3224
J . Phys. Chem. 1987, 91, 3224-3228
Transverse Nuclear Spin Relaxation of Fluorine-19 and Phosphorus-31 in PFO,*- in High Magnetic Fields Thomas C. Farrar* and Rafael A. Quintero-Arcayat Department of Chemistry, University of Wisconsin, Madison, Wisconsin 53706 (Received: December 15, 1986)
The low-frequency line in the I9F NMR spectrum of PF03,- is much broader than the high-frequency line while for the 31P NMR spectrum the high-frequency line is broader than the low-frequency line. The experimental conditions needed for the occurrence of such differential line broadening (DLB) in coupled spin systems are discussed. Experimental measurements of T I ,and the line widths for fluorine-19 and phosphorus-31 are reported for the PFO?- ion in water-ethylene glycol solutions. These results are compared to the theoretical predictions of Shimizu. Theory and experiment are in excellent agreement. The absolute sign of the spin coupling constant is negative, JPF= -870.0 0.5 Hz. It is shown that T I ,measurements of simple two-spin systems can be used to obtain accurate information about the chemical shift anisotropy of the two spins, the bond distance, and the molecular correlation time.
*
Introduction In principle, the Redfield density matrix theoryl of N M R relaxation tells one all there is to know about the behavior of simple spin systems in liquids. On the basis of the Redfield theory, Shimizu2 has shown that for a two-spin system, I-S, where both I and S have a spin of I/,, the relaxation behavior of the two lines in the I-spin NMR spectrum and the two lines in the S-spin N M R spectrum can be quite different, if more than one relaxation process is present (we shall sometimes refer to the two spins as I and S and sometimes as A and X, both conventions are used interchangeably). For example, if both the dipole-dipole interaction and the chemical shift anisotropy (CSA) interaction contribute significantly to the relaxation, then the longitudinal relaxation time, “TI”,and the transverse relaxation time, “T,”, can be very different for each of the four lines. The longitudinal relaxation of each of the four lines is rather complex and is described by a triple exponential function. The transverse relaxation, T,, of each of the lines is different and each is described by a single exponential function. When we refer to the T , and T2relaxation times in this paper we mean the longitudinal (spin-lattice) or transverse (spin-spin) relaxation times, respectively. The goal of the work reported in this paper was to carry out a careful experimental test of the Redfield theory as it applies to the transverse relaxation time, T,, for the “simple” two spin system PFO?-. As we shall see, the experimental results and the theory agree well. An earlier classic effort of such an experimental test was made in a series of elegant papers by Mackor and M ~ L e a n . In ~ their work they used CHFC1, as a model compound. Although they were able to show that the longitudinal relaxation was different for the two lines in the high-resolution fluorine-19 NMR spectrum, they were not able to see any differential transverse relaxation (or differential line broadening, DLB). CHFC1, is not an ideal model compound for such a test because the presence of the chlorine nuclei influences the transverse relaxation of both the proton and fluorine spins, and due to the low molecular symmetry the proton and fluorine have different correlation times. A comprehensive review article dealing with many theoretical and experimental aspects of N M R relaxation has been recently published by Vold and V ~ l d . The ~ review by Werbelow and Grant5 on dipolar relaxation in coupled spin systems covers some aspects of the use of the Redfield density matrix formalism. For this present study we have chosen PF03,- as a model compound. There are several reasons for this choice: (a) the chemical shift anisotropies of both fluorine and phosphorus have been measured6 and the anisotropies for both are rather large, (b) the P-F bond distance has been measured,’ (c) PF03,- is reasonably soluble in a D20-ethylene glycol-dlomixture, which Present address: AT&T Bell Laboratories, Room IC-252, Murray Hill,
NJ 07974. 0022-3654/87/2091-3224$01.50/0
TABLE I
parameter (ail
- .dP
(all
- ul)F
r
value
ref
-145 ppm f182 ppm 163 pm
6
6
I
