Chiral Lanthanide NMR Shift Reagents and Equilibria Rationale for the Observed Signals Robelt Rothchild The City University of New York, John Jay College of Criminal Justice, Toxicology Research and Training Canter, Department of Science, 445 West 59 Street, New York, NY 10019
Since their discovery by Hinckley in 1969 (1) NMR lanthanide shift reagents (LSR) have proven quite useful in providing spectral simplification and assisting structure determinations. The subject has been extensively reviewed (210). With the development of chiral LSR, it has been possible in many cases to achieve direct determinations of optical purity (enktiomeric excess) based on the observation of enantiomeric shift differences. The enantiomeric shift difference may he defined as the difference in chemical shift observed for the signals of corresponding nuclei in enantiomeric molecules in the presence of chiral LSR. Several reviews have focused on ihiral LSR applications (11,12). In general, the LSR binds to a basic site in the substrate in a Fast, reversible equilibrium, i.e., fast on the NMR time scale. Addition of achiral LSR to a sample solution usuallv provides a single set of absorption signals, the chemical-shifts reflecting the time average of the shiftsfor thefree,unhound substrate and for the substrate bound to LSR to form a "bound complex". The "bound complex" would be characterized hv its "bound shifts". but the actual observed shifts are weigked averages reflecting relative amounts of free substrate and substrate present as "bound com~lex".This depends on the concentr&ions and molar ratios bf LSR and substrate and the binding constants (or association constants) for LSR and substrate in the different species involved. Typical work at ambient temperatures involves association4ssociation that is fast enough on the NMR time scale so that one set of resonances is seen, rather than seeing separate signals for free versus bound substrate. When a mixture of substrate enantiomers is treated with an o~ticallvpure chiral LSR. one can often see seoarate sign& corr&ponding to the two enantiomers. ~ e a s u r k n e n t of peak intensities (bv peak heiehts or. better. hv areas) allows direct measure&& of relaiive amounts df sibstrati enantiomers and permits optical puritv determinations with no need for skple deriv&ization A d with no need for actual enantiomer resolution. In fact, each set of signals observed for the substrace enantiomers reflects a d y & n i c equilibrium 01' free substrate and bound complex for each enantiomer. The different chemical shifts for the enantiomers may reflect differences in binding constants or differences in geometry of the bound complexes of the two enantiomers, or both. We have found that students often have difficulty in understanding the origins of the enantiomeric shift differences. If the LSR is in rapid equilibrium with each of the substrate enantiomers, whv do vou not see onlv a single set of signals, representing averaged chemical shifts for both enantiomers? The simple analom presented here as a rationalization has served as a useful-way to clarify the situation. Our analoev illustrates the two eauations that describe the simple viLw of the dynamic equilfbria involved in which the two enantiomers of substrate rauidlv and reversiblv can bind to a n optically pure LSR, denoted R*-(LSR), toform 814
Journal of Chemical Education
lllusbatlons for me movingcandle analogy. Left: A candle m move between rwms A and B or between rwms C and D. Center: The "photographic time exposure" shows light Intensity in ma variws rooms in proponion to the times
swnt by. me candles. with hnizontal bars of lioM connenino mt, r w m s linked . ~~
by the oynamic processes.Right: The hMR specnal representation under 'last exchange cond lions" shows ring e 'peak pos Bans" reflening the l i m p averaged Chemcsl shins tar each of the wo equiloor a. Sea text.
