231 1
J. Phys. Chem. 1982, 86, 2311-2314
Correlation between the Stability and Structure of Diastereomeric Charge-Transfer Complexes in Solutlon. ( P ) - [7]Thiaheterohelicene and (S)- and ( R )-[ [(Tetranitrofiuoroenylidene)amino]oxy ]propionic Acid Pairs Hlroko Nakagawa, Hlsao Tanaka, Koh-lchl Yamada, and Hlroshl Kawarura Faculty of Phermaceuticai Sciences, Josai Universlty, Sakado, Saitama 350-02, Japan (Received: October 13, 1981; In Final Form: February 19# 1982)
The thermodynamic energetics of the diastereomericcharge-transfer (CT) complexes (P)-[7]thiaheterohelicene ((P)7TH)-(S)-[[ (tetranitrofluorenylidene)amino]oxy]propionic acid ((S)TAPA) and -(R)-[[(tetranitrofluorenylidene)amino]oxy]propionic acid ((R)TAPA)in tetrachloroethane solution were determined by a 'H NMR method. The (P)-(S) complex was more stable by 6AH = 1.03kJ/mol and 6AS = 1.40 J/(K mol) than the (P)-(R) complex. The structural surveying also carried out by a 'H NMR method indicated that the components of the (P)-(S)complex were better fitted than those of the (P)-(R)complex, with stronger electronic repulsion existing between the components of the (P)-(R)complex. Thus, the correlation between stability and structure of the title complexes was positively confirmed to offer a chirality discrimination mechanism in the diastereomers.
Scheme I
Introduction I t is well recognized that chiral discrimination occurs through interactions between two chiral moieties, producing enantiotopically or diastereotopically different circumstances.l Much effort has been devoted to the elucidation of molecular interactions which lead to the discrimination.'P2 Experimentally, enantiomeric interactions have been scrutinized by several thermodynamic quantities such as the free energy of crystallization,3the enthalpy of mixing: and the equilibrium constant in product formation,"* yielding differences between a racemate and its corresponding enantiomer. Discrimination of diastereomeric interactions, besides thermodynamic verifi~ation,"'~has been argued from the structural features of the diastereomers of chiral transition-metal complexes and organic compound^.^^-^^
(1)S.F. Mason, Annu. Rep. Bog. Chem., Sect. A, 73,53 (1976),and references cited therein. (2)D. P. Craig and D. P. Mellor, Top. Curr. Chem., 63, 1 (1976). (3)M. Leclercq, A. Collet, and J. Jacques, Tetrahedron, 32, 2831 (1976). (4) S. Takagi, R. Fujishiro, and K. Amaya, J. Chem. SOC.,Chem. Commun., 480 (1968). (5)H. Wynberg and B. Feringa, Tetrahedron, 32,2831 (1976). (6)S.E.Harnung, B. S. Soreneen, I. Creaser, H. Maegaard, U. Pfenninger, and C. E. Schaffer, Inorg. Chem., 15, 2123 (1976). (7)P. D. Tofferdell and M. Spiro, J. Chem. SOC..Farady Trans. 1,72, 1477 (1976). (8)C. D.Tran and J. H. Fender, J. Am. Chem. SOC.,102,2923(1980). (9)M. Newcomb, R. C. Helgeson, and D. J. Cram, J.Am. Chem. SOC., 96,7367 (1974). (10)B.Norden, Acta Chem. Scand., 26, 111 (1972). (11)K. Ogino, Bull. Chem. SOC. Jpn., 42, 447 (1969). (12)M.Yamamoto and Y. Yamamoto,Inorg. Nucl. Chem. Lett., 11, 833 (1975). (13)E.M. Arnett and S. P. Zingg, J. Am. Chem. SOC.,103,1221(1981). (14)Y. Kushi, M. Kuramoto, and H. Yoneda, Chem. Lett., 135,339, 663,1133 (1976). (15)T. Taura, H. Tamada, and H. Yoneda, Inorg. Chem., 17, 3127 (1978). (16)T. Tada, Y. Kushi, and H. Yoneda, Chem. Lett., 379 (1977). (17)T. Tada, Y. Kushi, and H. Yoneda, Bull. Chem. SOC. Jpn., 54, 1538 (198l),and references cited therein. (18)M. Kuramoto, Y. Kushi, and H. Yoneda, Bull. Chem. SOC.Jpn., 53, 125 (1981). 0022-365418212086-2311$01.25/0
U
(81 TA PA
(PI7TH