affords one a wide range of molecular correlation times over a reasonable temperature range. A summary of this information is given in Table I. Until quite recently most of the relaxation effects observed in N M R experiments were due to a single relaxation mechanism, usually dipole-dipole relaxation. A number of reports have been published in which dipolar relaxation and spin rotation relaxation are both present (see. ref 4), but in this case the correlation times (the molecular correlation time and the angular momentum correlation time) are totally different. In both cases the relaxation is relatively simple. For simple dipolar relaxation in a coupled I-S spin system (for example, HI3C=C-D, at low magnetic fields), the longitudinal relaxation can be described by double exponentials while a single exponential suffices for the transverse relaxation of either n u c l e ~ s . ~ ~ ~ For many N M R experiments done nowadays in higher magnetic fields (4.7 to 12 T, that is, 200 to 500 MHz for the proton resonance frequency), the chemical shift anisotropy (CSA) can also contribute substantially to both transverse (T2)and longitudinal ( T I )relaxation. In the event that both dipolar relaxation and CSA relaxation contribute significantly, the differential relaxation predicted by Shimizu, should be observed. And indeed such differential line broadening has been reported in several papers over the past year.*’, The data presented here serve as a careful experimental test of the theoretical predictions and show clearly that, when the CSA and dipolar contributions to the relaxation are comparable, interference effects arise, both spin-lattice and (1) Redfield, A. G. Ado. Magn. Reson. 1965,I , 1. (2) Shimizu, H.J . Chem. Phys. 1964,40, 3357. (3)Mackor, E.L.;McLean, C. J . Chem. Phys. 1965,42,4254.1966,44, 2708. Prog. N M R Spectrosc. 1967,3, 129. (4)Vold, R. L.;Vold, R. R. Prog. N M R Spectrosc. 1978,12,79. (5)Werbelow, L. G.; Grant, D. M. Adu. Magn. Reson. 1977,9, 189. (6) VanderHart, D. L.; Gutowsky, H. S.;Farrar, T. C. J . Chem. Phys. 1969,50, 1058. (7)Durand, P.J.; Granier, W.; Cot, L.; Caligne, J. L. Acta Crystallogr. Sect. B 1975,831, 1533. (8)Mayne, C. L.;Alderman, D. W.; Grant, D. M. J . Chem. Phys. 1975, 63,2514. (9)Farrar, T. C.;Quintero-Arcaya, R. A. Chem. Phys. Lett. 1985,122, 41. (10)Lunsford, J. H.; Rothwell, W. P.; Shen, W. J . Am. Chem. SOC.1985, 107, 1540. (1 1) Macura, S.; Brown, L. R. J . Magn. Reson. 1985,62,328. (12) Quintero-Arcaya, R. A.; Ph.D. Thesis University of WisconsinMadison, 1986.
0 1987 American Chemical Society
PF032-in High Magnetic Fields
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3225
spin state
Normally, it is not possible in a high-resolution N M R spectrum to determine the sign of J. As we show later, when DLB is present it is straightforward to obtain the absolute sign of J . In order to make any predictions about the spin-lattice or spin-spin relaxation behavior in solution we must use the density matrix approach. Since the theory for two spins has been worked out by Shimizu,z we will not repeat the details here but give just the final results for T2 (for details see ref 2 or ref 12). This theory is valid for an isolated, two-spin system where only intramolecular dipole-dipole (dd) and chemical shift anisotropy (CSA) relaxation processes are present. The theory, as used in this paper, further assumes that the motion of both spins can be described by a single molecular correlation time. All of these conditions are met by the PF032- anion. There are, of course, two different correlation times for the anion, one, T ~ related , to the motion about the C3, symmetry axis and one, T ~ related , to the two equivalent motions about the two axes which are orthogonal to one another and to the C3, axis. Since. only the changes in T~ can result in fluctuating magnetic fields at either the phosphorus or the fluorine nuclei, rc is the only relevant correlation time for longitudinal or transverse relaxation. The fluorine spectrum consists of two lines, F1 and F2, and, similarly, there are two lines, P1 and P2, for the phosphorus spectrum (see Figure 1). The transverse relaxation rate for the spectral line resulting from a transition between states i and j is denoted by -Rbp The transverse relaxation time, T2, is the inverse of the relaxation rate. Thus
Energy level Q4
A X
-
03
QZ
A2 P2
A1 e1
X1 P1
x2 P2
incras8ine
*-.--.--.-------------(II
T2(F2) = -1
Figure 1. The energy level diagram for a two-spin A-X system, both spin l/*. If JA-x > 0, the XI transition (low frequency) is between levels 1 and 2. If JATX< 0, the XI transition (the low-frequency transition) is between levels 3 and 4. The I9Fspectra and the 31Pspectra depicted at the bottom of the figure show all four lines to have equal heights, as is expected for low magnetic field strengths (Bo< 2 T).
