J. Phys. Chem. 1992,96, 5725-5733
5125
Ionic Strength Dependence of the Enantioselective Quenching of Tb( 2,6-pyridinedicarbo~ylate)~% Luminescence by Resolved Ru( 1,IO-phenanthroline):$ Roe1 B. Rexwinkel,f Stefan C. J. Meskers; Harry P. J. M. Dekkers,**+and James P. Riehl*g* Gorlaeus Laboratories. Department of Chemistry, Leiden University, Postbox 9502, 2300 RA Leiden. The Netherlands, and Department of Chemistry, University of Missouri-St. Louis, St. Louis, Missouri 631 21 (Received: February 24, 1992) The enantioselective excited-state quenching of r~c-Tb(2,6-pyridinedicarboxylate)~~[A,A-Tb(DPA)33-]by A-(-)-Ru(1,lO-phenanthroline):' [A-R~(phen)~~+] has been studied in aqueous solution (298 K) and in methanol (298 and 255 K) as a function of solution ionic strength. The ionic strength of methanol and water solutions were controlled through the addition of NaBr. The bimolecular rate constants for homochiral (A-A or A-A) and heterochiral (A-A) quenching were obtained by numerical fitting of the biexponential decay of Tb(DPA)3f luminescence in a series of time-resolved experiments. It is shown that the diastereomeric quenching reactions can be modeled by a kinetic scheme in which the luminophore and quencher form an encounter complex and then undergo a reactive step leading to energy transfer. In water, it is demonstrated that the ionic strength dependence of the quenching rates can be accurately described by the predicted ionic strength dependence of a pseudoequilibrium constant for the encounter complex. Experimental results for a wide range of ionic strengths are presented, and it is shown that the enantioselectivity of the quenching in water at room temperature does not depend on ionic strength. Results for enantioselective quenching in methanol (which are opposite in sign to those measured in water) do show variations in enantioselectivityat room temperature due to interference from racemization of the lanthanide complex, which can be suppressed at lower temperatures. The remaining ionic strength dependence is attributed to a situation in which the reaction becomes nearly diffusion controlled. A theoretical description of chiral recognition in both solvent system is developed through calculations of diffusion and dissociation rates using DebyeSmoluchowski and Eigen equations,respectively, and it is concluded that most of the observed enantioselectivityis due to chiral differences in the reactive step. The analysis also yields a charge product that is very close to the expected value of -6 for both solvent systems and a reactive distance of 1.1 nm. This latter result indicates that the observed quenching is due to very short-range interactions.
Introduction The enantioselective quenching of solutions of racemic lanthanide complexes with D3 symmetry, such as the tristerdentate Tb(2,6-pyridinedicarboxylate = DPA)33-, by optically active transition-metal complexes has been described in several recent publications.1d Although several different optically active species have been shown to enantioselectively quench the excited state of these lanthanide species, Ru( l,l0-phenanthroline = phen)?', the first complex discovered to effect chiral quenching in this manner, is especially suited for detailed study due to its ease of purification and stability to thermal or photo-induced racemization.'J The enantioselective quenching is usually observed through direct measurement of the steady-state or time-resolved circularly polarized luminesence (CPL) from excited lanthanide ions. In CPL spectroscopy one detects the usually small net circular polarization in the luminescence from optically active molecules.' In the case of lanthanide complexes such as Tb(DPA)33-, that occur as rapidly interconverting racemic mixtures in solution, A A, one measures CPL due to the generation of nonracemic excited state populations resulting from preferential quenching of one enantiomer over the other. In the steady-state experiments, the observed CPL is due to a time-averaged excited-state population difference! In more recent experiments, time-resolved CPL has been measured in the luminescence decay of an initially prepared racemic excited state.'-5 Recently we have demonstrated that it is possible to determine accurate decay constants for the homochiral (AA = +) and heterochiral (AA = -) quenching of Tb(DPA)33- by A-(-)-Ru(phen)?+ by a procedure in which the individual luminescence decay constants have been determined through a nonlinear least-squares fit of the luminescence decay curves in terms of a biexponential function? The primary advantage of this procedure over the measurement of the time-dependent CPL signal is the fact that one is able, in this case, to analyze the time decay of the total emitted intensity as opposed to the very small differential intensity. In studies of this type, the differential emission intensity at time t = 0 (when the total emission intensity is a maximum)
-
Leiden University. 'University of Missouri-St. Louis. To whom correspondence should be addressed.
is exactly 0 and reaches values of only a few percent of the total intensity in the tail of the decay. Of course, this type of analysis must be coupled with a measurement of circularly polarized luminescence in order to verify that the biexponential decay is indeed due to enantioselective quenching and not simply due to the presence of more than one species with differing emission lifetimes. Of particular interest to us is the observation that, in experiments involving the enantioselective quenching of Tb(DPA)33by resolved Ru(phen)3z+,the sign of the measured differential emission intensity has been shown to be opposite for experiments performed in water compared to identical experiments using methanol as a solvent.zv6 To date, the theoretical models for this enantioselective process have not yet been able to explain this solvent dependence,8 and clearly additional experiments are necessary in order to develop an accurate description of the kinetics and thermodynamics of this phenomenon. In the work reported here, we examine the diffusional nature of the chiral quenching of these two ionic species through measurement of the ionic strength dependence of the diastereomeric quenching rates.