Numerous works have clarified the details of chiral discrimination energetically or structurally; however, it seems that there exists no direct approach to correlate differences in energetics with those in structure. Establishment of the correlation is expected to provide a more detailed understanding of the discrimination mechanism and also should be useful for practical application toward the acquisition of purely chiral materials. We report here an attempt at correlating thermodynamic energetics with structural factors in the diastereomeric pairs (P)7TH-(S)TAPA and (P)7TH-(R)TAPA (see Scheme I). One of the components of the pair, TAPA, is well-known for its selectivity in chromatographicseparations of racemic carbohelicenesZ1and heterohelicenes.22 It functions by exerting the binding power of the electron-accepting tetranitrofluorenylidene moiety to the electron-donating helicene through charge-transfer interaction and also possesses the recognition ability of the oxypropionic acid moiety toward the helicene chirality. A few of the diastereomeric pairs formed through charge-transfer interaction have been treated energetibut seldom with respect to their discrimination mechanisms. (19) M. Kuramoto, Bull. Chem. SOC.Jpn., 52,3702 (1979). (20)M. Kuramoto, Y. Kushi, and H. Yoneda, Bull. Chem. SOC.Jpn., 51,3251 (1978). (21)F. Mikes and G. Boshart, J. Chromatogr., 149, 455 (1978);F. Mikes. G. Boshart. and E. Gil-Av. ibid... 122.. 205 (1976):J . Chem. Soc., Chem.' Commun.,99 (1976). (22)H. Nakagawa, S.Ogashiwa, H. Tanaka, K. Yamada, and H. Kawazura, Bull. Chem. SOC. Jpn., 54, 1903 (1981). (23)H. Wynberg and K. Lammertsma, J. Am. Chem. SOC.,95,7913 (1973). (24)A. Balene and H. E. Gottlieb, J. Chem. Soc., Perkin Trans. 2,350 (1981). I
0 1982 American Chemical Society
2312
The Journal of Physical Chemistv, Vol.
86,No. 13, 1982
In the course of our spectroscopicstudies%@on complex formation through CT interactions of heterohelicenes and tetracyanoquinodimethane (TCNQ), we have found that NMR prevails over other methods by giving the thermodynamic parameters for a weakly CT interactive system and allowing an estimation of the relative spatial orientation of the interacting components. Thus, we have analyzed the formation equilibrium of the diastereomers (P)7TH-(S)TAPA and (P)7TH-(R)TAPA by 'H NMR based on Foster's treatment; secondly, we have estimated the geometrical structure of the diastereomers by a modified 'H NMR method which gives structural parameters. And finally we have evaluated the correlation between the energetics and the geometry in these diastereomers to clarify the chiral discrimination mechanism in the CT interactive systems.
Nakagawa et ai.
01
02
0 3
C C
A lopm
Experimental Section Figwe 1. Relation between A/[A] and A in the diastereomer formath (A is for H5 of (P)7T*): (0)(P)7TH-(R)TAPA, (0) (P)7TH-(S)TAPA. (S)- and (R)TAPA were synthesized and purified ac[(P)7TH] = 2.48 X lo4 moi/dm3; (R)TAPA] = 2.644 X lo-', 4.181 cording to the procedure in the literature.% (P)7TH was X 6.427X lo-', 8.074 X 10- , 1.145X lo-', and 1.500X lo-' isolated from racemic 7TH by high-performance liquid md/dm3;and [(S)TAPA] = 2.609 X lo-', 4.273 X lo-', 6.408X lo-', chromatography with a column of silica gel bonded with 8.650 X lo-', 1.141 X lo-', and 1.499 X lo-' moi/dm3. SD in the (S)TAPA.22 The isolated compound showed = least-squares fit is 0.02-0.03. +2990, which indicates nearly 100% optical purity.22 NMR samples used for Foster's analysis were prepared as follows: 3.80 mg of a crystalline (P)7TH was dissolved in 3900 mm3 of 1,1,2,2-tetrachloroethane-l,2-dz(CzDzC14; Merck. Uvasol), including a trace of tetramethylsilane (Me,Si) as an