spinspin relaxation become complex, and the resonance lines are differentially broadened. The experimental data reported here are in excellent agreement with the predictions of Redfield density matrix theory over a wide range of molecular correlations times, down to and beyond the region where wOrc2 1, where wo is the nuclear precession frequency in rad s-l and 7, is the molecular correlation time in s rad-'. Analysis of either the TI and T2 data then allows one to determine: (a) the absolute sign of the indirect spinspin coupling constant, JIs, (b) the magnitude of the chemical shift anisotropies for both nuclei I and S, (c) the I-S internuclear bond distance, and (d) the molecular correlation time.
/R1313
The Rijij are in turn given by
Theory For a simple system of two unlike spins I and S where both the time-independent Hamiltonian (in I and S have a spin of units of angular frequency) may be written as H = -v/ZZ - vsSZ+ J/,yI*S (1)
the line widths are given by
and
and the wave functions are given by $1
= %%
$2
=
00, $3
= Pa,
$4
=
PP
(2)
where we have adopted the convention that the spin state of the I spin is always written first and the resonance frequency of the I spin is chosen such that is is greater than that of the S spin, that is wI > ws. The corresponding energy levels are then given by
Ei =
($ilHl$i)/($il$i)
(3)
It is straightforward to show that El = - ( 1 / 2 ) ( ~ / YS) + (1/4)J
+
E2 = -( 1/ 2 ) ( ~ /- v S )
- (1 /4)J E3 = + ( 1 / 2 ) ( ~ , - US) - (1/4)J E4
= +(1/2)(~/
+ vs) + (1/4)J
(4)
For the present case of PF032-where lvI - vsl >> IJlsl, the energy level diagram is as shown in Figure 1. Note that the relative spacing between the energy levels depends on the sign of JIs.
