A Molecular Mechanics Method for Predicting the Influence of Ligand

Chapter 6

Downloaded by PRINCETON UNIV on November 14, 2014 | http://pubs.acs.org Publication Date: February 11, 1999 | doi: 10.1021/bk-1999-0716.ch006

A Molecular Mechanics Method for Predicting the Influence of Ligand Structure on Metal Ion Binding Affinity Benjamin P. Hay Environmental Molecular Sciences Laboratory, Pacific Northwest National Laboratory, Richland, WA 99352 This paper presents a molecular mechanics method for the quantitative analysis of ligand binding site organization for metal ion complexation. For series of polydentate ligands bearing a constant number and type of donor atom, the method can be used to identify the connectivity that will yield the highest affinity for a given metal ion. The utility of the method is demonstrated through correlations of alkali and alkaline earth cation binding affinities with the ligand strain energies for five series of multidentate ether ligands.

A new methodology for the application and interpretation of molecular mechanics calculations in the structural design of ligands has been described recently (i). In this paper, this molecular mechanics methodology is used to analyze the differences in metal ion binding affinity for five series of polydentate ligands. These ligand series were selected for two reasons. First, each series of ligands consists of members that contain the same number of ligating donor groups, but vary in the way that the donors are connected together. Second, relative metal ion binding affinities have been determined for each series of ligands under a constant set of experimental conditions providing a consistent set of data for the comparison. Under such constraints, it is reasonable to expect that differences in metal complexation would largely result from structural factors. Correlations between metal ion binding affinity and ligand strain will demonstrate this to be so. A Description of the Methodology Complexation of a metal ion to a ligand often causes changes to the ligand's struc ture that introduce steric strain within the ligand. A design criterion for ligands that will complex metal ions more strongly is to choose a ligand structure that minimizes this strain, that is, ligands that are sterically efficient (2). In the approach described here, molecular mechanics calculations are used to define the degree of ligand binding site organization in terms of two ligand strain energies. This involves a consideration of two types of structural change: conformational reorganization and distortion of the binding conformer. The conformational mobility of the ligand can affect both its metal ion selectivity and binding affinity. As a result, the imposition of conformational constraints is an 102

©1999 American Chemical Society

In Metal-Ion Separation and Preconcentration; Bond, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.

103 often-cited criterion for metal-selective ligand design (2-6). Many ligands exhibit more than one conformer (different conformers are distinguished by gross changes to torsion angles, e.g., from gauche to anti). Different conformers of the same ligand can possess quite different cavity sizes and shapes. In such cases, the metal ion selectivity of the ligand will be compromised if different conformers prefer different metal ions. In addition, if the ligand prefers one conformer when uncomplexed and a different conformer when in a metal complex, then the ligand must undergo a conformational reorganization to form the metal complex. This process costs energy, which can significantly lower the observed binding affinity. The strain energy associated with this conformer change can be quantified with molecular mechanics calculations. Herein, the quantity AU is a strain energy defined as the change in ligand steric energy as it goes from the preferred uncomplexed conformer to the binding conformer. Further destabilizing ligand strain may occur on metal ion complexation to the binding conformer. Structural distortion may result from movements of the ligand donor atoms in an attempt to satisfy metal ion - donor atom distance preferences (cavity size mismatch (2,3,6)), stereoelectronic preferences of the metal ion (topology mismatch (4,6,7)), or ligand donor atom geometry requirements (lone pair and/or dipole misalignment (2,8)). The degree of structural distortion to the binding conformation upon metal ion complexation provides a measure of the ligand's complementarity for the metal ion (1). The principle of complementarity as originally stated is, "to complex, hosts must have binding sites which cooperatively contact and attract binding sites of guests without generating strong nonbonded repulsions" (9). A ligand with perfectly complementary binding sites will not experience unfavorable steric interactions (neither strong nonbonded repulsions nor distortions from preferred bond lengths, bond angles, and torsion angles) as a result of complexation. Metal ion complexation to noncomplementary binding sites will cause distortions to the ligand structure. This generates steric strain within the ligand. Herein, the quantity A U is a strain energy defined as the change in ligand steric energy as it goes from the uncomplexed binding conformer to the metal complex. The sum of the two structural reorganization components is defined as the ligand's reorganization energy, AU = AU + A U . This quantity is a molecular mechanics strain energy that provides a quantitative measurement of the degree of a ligand's binding site organization for metal ion complexation. Ligands that are poorly organized for binding will exhibit large AU values; ligands highly organized for binding will exhibit small A U values. A figand that is perfectly organized for binding, that is, constrained to a binding conformation with comp lementary sites, would exhibit a AU of zero.


