J . Phys. Chem. 1987, 91, 1546-1553
1546
Theoretfcal Models of Diastereomeric Noncovalent Electron-Transfer Complexes. A Thermodynamic and Conformational Investigation Basilio Pispisa,* Antonio Palleschi, and Gaio Paradossi Dipartimento di Chimica, Universitci di Napoli, 801 34 Napoli, Italy, and Dipartimento di Chimica, Universitii di Roma, 00185 Roma, Italy (Received: July 28, 1986) Some of the parameters that were used in the computational studies of noncovalent diastereomericelectron-transfercomplexes between L-adrenaline or L-dopa and [Fe(tetpy)(OH)$ ions anchored to enantiomeric ordered polypeptides have been revised (tetpy = 2,2’,2’’,2”’-tetrapyridyl). The changes were based on a more realistic approach in evaluating electrostatic energies by using a distance-dependent dielectric constant and partial atomic charges for each atom of reactants. The changes removed some discrepancies previously observed in computed conformations of the diastereomeric adducts with L-dopa and led to a satisfactory comparison between calculated and experimental “differential” thermodynamic functions of binding for both substrates. Furthermore, there is now no dominant steric effect that discriminates between DL and LL pairs. Instead, binding stereoselectivity results from a complex interplay of ionic and nonbonding forces. Both these interactions enable the redox centers in the diastereomers to experience a different mutual orientation and separation distance which account for kinetic stereoselectivity that predominates over thermodynamic stereoselectivity in the reactions investigated. Solvent reorganization energy changes associated with the diastereomerically related charge-transfer steps were calculated by the ellipsoidal cavity model for short-range electron transfer. These changes reflect the stereochemical control exerted by the ordered polypeptide matrices in the formation of diastereomeric pairs and are chiefly responsible for the observed topochemical phenomena.
Introduction Quantitative models for the forces governing molecular association are a challenging goal in theoretical physical chemistry and biochemistry. At variance with covalent association, noncovalent binding is rather easy to treat because reliable models of noncovalent forces have been successfully developed over the past years.14 Such forces are generally considered to be van der Waals, hydrophobic, hydrogen-bonding, and Coulombic interactions. In treating noncovalent association a major problem has been that of accounting for solvent effect^,^ but this problem may be partly circumvented when dealing with the formation of diastereomeric adducts. In such a case, only “differential” energetic contributions are relevant and most of solvent effects may be expected to cancel out upon binding if the modes of binding are similar. In the past few years we were interested in electron-transfer reactions between chiral species. On the basis of previous unsuccessful investigations6 we felt that, in order to observe stereoselectivity in the reaction, the redox couple must form a stable association complex in which the diastereomers have to experience definitely different steric constraints. We then thought to use transition-metal derivatives bound to asymmetric polymers as one of the reactants because the macromolecular ensemble can offer a more efficient discriminating environment for the redox chiral partner than that of a simple asymmetric molecule. The ultimate goal was, in fact, that of obtaining a system that could mimic the stereospecific activity of enzymic materials. With this line of reasoning, we employed [Fe(tetpy)(OH),]+ ions (FeT; tetpy = 2,2’,2’’,2’”-tetrapyridyl) anchored to sodium poly(L-glutamate) (FeTL) or poly(D-glutamate) (FeTD) as enantiomeric oxidant systems and L-ascorbic acid, L-catecholamines, and L-thiols as reductants, according to eq 1. While ascorbic P-Fe”’T+
+ A-
F=
P-Fe”T
+ A‘
(1)
acid and catechol derivatives were found to undergo, under suitable a stereoselective charge-transfer process with iron(II1) ion, very surprisingly the thiols (such as L-cysteine and reduced L-glutathione) did not. These latter results shall be reported in a separate paper, but they clearly indicate that the basic factors that produce stereochemical control are not yet easily foreseeable. Stereoselectivity apparently involves a delicate balance between opposing forces and must result from a complex interplay of both steric effects and ionic interactions. The knowledge of *Address correspondence to this author at the Universitl di Napoli.
