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Practical aspects of quantitative CIDNP using FT NMR
JOURNAL
OF
MAGNETIC
RESONANCE
40, 135-1.55
(1980)
Practical Aspects of Quantitative CIDNP Using FT NMR RONALD G. LAWLER AND PAUL Department
of Chemistry,
Brown
University,
Providence,
F. BARBARA Rhode
Island
02912
Received October 26, 1979 Two procedures have been devised for minimizing the distorting effects of relaxation on NMR spectra obtained from continuously reacting samples which exhibit CIDNP. The techniques employ (90-7)~ or (Pu,<-POt,S- tob.)Npulse sequences. These record the chemically driven component of the spectrum which develops a short time after the signal has been saturated by one or more rf pulses. The theory of the method is developed for several models of reaction kinetics and illustrated with experimental determinations of the absolute and relative CIDNP enhancement factors for ‘H and 13C spectra obtained from two thermally decomposing organic peroxides. It is found that the enhancement factors obtained from relaxation-free CIDNP spectra are in excellent agreement with predictions of the high-field radical pair theory. Errors arising from incomplete saturation are estimated and the compromise between signal/noise and removal of relaxation effects is discussed. INTRODUCTION
Since its discovery in 1967, chemically induced dynamic nuclear polarization (CIDNP) has become an important tool for the study of free radical reactions (1). The phenomenon is manifested by greatly enhanced NMR signals, in absorption (A) or emission (E), observed in molecules formed from radical intermediates. Most applications of CIDNP to data have employed only the sign of enhancement of NMR lines (A or E) rather than the magnitude. More quantitative determination of CIDNP enhancements is difficult because the observed intensity depends not only on the intrinsic enhancement due to the chemical reaction but also on the competition between the “chemical pumping” of the spin system and nuclear relaxation (2). Although cw NMR has been employed in most recent CIDNP investigations, it is inevitable that the ubiquitous FTNMR spectrometer will inherit the bulk of the future CIDNP workload. Nearly all CIDNP spectra published so far using either method, however, are of the “steady state” (SS) variety, recorded by using either low cw rf power or long waiting periods between rf pulses and small pulse angles. To extract intrinsic CIDNP intensities from SS spectra it is necessary to determine accurately both the rate of the reaction and the relaxation times of the nuclei of interest (2), a tedious undertaking even for simple NMR spectra. Furthermore, the complex kinetic behavior of many reactions and nonexponential relaxation in any but the simplest spin systems present added complications (3). We report here the use of two FT pulse sequences to record CIDNP spectra in which the intensity distortions arising from spin-lattice relaxation are greatly 135
0022-2364/80/100135-21$02.00/0 Copyright @ 1980 by Academic Press, Inc. All rights of reproduction in any form reserved Printed in Great Britain
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reduced. We also describe a protocol by which one may extract relative and absolute enhancement factors from such spectra without knowing the detailed kinetics of the reaction. The methods are variants of the “progressive saturation” (PS) (4) and “saturation-recovery” (SR) (5) techniques used to determine T1 values in normal spectra. In our case, however, we take advantage of the principle, first stated by Buchachenko and Markarian (6), that the magnetization of an initially saturated spin system depends at short times primarily on the rate of CIDNP production, i.e., is independent of Ti. A similar approach was employed recently (7) for samples excited by intermittent irradiation. We are concerned here, however, with applications to the commonly occurring cases in which the reaction rate cannot be easily controlled, e.g., continuous thermolysis, bimolecular redox reactions, continuous irradiation, etc.
THEORY
OF STEADY-STATE
CIDNP SPECTRA
In the absence of an rf field the magnetization of a chemically pumped spin system is affected by both the chemical reaction, r(t), which converts a reactant (R) into a “polarized” product (P*), and by relaxation, w(t), via transitions within the nuclear spin system. Relaxation redistributes and eventually destroys the polarization to give the “unpolarized” product (PO) R -
r(t)
P* w(t? PO.