conf

comp

reorg

conf

comp

reorg

reorg

Computational Methods Molecular mechanics calculations were conducted with the MM3(96) program (10) using an extended parameter set developed and extensively validated for ethers and their complexes with the alkali and alkaline earth cations (11-13). Conformations for the free ligands and their metal complexes were taken from crystal structure data where available. In the absence of crystal structure data, minimum steric energy conformations were determined by conformational searches using methods described elsewhere (14-16). Values of AU reported are the sum of AU and A U as defined above. In cases where no conformational reorganization is observed, A U is zero. Otherwise, A U is calculated as the difference in steric energy between the uncomplexed ligand conformer and the binding conformer of the ligand. A U is calculated as the difference in steric energy between the binding conformer and the bound ligand. The latter quantity is computed by (i) optimizing the metal ion complex, (ii) removing the metal ion, and (iii) obtaining the initial energy of the resulting structure. reorg

conf

comp

conf

conf

comp


104 Results and Discussion Potassium Formation Constants with Hexadentate Crown Ethers. The first series of ligands (1-11, Figure 1) were examined in a prior molecular mechanics study (17). Formation constants for potassium complexes (equation 1) have been reported for each of the ligands in the same solvent and at the same temperature (methanol solvent, 25 °C), providing a consistent set of data for comparison (18). These formation constants (log Κ values, Figure 1) span four orders of magnitude. +


K +L

KL

+

(1)

In the prior study (77), a linear correlation was obtained by plotting log Κ values against the difference in steric energy between the uncomplexed ligand and the potassium complex. Following the current methodology, AU values (see Figure 1) have been computed for potassium complexation by 1 -11 using conformations from ieorg

ο

ο

ο

1(6.1,3.98)

0 * ° ^ ° ^

ο

ο

ο

2(6.0,3.34)

0

^ Ύ

ο

^

ο

4 (5.4,4.07)

C

ο

0

3(5.9,4.01)

^

ο

ρ

5 (5.2,4.48)

ο.

.ο

J

C

7(4.0,5.88)

ο.

j

8(3.8,6.52)

k.O^

OH

10(2.6,8.20)

ο

ο

6 (4.1, 5.52)

Η

o

> o

9(3.3,6.91)

k.O^ 11(1.7,8.74)

Figure 1. Series of eleven hexadentate ether ligands. Parentheses contain the log Κ value and AU (kcal/mol) for potassium complexation, respectively. reorg


105 the prior study. A similar correlation is obtained when the log Κ values are plotted against AU values (Figure 2). In the AU values for 1 -11, the majority of the ligand strain occurs in the AU term. Structural distortions of the binding conformer on metal complexation result primarily from attempts to achieve preferred trigonal planar ether oxygen geometry rather than attempts to achieve preferred K-0 distances (11). For example, while 1 has a cavity that gives near optimal K-0 distances, the C-O-C groups do not point to the center of the cavity. In the D conformation, the oxygens are positioned alternately above and below the plane of the ring. When potassium occupies the cavity, the oxygens all move in such a way as to be more in the plane of the macrocycle, that is, to attempt to achieve trigonal planar geometries with respect to the metal ion. This structural change generates 3.98 kcal/mol of destabilizing ligand strain. Thus, the D conformation of 1 does not provide an optimum arrangement of ether donor groups for potassium complexation. Extrapolation of the linear correlation in Figure 2 to a A U value of zero suggests that a ligand with an optimum arrangement of six ether oxygen donor groups would exhibit a log Κ value of 8.8 in methanol, that is, a binding constant nearly three orders of magnitude higher than that of 1. reorg

comp


3d

3d

reorg

Figure 2. Plot of log Κ versus A U for potassium complexation by hexadentate ether ligands shown in Figure 1 (r = 0.986). reorg

Lithium Extraction Constants with 14-Crown-4 Derivatives. The second series of ligands (12 -16, Figure 3) consists of a set of five 14-crown-4 derivatives that differ in the alkylation of the ethylene and propylene bridges. Thermodynamic equilibrium constants (equation 2) have been determined for the transfer of Li C10 "from aqueous solution to nitrobenzene (Moyer, Β. Α.; Sachleben, R. Α., Oak Ridge National Laboratory, unpublished results). These extraction constants (log K values, Figure 3) span two orders of magnitude. +