internal reference; 300-mm3portions of the solution were taken out with a micropipet (Gilson, Pipetman Model P, k0.570in error) and put into six sample tubes containing crystalline (S)TAPAand six sample tubes containing crystalline (R)TAPA in various amounts (3-40 mg) which were weighed to a precision of mg with a microbalance. After complete dissolution, each solution was transferred into a 5-mm diameter NMR tube. The 'H NMR spectra of the 12 samples thus prepared and a sample containing only the (P)7TH solution were successively measured at a fixed temperature. Each spectrum was recorded with 100-200 scans on a JEOL PET 100 pulsed Fourier transform spectrometer system. The temperature of a given sample was regulated by a VT-3C variable-temperature unit and was read from an 30 35 40 h 5 Ohkura AM-1001 microvoltmeter connected to a copperconstantan thermocouple whose junction was placed inside T-I I k K the probe. The temperature was constant within ca. 1 K F W 2. Relation between In Kand T-' in the diastereomer formation: during a series of measurements. (0)(P)7TH-(R)TAPA, (0) (P)7TH-(S)TAPA. SD in the least-squares
5
Results and Discussion Energetics of the Diastereomers. Foster's treatment generates, in the present case, eq 1. Here, K is the A/[A] = -KA + KAc (1) equilibrium constant in the diastereomer formation and [A] represents the concentration of acceptor (S)- or (R)TAPA which was present in large excessz9in comparison with the concentration of the donor (P)7TH. A (= 6, - 6) is an observable net shift where 6, and 6 are the chemical shifts of the donor proton in the uncomplexed state and (25) K. Yamada, T. Yamada, and H. Kawazura, Chem. Lett., 933 (1978). (26) H. Tanaka, H. Nakagawa, K. Yamada, and H. Kawazura, Bull. Chem. SOC.Jpn., 6$ 3665 (1981). (27) R. Foster, Organic Charge-Transfer Complexes", Academic Press, New York, 1966, Chapters 5 and 6; "MolecularComplexes",Vol. 3, Elec Science, London, 1974, Chapter 3. (28) P. Block and M. S. Newman, Or.#.Synth., 48, 120 (1968). (29) Since a large exceas of either of the components is required in the use of Foster's equation, the concentration ratio of the acceptor to the donor was varied in a range of 1&100.
fit is 0.03-0.04.
TABLE I : Thermodynamic Parameters of (P)7TH-(S)TAPAand (P)7TH-(R)TAPA Complexes K(248 K), dm3/mol
A H , kJ/mol
AS,J / ( K m o l )
( P ) - ( S ) 6.78 * 0.06 -15.65 + 0.18 -47.01 + 0.67 ( P ) - ( R ) 5.04 + 0.08 -14.62 t 0.23 -45.61 f 0.85
in the complexing equilibrium, respectively, and it is assumed to be equal to Ac when all of the donor molecules are converted to the diastereomer. Hence, the parameter Ac is independent of the chosen reference and should become an intrinsic value for the structure of the diastereomeric complex (vide infra). Figure 1 shows the plots of A/[A] vs. A in the diastereomer formation of (P)7TH-(S)TAPA and (P)7TH(R)TAPA pairs at 248 K. The association constant K shown in Table I was determined from a least-squares fit of eq 1 for the linear plots in Figure 1. The parameter Ac
The Journal of Physical Chemistry, Vol. 86, No. 13, 1982
Distereomeric CT Complexes in Solution
TABLE 11: Intrinsic Shifts of the Protons of the Components in the Diastereomers (P)'ITH-(S)TAPA and (P)'ITH-(R )TAPA protona
1 2 3 4 5 1' 2' 3'
4' 5' 6'
hCs
ACR
A cR/ A cs
0.94 0.42 0.37
1.13 0.55 0.38 0.91 1.25 2.22 1.45 1.96 2.16 0.79 0.31
1.20 1.31 1.03 1.28 1.09 1.45 0.84 1.33 1.34 2.63 >10
0.71
1.15 1.53 1.72 1.47 1.61 0.30 0.02
2313
$
a For the numbers, refer t o the structural formulas of
7TH and TAPA. The 'HNMR signals of 7TH and TAPA were assigned according to ref 34 and 35,respectively.
