J. Phys. Chem. 1996, 100, 17655-17661
17655
Solvation of 1,4,7,10-Tetraazacyclododecane in Aqueous Solution As Studied by the Monte Carlo Method Supot Hannongbua Department of Chemistry, Faculty of Science, Chulalongkorn UniVersity, Bangkok 10330, Thailand ReceiVed: October 31, 1995; In Final Form: March 25, 1996X
The solvation structure of 1,4,7,10-tetraazacyclododecane (cyclen) in aqueous solution has been investigated using the Metropolis Monte Carlo scheme. Simulations have been carried out for a system containing 202 rigid particles, including one cyclen molecule, which is fixed at the center of the cube. With a volume of 201 water molecules at 298 K and 1 atm plus additional space occupied by the cyclen molecule, a periodic cubic volume of side length 18.28 Å was yielded. A cyclen-water pair potential has been developed based on ab initio calculations, while the MCY potential was employed to describe water-water interactions. Three hydration layers around the cyclen have been monitored and named the nearest-neighbor, inner hydration, and outer hydration shells. The corresponding numbers of water molecules lying in each shell are 2, 6, and 54, respectively. The two nearest neighbors are bound to the ligand cavity, one above and the other below the ligand plane, pointing one hydrogen atom to the center of the cavity. It was also found that each of them was solvated by three of the six molecules in the inner hydration shell of cyclen. In addition, significant solvent structure around the cyclen molecule has been observed up to 8-9 Å from the molecular center.
1. Introduction While chemists have agreed on the existence of the macrocyclic effect1,2san enhanced stability of macrocyclic ligand complexes as compared to their open-chain analogssefforts to establish more detailed contributions to this effect have led to conflicting results.3-5 The solvation effect1,2 was suggested to be one of the important factors contributing to such extra stability. This argument states that the cyclic nature of the closed-ring ligands physically prevents them from having as large a hydration number as their open-chain analogs. Therefore, less water molecules have to be removed from the hydration shell of the cyclic than from the open-chain ligands during complexation. There is no way to ascertain, on the basis of existing data, whether the macrocyclic effect is caused primarily by the solvent effect. Data on the solvation structure of this type of ligand are not available because it is too complicated to examine by the diffraction method.6 To overcome this problem, it is necessary to obtain information on the solvation structure of macrocyclic ligands at the molecular level. Recently, we have investigated the solvation structure of 1,4,7,10-tetraazacyclododecane (cyclen) in 18 mol % aqueous ammonia solution by means of Monte Carlo studies7 using an ab initio pair potential at the STO-3G level for cyclen-water and cyclen-ammonia interactions. A clear picture of cyclen’s solvation shell was obtained. Its nearest neighbors are two water molecules, located very close and pointing one O-H bond to the ligand’s cavity. The next solvation sphere accommodates four water molecules lying near to the four NH functional groups of cyclen and forming hydrogen bonds with the first two molecules. Beyond this shell, some ammonia molecules and structural properties of the solvent identical to those found for bulk water-ammonia mixture8-13 have been, respectively, detected. Similar investigation has been carried out in the past decade for a cyclen molecule in pure water, using also the Monte Carlo method, but with a GLO basis set for the ab initio calculations.14 The difference in the first-shell coordination X
Abstract published in AdVance ACS Abstracts, October 1, 1996.
