4316
Journal of the American Chemical Society
(4) (a) H. A. Bent, Chem. Rev., 68, 587 (1968); (b) N. W. Aicock. Adv. Inorg. Radiochem., 15, 1 (1972);(c) P. Murray-Rust, Spec. Rep. Chem. SOC., in press. (5) (a) R . E. Rosenfield, Jr.. and R. Parthasarathy, Abstracts of the American Crystallographic Association's 25th Anniversary Meeting, Charlottesville. Va., March 9-13, 1975, p 28; (b) R. E. Rosenfieid, R. Parthasarathy, and J. D. Dunitz, J. Am. Chem. SOC., 99, 4860 (1977). (6) 0. Kennard, D. G. Watson, F. H. Allen, W. D. S.Motherwell, W. G. Town, and J. Rodgers, Chem. Br., 11, 213 (1975). (7) User manual, Cambridge Crystallographic Data Centre, 1978. (8)D. N. Peak, W. L. Duax, C. Eger. and D. A. Norton, Am. CrysfaIIogr. Assoc. Abstr., 1 (summer, 1970). (9) In the Cambridge Crystallographic Data file. April 1978 update. (10) Figures l a and l b should be rotated about the C-X axes to give a true picture of the density. The volume of an annulus with limits rl, r,, 81, is 2.rr(r13 r23)(cos 81 - cos /I2). (1 1 ) These studies would have taken several man-years by manual methods (literature searching, punching coordinates, and checking errors) but required only -10 min computer time altogether on an IBM 370/165. (12) Geometrical correlations have been linked to the potential energy surface of molecules (ref 13).A similar argument has been used by Brown14 who plotted 0-H---0 interactions and suggested that the high frequency of occurence of linear arrangements corresponds to a potential minimum, (13) (a) H. B. Burgi, J. D. Dunitz, and E. Shefter, J. Am. Chem. SOC.,95, 5065 (1973); (b) H. B. Burgi, Angew. Chim., Int. Ed. Engl., 14,460 (1975);(c) P. Murray-Rust. H. 6. Burgi, and J. D. Dunitz, J . Am. Chem. SOC.,97, 921
/
101:15
/ J u l y 18, 1979
1
o2
-
(1975). (14) I. D. Brown, Acta Crystallogr., Sect. A, 32,24 (1976). (15) If the Boitzmann distribution governs the density of points,14 then the minimum at 8 = 180" might be -1.5-2.0 kcal mol-' below that of any configuration at 8 = 90'. However, it is dangerous to put too much confidence in the quantitative aspects of the distribution.
(16) In several cases in Figure la the iodine makes contact with two oxygen atoms of a neighboring molecule (e.g.. an ester).
Peter Murray-Rust* Department of Chemistry, Unirersity ojStirling Stirling FK9 4LA, Scotland W. D. Sam Motherwell Crystallographic Data Centre, Unicersity Chemical Laboratory Lensfield Road, Cambridge, England Receiced January 18, I979
Small Errors in C-H Bond Lengths May Cause Large Errors in Rotational Correlation Times Determined from Carbon-13 Spin-Lattice Relaxation Measurements Sir:
Measurements of spin-lattice relaxation times ( T i )of resonances of proton-bearing carbons in proton-decoupled 3C N M R spectra have been used extensively to study rotational motions of large molecules in solution.',' Because I3C-'H dipole-dipole interactions with directly bonded hydrogens provide an overwhelmingly dominant relaxation mechanism? (even at high magnetic field strengths3), it is necessary to know the values of the pertinent carbon-hydrogen bond lengths (rCH) in order to extract values of rotational correlation times ( T K ) from the measured TI I n this report we show that the widespread practice of setting rCH = 1.09 A (a typical value obtained from rotational spectroscopy) can cause very large errors in the value of T R . We show that small errors (2-3%) in the assumed value of rCH can result in values of T R in error by as much as a factor of 2. This sensitivity of T R to the choice of rCH is caused by the combined effects of the dependence of 1 / T I on r C H 6 and the nonlinear relationship between I /TI and T K (when dealing with large molecules a t typical magnetic field strengths; see Figure I ) . j W e show that the temperature dependence (at 14.2 kG) of the T I values and nuclear Overhauser enhancements ( N O E ) of the a-carbon resonances of aqueous hen egg-white lysozyme can be used to determine T R and rCH. We discuss the choice of magnetic field strength for maximizing the accuracy of T R when rCH is not known accurately. We show that the reported discrepancies between T R values measured a t 14.2 and 63.4 kG5 are elimi0002-7863/79/150l-4376$01 .OO/O
001
L-
10 o
10
IO-'
Figure 1. Semilog plots of'thcureticci1 (in seconds) and NOE (ratio of intcnaitica h i t h and without prototi dccoupling) vs. 713 (in seconds) for a "C spin undergoing I 3 C I~l l dipolc-dipole relaxation, in the case of isotropic rotational reorientation ,ind under conditions of proton d e ~ o u p l i n g . ~ Plots arc given for various ini,lpnctic ficld strengths. indicated in kilogauss. The N O E v;ilucs arc indcpcndcni of t h c choice o f the carbon-hydrogen distance.J Thc T I plots wcrc coiiiputcd lor a C-H group with r c =~ I .09 ( d i d curve:\) or 1.13 .& (d,i\hcd curLC\).