was 0.876 f 0.010 and 0.927 f 0.019 ppm for the (P)-(S) and (P)-(R)pairs, respectively.m These values were used as an invariant of temperature31 to further deduce the K values at other temperatures by referring to eq 1. Measurements of the A values for the diastereomeric pairs in the range of 233-323 K gave directly the corresponding K values which are shown in the van't Hoff plots in Figure 2. The enthalpy (AH) and entropy changes (AS) upon complexation were obtained from the slope and the intercept of the lines in Figure 2 through a least-squares analysis and are listed in Table I. From the table, the higher stability in the (P)7TH-(S)TAPA pair is evident from its K value. This can be reasonably confiimed by the fact that an increase of bonding energy (-AH) in the (P)7TH-(S)TAPA pair causes an increase of bonding entropy (-AS), indicating a stronger bond between the complexing species. The discrimination energies between both diastereomers do not seem to be large: 6AH = 1.03 kJ/mol, 6AS = 1.40 J / ( K mol), and 6AG = 0.61 kJ/mol (248 K). It is very interesting that such a small difference may result in explicitly different stereochemistries, as stated below, in both diastereomers. Structural Factors in the Diastereomers. In order to abstract the mutual orientation in the diastereomeric pair, determination of A, for all of the protons in the diastereomeric pairs is desired. This is due to the fact that AC embodies a long-range shielding effect imparted primarily from the aromatic moiety of the counterpart in the complex, and therefore Ac becomes a good index for the spatial location of relevant nuclei. The A, values were determined by measuring A's for all of the protons in an equimolar mixture of both components. In an equimolar mixture of donor (7TH) and acceptor (TAPA), the molar fraction of the associated complex formed is given by A/Ac. Hence, the equilibrium (30)These values determined by the concentration variation method do not coincide correctly with those (Table II) obtained by the equimolar method. This may be due to a difference in a dimensional standard between both methods. However, coincidence of the ratios AcR/@ (1.06 for the former and 1.09 for the latter) may reflect the validity of their values in both methods. (31) The invariability of Ap has been confirmed experimentally in the case of the charge-transfer complex between thiaheterohelicenes and TCNQ. See ref 26. (32) A proper measure is the ratio A$/A$, not the difference smce the latter may be kept small even in a large change of the geometry with respect to the protons in a weak local field and the same conflict exists with respect to the protons in a strong local field. (33) Shifts of the proton H5 of the (P)7TH donor were used for determination of the K and AC values because the shifts were largest. A similar result for the Ks was also obtained from the shifts of other protons of the donor.
(P)7TH-(S ITAPA
Flgure 3. Schematic drawing of the diasterometric complexes.
formula of the equimolar mixture (initial concentration C) is transformed to give Ac as follows: Ac = A[2KC
+ 1 + (4KC + 1)'/2]/(2KC)
Table I1 collects the A, values calculated by this equation (C= 3.31 X mol/dm3). In the Table, AcS and kRrefer to the inherent shifts of the protons in the diastereomers (P)7TH-(S)TAPA and (P)7TH-(R)TAPA, respectively. One can find the following distinct trends for the intrinsic shifts Ac's listed in Table 11, common to both diastereomers (P)7TH-(S)TAPA and (P)7TH-(R)TAPA (1) At's are all positive, indicating that all of the protons experience a net shielding upon diastereomer formation. (2) A6s for the ring protons of TAPA are larger than those for the ring protons of 7TH. This correlates well with the result expected from a long-range shielding effect due to the ring current which is accumulated with an increase of the number of aromatic rings. (3) In TAPA, AC'S for the ring protons are larger than those for the propionic chain protons. ( 4 ) In the propionic group of TAPA, A, for the methyne is larger than that for the methyl proton. (5) In 7TH, AC'S for the outer-periphery protons (H2 and H3) in the vicinity of the overlapped terminals are smaller than those for the protons (H1 and H5) near the central region of the molecule. These trends for the AC'S make it possible to depict the fundamental structure of the diastereomers as follows: the fluorenylidene plane of the TAPA molecule which faces the pseudoplane of the 7TH molecule is located on the central region of 7TH, apart from the staggered terminals. While the propionic side chain of the TAPA molecule is directed toward the staggered terminals, it is held far from the helicene plane. In the chain, the bulky methyl group (34) K. Yamada, S.Ogashiwa, H.Tanaka, H.Nakagawa, and H. Kawazura, Chem. Lett., 343 (1981). (35) A. Manmschreck, P.Roza, H. Brockmann,Jr., and T. Kemmer, Angew. Chem., 90,995 (1978).