wI is the resonance frequency of nucleus I (expressed in rad s-l), y I is the gyromagnetic ratio of nucleus I, r is the I-S internuclear distance, X is Planck's constant divided by 27r, Bo is the value of the dc magnetic field, and 6,is the CSA of nucleus I, and similarly for nucleus S. Note that in the above R, formulae, RIZI2 contains terms (6, - p ) which depend upon the difference between the CSA interaction and the dipolar interaction. R3434contains terms which depend upon the sum of 6x and p . In particular, since
Riziz - R3434 = ~ P S X I ~ J ( O+) 3J(wx)l
(12)
the DLB will increase as the magnetic field, Bo, increases and as , (see eq 11). Similar the molecular correlation time, T ~ increases
3226 The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 TABLE I1
temp,
F2
F1
P2
P1
OC
Rl313
R2424
R1212
R3434
-40.0
-19.0
+17.7
39 f 1 (25) [22.7 f 1.71
6.9 f 0.5 (4.5) [3.2 f 0 21
2.1
6.4 f 0.5 (3.8) [3.2 f 0.31
2.7 f 0.5 (1.2) (0.75 f 0.061
1.6 f 0.2 (0.50) [0.43 f 0.051
1.3 f 0 1 (0.16) [0.11 f 0.011
* 0.5
0
16.9 f 0.5
0
[]
Ali2 TIP
[I
calcd
1.2 0.5 (0.56) [0.69 f 0.011
2.1 f 0.5 (1.8) [1.9 f 0.11
Alp
calcd
1.2 0.2 (0.15) [0.13 f 0.011
1.2 f 0.2 (0.25) [0.24 f 0.021
calcd
*
TI,
TI0
comments, of course, hold for the A nucleus. Experimental Section The measurement of transverse N M R relaxation times is an exercise fraught with many opportunities for making e r r 0 ~ s . l ~In the present case we have measured T2 of each of the individual lines by three different methods: (a) direct measurement of the N M R line width of the frequency spectrum, (b) measurements using the Carr-Purcell-Meiboom-Gill (CPMG) pulse sequence, and (c) T I ,measurements using the standard T I ,pulse sequence (see ref 14 for details of these pulse sequences). Transverse relaxation parameters as determined by the CPMG method were always found to have values between the ones obtained from spin-locking experiments and those obtained from line shape experiments. The narrowest lines (and in our view the most reliable and accurate results) were obtained from the spin-locking, TI,, experiment. The results obtained at several different temperatures are summarized in Table 11. The T I ,measurements were taken with a small amount of yBl power, the 90" pulse time was in the range of 1 to 10 ms. Low power is needed such that only one of the lines in the spectrum is affected, in order to avoid cross relaxation effects (the Rijkrterm in the relaxation matrix [see ref 41). On the other hand, the 90" pulse duration should be short compared to T I and T,. Both of these conditions were met in the experiments done here. The line width measurements were done on a homemade 4.7-T magnet and spectrometer and on a Bruker AM-500 multinuclear spectrometer. The CPMG and T I ,experiments were done with the homemade spectrometer and an EN1 rf power amplifier was used as a final power amplifier into the probe. The current capability of the rf power amplifiers in N M R spectrometers designed for liquid-state measurements is usually not sufficient to give reliable values of T, or T I P .The EN1 was used at about half of its rated power output. A proportional control temperature apparatus was used to control the temperature of the cold N2gas which passed up over the sample and back again (a double pass gas cryostat). The temperature of the gas at the sample probe was controlled to about f 0 . 5 'C. A separate platinum resistor located about 3 cm below the sample was used to continuously monitor the temperature. As a further check on the temperature a platinum resistor was placed directly in an N M R tube filled with the same amount of solvent as the actual sample, and the temperature of the solvent in the rf coil was measured at the set temperature both before and after the relaxation time measurements. Great care was taken to measure and control the sample temperature since the stability and accuracy of the sample temperature is the source of the largest experimental uncertainty in all of these measurements. All CPMG and T I Pexperiments . were done on static (nonspinning) samples. A field-frequency lock was not used because of instabilities in the lock circuitry caused by the CPMG pulses or the spin-locking pulse. Since the homemade magnet had no inherent drift, we could work at night when there were no environmental disturbances and get excellent signal averaging results (13) Vold, R. L.; Vold, R. R.; Simon, H. E. J . Magn. Reson. 1973, 11, 283. (14) Farrar, T. C.; Becker, E. D. Pulse and Fourier Transform NMR; Academic: New, York, 197 1 .