nated (without invoking anisotropic rotations5 or internal librational motions6) when the corrected value of rCH is used. The appropriate choice of rC-11 for the interpretation of I3C relaxation data is the average ( r - 3 ) - i / 3for the vibrational ground state.' Only a f e N determinations of rotational motions from "C T Imeasurements have incorporated vibrational corrections for r c ~ . ' These . ~ estimates indicate that ( r - 3 ) - 1 / 3 may be 1-2% greater than rc values based on rotational spectra or electron diffraction In addition, results from N M R spcctroscopy i n liquid crystal solvents (which yields distance parameters related to ( suggest that, at least in some cases, the vibrational correction may be >2%.9 Furthermore, the reported frequency dependence of some I3C TI values has been used to suggest a value as large as 1.15 A for the Cc'- H bond length in some peptides.I0 Considcr a carbon ( w i t h a single directly bonded hydrogen) which i b part of a nioleculc undergoing isotropic rotational reorientation uith a corrclation time T R . Figure 1 shows theoretical plots of T I arid h O E vs. T R (in a range of T K values expected for ~nolccularweights between 10' and IO6), at 14.2, 23.5, and 63.4 k G . j 'The NOE values are independent of the choice of r( 11. For the T ,computations, rcH values of 1.09 (solid lines) and I . 13 A (dashed lines) were used. Let us assume that the truc values uf rcl{ and T K are 1.13 8, and 8 ns, respectivel>.Then the measured 7'1 at 14.2 and 63.4 kG will be 29.6 and 270 in>,respectively. I f \ L C use rCH = 1.09 8, in the interpretation of the data. Figure I will yield T R values of 18 ns (14.2 k G ) atid 10 11s (63.4 k C i ) . " Clearly, i f t h e true T R = 8 ns, an erroncous choice of rcl! is much more serious for T I data at 14.2 kG than fur data at 63.4 kG. In general, measured T Ivalues \\ hich are near thc miiiiiiium of the T i vs. T R curve may yield \cry erroneous v~ilucsof T R , unless rcH is known with great accur:icj. The minimum in the T I curves occurs a t T R values o t -2. 5 . and ti 11s at 63.4. 23.5, and 14.2 kG, respectively. Values of rK i n thc range 1 ~ 1 ns0 are expected for many substances ( i n "rioii\iscious'. solvents at room temperature) which I i i i ~ c riiulecular weights in the range 2000 to Clearl). \\hen I3C spin-lattice relaxation times 20 O W . ' I " arc u d t'or dcterriiining the T K values of such molecules, it is desirable tu chouse :I rnagnctic ficld strength which does not place 7'1 near the ~iiinimumin the T I VS. T R plot.