the two different hound (1:l) complexes, represented as RRXand S-R*. Since these two bound complexes have the same configuration in the LSR portion. R*. and different configurati&s in the substrate ~ortion,'the'complexesare related as diastereomers. That is, the complexes can have different geometries, different energies, and different chemical shifts. The crucial point is that there is no equilibrium interconverting R- and S-(substrate); racemization is not occurring, and likewise there is no interconversion between the R-R* complex and the S-R* complex. There is no "leakage" pathway between eq 1and eq 2. R-(substrate) + Re-LSR * R-R* (bound complex)
S-(substrate)+ R*-LSR +5-R* (bound complex) (2) In our analogy, we consider people moving between different rooms (see figure) carrying candles. One person can move back and forth between rooms A and B (but cannot get to rooms C or D). Another person can move between rooms C and D (hut cannot enter rooms A or B). The proportion of time spent in one room versus the other accessible room relates-to the equilibrium constant for the process or, in the case of the LSR process, the bindinz or association constants. The rate 01travel between the rooms would correspond to the kinetic rate constants, assumed "fast" on the NMR time scale. For the A-to-B equilihrium, we have represented the case where more time is spent in room B; on the average, there would be a higher level of illumination than in room A. Conversely, we have shown that in the C to D case, more time is spent by the person with the candle in room C than room D. The average light levels in the rooms are indicated in the central nortion of the firmre. - . corres~ondine to the sizes of the encircied regions. o u r assumption;hat t h e svstem is in the reaion of fast exchange for the NMH spectra means that we wiil observe a time-weighted average-single peak for eq 1(candle motion between rooms A and B) and a
separate single peak for eq 2 (candle motion between rooms C and D). For eq 1,this weighted average would place the candle toward room B and for eq 2 toward room C, as shown in the right-hand portion of the figure. The point is that the average chemical shift observed for the species containing the R-(substrate) must lie somewhere between the shifts for free and bound R-(substrate), whereas the observed shift for the species containing the S-(substrate) lies between the shifts of free and bound S-(substrate). The bound shifts of the diastereomeric complexes R-R* and S-R* may differ for geometric reasons and the observed time-averaged shifts may also reflect differences in the binding constants, i.e., relative amount of free versus bound substrate for each enantiomer. But since there is no "averaging" pathway between the diastereomeric hound complexes and no racemization pathways between the substrate enantiomers, there is no necessity for observation of only one absorption peak. We might consider a photographic time exposure of the moving candles for the situation we have pictured here. Clearly, the time exnosure would reveal a horizontal bar of lieht linkine rooms A and B, with more luminosity at the B iide, and second separate horizontal bar of light linking rooms C and D, with greater luminosity at the C side. No vertical or diagonal bars of light would be seen since there are no pathways between the upper rooms (analogous to eq 1) and the lower rooms (analogous to eq 2). As a consequence of the assumed fast exchange on the NMR time scale, one observes a single peak of intermediate chemical shift when two species with differing chemical shifts are in rapid equilibrium with each other (rather than the time-exposure photograph that might show two separate balls of light with luminosities proportional to the times spent by the candle between the two rooms). If slow-exchange conditions obtained in the NMR of a mixture of substrate enantiomers with an optical-
ly pure LSR, one might expect to see one signal for each bound complex, with areas proportional to relative amounts of these R-R* and S-R* complexes, and another single signal for the pair of free substrate enantiomers, since true enantiomeric species should have identical chemical shifts. These analogies have served well to clarify this question l ex~lainine related t o ~ i c involvs and should nrove h e l ~ f uin ing averaging observations. The subject is especially relevant as seen by several recent articles on chiral and achiral LSR (13,14). Acknowledgment Supporting funds have been provided, in part, from the U.S. Education Department Minoritv Institutions Science Improvement program Award no. ~008641165,National Science Foundation Instrumentation and Laboratory Improvement award no. USE-8851684, and the Sandoz Research Institute. Literature Cited
1. Hinekley, C. C. J Am. Chem. Soe. 1969.91.51W162. 2 CwkeriU,A. F.:Davies.0. L. 0.; Hmdcn, a. C.:Raekham, D.M.Chem.Reu. 1978.73, 553-588. 3. Kime, K. A,: Simra.R. E.AldtiehimAefa 1971.10 (4).5462. 4. n-. R R. 1" A s y m t r i c Smthos*; Monisan, J. D., Ed.: Academic: Nea York, 1983: Vol. 1, pp l?3-196. 5. Inagaki, F.; Miwwa,T. m . N u c l . Mwn. ReaahSpertmre. 1981,14,W-111. 6. h e n s o , J. R.;xavier. A. V. I" Syatemotics and the Pmpeniea of &heknthonides: Sinhs, S.P., Ed.;NATO AdvaneedStudy InatitutcSsries, Sedes C, no. 1W. Reidel: Dordrdt, Notherlands, 1983; pp 501-540. 7. Hofer, 0.In Topi- in SLereoehsmlstry; AUingu, N. L.; Eliel, E L., Eds.; WileyIntemience: NeaYork, 16'7%pp 111-197. s. Rinaldi, P. L.Plop. Nucl. Magn. Rem~.Speetraae.1982,15,291352. 9. Flockhart B. D. CRC Crit. Re". Anal. Chem. 1916.6 (1) 69-130. 1987. lo. Wenu1.T. J.NMR Shift ReogenC8; CRC:Bwa Raton, 11. Kutal,C.IoNucloarMogmticResa~neeShiftRaagents;Sieven.R.E.,Ed.;Acadsmic: Near York, 1973; pp 87-98. 12. Sulliuao. 0. R. In Topics in Stemoehemisfry; Elid, E. L.; AUinger, N. L., Eds.; Inteneienee: New York. 1978; pp 287329. 13. Lipkoaitz, K. B.; Mwney. J. L. J. Chem. Ed=. 1987.64.98fr986 14. Wenzel, T. J.; Russett, M.D. J. Chom. Edue. 1987,M,979-980.
Volume 66 Number 10 October 1989