Farrar and Quintero-Arcaya without a lock. Ninety degree pulses were adjusted by using either the null method or the Haupt method.15 The accuracy and precision of the CPMG and T I , measurements were checked by measuring T I ,T2,and T1,on a sample of ferric nitrate whose T I and T2values are known to be equal.I6 The concentration of the solutions was adjusted such that the T2 of the ferric nitrate solutions was very close to the T2value for the fluorophosphate solution. For the ferric nitrate solutions, the T I and T I ,values agreed to within 5% of one another. ( T I for the ferric nitrate solution at room temperature was 2.5 1 f 0.03 s.) At low temperature in a viscous sample it is rather difficult to adjust the magnet for a highly homogeneous field. For this reason we did the experiments in a 5.0" 0.d. N M R tube which was centered inside an 8.0-mm 0.d. N M R tube containing acetone-& Although this arrangement, which allowed field tuning on the relatively fluid acetone sample, was an improvement over tuning on the deuteriated ethylene glycol or water solvent, it still did not allow tuning the field homogeneity to the point where it did not contribute to line broadening in the fluorine or phosphorus spectra. This is evidenced by the fact that the line shape data all contain some systematic error.
Results and Discussion The results of the line shape and T I , measurements at three different temperatures are shown in Table 11. As can be seen, the T I , measurements give consistently smaller values for the relaxation rates, and consequently, consistently narrower values for the line widths ( A l p = -R2/7r). The CPMG measurements were much more accurate than the results from line shape analysis. The accuracy of the three methods increases in the order T 1 ,> CPMG >> line shape. For this reason we have used the TIPresults rather than the line width or CPMG results for the comparison with the theoretical predictions. The T I , results in Table I1 show clearly that the Redfield theory is in very good agreement with the experimental R,, values. Actual fluorine and phosphorus spectra at three different temperatures are shown in Figure 3. It is very satisfying to find that there is close quantitative agreement between theory and experiment even for relatively slow molecular motion ( w ~ T S , 1). One can clearly see from eq 7a-d that differential broadening is predicted. By using the data given in Table I, one can, using eq 7a-d, calculate the R,, v a l ~ e s . ~ J ~ This has been done and these values are listed in Table I1 as the "calcd" values. Having shown that eq 7a-d are valid, one can then use these equations with accurate R,, values to calculate the CSA values, internuclear distances, correlation times, and in favorable cases the components of the rotational diffusion tensor." At this point it would, we think, be helpful to explain in simple physical terms why one observes such differential broadening and to point out when one might expect samples to exhibit such differential broadening. One can best obtain a physical picture of the differential broadening by considering what happens in the solid state. Consider a single crystal of PF032-for the three orientations shown in Figure 2a. The resonance frequency for the phosphorus nuclei which are bonded to fluorine will change as a function of 0 as follows: fA
= fo - ( y p y F X 2 / r 3 ) (cos2 3 % - 1)
( 1 2a)
fB
=fo + ( y p y F X 2 / r 3 ) (cos2 3 % - 1)
(12b)
where fA and fB are the two frequencies in the phosphorus spectrum, 8 is the angle between the P-F internuclear vector and the magnetic field, Bo, and r is the P-F bond distance; the other constants are as defined in eq 7a-d. The negative sign cfA) goes with that half of the phosphorus nuclei, PA,which are spin coupled to a fluorine in the a-spin state and the positive sign cfB)goes with that half of the phosphorus nuclei, PB,which are spin coupled to fluorine nuclei in the @-spinstate, that is, those fluorine spins which (15) Haupt, E. J . Magn. Reson. 1982, 49, 358. (16) Abragam, A. Principles of Nuclear Magnetism; Oxford University: London, 1961; Chapter 8. (17) Koenigsberger, E.; Sterk, H. J . Chem. Phys. 1985, 83, 2723.