S0022-3654(95)03223-0 CCC: $12.00
numbers due to an artificial stability of the GLO energies, which are more than two times more negative than the STO-3G values,7,14 is clearly found. 2. Details of the Calculations 2.1. Cyclen-Water Potential Function. The cyclen-water pair potential was developed on the basis of ab initio calculations. Intramolecular geometries of cyclen and water molecules were taken from the literature15-17 and were used throughout. Due to a C2V symmetry of the cyclen molecule, only one-fourth of the whole space around the cyclen was taken into consideration. The water molecules were placed at numerous positions around the cyclen, where 0° e θ e 180°, 0° e φ e 90°, and 2 Å e r e 10 Å. Then ab initio self-consistent field (SCF) calculations were performed with and without correcting for basis set superposition error (BSSE), using the following default basis sets of the Gaussian 92 program:18 STO-3G, 3-21G, 6-21G, 6-31G, DZ, DZV, and DZP. The STO-3G basis set was, finally, selected (a detailed discussion is given in section 3.1). After SCF calculations were performed for about 1000 single water-cyclen configurations, the data were fitted to an analytical function of the form 3
32
∆E(L,W) ) ∑ ∑
Aijab
6 i)1 j)1 r ij
+
Bijab
+
rij12
Cijab rij4
+ qiqj
[ ] 1
rij
+
1
rij2
(1)
where i and j label atoms of water and cyclen molecules, respectively, Aij, Bij, and Cij are fitting constants, rij is the distance between an atom i of water molecule and an atom j of cyclen, and qi and qj are the net charges of atoms i and j in atomic units, obtained from the population analysis19 of the isolated molecules. Superscripts a and b on the fitting parameters have been used to classify atoms of equal atomic number but different environment conditions, for example HN, HC, and HC′ (see Figure 1). The second Coulombic term in the cyclen-water potential which has been successfully used for several cases14,20,21 leads to a distance dependent on the chargecharge interactions. © 1996 American Chemical Society
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Figure 1. (a, b) Orientations of the cyclen molecule in the coordinate system. (c) Definition of top, side, and plane regions.
The fitting procedure starts with 400 data points. The resulting analytical potential functions with the best fit for this set of the initial data were tested using an additional 100 randomly chosen points, outside the first set. Then, the test points were included into the fit. Another 100 points were, again, tested and then included. This procedure was repeated until consistency of the fitting parameters was yielded, leading to the total amount of about 1000 energy points of cyclenwater interactions. This self-consistent method was originally introduced by Jorgensen et al.22 2.2. Monte Carlo Simulations. Monte Carlo simulation has been carried out for a cyclen molecule in aqueous solution. The system contained 202 rigid particles, including one cyclen molecule, which is fixed at the center of the cube, and 201 water molecules. The volume of the 201 water molecules at an experimental density of 1 g‚cm-3 at 298 K and 1 atm, plus additional space occupied by the cyclen molecule (the volume of its solvation sphere7,14 is estimated as a cylinder of height 3 Å and radius 5 Å), yielded a periodic cubic volume of side length 18.28 Å. A spherical cutoff for the site-site interaction potentials was applied at half of this length. The starting configuration of the water molecules was randomly generated. The MCY23 potential was employed to describe water-water interactions. After equilibration, 8 × 106 configurations were generated and stored for subsequent analyses, which were carried out by averaging over groups of 1.6 × 104 configurations evenly spaced throughout the whole simulation history. 3. Results and Discussion 3.1. Cyclen-Water Potential Function. In Table 1, the