the structural features of the diastereomeric encounter complexes is, therefore, of paramount importance for a better understanding of the phenomenon, and conformational energy calculations may be a valuable tool for the purpose. It is the aim of this paper to present hypothetical noncovalent models of FeTD-L-catecholamines and FeTL-L-catecholamines diastereomeric electron-transfer complexes undergoing stereoselective reaction. Models of this kind were already reported by us9 but those presented here are based on new computational results where electrostatic energies were estimated by using a distance-dependent dielectric constant, corrected for the ionic strength of the medium through the inverse of Debye-Huckel screening length. Using the calculated interaction energies and the molecular parameters of the models, we were able to reproduce the experimentally determined differential thermodynamic functions for the formation of these complexes and offer a structural and energetic model to account for, at least partially, the observed topochemical effects. For the sake of comparison with computed values, we also summarize here some of the experimental material previously reported,9atogether with new results on the structural features of the oxidant systems and on the thermodynamics of formation of the diastereomeric complexes. Experimental Section Materials. Quaterpyridineiron(II1) complex ions and polypeptides were obtained as already reported.’3l0 L-Adrenaline (BDH) and L-dopa (Merck) were analytical-grade reagents and used as such. Concentrations were determined by UV absorption? (1) Platzer, K. E. B.; Momany, F. A.; Scheraga, H. A. Int. J . Peptide Protein Res. 1972, 4, 187. Pincus, M. R.; Scheraga, H. A. Arc. Chem. Res. 1981, 14, 299. (2) Levitt, M.J. Mol. Biol. 1974, 2, 393. (3) (a) Case, D.;Karplus, M. J . Mol. Biol. 1978, 123, 697. (b) McCammon, J. A,; Wolynes, P. G.; Karplus, M. Biochemistry 1979, 18, 927. (4) De Tar, D.F. J . Am. Chem. SOC.1981, 103, 107. (5) Gilson, M. K.; Rashin, A.; Fine, R.; Honig, B. J. Mol. Biol. 1985, 183, 503. Zauhar, R. J.; Morgan, R. S. Ibid. 1985, 186, 815. (6) Grossman, B.; Wilkins, R. G. J . Am. Chem. Sor. 1967, 89, 4230. Sutter, J. H.;Hunt, J. B. Ibid. 1969, 91, 3107. Kane-Maguire, N. A. P.; Tollison, R. M.; Richardson, D. E. Inorg. Chem. 1976, 15, 499. (7) (a) Barteri, M.;Pispisa, B. J. Chem. SOC.,Faraday Trans. I 1982, 78, 2073. (b) Ibid. 1982, 78,2085. Makromol. Chem., Rapid Commun. 1982,
3, 715. (8) (a) Pispisa, B.; Barteri, M.; Farinella, M. Inorg. Chem. 1983,22, 3166. (b) Pispisa, B.; Farinella, M. Biopolymers 1984, 23, 1465. (9) (a) Pispisa, B.; Palleschi, A.; Barteri, M.; Nardini, S . J. Phys. Chem. 1985, 89, 1767. (b) Pispisa, B.; Palleschi, A. Macromolecules 1986, 19,904. (10) Branca, M.; Pispisa, B.; Aurisicchio, C. J . Chem. Soc., Dalton Trans. 1976, 1543. Cerdonio, M.; Mogno, F.; Pispisa, B.; Vitale, S . Inorg. Chem. 1977, 16, 400.
0022-3654/87/209 1- 1546%01 .50/0 0 1987 American Chemical Society
Diastereomeric Noncovalent Electron-Transfer Complexes those of the polymer [PI being referred to monomeric units (monomol/L). Tris buffer (Sigma) was employed in the chloride form, at a concentration of 0.05 M (pH 7.01 f 0.03). Under the experimental conditions used, the degree of association of FeT ions by polypeptides is higher than 93%" All measurements were carried out on freshly prepared solutions, using doubly distilled water. Methods. Electron-transfer reactions were carried out in aqueous solution a t 26 "C and pH 7 (0.05 M Tris buffer), measuring the absorption of adrenochrome or dopaquinone at 320 or 475 nm,12aaccording to the r e a ~ t i o n ~ , ' ~ ~ H202
+ A(0H)O-
FeTL
A(O2)
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
1547
Channel-number 100
i 0.0c
200 I
400
300
I
I
I
I
+ H2O + OH-
where A(02) denotes quinone. Under the experimental conditions used, the rate of electron transfer from catecholamines to iron(II1) in FeTL or FeTD systems (eq 1) was found to be [H202]independent, within the range of [H202], = 1 X 104-1 X lo-* M.*q9 In fact, hydrogen peroxide simply oxidizes the reduced iron ion and substrate radical in subsequent fast steps, thus allowing one to follow the kinetics by measuring the formation of quinones, as already de~cribed.~" The temperature dependence of specific rates was measured in the range of 13-26 OC, the a-helical content in the polypeptide matrices being not practically affected by this temperature ~ariation.'~Steady-state kinetic measurements were M), with varying initial conperformed at fixed [C], (1 X centrations of substrates within the range of 5 X 10-5-5 X