[II
During a reaction the changing chemical and physical properties of the sample will generally impart a time dependence to both r and w. Furthermore, only in idealized cases will these two processes be adequately described by first-order kinetics. In what follows we ignore complicating effects of CIDNP on pulsed NMR spectra which may arise in homonuclear spin systems at very short times (8) or when large pulse angles are employed (9). The first effect is seen only in experiments where the chemical and rf excitations of the sample are phase coherent. It is absent when chemical excitation is continuous, is reduced when several nuclei are present, or may be eliminated by jitter in the timing of light and rf pulses. The second effect is easily circumvented, but with some loss of sensitivity, by employing pulse angles less than 30” or so. In the absence of the above effects the observed intensity,’ Li, of a line i extracted from a free-induction decay taken at time t is proportional to the population difference between two energy levels of the nuclear spin system. For such a “simple line” (12) in a spectrum exhibiting CIDNP we may write (13) dLi/dt = EidLP/dt+EidLP/dt-
T;: (Li-Lp)-r
Aik(Lk -Li). k
I21
’ We prefer to discuss the experimentally observed line intensities rather than population differences (10) or magnetizations (11). In doing so we assume that degeneracy factors and “intensity borrowing” effects in spin-coupled systems have been properly included in the definitions of Li and the relaxation parameters in Eq. [2].
QUANTITATIVE
If the transition
CIDNP USING FT NMR
137
i is between nuclear spin states a and b
T;; = 2 Aik
=
wab
(!i>(
+ ($1 c”
c
Wac
-
(wac
+
wbc),
I31 WI
wbc).
A superscript zero denotes thermal equilibrium, Ei (with a value between 0 and 1) determines the contribution to Li from thermal polarization in the reactant,2 and Ei is the (possibly time dependent) enhancement factor arising from CIDNP. The fourth term on the right-hand side of Eq. [2] arises from coupling between line i and other lines which share state a or state b. This term may become important either if the differential relaxation probability, Aik, is especially large (14) or if Ek is much larger than Ei (15). Such effects probably contribute to nearly all steady-state spectra, but we ignore them for simplicity in what follows. They are removed along with other relaxation effects by use of the pulse sequences described in later sections. The steady-state solution of Eq. [2] in the limit where coupled relaxation is negligible becomes (L~)ss = Lp + Tli(Ei + Ei)(dLP/dt).
[41
The observed intensity under these conditions thus follows the intensity of the unpolarized spectrum dLP/dt, i.e., the rate of reaction. A typical series of spectra obtained under steady-state conditions is shown in Fig. 1. Rearranging Eq. [4] we obtain the following expression for Ei. Ei = T;: [Li(t)ss-LLP(t)][dLP/dt];‘-&i.
[51
We see that even in the absence of the complicating effects of coupled relaxation, a determination of Ei from a steady-state spectrum requires knowing, in addition to
H-4,
0
50
100 150 SEC
200
4
II
3
2 km
1
0
FIG. 1. Typical steady-state spectra obtained during thermolysis of peroxide (1) in hexachloroacetone at 120°C. H-2 and H-4 are methylene Each spectrum was obtained from a single 20” pulse taken at intervals moment the sample was placed in the heated probe. The time dependence
t-butylacetyl-m-chlorobenzoyl protons identified in Scheme 1. of 20 set and beginning at the of peak H-4 is shown at the left.
* The contribution to L arising from the reactant and described by E will in general depend on the relaxation time of the reactant, TR, as well as on r and Tl. Thus E will take on the values 1 or 0 if T, is much shorter or much larger than Tl, respectively. The value of E for intermediate cases is given by E = I- T,( TR - TJ’[exp( - T/ TR) -exp( - r;/Tr)][l - exp( - T/T,)]-‘. It is assumed that both the reactant and product lines are initially fully saturated.