4

ex

Li

+ (aq)

+ C10

4

(aq)

+ L

(org)

LiL

+ (0rg)

+ ClO 4

(0rg)


(2)

106

Λ ο c U

12(0.81,5.27)

13(0.10,7.94)

14 (-0.31,8.93)

αΡ0:ο


QO^OJO

15 (-1.1,10.99)

16 (-1.3,10.65)

Figure 3. Series of five 14-crown-4 ligands. Parentheses contain the log K value and AU (kcal/mol) for lithium complexation, respectively.

ex

reorg

Values of AU were calculated for this series (see Figure 3). In this case, con formations for the uncomplexed ligands 12 -16 and for lithium complexes with 12 15 were taken from crystal structures (19-21). A conformational search was performed to locate the lowest steric energy lithium complex for 16. A plot of log K versus AU (Figure 4) provides a second example of how ligand strain correlates with metal ion binding affinity. reorg

ex

rçorg

£

0

ο

AUreorg Figure 4. Plot of log K versus AU for lithium complexation by the 14-crown-4 ligands shown in Figure 3 (r = 0.978). e x

reorg


107 In 12 -16 both AU and A U contribute to the AU values. In all cases the ligand undergoes a conformational change prior to lithium complexation. The highest log K occurs with 12, which exhibits the lowest AU (0.97 kcal/mol), while the lowest log values occur with 15 and 16, which exhibit the highest values of AU (3.88 and 6.43 kcal/mol, respectively). In addition to the ligand strain associated with conformational reorganization, lithium complexation to the binding conformer adds from 4.30 to 6.77 kcal/mol additional ligand strain in the A U term. In the 14crown-4 binding conformation, the lithium perches atop the four oxygens, and no change in ligand structure is required to attain preferred Li-0 distances. Thus, as with the previous example, the A U contribution primarily results from ligand distortion as the four ether donors attempt to achieve their desired orientation with respect to lithium. Extrapolation of the linear correlation in Figure 4 to a A U value of zero suggests that a ligand with an optimum arrangement of four ether donor groups would exhibit a log K value of 2.8 under these conditions, that is, an extraction constant two orders of magnitude higher than that of the current best member of the series, 12. conf

comp

reorg

ex

conf

ponf

comp

comp


reorg

ex

Lithium Formation Constants with 14-crown-4 Derivatives. The third series of ligands (17 - 21, Figure 5) is a set of five 14-crown-4 derivatives that differ in the alkyl substitution on one ethylene bridge. Solvent extraction studies showed that the extraction efficiency for lithium decreased in the order 17 > 18 > 19 > 20 > 21 (22). Formation constants for lithium complexation by 18 - 21 (equation 3) were determined in cyclohexanone at 80 °C (22). The ordering of the formation constants (log K, Figure 5), which span nearly two orders of magnitude, parallels that of the extraction efficiencies. +

Li + L

LiL

+

(3)

Values of AU were calculated for this series (see Figure 5). In the absence of crystal structure data, conformer searches were performed to identify the low energy forms of the uncomplexed ligands and their lithium complexes. A plot of log Κ versus A U ^ (Figure 6) provides a third example of how ligand strain correlates with metal ion binding affinity. Although a log Κ value was not reported for the ligand with the lowest AU , 17, calculation results are consistent with the observation that 17 gives the highest extraction efficiency for this series. The correlation shown in Figure 6 yields an estimate of log Κ = 4.5 for lithium complexation by 17 in cyclo hexanone at 80 °C. reorg

reorg

Φ /-O

OOO Ο Ο

O-^

O-v

\_J 17 (n.a., 6.43)

r-0

\-J 18 (3.8,7.04)

Ο-Λ

r-O

r-0

O-^

\—/ 19 (3.7,7.93)

O-v

\ ι \ / 20(2.6,8.99) 21(2.1,9.70) i Figure 5. Series of five 14-crown-4 ligands. Parentheses contain the log Κ value and AU (kcal/mol) for lithium complexation, respectively. reorg



108

Strontium Distribution Coefficients with Dicyclohexano-18-Crown-6 Derivatives. The fourth series of ligands (22 - 26, Figure 7) are a set of five dicyclohexano18-crown-6 derivatives that differ in the stereochemistry of the cyclohexyl rings and the placement of t-butyl substituents. Distribution coefficients (equation 4) have been determined for strontium extraction from 1 M nitric acid to 1-octanol (Dietz, M . L., Argonne National Laboratory, unpublished results). The distribution coefficients (log D , Figure 7), which span two orders of magnitude, were determined under identical conditions (solvent composition, reagent concentrations, and temperature) and were corrected for the formation of aqueous phase complexes. Sr