M.9 Calorimetric measurements were carried out at 25 OC and pH 7, using a 10700-2 LKB batch microcalorimeter. The enthalpies of pairing (Table 11), under conditions where the association of substrates to the oxidant systems (at a complex to polymer-residue ratio [C]/[P] = 0.20) is virtually complete, were obtained from the observed heats after correction for dilution effects and normalization for polymer concentration. (AHdil = 78 cal/monomol for the oxidant system at [PI = 1 X M and around -2 cal/mol M; pH 7). Several for substrates buffered solutions at 2 X calorimetric measurements were performed for each run to obtain consistency in results. Mossbauer spectra of freeze-dried solutions of oxidant systems at [C]/[P] = 0.20 were recorded at room temperature with a 57Co-in-Rhsource and a constant-acceleration Elscint spectrometer, connected with a 520-channel Laben 4096 unit and calibrated by Na2[Fe(CN)5NO].2H20absorber. The spectra were fitted to Lorentzian lines by using a computer program. While Mossbauer parameters reflect the structure of the powder, optical and chiroptical data of the solution obtained by dissolving again the powder in water are in good agreement with those of the original mixture. This would suggest that the oxidant system in the solid sample basically retains the features of that in solution, an hypothesis consistent with the stability of the rather rigid structure of the material at [C]/[P] = 0.20 (see later) and with the mild conditions employed in freeze-drying the sample. Other apparatuses were already
Results and Discussion Structural Features of the Oxidant Systems. Quaterpyridineiron( 111) ions form an inner-sphere complex with sodium poly@-glutamate) (FeTL) or poly@-glutamate) (FeTD), in which the coordination of an apical site of FeT by a y-carboxylate group of side chains of the polymer occurs.11 In addition, progressive binding of FeT ions by the polyelectrolyte (pH 7) determines a coil-to-a-helix transition and aggregation phenomena where the iron molecules very likely act as bridging groups between helical segments of different chains or the same chain after partial f ~ l d i n g . ~At. ~high complex to polymer-residue ratio, e.g. [C]/[P] = 0.20, the enantiomeric oxidant systems exhibit therefore a folded, rather compact, structure where most of FeT ions are (1 1) Branca, M.; Pispisa, B. J . Chem. SOC.,Faraday Trans. I 1977, 73, 213. (12) (a) Martin, R. B. J . Phys. Chem. 1971, 75, 2657. (b) Heacock, R. A. Chem. Reo. 1959, 59, 181.
'.O
t
I1 -3
V I
I
-2
-1
I
I
I
I
0
1
2
3
Source velocity, mm /s
Figure 1. Typical room temperature Mossbauer spectrum of freeze-dried solutions of the FeT-poly(g1utamate) system a t a complex to polymerresidue ratio of about 0.20. The solid line is the (single) Lorentzian curve generated with the parameters given in the text.
shielded by the ordered polypeptide matrix.I3 This picture was recently confirmed by Mossbauer spectra of freeze-dried solutions of FeTL at [C]/[P] = 0.20 (Figure 1). They show two iron(II1) sites, one with an isomer shift (6) of 0.51 mm/s and a quadrupole splitting (A) of 0.71 mm/s and the other with 6 = 0.75 and A = 1.72 mm/s (errors within 3~0.03mm/s), the ratio between the two sites being around 2:l.14 Accordingly, Figure 2 illustrates the molecular model of FeTL at high [C]/[P] ratio, as obtained by conformational energy calculations partially based on available X-ray data, with the deepest minimum of total energy given as a sum of electrostatic and nonbonding energy terms.9a The observed values of isomer shifts suggest that the first iron(II1) site has a lower coordination number than the second.15 The first site may be thus assigned to the "buried" active centers because the oxygen atoms 0, and 0, of side chains of polypeptide lie on the axis normal to the equatorial plane of the complex, but at a separation distance of 2.34 and 2.50 %, from the central metal ion, respectively, as compared to an average length of 2.10 %, for the four Fe-N(pyridine) bondsSgaThe second iron(II1) site may be assigned to the pseudo-octahedral centers exposed to the bulk solvent (Figure 2). Kinetic and Thermodynamic Stereoselectivity. We have already proved9 that electron transfer from catecholamines I and I1 (Chart I) to iron(II1) in FeTD or FeTL system (eq 1) takes place intramolecularly within a precursor complex, i.e.