The Journal of Physical Chemistry, Vol. 91, No. 12, 1987 3227
PF032- in High Magnetic Fields
F19-188MHZ
P31-81 MHz
T('C)
:
PA
I
Figure 3. Actual fluorine-19and phosphorus-31 NMR spectra at temperatures of -30, -40, and -50 OC at a magnetic field of 4.7 T. The lowest spectrum is for phosphorus at a magnetic field of 1 1.5 T. For all of the spectra the frequency increases from right to left.
rienced by the PA and PB nuclei as a function of 0 will be very different. In Figure 2b we show the single crystal spectra for 31P for the three different orientations, 6' = Oo, 54.7O, and 90°. The frequency of the two lines is now given by f0
e
t PB
- oo
PA
I
e
PB
PA
e
* 54.70
= 800
I
C increasing
PA fB
. I
-
dp p > 0
Po
-
(7pf/r3)(3c0828- 1)
Po + (rpf/rf)(3cos2e- 1)
-
d p ( 3 ~ 0 8 -~ 01)
- d p (3~08'0 - 1)
0 and d p < 0
Figure 2. (a, top) The phosphorus spectrum for a single-crystalsample of PFO?-, at three orientations of the PF internuclear vector with respect to the Bo magnetic field, Oo, 5 4 . 7 O , and 90'. The dotted line in the spectra are for those phosphorus nuclei, PB, which are bonded to a fluorine in a &spin state. The dashed line in the spectra are for those phosphorus nuclei, PA,which are bonbded to a fluorine in an a-spin state. The spectra are shown for the hypothetical case in which the CSA for the phosphorus is zero. In this case, the local field variations, APAand APB, for the PAand PBnuclei are equal. The hatched lines indicate the range of the local field variations. (b, bottom) The conditions are the same as in (a), except that the CSA and the dipolar interactions are about equal. This is the situation for the PF03*-at a field of about 6.3 T. Here the local field variation for the PAnuclei is about twice what it is for the case of zero CSA. The PBnuclei experience almost no local variation since the CSA and dipolar effects almost cancel one another.
are aligned antiparallel to Bo. If the phosphorus chemical shift is isotropic (& = 0, see eq 9), then for a single crystal sample for which 8 = Oo, we get a maximum phosphorus splitting of the two lines of 2p. At 8 = 5 4 . 7 O , the two lines coalesce and at 0 = 90° the splitting is p . The spectra of these three orientations are depicted in Figure 2a. The hatched lines below the spectra show the total variation in the magnetic field at the PAand PB phosphorus nuclei, arising from the dipolar interaction with the fluorine. If the phosphorus and/or the fluorine chemical shifts are anisotropic (which for PF03*- they are), then the local field expe-
f(A/B) = f o (F)( y p y F X / 2 r 3 ) ( cos2 3 0 - 1) - 6p(3 cos2 6' - 1) (13) If the magnitude of the dipolar and CSA terms are about equal, then one of the lines in the single crystal spectrum will experience almost no change in frequency as a function of 0, since any change in the local field due to the dipolar term will be canceled by the CSA term. The other line will experience a change almost twice as great since local fields generated by the dipolar and CSA terms add constructively. For PF032-the phosphorus CSA, (ull- ( T ~ ) ~ = -145 ppm (see ref 6 ) . In this case the total range of magnetic fields experienced as a function of 0 is quite small for the PA nuclei. At a field of 6.3 T the "dipolar" field for the PA nuclei is approximately independent of orientation. For the PBnuclei the local field changes at about twice the rate as would be expected for the dipolar interaction alone. In other words, the dipolar field fluctuations at the PAnuclei due to changes in orientation are largely cancelled by field changes of the opposite sign due to the CSA. The hatched lines below the spectra in Figure 2b show schematically this very small range in the local field for the PA nuclei and the twofold greater range in the dipolar field for the PB nuclei. When the P F O t - molecules begin to move, the magnetic fields at the PA and PB nuclei are modulated by the molecular motion. And it is the magnitude of this motion-induced magnetic field modulation (represented by the hatched lines in Figure 2, a and b) that couples the precessional motion of the nuclear spins to the molecular motion and brings about relaxation of the nuclear spin system. When the CSA and dipolar interactions are comparable, as they are in the present case (Figure 2b), relatively little magnetic field modulation occurs at the PAnuclei. Consequently, they will have very long relaxation times, even for slow molecular motions where W ~ T , 1. The PBnuclei, however, will experience much larger than normal magnetic field