TABLE 1: Final Optimization Parameters for the ith Atoms of 1,4,7,10-Tetraazacyclododecane (Cyclen) Interacting with the jth Atoms of Water (Water, qO ) -0.366, qH ) 0.183; Cyclen, qN ) -0.315, qC ) -0.005, qHN ) 0.141, qHC ) 0.033, qHCm ) 0.059, in atomic units) i-j
A (Å6 kcal/mol)
B (Å12 kcal/mol)
C (Å4 kcal/mol)
N-O C-O HC-O HC′-O HN-O
-1
-0.181 044 × 10 -0.908 842 × 102 -0.846 894 × 103 -0.157 559 × 10-1 -0.421 048 × 10-1
106
0.231 435 × 0.207 043 × 107 0.319 998 × 106 0.221 200 × 104 0.773 339 × 103
0.330 232 × 102 0.405 301 × 102 0.607 378 × 101 0.864 485 × 101 0.202 690 × 102
N-H C-H HC-H HC′-H HN-H
-0.308 072 × 102 -0.105 299 × 103 -0.222 826 × 100 -0.450 320 × 10-2 -0.109 231 × 10-1
0.788 451 × 102 0.591 790 × 105 0.477 655 × 104 0.338 516 × 100 0.157 351 × 104
0.175 571 × 102 0.159 690 × 102 0.203 789 × 102 0.172 227 × 102 0.157 515 × 102
fitting parameter values are summarized. The fitted and the SCF energies in the configuration where the minimum of the pair potential takes place (the water molecule lies on the z-axis and points one O-H bond toward the cavity of cyclen) are depicted in Figure 2. In this context, the influences of the small basis set and of the BSSE have also been taken into consideration. The results of the calculations for various basis sets are compared in Table 2. As far as the molecular dipole moments, the stabilization energies, and the corresponding distances along the z-axis from the O atom (of water) to the center of cyclen’s cavity are concerned, the STO-3G basis set gives results comparable to those from the DZP basis set, while the computation time is about 64 times less. Since the cyclen-water potential curve near the minimum is quite broad (Figure 2), the observed shift of the distances to the minima and changes of the corresponding
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J. Phys. Chem., Vol. 100, No. 44, 1996 17657
TABLE 2: Total Energy (E in atomic units), Molecular Dipole Moment (µ in debye), Optimal Stabilization Energy with and without BSSE Correction (∆E and ∆EBSSE in kcal‚mol-1), Corresponding Distance from the O Atom (of Water) to the Center of Cyclen’s Cavity (r and rBSSE in Å, See Figure 1), and Time Required (CPU Time in min, for Cyclen-Water Dimer on an IBM RISC 6000 Workstation), Calculated from Various Basis Sets H2O
H2O-cyclen
basis set
µ
E
E
r
∆E
rBSSE
∆EBSSE
CPU time
STO-3G 3-21G 6-21G 6-31G DZV DZ DZP exptl
1.73 2.44 2.41 2.63 2.68 2.68 2.23 1.85a
-74.962 93 -75.585 39 -75.887 87 -75.983 99 -76.009 22 -76.009 28 -76.046 51
-525.818 49 -529.310 89 -531.606 89 -532.021 57 -532.099 30 -532.101 60 -532.401 95
2.78 2.62 2.64 2.76 2.81 2.84 2.93
-5.52 -17.26 -16.57 -12.38 -10.28 -10.16 -7.04
2.92 2.90 2.91 2.88 2.94 2.95 3.01
-2.97 -7.30 -7.09 -8.16 -7.95 -7.93 -5.49
5 17 18 31 72 90 320
a
The experimental dipole moment for water, taken from ref 24.
Figure 3. Radial distribution functions and corresponding running integration numbers from O (solid line) and H (dashed line) atoms of water molecules to the center of mass of cyclen for the entire space around cyclen. Figure 2. Cyclen-water stabilization energies obtained from the STO3G ab initio calculations (circle) and from the potential function (line) with the fitting parameters given in Table 1, where the water molecule lies along the z-axis (see Figure 1) and points one hydrogen atom toward cyclen’s cavity.