Experimental Section Tb(II1) solutions were prepared from TbC13 (Aldrich). 2,6Pyridinedicarboxylic acid (DPA) was obtained from Janssen Chimica and used without further purification, and A-(-)-Ruhen)^^' was prepared by a procedure described previo~sly.~ Methanol was purchased from Janssen Chimica. The water content of the methanol was estimated to be approximately 0.5% through density measurements. All samples were prepared from stock solutions of Tb(dpa)?- and Ru(phen)32-. The concentrations were determined spectrophotometrically. Solutions of varying ionic strength were prepared by weighing different amounts of NaBr (J.T. Baker) in dry, clean cuvettes and then adding 3 mL of stock solution to each. In all experiments the Tb(DPA)33- emission was monitored at 543 nm, corresponding to the most intense component of the 5D4 'F5 emissive transition of Tb(II1). The luminescence was monitored following repeated short (1 ps) excitation pulses (hXc = 300 f 20 nm). Acquisition of decay data was determined when the total number of photon counts in the first time channel reached a value of lo6. The decay curves were analyzed by a nonlinear least-squares curve-fitting procedure based on the Levenberg-
-
0022-3654/92/2096-5725$03.00/00 1992 American Chemical Society
5726 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 10
1
"
"
"
"
'
the lanthanide complexes interconvert rapidly on a laboratory time scale, between the A and A forms, but that the excited state decay rate is much faster than the racemization rate. The final state of the quencher species is indicated by QA', and that of Ln* by Ln'; ko denotes the decay rate in the absence of quencher, and k,+ and k,- are, respectively, the bimolecular rate constants for quenching of the A and A enantiomer of the excited lanthanide complex. If k; is not equal to kq+, then the excited-state concentrations of the rare-earch enantiomers will not be equal at all times after an unpolarized excitation pulse. The degree of enantioselectivity in the quenching process is designated E, and is defined as follows:3
1
Residuals
(6)
5
4
0
-5
I
.
I
"
,
'
,
"
.
"
,
'
,
1
I
,
J
-1
'
6
2
\
5
c C 2
0 0 C
0 c 0
4
E, =
P
v 0,
3
2
1 i = 255K 5.0
Time ( m t e c . )
Figure 1. (A) Total luminescence decay measured at 543 nm of a 0.7 mM solution of Tb(DPA),> in methanol at 255 K following the addition of 2 gM h-(-)-R~(phen),~+.The solid line is the result of a numerical tit to the function&) = lo[exp(-klt) exp(-k2t)] 1,. Results from fit: k, = 965 4 and k2 = 824 2. The ionic strength of the solution was set equal to 8.5 X lo-, mol/kg through the addition of NaBr. (B) Weighted residuals from the monoexponential fit. (C) Autocorrelation
*
+
*
+
function of the weighted residuals.
Marquardt algorithm.I0 The time-dependent luminescence was fitted to a function of the form f i r ) = A[exp(-klt)
+ exp(-k2t)] + I d c
Theory A. Kinetics. A simple kinetic scheme for the enantioselective quenching of a racemic rare-earch complex by a chiral quencher complex is given in eqs 2-4. We assume that in the ground state A-Ln + hvabs A-Ln* A-Ln + hvab A-Ln* (2)
-
ko
A-Ln
+QA A-Ln* + Qa A-Ln*
-
A-Ln'
+ QA'
A-Ln'
+ Qat
k;
ks'
-
A-Ln*
kQ
A-Ln
Ln*:QA] denotes the heterochiral encounter complex, and k, describes all processes occurring after energy transfer except energy back-transfer. A similar scheme can be written for the corresponding homochiral process; however, for simplicity of notation, we do not specify the homo/heterochirality of the quenching processes, i.e., we drop the and - superscripts in this and the next section. In addition, it is reasonable to assume, for our system, that 4 is much larger than k,, and thus back-transfer will be neglected. Making the usual steady-stateapproximation for [Ln*:QA],we can write down a simple expression for the time dependence of the quenching of lanthanide ion luminescence:
+
(1)
in which A, k l , kZ,and Idc were allowed to vary. The appropriateness of the use of this function has been discussed previously.* Figure 1 contains the results for a typical biexponential fit. In this figure we have plotted the log of the measured emission intensity, the weighted residuals, and the autocorrelation function of the residuals. The solid line in Figure 1A represents the best fit of the decay data. Goodness of fit was also checked by examination of the residuals (Figure lB), which should be randomly distributed around 0, and by the autocorrelation function of the residuals (Figure l C ) , which should look like a delta function around 0. The luminescence instrument used for the work reported here is a custom-built spectrometer capable of recording the time dependence of both the total and circularly polarized luminescence.l1,l2 Measurements at low temperatures were performed by placing the cuvette containing the sample of interest in an Oxford instruments cryostat.