0 1979 Americdn Chemical Society
4377
Communications to the Editor Table 1. a-Carbon Spin-Lattice Relaxation Times and Nuclear Overhauser Enhancements a t 14.2 kG for Aqueous Hen EggWhite Lysoiyme" t em p,
temp,
"C
TI,s'
NOE'
"C
TI,^"
NOE'
22 25 29 35 37 40
27.9 21.4 29.0 30.9 28.7 28.9
1.43 1.45 I .42 1.62 1.51 1.55
44 46 49 50 57 62
26.3 28.3 26.2 28.8 28.7 32.5
1.68 I .87 I .hO I .74 I .72 I .96
( I Hen egg-white lysozjme (six times crjstallized) h a s obtained from Miles Laboratories, Elkhart, Ind. The sample was 7 inM protein in H?O (0.1 M NaCI). At temperatures u p to 50 "C. the pH u a s adjusted to -3.0, a value low enough to prevent appreciable self-association ( R . S. Yorton and A . Allerhand. J . B i d . Cheti/,,252, 1795 (1977), and references cited therein). but high enough to avoid unfolding of the protein. The pH p i i s raised to 5.0 for measurements above 50 "C. Carbon-13 Y M R spectra wcre obtained casentiallq a s described by E. Oldfield, R. S. horton. and .A. 4llcrhand. ihid.. 250, 638 I ( I 975). 71 values were measured from partiallq relaxed Fourier transform ( P R F T ) I\r M R spectra.' Typicall\. cleven P R F T spectra Mere used at each tenipernture. and the observed intensities of the m-carbon envelope here anall7ed v.ith the use o f an exponential fit (see M . Sass and D. Zieso\r, J . ,i.ln,q/r. Ro.yo/i., 25, 263 (1977)). Estimated random error is % 10%. We define the YOtj as the ratio of intensities nith and without proton decoupling. The h O E values were measured with the use of gated proton dccoupling (see R. Freeman, H. D. W . Hill, and R. Kaptcin. ihid.. 7, 327 ( I 972)). Estimated random error is f 10%.
i
-
f0 9 -
'
8 C
7 L 6-
' 0
54-
,'
0
0
. . j O'
0
TR (ns)
,
0
,
I
0
0
.' 2 -
"
We now show that measurements of T I values at or near the minimum of the T i vs. 7~ curve can be used for estimating the proper value of r C H (for use in the analysiz of T I data at any magnetic field strength), if the corresponding NOE values are also measured. I n Table I we show the t e m p m t u r c dependence of the T I and N O E values (at 14.2 kG) of the (Y carbons of 7 m M hen egg-white lysozyme in H 2 0 (with 0.1 M NaCl).l3 The N O E value gradually increases from - I .4 a t 22 "C to -2.0 at 62 "C. On the basis of the N O E curve f o r 14.2 kG (Figure 1 ) we conclude that T R changes from about 7 ns at 22 "C to -3 ns at 62 "C. For this range of T R values, T I (at 14.2 kG) should be nearly invariant and very close to the minimum T I (see Figure I ) . Indeed, the experimental T I values are mentially independent of temperature (Table I ) . We e30:1). N M R shows a single doublet, 6 1.01 for 9, whereas the exo methyl isomer, obtained by partial equilibration of 9, shows this methyl group at 6 I .20. At this point, all four critical centers corresponding to C ( 13), C(14), C(17), and C(20) i n steroid numbering have been created with the correct relative configuration. Baeyer-Villiger oxidation using basic hydrogen peroxide gives initially the unrearranged hydroxy acid which upon direct subjection to TsOH in benzene is converted into the rearranged IR 1780, 1655 crn-l; N M R 6 5.43 (d, J = 7 Hz, lactone 1 H ) , 4.55 (br S, 1 H ) , 1.28 (d, J = 7 Hz, 3 H), 1 . 1 1 (s, 3 H ) . After reduction to the diol, reaction with 1 equiv of tertbutyldimethylsilyl chloride allowed selective protection of the primary alcohol. Transposition of the chirality of the allyl alcohol unit to an allylic inverted carbon unit envisioned the use of allylic alkylation via organopalladiuni chemistry12,'3or [ 3.31-sigmatropic rearrangement. Attempts to effect a modified Claisen rearrangement ( C l a i s e n - J ~ h n s o n 'ortho ~ ester or Claisen-Ireland-Arn~Id'~enolate) failed presumably because of steric crowding. On the other hand, the much less 0 1979 American Chemical Society