fluctuations and as a result will have short relaxation times. Since = -R,/n = l/(nT2), we see a differential broadening of the two lines (see Figure 3). Normally, one cannot determine which of the lines in a highresolution NMR spectrum are associated with the transitions between the various energy levels. For example, in Figure 1 it is not usually possible to determine whether the P 2 phosphorus line arises from the transition between energy levels 1 and 2 or between levels 3 and 4. However, when DLB is present one can easily determine which line is associated with the transition between the energy levels. In the present case we know from an independent experiment6 that the phosphorus CSA, (ull- u ~ ) ~ = -145 ppm. From eq 7c and 7d (where = 6,) then, we know that R1212 > R3434.Consequently, the broader line in the spectrum is associated with the R , 2 1 2transition. In the present case it is the high-frequency, P,, phosphorus line which is broad. Therefore
,
,
3228
J. Phys. Chem. 1987, 91. 3228-3233
the sign of JPF must be negative. Since SF is positive, it is the low-frequency line in the fluorine spectrum which is broad. In summary, we have shown that over a wide range of correlation times (lo-" 2 7,2 lo-'), the experimental and theoretical values of the transverse relaxation times for both the fluorine- 19 and the phosphorus-3 1 relaxation times in PFOj2- solution are in excellent agreement. We have shown unequivocally that the is negative, in absolute sign of the spin-coupling constant, JPF, particular JpF= -870.0 f 0.05 Hz, at room temperature in an ethylene glycol-water solution. In favorable cases such as PF0,2(or HI3C-X3, where X is nonmagnetic), relatively straightforward measurements of the transverse relaxation time as a function of temperature should be able to provide accurate measurements of the CSA for both nuclei, the internuclear distance and the correlation time. One can expect in coupled spin systems to see such differential line broadening under the following conditions: (a) When 100 2 2 0.01. Therefore nuclei such as phosphorus-3 1, carbon-1 3, nitrogen-15 , fluorine-19, silicon-29, selenium-77, platinum-195, and so on are likely candidates for DLB. (b) When the magnetic field strength is equal to or greater than 4.7 T, or until the point is reached where 6, >> p . (c) When the molecular motions are relatively slow. DLB becomes most pronounced when W ~ = T 1. ~ Therefore spin systems in macromolecules," or absorbed on high surface area materials,I0 or in other environments where their molecular motions will be slow, are most likely to exhibit DLB. (d) When the two relaxation processes (in the present case, dipolar and CSA) have a common correlation time. (e) When intramolecular relaxation is the dominant relaxation. That is, intermolecular relaxation, which usually involves an in-
dependent correlation time, will tend to mask the differential broadening. A simple but, we believe, very significant consequence of the present work is the positive identification of CSA as an important NMR relaxation mechanism in coupled spin systems when working in high magnetic fields (Bo2 4.7 T). Since the relaxation of both the individual and the total magnetizations in a multiplet can be strongly affected by the relative orientation of the chemical shift and dipolar tensors,l8 care should be taken to include this parameter in any calculations. For a coupled spin system the relaxation is complex but can be completely analyzed by using density matrix theory. For experiments in which one of the spins is decoupled it is not yet clear how to interpret the relaxation results; care should be taken in attempts to measure molecular parameters, such as correlation times, in such experiments at high fields. In the present case it is also possible that the indirect spin coupling tensor (J)has a significant anisotropy. In this event the dipolar parameter, p , defined in eq 10 should be modified to include the anisotropic J term. Finally, we should note that quite recently DLB has also been observed for proton spectra.Ig
Acknowledgment. We acknowledge the help of Marvin Kontney with the rf electronics and Ilene Locker for many helpful discussions, suggestions, and comments. We gratefully acknowledge the fellowship support of the DuPont Co., the Venezuelan Conicit program, and the National Science Foundation Grant No. CHE-8306696. (18) Farrar, T. C.; Adams, B. R.; Grey, G. C.; Quintero-Acaya, R. A,; Zuo, Q. J . Am. Chem. SOC.1986, 108, 8190. (19) Anet, F. A. L. J. A m . Chem. SOC.1986, 108, 7102.