A-Ln*
kq+ + k,-
I 10
1
0.0
k,+ - k i
If homochiral quenching dominates over heterochiral quenching, a positive value of E, is expected, and, obviously, a negative value will be obtained if the reverse is true. It is useful to express the quenching process (given as the third reaction in the scheme given above) as a diffusional step (kdiff or kdiff+), resulting in the formation of an encounter complex, followed by competing pathways for dissociation of the encounter complex ( k a - or k a f ; ' )or energy transfer (kn-) to the quencher and back transfer (k-;). This is illustrated in eq 6, where [A-
1
*3
Rexwinkel et al.
(3)
(4)
The observed rate constant is given by the following expression:
kobs = ko
+ ~,[QA]
(8)
where from eq 7 it can be seen that
k, =
kdiffket ket + k-diff
(9)
Alternatively, eq 9 may be written as follows:
where K = (kdiff/k4iR) is the equilibrium constant for formation of the encounter complex. Three kinetic regimes can be identified from the discussion given above. In regime I, k,, > kdiff,and the quenching process is diffusion controlled, that is, the observed rate constant is a measure of diffusion to form encounter complexes. In this case, the overall quenching rate is insensitive to k,,,and kq = kdiff (12)
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5121
Enantioselective Quenching of Lanthanide Complexes Between these two limiting cases, the quenching rate becomes increasingly sensitive to the rate of diffusion (regime 111). If k,, is of the same order as kAiff,then the reaction can be described as ‘nearly diffusion controlled”. In this case, the quenching rates are slightly smaller than kdiffand moderately sensitive to k,,. B. Theoretical Expressiom for the Rate Co~tants.Chiorboli et al.I3 have developed expressions for both the diffusion and dissociation of ionic encounter complexes in solution as a function of ionic strength and various solvent parameters. kdiffcan be calculated from the Debye-Smoluchowski equation
to structure have been included. Even with these fairly severe approximations, the expressions for kdiffand kAiffappear to give reasonably reliable results, although the calculations are nontrivial, e.g., one needs to perform the numerical integration over the interaction distance. These expressions do seem to yield results that more closely model experimental data than other more tractable expressions.lj C. Ionic Strength Dependence of kq+and k 0.05; in the very low [~IJ(DPA)~*] ionic strength solutions the concentration of [Tb(DPA)3'] was decreased and no NaBr was a d d d [Ru(phen)p2'] = 0.2-1.8 pM. kdiRis calculated as in Figure 4. Also plotted in this figure is the degree of enantioselectivity, E,,. ps = 787 kg m-3, and D = 32.63.)"J8 However, the quenching rate constants have increased significantly from that observed in water. At the lowest values of ionic strength, the ratio kdiff/kq is only 7.5, implying that in these solutions, we must treat the system with a kinetic analysis appropriate for regime 111. We also note that Ep is not a constant over the full range of ionic strengths. To determine if racemization of the lanthanide complex is competing with quenching at high values of ionic strength, a small amount of the ruthenium complex was added to the cuvette corresponding to the last points in Figure 5. As indicated in eq 8,addition of quencher has the effect of increasing the quenching rate but has no effect on the racemization rate. Following this addition, the value for lE,l increased to the value obtained for the low ionic strength solutions, and, therefore, it is concluded that under these conditions racemization can no longer be neglected. We also observe a significant decrease in enantioselectivity at low values of ionic strength. This, we believe, is due to the fact that we are no longer in kinetic regime I as discussed in more detail below. To suppress racemization, we have performed a series of experiments in a cryostat at 255 K. These results are presented in Figure 6. To calculate kdiff, values for viscosity, density, and dielectric constant for methanol at this temperature were obtained from polynomial fits of tabulated reference data (for methanol at 255 K, Q = 1.132 X kg m s-', ps = 828 kg m-3, and D = 42).'7-2'As can be seen in this figure, E, is now constant over the range of ionic strengths selected. It should be noted, however, that the value obtained (-0.17),is significantly different than that obtained at room temperature (-0.28). This constitutes the first evidence that the degree of enantioselectivity in the quenching process of lanthanide trischelates is temperature dependent.
Discussion The two expressions presented above for the ratio of homochiral to heterochiral quenching (eqs 23 and 28) display a complex dependence on molecular dimensions (rLn,rQ, uLnrand uQ)and distances (a+and u-). To use these equations to model the effects measured in this work, it is necessary to develop an understanding of the size and shapes of the two species involved, and, ultimately,
Rexwinkel et al.