P-FeII'T-A
k,
(slow)
P-Fe"T
+ A'
The parameters of steps 2 and 3, as obtained by kinetic data in the steady-state approximation, are reported in Table I for the (13) Paradossi, G.; Pispisa, B.; Rizzo, R.; Barteri, M. Biopolymers 1986, 24, 1249. (14) The spectrum consists of three lines positioned at -0.48,0.14, and 1.24 mm/s, with intensity of 0.3,0.8, and 0.3, respectively. According to the width of the bands and to the fitting parameters of the Lorentzian curve (Figure 1) the internal doublet (in the central band) is that due to hemin-like quaterpyridineiron(II1) ions sandwiched between helical segments of polypeptideIs (see above and Figure 2). The bands in the spectrum also show a broadening that is suggestive of some kind of disorder in the sample. We believe that this disorder arises from slightly different microsymmetries in the iron(II1) sites, as one would expect for this type of polymeric material. A similar broadening was recently observed in Mbsbauer spectra of iron(II1) carboxylate derivatives having polymeric features, where the metal site is present in a variety of slightly different environments.I6 (15) Fluck, E. In Chemical Applications of Mossbauer Spectroscopy, Goldanskii, V. I., Herber, R. H., Eds.; Academic: New York, 1968; Chapter 4. (16) Dziobkowski, C. T.; Wrobleski, J. T.; Brown, D. B. Znorg. Chem. 1981, 20, 671.
Pispisa et al.
1548 The Journal of Physical Chemistry, Vol. 91, No. 6, 1987
TABLE I: Kinetic and Activation Parameters of Intramolecular Electron Transfer from L-Catecholamines to Iron( 111) in the Diastereomeric Complexes“ [CI / [PI oxidant 103ket,s-1 1o-2&l, M-’ ketDL/ketLLC koDL/koLL“ AHSet,kcal/mol ASSet,cal/(mol-deg) L-Dopa FeTD 0.01 25.3 f 2.7 24.2 f 2.3 1 1 FeTL 0.20
FeTD FeTL
18.5 i 2.1 7.2 f 0.8
18.2 f 2.0 12.1 f 1.3
0.01
FeTD FeTL
35.8 f 2.7
37.7 f 3.8
1
1
0.20
FeTD FeTL
31.1 f 3.2 9.4 f 1.1
10.4 f 1.3 7.7 f 0.9
3.3 f 0.5
1.4 f 0.2
2.6 f 0.4
1.5 f 0.2
17.4 f 1.0 17.5 f 1.3
-8 f 3 -10 f 4
16.6 f 1.0 16.6 f 1.3
-10 f 3 -12 f 4
L- Adrenaline
“ 25.9 OC, pH 7, 0.05 M Tris buffer. stereoselectivity .
Complex-to-polymer-residue ratio of the oxidant systems.
s
Kinetic stereoselectivity. “Thermodynamic
TABLE 11: Thermodynamic Parameters of Diastereomeric Electron-TransferComDlexes Undergoing Stereoselective Reaction“ AH’,’ AS0,d complex kcal/mol kcal/mol cal/(mol*deg) FeTD-L-dopa -4.46 0.9 18 FeTL-L-dopa -4.22 1.2 18 FeTD-L-adrenaline -4.13 0.9 17 FeTL-L-adrenaline -3.95 1.3 17
’
“25 O C , pH 7, 0.05 M Tris buffer; [C]/[P] = 0.20 for FeTD and FeTL systems. bFrom Table I; errors within f0.07 kcal/mol. CFrom microcalorimetric measurements; errors within f0.1 kcal/mol. Errors within f l eu.