Dual Fluorescence of Isobacteriochlorins Fritz A. Burkhalter, Erich C. Meister, and Urs P. Wild* Physical Chemistry Laboratory, Swiss Federal Institute of Technology, ETH- Zentrum, CH-8092 Zurich, Switzerland (Received: December 15, 1986)
Room-temperature solutions of two synthetic isobacteriochlorins are shown to have dual fluorescence with 0-0 bands near 635 and 585 nm. The full two-dimensional fluorescence intensity as a function of the excitation and emission wavelength is presented. It is concluded that the dual fluorescence results from two different tautomeric forms which involve a diagonal and an adjacent arrangement of the two free base hydrogens. The long-wavelength fluorescence has a lifetime of about 3 ns, and the short-wavelength emission has a lifetime of about 8 ns. Semiempirical calculations of the QCFF/PI and the CNDO/CI type were performed in order to discuss the absorption spectra of the different tautomers.
1. Introduction The chromophore of siroheme, closely related to a naturally occurring intermediate in the vitamin B,2 biosynthetic pathway and a prosthetic group in redox enzymes, has been shown to be of the isobacteriochlorin type.I Several substituted model compounds have been synthesized by Chang,* Battersby et and Eschenmoser et al. 4,5 A significant change of the vibrational structure in the visible and UV absorption spectra of several isobacteriochlorins was observed by Chang2 as a function of temperature. It was suggested that, at least, two tautomeric forms are in rapid equilibrium at (1) Murphy, M. J.; Siegel, L. M. J. Bioi. Chem. 1973, 248, 691 I . (2) Chang, C. K. Biochemistry 1980, 19, 1971. (3) Battersby, A. R.; Jones, K.; McDonald, E.; Robinson, J. A,; Morris, H. R. Tetrahedron Lett. 1977, 2213. (4) Montforts, F. P.; Ofner, S.; Rasetti, V.; Eschenmoser, A,; Woggon, W.-D.; Jones, K.; Battersby, A. R. Angew. Chem., Int. Ed. Engl. 1979, 18, 675. (5) Naab, P.; Lattmann, R.; Angst, C.; Eschenmoser, A. Angew. Chem., Int. Ed. Engl. 1980, 19, 143.
0022-3654/87/2091-3228$01.50/0
room temperature. The two strongest absorption bands near 590 and 370 nm were tentatively assigned to the principal form, with two diagonally located free base hydrogens in the center, whereas the long-wavelength band at 635 nm and the shoulder at 400 nm, which disappear upon cooling of 2-methyltetrahydrofuran solutions to 77 K, were assigned to a form with the two free base hydrogens bound to adjacent pyrrolic nitrogens (Figure 2 ) . The study of the light-induced shifts of the free base hydrogens in porphyrins and related ring systems has lead to a series of exciting result^.^-^ Using hole burning at low temperatures, we could follow the photoconversion even in porphine, where the two forms are equivalent from the molecular symmetry standpoint and the small difference in the transition energies results only from (6) Gorokhovskii, A. A.; Rebane, R. K.; Rebane, L. A. JETPLett. (Engl. Transl.) 1974, 20, 216. (7) Voelker, S . ; Macfarlane, R. M. IBM J . Res. Deo. 1979, 23, 547. (8) Burkhalter, F. A.; Suter, G. W.; Wild, U. P.; Samoiienko, V. D.; Rasumova, N. V.; Personov, R. I. Chem. Phys. Lett. 1983, 94, 483. (9) Wild, U. P.; Bucher, S. E.; Burkhalter, F. A. Appl. Opt. 1985, 24, 1526.
0 1987 American Chemical Society