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the observed intensity, (Li)ss, three other quantities: Lp, Tri, and the reaction rate, dL?/dt, all at the time of measurement of (Li)ss. If the CIDNP intensity is large the corrections for Lp and ei will be unimportant. Furthermore, since dL’/dt will differ at most by a constant factor for each line in the spectrum of a given reaction product the relative enhancement factors of two such lines will be given by
[61
(EiIEj) -(T1jlT,i)[(Li)ss-LPI[(Lj)ss-LPI-’.
However, even in this case an accurate determination of the ratio of the Tl values is required. It is thus not surprising that little use of the magnitudes of enhancement factors has been made. Steady-state CIDNP spectra are of qualitative value only. A series of such spectra may be used, however, as in Fig. 1, to obtain an estimate of the time span during which data should be collected when the pulse schemes described below are applied. PROGRESSIVE
SATURATION
Theory
The key to minimizing relaxation effects in CIDNP spectra lies in making all but the second term in Eq. [2] as small as possible. In strongly enhanced spectra the contributions of ei and Lp are small. The relaxation terms may therefore be made small by recording the spectrum only when Li is small, e.g., before significant relaxation has taken place following a 90” pulse or saturating pulse sequence. Equation [2] may be integrated over the range of time 7=t,-tn-1
between application of a saturation pulse at tnel and observation of an FID at t,. The intensity, L, of the line obtained from the FID is
L(L) -L”(tn-dl -exp(-~/T~)l+[L”(t,)-Lo(t,-~)l xi1 + (TI/T)(~- 1X1-exp( - 4 Tdl) +[L”(~n)-Lo(t,-~)l(T~I~)E[l--xp(-~/T~)l.
[71
We have continued to ignore Aik and it is assumed that E, T,, and dL’/dt are varying slowly enough that they may be considered constant during the 7 epoch. For convenience the subscript i has been dropped here and in what follows. The variation of L during a string of 90” pulses is shown in Fig. 2a for two different values of 7 and is compared with the corresponding changes under steady-state conditions for a first-order reaction. Equation [7] may be summed over a series of N equally spaced FIDs collected between times tl and tN following 90” pulses applied at to through tN-l. Intensity cc f L(t,,) = SL”+SLo[l
-exp(-T/TI)]
?I=1
x {[E.+ (E - ~)](T,/T)
+ N(L”)(SLo)-‘},
l-81
QUANTITATIVE
139
CIDNP USING PTNMR HALF-LIVES
4
I
2
3
t/T,
FIG. 2. (a) Calculated time dependence of CIDNP intensity during a string of 90” pulses applied to a first-order reaction with rate constant k. Times are given in units of 7’i. Values of KT,, E, E,and r/T1 used in Eq. [6] are as shown. The evaluation of intensity under steady-state conditions, i.e., using a very small pulse angle, is shown by the dashed line. (b) Summed intensity of lines in (a) using Eq. [7].
where
SLO = E, [LO(a) -LO@,-l)] =Lo&v)-LOOo),
N(LO>= c” LO(t,-l), n=l
Pal Pbl
and we have assumed that E and T1 do not change during the reaction. For large N,
N(LO) = 7-l I
c-1 fo
Lo(t) dt.
[9cl
It is useful to consider four practical limiting situations in which Eq. [8] would apply.
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Stable Sample L’)(t,)
= I/(?to)
for all n,
Intensity a N[ 1 - exp( - T/ T,)]LO( to),
[loal
which is simply the expression employed to determine T, by the saturation-recovery method using perfect 90” pulses (5). No CIDNP E = 0,
Intensity aSLo{
+ (E - l)(T,/~)[l
-exp( - ~/Ti)l} +N(L’)[l
-exp(r/Ti)].
[lob1
It is interesting to compare Eqs. [lOa] and [lob] for the case r < Ti. In this limit Eq. [lob] becomes Intensity a N(L’)(r/
7’i) + e&5’.