“
Figure 2. Molecular model of FeTL oxidant system, under conditions where it exhibits stereoselective activity (see text). The oxygen atoms of the side chains of poly(L-glutamate) closest to Fe(II1) are indicated as O1and 02.Two types of active sites are shown, in agreement with Mossbauer data. The reaction centers capable of stereoselective process are thought to be those FeT ions sandwiched between a-helical segments of polypeptide.
two extreme conditions of [C]/[P] = 0.01 and 0.20 of the enantiomeric oxidant systems.9a From the results it appears that (1) remarkable stereoselective effects in the reactions investigated occur only on increasing the [C]/[P] ratio of the oxidants; (2) chiral discrimination is chiefly observed in step 3 since ketDL/ketLL is definitely higher than KODL/KOLL; (3) when looking at the activation parameters of the stereoselective electron-transfer step the uncertainty in AH*,, and AS*,,values makes it impossible, unfortunately, to establish which term is the major contributor to kinetic stereoselectivity. Moreover, the slightly negative values of AS*et(--lo eu) might indicate some nonadiabatic character in the transfer.” This hypothesis must be accepted with reser(17) Sutin, N. In Tunneling in Biological Systems, Chance, B., De Vault, D. C., Frauenfelder, H., Marcus, R. A., Schrieffer, J. R., Sutin, N., Eds.; Academic: New York, 1979; p 201. Brunschwig, B. S.; Creutz, C.; Macartney, D. H.; Sham, T. K.; Sutin, N. Faraday Discuss. Chem. SOC.1982, 74, 215.
Vations, however, because nuclear tunneling effects cannot be ruled out.lBa The reactions investigated involve aromatic compounds whose vibrational states cannot be assumed to be totally excited, as usually done for metal-ligand moieties.19 On the other hand, negative values of AS*,will also result if A S o , the thermodynamic entropy change for the electron transfer (step 3), is sufficiently negative. 8b We next investigated the thermodynamics of formation of the diastereomeric pairs undergoing stereoselective reaction (Table 11). The main inferences to be drawn are the following. (1) The energetics of chiral discrimination in step 2, W L L - N o D L ,are around 300 cal/mol, a finding that substantiates the idea that the observed stereoselectivity is characterized by modest thermodynamic effects. Interestingly, a similar binding discrimination was recently observed when chiral organic ions form diastereomeric pairs.*O This is not surprising because diastereomeric discrimination energies in solution are commonly of the same order (-0.2-0.5 kcal/mol) as those differentiating “active” from “racemic” enantiomeric contacts in the solid phase.21 (2) Diastereomeric discrimination entropies, M O L L - A S O D L , are negligibly small, as one would expect if the modes of binding are similar, but for each pair the entropy effects due to reduction in molecular degrees of freedom are overbalanced by those arising from solvent r e l e a ~ e . ~ ~ ~ ~ ~ From the results we can draw the following conclusions. A remarkable stereoselectivity in the electron-transfer reactions investigated (eq 1) is observed only when structurally ordered and partially shielded reaction centers prevent easy approach for redox (18) (a) Marcus, R. A. In Tunneling in Biological Systems, ref 17, p 109. (b) Marcus, R. A.; Sutin, N. Znorg. Chem. 1975, 14, 213. (19) If one takes into account the following process:
-oc-c=c-co-
I
I
-e +e
.. . -. . . . . ..
oc-c-c-co
I I
the mean stretching frequency of catecholic moiety results to be about 1350 cm-’ since the valence vibrations are as follows: C-O(H) = 1220 cm-I (degeneracy 2) and C=C (aromatic) = 1630 cm-I. (20) Arnett, E. M.; Zingg, S. P. J. Am. Chem. SOC.1981, 103, 1221. (21) Mason, S. F. In Optical Activity and Chiral Discrimination, Mason, S . F., Ed.; Reidel: Dordrecht, 1979; Nato Advanced Institutes Series, p 319. (22) Pispisa, B.; Paoletti, S. J. Phys. Chem. 1980, 84, 24. (23) Matthew, J. B.; Weber, P. C.; Salemme, F. R.; Richards, F. M. Nature (London) 1983, 301, 169.
The Journal of Physical Chemistry, Vol. 91, No. 6, 1987 1549
Diastereomeric Noncovalent Electron-Transfer Complexes
CHART I: Partial Atomic Charges Used for the Reactants. In Both Substrates, the OH Group Was Treated as a United Atom 0 023
-0 028;
- 0 009c H/
0 023
0 023
/c\
H\
‘
N O ;
\c/
0
392 \,
0 278 ‘, Fell’ I 894 I‘
0277
\C(HI
- 0 092
A - 1 309
#‘
N l O 397
-0 o o 9 j
I
- 0 02EC
Fel,l*yi2 50
AI
/
0 277
( 2 34 A I 0 576 l o - 7 265
H/ \c//c-” 0022 -00091 H 0 023
FeT-poly (glutamate) -0 183
- 0 183
OH
OH
0.176
?