energies due to the BSSE for all basis sets are within fluctuations due to thermal effects at room temperature (0.6 kcal‚mol-1). Without BSSE corrections, the STO-3G energy of -5.52 kcal‚mol-1 is surprisingly consistent with that of the DZP set with the BSSE corrections. Taking into account all the data given above, it is clear that STO-3G should be a sufficiently reliable basis set for the system under consideration. In addition, the selected basis set gives the best value of the dipole moment of water molecule, in comparison with experimental data.24 The good agreement between the fitted and the SCF energies is shown in Figure 2. The small value of this function at the distance of about 7 Å justifies that correction of the Coulombic interactions beyond the cutoff distance in the Monte Carlo simulations is not necessary. Some comments should be made concerning the previous cyclen-water potential functions developed by our group during the past decade.25 The GLO basis set26 was employed, due to limits on computing power, leading to the optimal stabilization energy of -12.2 kcal‚mol-1 at 2.6 Å. An artificial stabilization caused by the GLO basis set, compared to the energy of -5.5 kcal‚mol-1 from the STO-3G set, shows that the potential function needed to be redeveloped. 3.2. Investigation Model. Due to complexity of the ligand, the radial distribution functions (RDFs) between atoms of cyclen and those of water molecules overlap each other. Therefore, the position and orientation of solvent molecules are hard to evaluate. In order to overcome these difficulties, space around cyclen was divided into three regions, top, side, and plane. A picture of this division is shown in Figure 1c, where the side region is the rest of the space after subtracting the total volume
by the top and the plane regions. Consequently, the RDF for each region with respect to center of mass of cyclen has been investigated separately. The notation gxy(r) has been used, where x can be either the ligand’s atoms (C, N, HN, HC, and HC′) or the center of mass of cyclen and y denotes the O or H atoms of the water molecule. In addition, subscript x can be either T, S, P, or E for the RDFs from the center of mass of cyclen to the water molecules situated in the top, side, plane or entire region, respectively. 3.3. The Entire Solvation Shell of Cyclen. In Figure 3, total RDFs referring to the center of the cavity of cyclen, gEO(r)sthe probability of finding oxygen atoms of water in the region E relative to center of mass of cyclensand gEH(r), and the corresponding running integration numbers are depicted. Although the cyclen-water interaction is rather weak, it is clear from this plot that significant solvent structure around the cyclen molecule was observed up to 8-9 Å from the molecular center. However, it is interesting to note here that, due to the disklike structure of the cyclen molecule, some of the long-range structure beyond 7 Å is the contribution of water molecules situated in the first solvation shell and in the molecular plane of cyclen (see section 3.6). Three shells of solvation were exhibited by the three broad gEO(r) peaks, centered at about 2.7, 4.6, and 6.4 Å. Their coordination numbers, integrated up to the corresponding minima of 3.8, 5.1, and 7.9 Å, were 2, 8, and 62 water molecules, respectively. The appearance of the gEH(r) first peak ranging from about 1.4 to 2.8 Å with a coordination number of 2 means that each of the two water molecules corresponding to the gEO(r) first peak point one hydrogen to the center of the cyclen. The other hydrogen atoms of these water molecules were then tilted away from cyclen’s cavity and yielded a pronounced gEH(r) peak between 2.8 and 3.5 Å. Due to a weak cyclen-water interaction, the orientations of hydrogen atoms belonging to water molecules under the second
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Figure 5. Distribution of the angle R, defined in the text, for water molecules situated in the first nearest-neighbor sites of cyclen above and below the ligand plane.
Figure 4. Radial distribution functions and corresponding running integration numbers from O (solid line) and H (dashed line) atoms of water molecules to the center of mass of cyclen for the top, side, and plane regions (see also Figure 1).