5730 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992
20
19
18
17
21
I
0
0.0
0.2
0.1
0.3
0.4
0.5
0.6
Figure 8. Plot of the homochiral and heterochiral quenching rate constants versus the ionic strength dependence predicted by eq 20 (see text) for the quenching of Tb(DPA)33- luminescence by (-)-Ru(phen)?+ in water at 298 K. Parameters used are the same as in Figure 4. 18 0.00
0.05
0.10
0.15
0.20
0.25
sqrt(I4 Figure 6. Plot of the homochiral (kq+)and heterochiral (kc)quenching constants, and the calculated diffusion constant (kdiff)as a function of p 1 / 2in methanol at 255 K. The ionic strength was adjusted with NaBr; [Tb(DPA)?-] = 0.74 mM;[Ru(phen)?+] = 2.1 p M . kdiffis calculated as in Figure 4. Also plotted in this figure is the degree of enantioselectivity, Eq. 2+
3A-Tb@PA)3
A-R~(phen)~
5
4
3
2
1
0
0 0
02
04
0.6
0.8
1.0
1.2
fi
Figure 7. Space-filling models of Tb(DPA)33-and R ~ ( p h e n ) ~ ~ + .
to understand the ways in which the two charged complexes are able to fit together in diastereomeric pairs. As a first step, in Figure 7 we show space filling models of the two D3 complexes in two different orientations, looking down the C3axis and looking down one of the C2axes (which are, of course, perpendicular to the C3 axis). The approximate models are based on crystal structures of related compounds. As presented above, in regime I, a plot of In kq versus (e2/ 2DkBT)f(p,a)should yield a straight line with slope equal to the charge product -zL,zQ, and an intercept equal to In [4000~a~(rL, 4- rQ)NAket/3].To calculatef(p,a), we need to know a, the distance at which energy transfer occurs, and uLnand BQ, the sum of the radii of the reacting species plus dominant counterion. In these experiments the dominant counterions are Na+ (r = 0.12 nm) and Br- (r = 0.20 nm). Calculations have shown, in fact, that the results of the modeling presented here are quite insensitive to small changes in B, and, therefore, for simplicity we have set
0
20
40
60
80
100
K (M-') Figure 9. Plot of the homochiral and heterochiral quenching rate constants versus K calculated from eq 18 for the quenching of Tb(DPA)33luminescence by ( - ) - R ~ ( p h e n ) ~in ~ +water at 298 K.
= 0.8 nm for all the calculations that follow. The ULn = nonsphencal shapes of the two species involved strongly suggest that simply using a value of a equal to the sum of the maximum radii of the two complexes would not be an accurate description of the donor:acceptor complex, and this was, indeed, observed if a value of a = 1.4 nm was used inf(p,a). The "best" value of a was determined by plotting the function given above and selecting the value of a (1.1 f 0.1 nm) that gave the best straight line through the data points. This best fit is given in Figure 8 for both the homochiral and heterochiral quenching rates for the aqueous data. The range of ionic strengths is also displayed in this figure, and it should be noted that low values of ionic strength correspond to the large K values. As can be seen, parallel straight lines are observed. The slopes of these two lines, obtained from simple linear regression, are 5.69 (+) and 5.74 (-) and yield a charge product very close to the expected value of -6 for point charged spheres representing Tb(DPA)33-and Ru(phen)?' ions. From the intercepts of the linear regression, using the values for the parameters given above, one can calculate ket+(6.0 X lo6s-') and ka- (4.7 X lo6s-l). Additional evidence that for water solution we can use an analysis based on kinetic regime I, is provided in Figure 9, in which we plot kq versus the stability constant K. K was calculated using the same values for rLn,'Q, uLn,BQ,and a as used in the calculation presented in Figure 8, and the charge product was set equal to -6. Again straight lines are obtained, indicating that the assumptions that K is independent of the chirality of the ion-pair, and that all the chiral discriminationis
The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 5731
Enantioselective Quenching of Lanthanide Complexes 22
TABLE I:
Calculated Ionic Strength Dependence of E , for Quenching of Tb(DPA),* by Ru(phen)?+ in Water at 298 K Using Eqs 23 md 28“ calcd using eq 28 calcd using eq 23
~~~~
21
E,
3, nm Aa, nm (g = 1.68
i‘
l9
18 I 0.6
0.8 1.0 1.1 1.2 1.4 1.5
I
0.7
0.8
I
0.9
I .o
F m e 10. Plot of the homochiral and heterochiral quenching rate constants versus the ionic strength dependence predicted by eq 20 (see text) for the quenching of Tb(DPA)t- luminescence by (-)-Ru(phen),*+in methanol at 255 K. 12,
-I I
0
al v)
ca 0 7
W
0-
Y
I
1
, .
