radial distribution function of acetonitrile solvent sites at zero charge about 0 7 of dibenzo-18-crown-6. (b) Same as (a) but at full solvent charge.
reproduced. For both water and carbon tetrachloride, the solvent structure about the ether sites ( 0 1 and 0 4 ) nearest to the benzyl groups have been significantly perturbed. For water, the hydrogen distribution about the remaining oxygen (07) that is furthest removed from the benzyl groups does not deviate considerably from the parent 18-crown-6 case until about 6 A. In contrast, the effects in the case of carbon tetrachloride are much more immediate. These dissimilarities may be attributed to the fact that CC4 is a bulkier solvent than water. Also, CC4 is governed primarily by steric considerations as opposed to water where specific interactions are important. Consequently, the local order of water at 0 7 is maintained whereas that for CC4 is not. In the latter case, the presence of the benzyl groups induces a change in the solvent structure that is propagated over a greater distance. Figures 13a,b and 14a,b show the radial distribution functions for the solvation of dibenzo-18-crown-6 in acetonitrile. The solvent structure about the most removed ether sites (07 in Figure 14a,b) is not affected very much by the introduction of the benzyl groups to the principal ring (see Figure 6a,b). From Figures 13b and 14b, however, the acetonitrile at full charge appears to be better structured about the ether sites (01 and 0 4 ) adjacent to the benzyl groups rather than about the distant 0 7 ether sites. This is evidenced by the fact that gO-CH3 is sharper and higher and g o - N is displaced outward. We attempt to clarify this point a bit more by showing the acetonitrile structure about the crown methylene groups to which the benzyl groups are attached. Figure 15a shows gCH2-CH3, gCH2-C. and
I '
'
5
10
15
r [angstroms]
Figure 15. (a) Radial distribution function of acetonitrile solvent sites at full charge about methylene site adjacent to 0 1 of D3d 18-crown-6. (b) Same as (a) but for dibenzo-18-crown-6.
before the benzyl groups are introduced, and Figure 15b depicts results for dibenzo-18-crown-6. gCH2-N in Figure 15b is much depressed and shifted outward compared to Figure 15a. This is due to the unfavorable electrostatic interactions between the nitrogen end of acetonitrile and the negative charges in the plane of the benzyl ring. This behavior is manifested in go-N by the disappearance of the 4.4 8, peak in Figure 6b (the D3d 18-crown-6 case) from Figure 13b (the dibenzo-18-crown-6 case), resulting in greater acetonitrile structure about the ether sites adjacent to the benzyl groups of dibenzo- 18-crown-6. gCH2-N
V. Concluding Remarks We have performed XRISM calculations for two important configurations of the 18-crown-6 macrocycle in water, carbon tetrachloride, and acetonitrile. We see that, in water, our results compare quite well with previous free energy perturbation calculations which are computationally much more demanding. We determine the water structure about the D3d and Ci conformations of the crown and find the D3d conformer to be significantly better coordinated. In carbon tetrachloride, the relativity stability of the two crown configurations is dominated by their internal rather than their solvation energy differences. Further, we demonstrate how the relative stability of the two conformers are inverted as a function of solvent polarity in acetonitrile. In contrast to the much more specific hydrogen bonding which stabilizes the D3d conformer in water (compare Figures 3a and 6b), the electrostatic interactions between acetonitrile and 18-crown-6 are sufficient to stabilize the D3d
XRISM of Simple Crown Ethers conformer in water (compare Figures 3a and 6b), the electrostatic interactions between acetonitrile and 18-crown-6 are sufficient to stabilize the D3d conformer in solution. We attribute this to the strong rotational ordering induced by the electrostatic interactions of the acetonitrile molecules about the D3d conformer. The entropy of solvation substantiates this interpretation with a large entropy loss for the D3d conformer. Hydrogen-bonding interactions are, therefore, not a necessary prerequisite for stabilizing the D3d conformer in solution. The solvent coordination numbers seem to imply that two acetonitrile solvent molecules are binding on either face of the D3d conformer in accord with crystallographic information. Last, the addition of lateral groups in creating dibenzo-18-crown-6 appears to have a relatively local effect on the solvent structure about the solute. Acknowledgment. Partial financial supporr for this work was provided by ZENECA FCMO (UK) and the National Science Foundation via a NYI award to A.K.C. References and Notes (1) Jorgensen, W. L. J. Phys. Chem. 1983, 87, 5304. (2) Jorgensen, W. L.; Buckner, J. K. J. Phys. Chem. 1987, 91, 6083. (3) Rebertus, D. W.; Beme, B. J.; Chandler, D. J. Chem. Phys. 1979, 70, 3395. (4) Zichi, D. A.; Rossky, P. J. J. Chem. Phys. 1986, 84, 1712. (5) Chandler, D.; Pratt, L. R. J. Chem. Phys. 1976, 65, 2925. (6) Pratt, L. R.; Chandler, D. J . Chem. Phys. 1977, 66, 147. (7) Pratt, L. R.; Chandler, D. J. Chem. Phys. 1977, 67, 3683. (8) F’ratt, L. R.; Hsu, C. S.; Chandler, D. J. Chem. Phys. 1978, 68, 4202. (9) Amis, E. S. Solvent Effects on Reaction Rates and Mechanisms; Academic Press: New York, 1966. (10) Hsu, C. S.; Pratt, L. R.; Chandler, D. J. Chem. Phys. 1978, 68, 4213. (11) Yu, H. A.; Pettitt, B. M.; Karplus, M. J. Am. Chem. SOC.1991, 113, 2425. (12) Brooks, C. L., III; Karplus, M.; Pettitt, B. M. Proteins: A Theoretical Perspective of Dynamics, Structure, and Thermodynamics;John Wilev & Sons: New York. 1988. (13) Ranghino, G.; Romano, S.; Lehn, J. M.; Wipff, G. J. Am. Chem. SOC.1985, 107, 7873. (14) Wipff, G.; Weiner, P.; Kollman, P. J. Am. Chem. SOC. 1982, 104, 3249. (15) Gehin, D.; Kollman, P. A,; Wipff, G. J . Am. Chem. SOC.1989, 111, 3011. (16) Grootenhuis, P. D. J.; Kollman, P. A. J . Am. Chem. SOC.1989, 111, 2152. (17) Ha, Y. L.; Chakraborty, A. K. J. Phys. Chem. 1993, 97, 11291. (18) Ha, Y. L.; Chakraborty, A. K. J. Phys. Chem. 1991, 95, 10781. (19) Cram, D. J. Science 1988, 240, 760. (20) Lehn, I. M. Science 1985, 227, 849. (21) Wipff, G.; Kollman, P. A,; Lehn, J. M. J. Mol. Struct. 1983, 93, 153. (22) Christensea, J. J.; Hill, J. 0.;Izatt, R. M. Science 1971, 174, 459. (23) Ha, Y. L.; Chakraborty, A. K. J. Phys. Chem. 1992, 96, 6410. (24) Pedersen, C. J. J . Am. Chem. SOC.1967, 89, 7017. (25) Pedersen, C. J. J . Am. Chem. SOC.1970, 92, 391.
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