Ds^lS^KorgyiS^Kaq)

(4)

Values of A U were calculated for this series (see Figure 7). Conformer searches were performed to identify the low energy forms of the uncomplexed ligands and their strontium complexes. In the case of 24 and 25, calculated global minimum conformations for both the free ligands and their strontium complexes are fully consistent with available crystal structure data (23-34). A plot of log D versus AU (Figure 8) provides a fourth example of how ligand strain correlates with metal ion binding affinity. In 22 - 26 both AU and A U contribute to the AU values. However, in all cases, it is the A U term that dominates and, as with the potassium complex of 1, structural distortion to the binding conformer arises primarily from attempts to meet the preferred planar orientation of the ether donor groups. Extrapolation of the linear correlation in Figure 8 to a A U value of zero suggests that a ligand with an optimum arrangement of six ether donor groups would exhibit a log D value of 6.8 under these conditions, that is, a D value five orders of magnitude higher than that of the current best member of the series, 22. reorg

sr

reorg

conf

comp

reorg

comp

reorg

Sr

Sr


109

Κ, ο


22 (0.88,10.67)

Q

ο

ο ο

23 (0.42, 11.59)

Ο.

ο

Ο

ο ο-^ ο ο

Ο

24 (0.55,11.53)

α

25 (0.11,11.92)

Ω c 1 ο ο

ο

ft 26 (-1.54,15.03)

Figure 7. Series of five dicyclohexano-18-crown-6 ligands. Parentheses contain the log D value and A U for strontium complexation, respectively. Sr

reorg


110 Sodium Formation Constants with Hexadentate Polyether Ligands. The fifth collection of ligands (27 - 34, Figure 9) is a set of eight hexadentate polyethers bearing combinations of aliphatic and methoxyaryl ether donors. Formation con stants for sodium complexation (equation 5) were determined in water-saturated chloroform (9,35-37). These formation constants (log Rvalues, Figure 9) span ten orders of magnitude. +

Na picrate" + L = ^

+

(NaL) picrate"

Values of AU were calculated for this series (see Figure 9). With the exception of 27, for which there are crystal structures of the free ligand and the sodium complex (38), conformer searches were performed to identify the low energy forms of the uncomplexed ligands and their sodium complexes. A plot of log Κ versus AU (Figure 10) provides a fifth example of how ligand strain correlates with metal ion binding affinity. reorg


(5)

reorg

27 (14.1, 0.94)

30 (8.6,4.72)

32 (5.7, 8.33)

28 (9.9, 3.35)

29 (9.2,4.54)

31 (7.2,7.85)

33 (5.1, 9.29)

34 (3.4, 9.98)

Figure 9. Series of eight hexadentate ether ligands. Parentheses contain log Κ and AU (kcal/mol) for sodium complexation, respectively.



Ill

The correlation shown in Figure 10 strongly suggests that the different sodium binding affinities observed with this series of ligands are primarily due to steric rather than electronic effects. From this result it may be inferred that the two types of ether donor groups that occur in these ligands (i.e., aliphatic and conjugated), have a similar Lewis basicity. This inference is supported by the measured gas phase proton affinities for ethoxyethane (200.3 kcal/mol) and methoxybenzene (200.2 kcal/mol) (39). While the modeling results indicate that the weakest ligands, 32 - 34, undergo conformational reorganization prior to binding, 27 - 31 do not. In all cases, it is the AU term that makes the largest contribution to AU^ . Unlike the preceding crown ether examples, ligand structural distortion on sodium complexation is caused by attempts to satisfy both Na-0 distance and oxygen orientational preferences. This difference is caused by the fact that in 27 - 34 the metal ion resides in the center of a three-dimensional cavity that is not always sized correctly, whereas in 1-26, the metal ions examined in this study either fit nicely within the two-dimensional cavity (K and Sr"*") or perch above it (Li ). Ligand 27, often cited for its high degree of preorganization, exhibits the lowest value of AU observed of the 34 cases examined in this study, 0.94 kcal/mol. The correlation in Figure 10 suggests that it is not possible to achieve significant further enhancement of sodium binding affinity by altering the connectivity of six ether donor groups. comp

+

org

2

+

Conclusions For the polyether ligands examined in this study, ligand strain may arise from both conformational reorganization and structural distortion of the binding conformer. The latter component is always present and is often the major contribution to the ligand strain. With the alkali and alkaline earth cations, structural distortion of the binding conformer occurs as the ligand attempts to satisfy M-O distance preferences In Metal-Ion Separation and Preconcentration; Bond, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.