and the third gEO(r) peaks are not substantially influenced by the cyclen molecule. Consequently, this causes an overlapping of their hydrogen RDFs and leads to an expanded gEH(r) peak from 3.8 to 8.2 Å. Broadening of all gEO(r) and gEH(r) peaks, as well as nontruncation of all minima, can also be understood from the water-water and cyclen-water interactions, since their magnitudes in the optimum of -5.7 kcal‚mol-1 9 and -5.5 kcal‚mol-1,7 respectively, are rather similar configurations (for the later case, the water molecule lies above molecular plane of cyclen and points one O-H bond to its cavity). For easier monitoring, the three hydration layers around cyclen, corresponding to the first three gEO(r) peaks, are named the nearest-neighbor, inner hydration, and outer hydration shells, respectively. More detailed characteristics of the solution have been extracted from the RDFs with respect to the center of mass of cyclen for separate regions and are plotted in Figure 4. It is clear from these RDFs that the 2 nearest neighbors are located only in the top region, 6 molecules from the inner hydration shell (subtracting the integration number under the second peak of gEO(r) by that under the first one) are mostly in the top region, and 54 outer shell molecules (subtract 62 by 6 and 2) lie in all three regions. Integrating gTO(r) and gSO(r) up to the minimum after the second peak in gEO(r) (5.1 Å) yields coordination numbers of 7.2 and 0.8, respectively. That means that among 6 water molecules in the inner hydration shell (excluding the 2 nearest neighbors), 5.2 of them (subtract 7.2 by the 2 water molecules lying only in the top region) are in the top region. With the same calculations, 54 water molecules in the outer hydration shell include 14.7, 31.3, and 8.0 molecules from the top, side, and plane regions, respectively. As it is known that the ab initio pair potential is parametrized on the basis of the gas phase dipole moments. Several attempts
have been made in inclusion of the polarization effect, up to quadrupole moments, in the liquid phase simulations.27-32 The results show that this effect leads to an increase of the molecular dipole moments and, consequencely, more pronounced RDFs and the decrease of the dynamic properties. In addition, change of the coordination numbers has never been reported. This indicates clearly the reliability of the hydration picture observed in this study. 3.4. The Nearest Neighbors of Cyclen. A comprehensive investigation of the precise orientation of the two molecules nearest to the cyclen molecule has been made by computing the distribution of the angle R, formed by the dipole moment vector of the water molecule and a vector pointing from the oxygen atom to center of cavity of cyclen. The results are displayed in Figure 5. A pronounced peak with a maximum of 49° signifies that the two nearest neighbors approach the ligand from opposite sides by pointing one O-H bond to the ligand’s cavity (an exact value where the O-H bond lies on the z-axis is 52.25°; see Figure 1). Coordinates of hydrogen atoms of the two water molecules which do not point to cyclen’s cavity have been projected onto the xy-plane and are plotted in Figure 6, in order to examine their orientation and rotation around the z-axis (see Figure 1). The base of the plot denotes cyclen’s molecular plane. The xy-coordinates of the four hydrogen atoms of the NH functional groups of cyclen are marked by arrows, where two of them are above and the other two are below the ligand plane. The densities, above and below the plane, represent probability densities of the hydrogen for the water molecules above and below the plane, respectively. It is clear from this plot that the favorite orientation of the nearest neighbors of cyclen is to point the dipole moment (or one O-H bond) as far as possible from the opposite NH groups; i.e., one of the O-H bond lies in the plane perpendicular to the vector pointing from one to the opposite NH group. During the whole run, eight million configurations sampled every 500 configurations, rotation around the z-axis was not detected. 3.5. The Inner Hydration Shell of Cyclen. Since the NH functional groups of cyclen are expected to be solvated by water molecules due to their hydrophilicities, RDFs with respect to the NH functional group have been considered. The calculated gNO(r), gNH(r), gHNO(r), and gHNH(r) and the corresponding coordination numbers have been drawn in Figure 7. The gNO(r) shows a sharp first peak at 2.98 Å, and the running integration number up to the first minimum of 3.32 Å is 1.2. Since distances from the N atoms (of cyclen) to O atoms (of water) of 2.98 Å are identical to those from the N atoms to points lying on the z-axis at z ) (2.69 Å (see Figure 1), the
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J. Phys. Chem., Vol. 100, No. 44, 1996 17659
Figure 8. Distribution of the angle β, defined in the text, for water molecules lying not further than 3.32 Å (first minimum of gNO(r) shown in Figure 7) from the N atom of cyclen.
Figure 6. Projection onto the xy-plane of one of the hydrogen coordinates, which is not pointing toward the ligand cavity (see the attach of Figure 5), of water molecules situated in the first nearestneighbor sites of cyclen. Locations of the four NH functional groups of cyclen above and below the ligand plane are denoted by arrows. Positive and negative density are for atoms above and below the plane, respectively.