The first term is analogous to Eq. [lOa] except for the replacement of L” by its average value. The second term represents the contribution to Lo from polarization in the reactant and might persist even at values of r short enough to make the first term negligible, provided that the reactant molecule is either not saturated or recovers rapidly from saturation.* Overlapping CIDNP and Thermal Polarization LO(t&
in the Product
LO(thr).
If we restrict ourselves to the case r < Ti, we have approximately Intensity a EL”(tN) + eL”(tN) + N(L0)(7/ T,).
[1Ocl
The first term is the one of usual interest in CIDNP studies, but we see that no matter how short r is, the second term will also contribute to the accumulated signal. Since E is typically several hundred, however, but E is not expected to exceed unity, the second term may usually be ignored. The third term represents overlap of the polarized spectrum with “unpolarized” product. Although it would appear from the form of this term that it could be reduced to arbitrarily small size by using a very small value of r, the situation is complicated. This term will continue to grow in size with increasing number of scans once the reaction is over. For a large number of scans the magnitude of this term may be determined by evaluating the integral in Eq. [SC] for various kinetic models. First-order formation: Lo(t) = L”(oO)[l -exp( - kit)],
N(L”>(dTd= (Tmax/TdLo(~){l-[l-exp(-klT,,,)l(klT,,)-‘}, where T,,, = NT.
[lla
QUANTITATIVE
CIDNP
USING
FT NMR
141
Second-order formation: LO(t) = L0(00)t[T2 + t]-.l,
N(L0)(~/T~)=(T,,,/~~)L'(~){l-(~2/~max)ln[l+(~,,,/~~)l}r
[lib
where 7T1 = k2R(0); k2 is the second-order rate constant and R(0) is the initial concentration of reactant. We see from Eqs. [ 11 a] and [ 11 b] that, as predicted, the overlap term continues to grow in magnitude with increasing number of scans beyond the time that the reaction is over, i.e., for T,,,,, greater than k;’ or 72 for the above models. Thus it is obviously desirable to stop the accumulation once the reaction is over (see Practical Considerations below for further discussion of the optimum number of scans). Overlapping CIDNP and Thermal Polarization
in the Reactant3
LO(to) >>LO(t&
In this case dL’/dt in Eq. [2] is negative. When allowance is made for this, Eq. [8] becomes, in the short T limit, Intensity ccL”(tO)[e + E] + N(L”>(7/ T,).
[10dl
This differs from Eq. [lOc] only in the interpretation given to the last term. Here again this overlap term may be evaluated for specific kinetic models. First-order decay: Lo(t) = Lo(O) exp( - klt),
N(L’)(d Td = CT,,,/ TI)L~(O)II~ - exp(- kl T,,,)l(kl T,,J’. In this case the overlapping term of scans but approaches a limiting will decrease in magnitude for Reactions other than first-order
[llcl
does not continue to grow with increasing number value, L’(O)(k, TJ’ for T,,, > k;‘. Thus this term either a fast reaction or a long relaxation time. should produce qualitatively similar results. Applications
Relative Intensities
The usefulness of the progressive saturation method is illustrated by comparing the two carbon-13 spectra shown in Fig. 3. The chemical reaction is the decomposition of 0.5 M t-butyl-acetyl-m-chlorobenzoyl peroxide, 1, in hexachloroacetone (HCA) at 120°C (Id). The reaction products and assignments of carbon-13 lines are given in Scheme 1. Both spectra were obtained over a total reaction time, 3 We ignore the possibility that a line from an unreactive compound, e.g., solvent, may overlap the line exhibiting CIDNP. This situation is best avoided, of course, since N(L’) can become very large. If this is not possible, the overlapping spectrum may in principle be subtracted since its intensity is related to the number of scans via Eq. [lOa]. In practice, however, the widths and positions of lines in reacting and nonreacting samples are seldom identical. Incomplete cancellation of slightly shifted lines can also introduce line distortions which might be incorrectly interpreted as arising from lines exhibiting CIDNP.