I
. ,
t
n
I
.
l o8
,
1
,
6i
0 kq-
0 0
4
i
,
i
i
z t
1
ii
2
0
1
0
200
400
600
800
1000 1200 1400
K (M-’) Figure 11. Plot of the homochiral and heterochiral quenching rate constants versus K calculated from eq 19 for the quenching of Tb(DPA)$in methanol at 255 K. luminescence by (-)-R~(phen)~*+
in k,,, are appropriate ones for this set of results. The slopes of the two lines in this figure yield k,, directly; k,: = 5.3 X lo6 s-’, and k,; = 4.2 X 106 s-I. These results are close to those obtained above. In Figures 10 and 11 we plot similar graphs for the chiral quenching in methanol at 255 K. In the calculation of K, we have used the same values for the distance parameters as used for the aqueous solutions. The slopes of the two straight lines in Figure 10 yield charge products of -4.46 for the homochiral quenching and -4.50 for the heterochiral quenching. From the intercepts one obtains values of k,; = 3.4 X lo6 s-’, and k,+ = 2.4 X lo6 s-l. The slopes are considerably lower than that observed in water; however, this does not necessarily imply that the charges on the ions involved are different in methanol than in water, since, as mentioned above, at low values of ionic strength the system cannot be described by the formalism of regime I. In other words, k, does not equal Kk,. If the last two points in Figure 10 are omitted, where the deviation is most serious, charge products of -5.2 are obtained. The nonlinearity seen in Figure 11 is another indication that the quenching in methanol can not be modeled by regime I kinetics over the range of ionic strengths considered in this work. The fact that similar values for zL,,zQ are obtained in water and methanol suggests that the nature of the ionic species involved are essentially the same in these two solvents. We have previously demonstrated that the structure of the Tb(DPA)33-complex is essentially the same in methanol and in water through a comparison of the circularly polarized emission spectra of this species
0.082 0.184 0.282 0.439 0.97 1.276
mol/kg) Aa, nm
-0.04 -0.14 -0.22 -0.33 -0.62 -0.73
0.0575 0.105 0.139 0.183 0.310 0.404
(g
E, = 1.68 mol/kg) 0.12 0.02 -0.02 -0.07 -0.16 -0.22
auLn= UQ = 0.8 nm; 3 = (a+ + a-)/2, and Aa = a+ - a-. Aa was selected so that under conditions of zero ionic strength, E, = 0.12 (see eqs 24 and 29).
in these two solvents.* Also consistent with this observation is the fact that the same value for the separation of the charged species in the encounter complex (a = 1.1 nm) provides a good fit in both analyses. As shown in Figure 5 , at room temperature lEql decreases in methanol solutions as the ionic strength decreases. If the system must be described as “nearly diffusion controlled” then eq 10 must be used instead of the simple eq 11. This equation can be rearranged to solve for Kk,, as follows:
One can then “correct” the measured k, constants for diffusion effects by calculating kdinand performing the subtraction indicated in eq 32. If one makes the reasonable assumption that kdiffdoes not depend upon the chirality of the diffusing ion, then to get a value of -0.28 for E, from the first point in Figure 5 , one needs a value of kdirrapproximately 4 times smaller that calculated from the DebyeSmoluchowski equation (eq 13). This is well within the accuracy expected for this equation in methanol. As seen from eq 20, the enantioselectivity in the quenching process can, in principle, arise from K+ being unequal to K”, or k,: being unequal to ke;, or a combination of these effects. The first of these possibilities corresponds to a difference in the equilibrium concentration of homochiral versus heterochiral encounter complexes, and the second inequality corresponds to specific chiral selectivity in the energy transfer step. In the data presented in Figures 8-1 1, it has been implicitly assumed that the enantioselectivityis entirely in the energy-transfer step and that the equilibrium concentration of homochiral and heterochiral encounter complexes are equal. Examination of the ratio K+/K (see eq 20) shows that this ratio can only be different from unity if a+ does not equal a_. To evaluate this effect, we have performed a large series of model calculations in which the effect of variations in a+ and a- on the ionic strength dependence of E, has been determined. In these calculations it has been assumed that all of the enantioselectivity is due to these differences, i.e., k,: = k,;. The procedure used was to fix the value of cf = (a, + 4 / 2 , and solve for the value of Aa = a+ - a- such that E, at infinite dilution, as calculated indirectly from eqs 24 or 29, equals the observed value of 0.12. Using these values of rT and Aa, E, was calculated from eqs 23 and 28 for various values of p in the range 0-1.68 mol/kg. A wide range of values of a+ and a_,uLnand uQ were sampled, all obeying the condition that Eq(p=O) = 0.12. No discontinuities were found in plots of calculated E, versus p. Representative results are given in Table I for calculations in which uLn= uQ = 0.8 nm. In this table we report the value of ha required to produce an E, value of 0.12 at zero ionic strength, assuming the various values of cf shown. Also given in this table is the calculated value of E, at p = 1.68 mol/kg. It can be seen from the tabulated results that eq 29, and to a somewhat lesser extent eq 24, require large differences between a+ and a- to produce a value of Eg(p=O) equal to 0.12. These results also show the degree of enantioselectivity is predicted to depend strongly on the ionic strength of the solution. Using eq 28, this dependency