Figure 9. Projection of oxygen coordinates of water molecules which lie above the ligand plane and within the O-O distance of 3.5 Å from the nearest neighbor of cyclen onto the xy-plane. The location of the two NH functional groups of cyclen, those lying above the ligand plane, are denoted by arrows.
Figure 7. Radial distribution functions and corresponding running integration numbers from O (solid line) and H (dashed line) atoms of water molecules to N and H atoms of cyclen.
appearance of the first gNO(r) peak is clearly a contribution from the two water molecules in the nearest-neighbor shell. Further confirmation of this conclusion is demonstrated by the distribution plot given in Figure 8, where angle β is defined by the N-H bond and the vector pointing from the nitrogen atom of cyclen toward the oxygen atom of water, which situated under the gNO(r) first peak. The angle β of 65°, where a sharp maximum takes place, is equivalent to that where the oxygen atom is on the z-axis at z ) (2.56 Å, i.e., the coordination sites of the two nearest neighbors. The small and well-defined peak in gNH(r) at 2.32 Å of the gNH(r) with the integration number up to the next minimum of 0.8 can then be assigned to contribution from the hydrogen atoms of the two central water molecules pointing to the ligand’s cavity. Considering the gNO(r) second peak centered at about 3.7 Å, the integration number up to the broad minimum at 3.90 Å is
3.0. Two water molecules around each NH functional group (excluding one nearest-neighbor molecule) are surely not coordinated to the NH groups via hydrogen bonds. The reasons for this is that the peak is not well defined and at this distance hydrogen bonding will not take place. A conclusion which seems secure is to tentatively assign them to the first coordination shell of the nearest-neighbor water molecules. To reveal the geometrical arrangement of these water molecules, the coordinates of oxygen atoms which lie above xy-plane and within an O-O distance of 3.5 Å (a value taken from first minimum of the O-O RDF of water) from the nearest-neighbor water molecule have been projected into the xy-plane. The result is shown in Figure 9, where xy-coordinates of the two hydrogen atoms of the NH functional groups of cyclen that are located above the ligand plane are denoted by arrows. Some useful information can be extracted from the probability density plot, showing a set of three maxima with xy-coordinates of {+,+}, {-,+}, and {-,-}. (i) These three water molecules are in the first solvation shell of the nearest-neighbor water molecule, as they are within the first minimum of the gOO(r) of water. (ii) The nearest-neighbor water molecule points one hydrogen atom to form a hydrogen bond with the water molecule which is located in the {-,-} quadrants, as the probability densities of both coordination sites (hydrogen atom of the former water molecule and oxygen atom of the latter) lie at similar
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Figure 10. Proposed model for the solvation of cyclen in aqueous solution.