H
- 0.025t
&-0,025
I - 0.005
0.021
0.021 H0.037
I - 0 . 0 4 4 c’
1‘
0.052
-0.169
0.047
!.36,0
H-C-C%
I‘ H 0.052
0.004c
0 t
I
I
0.057 0.313
HI’H ‘ H
IH‘
’c
;’‘ c1
-0.110
0’030
0.055
6 0.500 9.0.250
Adrenaline ( II I
partners. The hindered accessibility of active sites makes the chiral residues of the helical polypeptide behave as primary sites of binding for substrate molecules. This ensures different steric constraints that affect the binding properties and stereochemical features of diastereomeric precursor complexes differently. The former do not much contribute to chiral discrimination in contrast with the latter, but in either case stereoselectivity must be coupled with a remote attack mechanism on the central metal ion because it involves a polymer-assisted pathway to the active site. This is the reason why we cannot observe an entirely stereoselective process. The active centers exposed to the bulk solvent (Figure 2 ) are, in fact, responsible for a parallel nonstereosejectiva route to products, like that observed when using the oxidant systems at a very low complex-to-polymer ratio (Table I). A direct attack mechanism through the “open” (axial) position of the bound FeT ions9 leads to conformationally mobile adducts, owing to the degrees of freedom of internal rotation of the bulky substituents, and hence to a negligible sterical discrimination between the diastereomeric pairs. Conformational Energy Calculations. The geometric and steric constraints that control the formation of diastereomeric adducts undergoing stereoselective electron transfer were evaluated by conformational analysis. As in earlier calculation^,^ two types of van der Waals potential functions, i.e. Buckingham (B) and 12-6 Lennard-Jones (LJ) type functions, besides electrostatic and hydrogen bond energy terms were used. However, we changed the Coulombic expression
-0.030
0.450
H
0.232
0.268
Dopa ( I I
I I
-0.356
I H-C-OH
- 0.687
0
\ N - C - C ‘0.064 I
-0.0246
\H
H/
0.020 -0.384
GLU
where k is the inverse of the Debye-Hiickel screening length (0.07 at 25 OC and p = 0.04 M ) and R , (A)the separation distance of the pertinent atoms i a n d j . The dielectric constant was thus interpreted as the numerical, dimensionless, value of the distance (RtI,)between nonbonded atoms i and j , corrected for the ionic strength of the medium through the k factor. The reason for this change is threefold. First, earlier calculations showed a discrepancy in the closest separation distance of the redox centers ( R ) in the computed conformations of the diastereomeric adducts with L-dopa. According to kinetic results (Table I), the DL reaction is faster than LL so that one would expect the catecholic O--Fe separation distance to be shorter for DL than for LL diastereomer. This was indeed the case for the complexes with L-adrenaline (RDL= 7 . 0 and R L L = 7.5 A) but not for those with L-dopa (RDL= 7.0 and R L L = 5.8 A).9bSecond, earlier data showed that both substrates and the enantiomeric oxidant systems fit together in the close environment of the active sites with remarkable precision. A reduction in the local dielectric constant is therefore predictable as a result of solvent exclusion on molecular a s s o ~ i a t i o n . The ~ ~ ~use ~ ~of a dielectric constant of 78.59 was thus a poor approximation even considering “differential” Coulombic contributions. Third, recent molecular mechanics calculation^^^^^^ were performed using e = R’,,, this choice being claimed to be numerically valid in the regions of the most important interactions, Le. those shorter than 5 8, where e < 5. However, in modeling our association process we carried out several minimizations by starting not only from different mutual orientations of the reactants but also from different di-
(4)
by expressing the dielectric constant as follows: e’ = e(1 + kRij); e = R’,. 11
(5)
(24) Warshel, A. J . Phys. Chem. 1979.83, 1640. (25) Blaney, J. M.; Weiner, P. K.; Dearing, A,; Kollman, P. A,; Jorgensen, E. C.; Oatley, S. J.; Burridge, J. M.; Blake, C. C. F. J. Am. Chem. SOC.1982, 104, 6424.
Pispisa et al.
1550 The Journal of Physical Chemistry, Vol. 91, No. 6, I987 TABLE III: Electrostatic Energies of Diastereomeric Pairs (kcal/mol) in the Deepest Minimum of Total Interaction Energya ~coul
diaster
Ucoul (E = R