5732 The Journal of Physical Chemistry, Vol. 96, No. 14, 1992 is always present. If eq 23 is employed, the dependence is much weaker, and, in the case in which one selects u and is values that are equal (e.g., the first entry in Table I), no dependence on ionic strength is found. This latter situation, however, does not apply to our system, since the results are best fit with a value of = 1.1 nm, Le., the third entry in Table I. As presented above, in the quenching experiments performed in aqueous solutions, Eq appears to be constant (0.12 f 0.01) over the entire range of ionic strength used. Both eqs 28 and 23 can reproduce this constant result only if Aa is chosen to be smaller than 0.01 nm (for the assumed values of ii = 1.1 nm and uLn = UQ = 0.8 nm). It is concluded, therefore, that either (a) most of the observed enantioselectivity in the system under study here is due to differences in k,, and not to differences in K or (b) that the expressions for K (eqs 18 and 25) are inadequate or incomplete. Both of these possibilities must be considered. The energy-transfer step in the kinetic scheme (6) has been described by Richardson et a1.8 as an activated process:
k,,+ = k,,+ exp(-AG+*/kT)
(33)
The underlying assumption is that the encounter complexes are sufficiently long-lived and structurally flexible so as to allow for reorientational motions of the Ln* and Q complexes. Specific orientations ard presumed to be necessary (activation with associated free energies AG+* and AG-*) for the actual electronic energy transfer (rate constant k,,) to occur. In this picture the enantioselectivityin the quenching can be due to differences in energy-transfer rate constants (due to chiral electronic overlap effects), or a nonzero differential free energy of activation, or a combination of these effects. In a study of enantioselective quenching of Tb(DPA)33-and E u ( D P A ) ~ ~by- Co(II1) ethylenediamine complexes, Richardson et aL8 have estimated the magnitude of the chiral electric dipolemagnetic dipole interactions for their system using a reactive configuration consisting of collinear trigonal axes. These authors have demonstrated that the resultant enantioselectivitydue to chirality in kd is proportional to the product of gak(quencher)gl,,(donor), and can, in principle, be very large. Although this source of enantioselectivitymay be possible for the &(en)$+ studies, we do not think that it provides a satisfactory picture for the results presented here. One reason for this conclusion is that an extremely large value for gabwould be necessary to explain the observed enantioselectivity. The largest absorption dissymmetry value observed for R ~ ( p h e n ) ~is~approximately + 0.01,22and although, in principle, larger values of gab can be obtained for selected orientations, we do not believe that sufficiently large values of gabor glmare available to explain the large enantioselectivityobserved in our work. We thus conclude that the enantioselectivity for the system under study here must be associated with differences in AG+*and AG-*. It has been argued* that, for reactants with relatively smooth spheroidal shapes, such as C ~ ( e n ) and ~ ~ +Ln(DPA)33-,that the chiral discriminatory parameter, Aa, would be expected to be quite small. Nevertheless, there is experimental evidence for chiral discrimination in stereuselective interactions between such species. For example, Gillard has described a number of enantiomeric resolutions using large differences between the aqueous solubilities of the diastereomericsalts of metal chelate complexes of complexes that can be described as ~ p h e r o i d a l . For ~ ~ example, C O ( O X ) ~ ~ has been resolved using A - ( + ) - c ~ ( e n ) ~ and ~ + ; A-(+)c~(en),~+ and A-(-)Rh(en)32+have resolved a number of other trisoxalate complexes of transition metals. These resolutions reflect the chiral discrimination in lattice energies and strongly suggest that there may well be a substantial thermodynamic enthalpy difference between homochiral and heterochiral ion pairs. Using the shape criterion, chiral discriminatory interactions in ion pairs, a fortiori, could not be neglected for Ln(DPA)>- and Ru(phen):+, the latter having particularly large propellor blades (see Figure 7) and not at all spheroidal. In the conceptual framework of Richardson et a1.* such an enantioselective enthalpy effect would enter through the constant K. If in the encounter complex the Ln* and Q species are close, the enthalpy of formation may involve contributions from
Rexwinkel et al. terms other than the pure point-charge Coulombic interactions considered so far. Formally, one might account for this by extending the work term in K (see eq 18 or 19) with a term w ” representing these additional interactions. Operative at short-range only, w”would not appreciably depend on ionic strength but might be very “chiral”. This chirality would not arise from the ratio a+/a- being different from unity, and, therefore, might accommodate the experimentally found insensitivity of Eq toward ionic strength. Obviously, the importance of such a w” term to chiral discrimination critically depends upon the “tightness” of the reactive donor:quencher complex, and a discussion of the possible alignment of the donor:quencher complex is appropriate. As mentioned above, the propeller shaped Ru(phen)?+ and Tb(DPA)33-species as displayed in Figure 7 are not smooth spheroids; at best one might describe them as oblate spheroids with equatorial radii of 0.67 and 0.66 nm, respectively, and polar radii of 0.35 and 0.30 nm. Thus, the value of a, 1.1 nm, obtained above is, in fact, less than one would predict for “contact” along the C2axes (i.e., the sum of the equatorial radii, 1.4 nm) but greater than that predicted for contact along the C3axis (Le., the sum of the polar radii, 0.65 nm). Therefore, for an approach of luminophore and quencher along the collinear C3 axes, energy transfer may be occurring at distances larger than the contact distance, and, thus, may occur without removal of solvent molecules. This picture may lead to an opportunity to explain the unusual solvent dependence observed in this system. The differential solvating abilities of methanol and water may result in significant differences in the preferred relative orientation of homochiral and heterochiral donor:quencher ion pairs in the energy-transfer step. This aspect of the enantioselective quenching, as well as the study of the relative contributions of enthalpy and entropy effects through temperaturedependent measurements, requires more experimental work.