locations (the maxima at xy-coordinates {-,-} in Figures 6 and 9). (iii) Two water molecules, centered at the locations {+,+} and {-,+}, coordinate to the nearest-neighbor water molecule via hydrogen bonds but do not coordinate to the NH functional groups, since the N-O distance of about 3.7 Å (distance to the gNO(r) second peak shown in Figure 7) is too far to form hydrogen bonds. However, the hydrophilic nature of the NH groups, which are very close to these two maxima (Figure 9), will help to stabilize the hydrogen bonds mentioned in (iii). (iv) Due to this fact, the two hydrogen bonds stated in (iii) are more stable than that in (ii). This is exhibited by more pronounced maxima than for the {-,-} peak. Taking into account all the above data, the position and orientation of all water molecules in the nearest-neighbor and inner hydration shells of cyclen have been sketched in Figure 10. It is now possible to clearly assign that the three molecules up to the minimum of gNO(r) at 3.9 Å arise from the nearestneighbor water molecule, the molecules at xy-coordinate {-,-}, and that lying close to each NH group (see Figure 9). 3.6. The Outer Hydration Shell of Cyclen. According to the clear picture of geometrical arrangements of the two water molecules in the nearest-neighbor and the six molecules in the inner solvation shell of cyclen (which is more precisely the first coordination shell of the first two molecules), it is now possible to state definitely that the outer hydration shell of cyclen (third peak of gEO(r) plotted in Figure 3) is a combination of the third hydration shell above or below the ligand plane (top and side regions) and the first hydration shell around the CH2 functional groups. The RDFs with respect to C, HC, and HC′ shown in Figure 11 are quite broad, indicating hydrophobicity of the CH2 groups. However, the existence of a peak structure proves that the cyclen molecule still influences the solvent structure significantly, also at larger distances from the CH2 groups. The outer hydration shell takes place at a large distance and includes a larger number of water molecules. Also the cyclenwater interaction, especially around the CH2 groups, is very weak. These factors lead to the overlap of the RDFs from all centers. Therefore, orientational information cannot be readily extracted for this hydration sphere. 3.7. Comments on the Macrocyclic Effect. Only two water molecules were found to attach to the cyclen molecule (L). Suppose that cyclen’s open-chain analog (L′) was solvated by four water molecules while complexes of both cyclic (MLn+)
Figure 11. Radial distribution functions and corresponding running integration numbers from O (solid line) and H (dashed line) atoms of water molecules to C, HC, and HC′ atoms of cyclen (see text for details).
and open-chain ligands (ML′n+) were solvated by the same number of water molecules, y. Then the exchange reactions are +
+
M(H2O)nx + L(H2O)2 f ML(H2O)ny + (x + 2 - y)H2O (2) +
+
M(H2O)nx + L′(H2O)4 f ML′(H2O)ny + (x + 4 - y)H2O (3) where x is the coordination number of the n-fold charged cation (Mn+) and y is expected to be lower than 4.1,2 It is obviously seen that more water molecules, x + 4 - y, have to be removed from the hydration shell of the open chain than from the cyclic ligands during complexation. This is in good agreement with the argument originally reported by Paoletti and Hancock3,4 that the space around the cyclic ligand can accommodate less water in comparison with the open-chain analog. In terms of enthalpic contribution, it is not clear whether the energy required for breaking some hydrogen bonds could lead to the higher stability of the L than the L′ complexes on the order of a million times. Considering the entropic change during complexation of both the solvent and the ligand, the former one is expected to increase for both cyclic and open-chain ligands due to the formation isolated species. The latter parameter, the entropic change of open-chain ligand, is clearly higher than that of cyclic ligand which is already in the geometry suitable for complexation. However, Margerum and co-workers33,34 have reported that the difference in the total entropic change according to the exchange reactions 2 and 3, where L and L′ are 1,4,8,11-tetraazacyclododecane and its open-chain analogs, is 16 cal K-1 or 4.8 kcal‚mol-1 at 298 K. This value is estimated tentatively to be equivalent to or slightly less than enthalpic requirement for
Solvation of Cyclen in Aqueous Solution breaking some hydrogen bonds between the open-chain ligand and water molecules. Taking into account the data given above, it seems secure to conclude according to our results that the entropic and enthalpic contributions (solVation effect) partially support the existence of the macrocyclic effect. Acknowledgment. Financial support from the Computational Chemistry Unit Cell by Chulalongkorn University and the generous supply of computer time by the Austrian-Thai Center for Computer-Assisted Chemical Education and Research, in Bangkok, are gratefully acknowledged. The author thanks Dr. David Ruffolo for proofreading the manuscript and for helpful comments. References and Notes (1) Carbiness, D. K.; Margerum, D. W. J. Am. Chem. Soc. 1969, 91, 6540. (2) Carbiness, D. K.; Margerum, D. W. J. Am. Chem. Soc. 1970, 92, 2151. (3) Fabbrizzi, L.; Paoletti, P.; Lever, A. B. P. Inorg. Chem. 1980, 15, 1502. (4) Hancock, R. D.; McDougall, G. J. J. Am. Chem. Soc. 1980, 102, 6551. (5) Smith, G. H.; Margerum, D. W. J. Chem. Soc., Chem. Commun. 1975, 807. (6) Ohtaki, H.; Seki, H. J. Macromol. Sci., Chem. 1990, A27, 1305. (7) Udomsub, S.; Hannongbua, S. Submitted for publication. (8) Hannongbua, S.; Ishida, T.; Spohr, E.; Heinzinger, K. Z. Naturforsch. 1988, 43a, 572. (9) Kheawsrikul, S.; Hannongbua, S.; Kokpol, S. U.; Rode, B. M. J. Chem. Soc., Faraday Trans. 2 1989, 85, 643.