112 and oxygen orientation preferences. As noted elsewhere (11), in crown ethers such as 1 - 26, it is the attempt to achieve trigonal planar oxygen geometry (i.e., the attempt to align the ether dipoles with the metal ion) that is the major cause of the structural distortion. Therefore, an important criterion in ligand design for enhanced complex stability is to choose a connecting structure that provides the preferred orientation of the donor atoms with respect to the metal ion. When the binding conformation fails to provide preferred donor atom geometries, significant decreases in complex stability will result. The ethylene bridges that occur in the majority of polydentate ethers prevent the oxygen donor groups from achieving their preferred trigonal planar geometries (1,8). It can be concluded that the design of polydentate ether ligands to achieve the highest metal ion binding affinity must involve the use of other connecting structures, for example, the methoxyaryl groups in 27. This paper has presented a molecular mechanics method for the assessment of the degree of ligand binding site organization for metal ion complexation. The method involves the determination of ligand strain incurred on complexation of a metal ion. The five examples presented here demonstrate that the quantity A U is a very useful tool in predicting the relative metal ion binding affinity for series of polyether ligands bearing the same number of donor groups. reorg

Acknowledgments This research was supported in part by the Efficient Separations and Processing Crosscutting Program of the Office of Science and Technology, within the U. S. Department of Energy's Office of Environmental Management, and in part by the Environmental Management Science Program under direction of the U . S. Department of Energy's Office of Basic Energy Sciences (ER-14), Office of Energy Research and the Office of Science and Technology (EM-52), Office of Environmental Management. Pacific Northwest National Laboratory is operated for the U. S. Department of Energy by B attelle Memorial Institute under Contract DEAC06-76RLO 1830. Literature Cited (1) (2) (3) (4) (5)

Hay, B. P.; Zhang, D.; Rustad, J. R. Inorg. Chem. 1996, 35, 2650. Hancock, R. D.; Martell, A. E. Chem. Rev. 1989, 89, 1875. Cram, D. J. Angew. Chem., Intl. Engl. Ed. 1986, 25, 1039. Potvin, P. G.; Lehn, J.-M. Prog. Macrocycl. Chem. 1987, 3, 167. Garrett, T. M.; McMurray, T. J.; Hosseini, M . W.; Reyes, Z. E.; Hahn, F. E.; Raymond, Κ. N. J. Am. Chem. Soc. 1991, 115, 2965. (6) Busch, D. H. In Transition Metals in SupramolecularChemistry;Fabbrizzi, L.; Poggi, A. D., Eds.; Kluwer Academic Publishers: Dordrecht, The Netherlands, 1994,p55. (7) Pletnev, I. V. Russ. J. Coord. Chem. 1996, 22, 333. (8) Hay, B. P.; Rustad, J. R. Supramol. Chem. 1996, 6, 383. (9) Cram, D. J.; Lein, G. M . J. Am. Chem. Soc. 1985, 107, 3657. (10) The program may be obtained from Tripos Associates, 1699 S. Hanley Road, St. Louis, MO 63144 for commercial users, and it may be obtained from the Quantum Chemistry Program Exchange, Mr. Richard Counts, QCPE, Indiana University, Bloomington, IN 47405, for non-commercial users. (11) Hay, B. P.; Rustad, J. R. J. Am. Chem. Soc. 1994, 116, 6316. (12) Hay, B. P.; Yang, L.; Lii, J.-H.; Allinger, N. L. THEOCHEM, J. Mol. Struct. 1997, in press. (13) Hay, B. P.; Yang, L.; Zhang, D.; Rustad, J. R.; Wasserman, E. THEOCHEM, J. Mol. Struct. 1997, in press. In Metal-Ion Separation and Preconcentration; Bond, A., et al.; ACS Symposium Series; American Chemical Society: Washington, DC, 1999.