S-ry In water solutions at 298 K we have shown that the kinetics of the quenching of Tb(DPA)33-by Ru(phen)?+ can be described as the formation of a diffusional preequilibrium followed by a slower energy-transfer step. The ionic strength dependence of the quenching rate constants have been shown to be accurately modeled by the predicted ionic strength dependence of diffusion of a +2 and -3 charged species. Furthermore, the value of the parameters, a+ and u- (1.1 nm), shows (for the first time) that the energy transfer between the lanthanide complex and Ru(phen)?’ occurs through a short-range interaction. The fact that both the homochiral and heterochiral quenching rate constants display the same ionic strength dependence, is consistent with a picture of a moderately tight ion pair in which the influence of secondary ions may be neglected. Analysis of quenching data in methanol at 298 K required consideration of two additional effects. At this temperature, racemization of the lanthanide complex is approximately 5 times that measured in water and cannot be neglected in high ionic strength solutions where the diffusion of ions is slowed. This racemization tends to decrease the observed enantioselectivity as measured in Eq values. Experiments performed at 255 K show constant values of Epat these ionic strengths. In addition, one must consider “near diffusion controlled” kinetics at low values of ionic strength in order to explain the variation in enantioselectivity observed under these conditions. Acknowledgment. This work has been supported by grants from the National Science Foundation, Division of International Programs (INT-8912621 to J.P.R.), NATO international collaborative research grant (H.P.J.M.D. and J.P.R.), and the National Institutes of Health (GM42194-01 to J.P.R.). References and Notes (1) Metcalf. D. H.; Snyder, S.W.; Wu, S.;Hilmes, G. L.; Riehl, J. P.; Demas, J. N.; Richardson, F. S. J . Am. Chem. Soc. 1989, 111,3082-3083. (2) Rexwinkel, R. B.; Makers, S. C. J.; Riehl, J. P.; Dekkers. H. P. J. M. J . Phys. Chem. 1992, %, 1 1 12-1 120. (3) Metcalf, D. H.; Snyder, S. W.; Demas, J. N.; Richardson, F. S. J . Am. Chem. Soc. 1990, 112, 5681-5695.
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J. Phys. Chem. 1992, 96, 5733-5738 (4) Metcalf, D. H.; Snyder, S. W.; Demas, J. N.; Richardson, F. S.J . Phvs. Chem. 1990.94. 7143-7153. 1 5 ) Metcalf, D.'H.;.Snyder, S. W.; Demas, J. N.; Richardson, F. S.Eur. J. Solid S f a f eInorg. Chem. 1990, 28, 57-64. (61 Wu. S.: Bedard. T. C.; Riehl. J. P. Coll. Czech. Chem. Commun. 1991, 56,'3625-3027. (7) Riehl, J. P.; Richardson, F. S.Chem. Rev. 1986, 86, 1 . (8) Richardson, F. S.; Metcalf, D. H.; Glover, D. P. J. Phys. Chem. 1991, 95,6249-6259. (9) Gillard, R. D.; Hill, R. E. E. J. Chem. Soc., Dalton Trans. 1974,1217. I101 Press. W. H.: Flannerv. B. P.: Teukolsky, S.A,; Vetterling, W. T. Numerical Recipes; Cambridge University Press: Cambridge, 1986. (1 1) Blok, P. M. L.; Schakel, P.; Dekkers, H. P. J. M. Meas. Sci. Technol. 1990, I, 126-30. (12) Rexwinkel, R. B.; Schakel, P.; Meskers, S. C. J.; Dekkers, H. P. J. M., to be published. (13) Chiorboli, C.; Indelli, M. T.; Scandola, M. A. R.; Scandola, F. J . Phys. Chem. 1988, 92, 156-163.