J. Phys. Chem. 1982, 86,2314-2321
2314
is outermost, and the geminal methyne proton is closer to the plane. Certainly, this structure is also acceptable energetically since its geometry is considered to be the most suitable one among those which maintain an effective CT-attractive interaction between both aromatic planes of 7TH and TAPA. This structure also minimizes an electronic repulsive interaction between the propionic chain of TAPA and the 7r-electron cloud of 7TH. The small discrimination energies (loc. cit.) are understood by a resemblance of both diastereomers in this basic geometry. On the other hand, a structural difference can be recognized in terms of the ratio AcR Acs where a deviation from unity provides a measure3 of the structural discrepancy. Table I1 indicates that all of the values of A C R / k Sfor the ring protons of 7TH and TAPA are near to unity (the mean value being 1.21 in a range of 0.84-1.45) while the values for protons in the propionic group are far from unity. Thus, a major difference in the geometries of the two diastereomers should exist in the arrangement of the propionic group of TAPA toward the staggered plane of 7TH. Judging from the large AcR/AcS values in the propionic group, one can guess that the chiral moiety in
4
the (R)TAPA component is located close to the upward winding terminal of (P)7TH, while that in the (S)TAPA component is kept over the upper side of the downward terminal. Such a change in the location of the chiral moiety from one diastereomer to the other may cause a slight change in the overlapping mode between both aromatic planes of TAPA and 7TH, thus leading to the s m a l l up and down shifts about unity in the AcR/ Acs values for the ring protons. On the basis of the above discussion, we can illustrate the two diastereomeric pairs (shown in Figure 3) where a different feature in the allocation of the chiral moiety is stressed. The spatial orientation thus inferred correlates well with the previously determined energetics: the (P)7TH-(R)TAPA pair may have a tendency to be destabilized by an electronic repulsion between the propionic acid moiety of TAPA and the (P)7TH terminal, while the (P)7TH-(S)TAPA pair may avoid such a repulsion and be stabilized through a net charge-transfer interaction. In conclusion, the stability difference in the present diastereomeric pairs is confirmed consistently from both thermodynamic and structural parameters.
Rate Theory for Gated Diffusion-Influenced Ligand Binding to Proteins Scott H. Northrup,’ Fahlmeh Zarrin,+ Department of Chemistry, Tennessee Technological University, Cmkeville, Tennessee 3850 1
and J. Andrew McCammon’ mpartment of Chemistry, University of Houston, Houston, Texas 77004 (Received: November 18, 1981; In Final Form: February 4, 1982)
The rate of binding of ligands to proteins may be determined not only by the relative diffusion rate of species through the solvent medium but also by the accessibility of the binding site. Because of the inherent flexibility and internal motion of proteins, this accessibility may fluctuate on the time scale of reaction, thereby causing the intrinsic reactivity of the protein to be a time-dependent quantity. Here, we present a general formulation of the kinetics of such gated reactions. Approximate analytical expressions for the rate constant are obtained for important limiting cases. These compare favorably with exact numerically obtained values for the gated reaction rate constant over a wide range of system parameters.
species due to stereochemical orientation or other static I. Introduction geometric features of binding sites.’G17 The binding of ligands to proteins often occurs sufficiently rapidly that the rate of diffusional transport of species can influence the overall rate.’ Much attention (1) C. R. Cantor and P. R. Schimmel, “Biophysical Chemistry”. Part has been focused on these so-called diffusion-influenced 111, ‘The Behavior of Biological Macromolecules”,W. H. Freeman, San reactions.2 Since the early theory of Smoluch~wski,~ Francisco, 1980. (2)R.M. Noyes in ‘Progress in Reaction Kinetics”, Vol. 1, Pergamon, generalizations have been made to include a number of New York, 1961, Chapter 5. important and interesting features: the influence of (3)M. v. Smoluchowski, Phys. Z.,17,557 (1916). (4)S.H. Northrup and J. T. Hynes, J. Chem. Phys., 68,3203 (1978). short-range activation barriers on the intrinsic reactivity (5)S.H. Northrup and J. T. Hynes, J. Chem. Phys., 71,871 (1979). of juxtaposed particle^;^ the modulation of encounter rates (6)P. Debye, Trans. Electrochem. SOC.,82,265 (1943). due to interparticle potentials extending beyond the col(7) J. M. Deutch and B. U. Felderhof, J. Chem. Phys., 59,1669(1973). (8) P. G. Wolynes and J. A. McCammon, Macromolecules, 10, 86 lision separation (arising from solvent structural effects5 (1977). and/or electrostatic interactions6);short-range modulation (9)R. Samson and J. M. Deutch, J . Chem. Phys., 67,847 (1977). of the diffusion rate due to hydrodynamic interaction^;^^^,^ (10)H. Sano, J . Chem. Phys., 74, 1394 (1981). effects of competition between reactants for a depleted (11)K. Solc and W. H. Stockmayer, J . Chem. Phys., 54,2981 (1971). (12)W. Scheider, J. Phys. Chem., 76,349 (1972). population of coreactant~;~J~ and anisotropic reactivity of ‘Department of Chemistry, University of Wyoming, Laramie, WY.
(13)K. S.Schmitz and J. M. Schurr, J . Phys. Chem., 76,534 (1972). (14)M. Doi, Chem. Phys., 11, 115 (1975). (15)T.L. Hill, Proc. Nut[. Acad. Sci. U.S.A., 72,4918 (1975). (16)R. Samson and J. M. Deutch, J . Chem. Phys., 68, 285 (1978).
0022-3654/82/2086-23 14$01.25/0 0 1982 American Chemical Society