113 (14) Hay, Β. P.; Rustad, J. R.; Zipperer, J. P.; Wester, D. W. THEOCHEM, J. Mol. Struct. 1995, 337, 39. (15) Paulsen, M. D.; Hay, B. P. THEOCHEM, J. Mol. Struct. 1997, in press. (16) Paulsen, M. D.; Rustad, J. R.; Hay, B. P. THEOCHEM, J. Mol. Struct. 1997, in press. (17) Hay, B. P.; Rustad, J. R.; Hostetler, C. J. J. Am. Chem. Soc. 1993, 115, 11158. (18) Izatt, R. M . ; Bradshaw, J. S.; Nielsen, S. Α.; Lamb, J. D.; Christensen, J. J. Chem. Rev. 1991, 91, 1721. (19) Buchanan, G. W.; Kirby, R. Α.; Charland, J. P. J. Am. Chem. Soc. 1988, 110, 2477. (20) Burns, J. H.; Sachleben, R. Α.; Davis, M. C. Inorg. Chim. Acta 1994, 223, 125. (21) Sachleben, R. Α.; Burns, J. H. J. Chem. Soc., Perkin Trans. 2 1992, 1971. (22) Kohiro, K.; Kaji, M.; Tsuzuke, S.; Tobe, Y.; Tuchiya, Y.; Naemura, K.; Suzuki, K. Chem. Lett. 1995, 831. (23) Burns, J. H.; Bryan, S. A. Acta Cryst., Sect. C 1988, 44, 1742. (24) Damewood, J. R., Jr.; Urban, J. J.; Williamson, T. C.; Rheingold, A. L. J. Org. Chem. 1988, 53, 167. (25) Dvorkin, Α. Α.; Fonar, M . S.; Malinovskii, S. T.; Ganin, Ε. V.; Simonov, Υ. Α.; Makarov, V. F.; Kotlyar, S. Α.; Luk'yanenko, N. G. Zh. Strukt. Khim. 1989, 30, 96. (26) Dvorkin, Α. Α.; Simonov, Υ. Α.; Suwinska, K.; Lipowski, J.; Malinovskii, T. I.; Ganin, Ε. V.; Kotlyar, S. A. Kristallografiya 1991, 36, 62. (27) Dvorkin, Α. Α.; Fonar, M . S.; Ganin, Ε. V.; Simonov, Υ. Α.; Musienko, G. S. Kristallografiya 1991, 36, 70. (28) Fonar, M. S.; Simonov, Υ. Α.; Dvorkin, Α. Α.; Malinovskii, Τ. I.; Ganin, Ε. V.; Kotlyar, S.; Makarov, V. F. J. Inclusion Phenom. Molec. Recognit. Chem. 1989, 7, 613. (29) Fraser, M. E.; Fortier, S.; Markiewicz, M . K.; Rodrigue, Α.; Bovenkamp, J. W. Can. J. Chem. 1987, 65, 2558. (30) Krasnova, N. F.; Dvorkin, Α. Α.; Simonov, Y. Α.; Abashkin, V. M.; Yakshin, V. V. Kristallografia 1985, 30, 86. (31) Krasnova, N. F.; Simonov, Y. Α.; Bel'skii, V. K.; Fedorova, A. T.; Yakshin, V. V. Kristallografiya 1986, 31, 1099. (32) Navaza, Α.; Villain, F.; Charpin, P. Polyhedron 1984, 3, 143. (33) Rath, N. P.; Holt, Ε. M. J. Chem. Soc., Chem. Commun. 1986, 311. (34) Simonov, Y. Α.; Malinovskii, T. I.; Ganin, Ε. V.; Kotlyar, S. Α.; Bocelli, G.; Calestani, G.; Rizzoli, C. J. Inclusion Phenom.Molec.Recognit. Chem. 1990, 8, 349. (35) Koenig, Κ. E.; Lein, G. M.; Stuckler, P.; Kaneda, T.; Cram, D. J. J. Am. Chem. Soc. 1979, 101, 3553. (36) Katz, H. E.; Cram, D. J. J. Am. Chem. Soc. 1984, 106, 4977. (37) Artz, S. P.; Cram, D. J. J. Am. Chem.Soc.1984, 106, 2160. (38) Trueblood, Κ. N.; Knobler, C. B.; Maverick, E. F.; Helgesen, R. C.; Brown, S. B.; Cram, D. J. J. Am. Chem. Soc. 1981, 103, 5594. (39) Lias, S. G.; Liebman, J. F.; Levin, R. D. J. Phys. Chem. Ref. Data 1984, 13, 695.


A Molecular Mechanics Method for Predicting the Influence of Ligand

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