(14) Eigen, M. 2.Phys. Chem. (Munich) 1954, J , 176. (15) Fuoss, R. M. J . Am. Chem. SOC.1958,80, 5059. (16) Sutin, N . Prog. Inorg. Chem. 1983, 31, 441. (1 7) Handbook of Chemistry and Physics, 50th ed.;The Chemical Rubber Company: Cleveland, OH, 1969. (18) Timmermans, J. Physical Chemical Consfants of Pure Organic Compounds; Elsevier: New York, 1950. (19) Infernational Crifical Tables of Numerical Dura: Physics, Chemisfry, and Technology; National Research Council of the USA; McGraw-Hill: London, 1958. (20) Viswanath, D. S.;Natarjan, G. Databook on rhe yiscosify ofliquids; Hemisphere Publishing: New York, 1989. (21) Lax, E. Taschenbuch for Chemiker und Fysiker; Springer-Verlag: Berlin, 1967. (22) Blok, P. M. L.; Cartwright, P. S.;Dekkers, H. P. J. M.; Gillard, R. D. J. Chem. SOC.,Chem. Commun. 1987, 1232-1233. (23) Gillard, R. D. In Optical Acfivifyand Chiral Discrimination; Mason, S . F., Ed.;D. Reidel: Dordrecht, 1979.
Guest Molecule Dynamics in Thiourea Inclusion Compounds As Studied by 13C MAS NMR Spectroscopy Klaus Miiller Institut fiir Physikalische Chemie, Pfaffenwaldring 55, 7000 Stuttgart 80, Germany (Received: March 16, 1992)
Thiourea inclusion compounds with four cycloparaffins (1,l-, cis-l,2-, and cis-1,4-dimethylcyclohexaneand cis-decalin) are studied by dynamic IgCmagic angle spinning NMR spectroscopy. Variabletemperatureexperiments are performed in order to evaluate the specific molecular features of the guest compounds. By a quantitative line shape analysis of these experiments the ring inversion process of the guest molecules can be established as the dominant relaxation mechanism in all systems investigated. The direct comparison with former investigations on the neat guest compounds reveals significant deviations in the activation parameters for cis- 1,4-dimethylcyclohexaneand cis-decalin. The differences are explained by molecular interactions between the thiourea host matrix and the hydrocarbon guests where rather sterical reasons than polar guest-host interactions are of importance. They primarily originate from the respective orientations of the guest molecules along with the spatial restrictions imposed by the thiourea host lattice.
Introduction Inclusion and intercalation compounds represent suitable systems to study the nature of molecular guest-host interactions.' Among these, urea and thiourea inclusion compounds particularly have been investigated which, with respect to the molecular structure, behave very similarly." X-ray diffraction studies have shown that both compounds build up hexagonal channel structures (see Figure la) which are distinguished by the actual size of the cross-sectional area.39637 Thus, the smaller urea channel is appropriate to store linear and branched hydrocarbon chains2while the thiourea channel diameter of about 7 A is large enough to accommodate bulky molecules such as substituted and unsubstituted cyclic hydrocarbons) or even metallocenes.* It is interesting to note that generally the guest molecules within these channels are expected to be positionally but not necessarily orientationally ordered. A prerequisite for the understanding of both the stability of these inclusion compounds and some unusual material properties9 is the precise knowledge of the molecular behavior of the guest species. In this respect, several studies have been published dealing with the evaluation of the structural and dynamic features of the guest molecules within such comple~es.'"~~ For the class of the thiourea inclusion compounds, the cyclohexane/thio~rea'~-~*~~*~~ and f e r r o c e n e / t h i o ~ r e asystems ~ ~ ~ ~ are very well characterized by X-ray and NMR investigations while the information on other systems, like substituted cyclic hydrocarbons, is rather limited. So far, it could be shown that monosubstituted cyclohexanes with polar substituents prefer a con-
formational state within the thiourea host lattice which is different from that usually encountered in liquid or gas Thus, bromo- and chlorocyclohexane in thiourea exhibit a high tendency to the axial conformation with an amount of 90-958, almost independent from t e m p e r a t ~ r e .As ~ ~the most probable explanation for this phenomenon polar guest-host interactions rather than sterical reasons have been considered since the nonpolar methylcyclohexane, although having a larger molecular size, still prefers the equatorial conformati~n?~*~~ Similar results have been reported from IR investigations on dihalocyclohexanesin thiourea?I However, in that case spatial constraints due to the limited cross-sectionalarea of the thiourea host lattice might be responsible for the stabilization of the axial conformation. First informations about the dynamic properties of the guest molecules in thiourea inclusion compounds have been obtained from former differential scanning ~alorimetry,'~ 14N nuclear quadrupole resonance, and IH NMR experiments'0-18*20 which implied a high degree of conformational flexibility of the un~ ) when substituted cycloparaffin guests (C6HI2to C ~ H I even trapped within the thiourea channels. This was confiied recently and by 2Hand 13CNMR investigations on both un~ubstituted~~ monosubstitutedg0cyclohexanes. By a quantitative line shape simulation it could be shown that the internal ring interconversion process of the cycloparaffin guests is the dominant relaxation mechanism between about -100 OC and room temperature with Surprisingly, the rate constants in the order of k lo2-lo6 kinetic parameters did not show any evidence for a remarkable influence of the host lattice on the internal guest molecule dy-
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0022-365419212096-5733$03.00/00 1992 American Chemical Society