J. Phys. Chem., Vol. 100, No. 44, 1996 17661 (10) Hannongbua, S. Aust. J. Chem. 1991, 44, 447. (11) Khewsrikul, S.; Hannongbua, S.; Rode, B. M. Z. Naturforsch. 1991, 46a, 111. (12) Hannongbua, S.; Rode, B. M. Chem. Phys. 1992, 162, 257. (13) Hannongbua, S.; Kerdcharoen, T.; Rode, B. M. J. Chem. Phys. 1992, 96, 6945. (14) Hannongbua, S.; Rode, B. M. J. Chem. Soc., Faraday Trans. 2 1986, 82, 1021. (15) Benedict, W. S.; Gailar, N.; Plyler, E. K. J. Chem. Phys. 1956, 24, 1139. (16) Hannongbua, S.; Rode, B. M. Inorg. Chem. 1985, 24, 2577. (17) Rode, B. M.; Hannongbua, S. Inorg. Chim. Acta 1985, 96, 91. (18) Gaussian 92/DFT, ReVision F.4; Gaussian, Inc.: Pittsburgh, PA, 1993. (19) Mulliken, R. S. J. Chem. Phys. 1955, 23, 1833, 1841, 2338, 2343. (20) Hannongbua, S.; Rode, B. M. J. Sci. Soc. Thailand 1986, 11, 135. (21) Bolis, G.; Clementi, E. J. Am. Chem. Soc. 1977, 99, 5550. (22) Jorgenson, W. L.; Cournoyer, N. E. J. Am. Chem. Soc. 1978, 100, 4942. (23) Matsuoka, O.; Clementi, E.; Yoshimine, M. J. Chem. Phys. 1978, 64, 1351. (24) Benedict, W. S.; Plyler, E. K. Can. J. Phys. 1957, 35, 1235. (25) Hannongbua, S.; Rode, B. M. Z. Naturforsch. 1985, A40, 644. (26) Ahlrichs, R. Theor. Chim. Acta (Berlin) 1974, 33, 157. (27) Ahlstroem, P.; Wallqvist, A.; Engstroem, S.; Joenssen, B. Mol. Phys. 1989, 68, 563. (28) Rullman, J. A. C.; van Duunen, P. Th. Mol. Phys. 1988, 63, 451. (29) Cailliol, J. M.; Levesque, D.; Weis, J. J.; Perxyns, J. S.; Patey, G. N. Mol. Phys. 1987, 62, 1225. (30) van Belle, D.; Couplet, I.; Prevost, M.; Wodak, S. J. J. Mol. Biol. 1987, 198, 721. (31) Weber, T. A.; Stillinger, F. H. J. Phys. Chem. 1982, 86, 1314. (32) Goodfellow, J. M. Proc. Natl. Acad. Sci. U.S.A. 1982, 79, 4977. (33) Hinz, P. F.; Margerum, D. W. Inorg. Chem. 1974, 2941. (34) Hinz, P. F.; Margerum, D. W. J. Am. Chem. Soc. 1974, 96, 4993.
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