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I
I
I
1
+
t30
120
110
C-7
I
150 t40
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I ’ c-4
I 00
1 70
1
1 60
I 50 pm
I 40
I 30
J 20
FIG. 3. Carbon-13 CIDNP spectrum of sample whose ‘H spectrum is shown in Fig. 1. The spectrum was obtained using N successive 90” pulses separated by r, as indicated. Note that the lower spectrum has been attenuated four-fold relative to the upper. Assignments of lines are given in Scheme 1. Broadband ‘H decoupling was employed.
NT, of 120 sec. The upper spectrum comes close to that expected under steady-state conditions since the 20 set between pulses is comparable to the longest relaxation time in the spectrum (ca. 20 set for C-l), whereas the lower spectrum has employed a value of T shorter than the shortest TI (ca. 3 set for C-2) and should be close to an “unrelaxed” spectrum. The intensities of unpolarized lines are lower than the noise R’COaO&R
(1) + [R’C02. .R]
[R’C02. .R] -+ R’-C02-m-C-(CH,), C-l c-2 c-3 H-2
Pair formation (2)
Coupling
[R’C02. .R] + CO2 + R’-CH&-(CH& C-6 C-l
Coupling
[R’COc. .R] + R’COI.+.R
Cage escape
HCA+.R
-a Cl-CH2-C-(CH& c-4 c-5 H-4 R’ = m -CICbHd,
Scavenging
R = CHPC(CH3), SCHEME
1
QUANTITATIVE
EFFECT
CIDNP
USING
TABLE 1 ON RELATIVE CIDNP INTENSITIES OF VARYING PROGRESSIVE SATURATION METHODS
Intensity ratio Calculatedi’ “Unrelaxed”’ “Steady state”e
C-l/C-2 0.5 0.5 *Old 2.6~tO.5
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F-l- NMR
(C-3 + C-7)/(C-2 + C-6) -0.34 -0.41 f 0.08 -1.60+0.13
7 USING
THE
c-5/c-4 -0.34 -0.35 i 0.03 -0.60 + 0.10
a Experimental data are derived from carbon-13 spectra similar to those shown in Fig. 3. The pertinent reactions are shown in Scheme 1. b It is assumed that the CIDNP intensity is proportional to the hyperfine-coupling constant of the nucleus in the intermediate radical pair. This approximation (13, 18) is valid for net polarization when Ag& is greater than the hyperfine-coupling constant of the polarized nucleus. Since the 13C hyperfine-coupling constants have not been determined by EPR for neopentyl or benzoyloxy radicals, these parameters were estimated. It was assumed that the 13C hyperfine-coupling constants for the ethyl radical (A, = +40 G and A, = -13.5 G) (17) are a reasonable estimate to those for neopentyl radical. For the carbonyl carbon (C-l) in the benzoyloxy radical, the estimated value was -20 G. This is the theoretical estimate (18) based on the assumption tha: benzoyloxy is a planar r radical. ’ 7 = 1.2 set; N = 100 scans. d Average of ratios obtained from spectra of three samples. Error estimate is one standard deviation. e T = 20 set; N = 6 scans.
level in these spectra and may be ignored. As expected, the noise level in the lower spectrum is 4 times that of the upper since nearly 16 times as many spectra were averaged in the former case. The actual signal intensity, however, is substantially lower in the upper spectrum for all but C-l. This reflects the loss of intensity due to relaxation when r > T1. Table 1 summarizes the ratios obtained for three groups of lines in the spectra under “unrelaxed” and “steady-state” conditions. As expected, the relative intensities obtained using a small value of r are in much better agreement with theoretical predictions than are those obtained under steady-state conditions. The differences are especially large for the ratio C-l/C-2 because the values of r1 differ by nearly an order of magnitude. Indeed, examination of Eq. [8] in the limit where thermal polarization is negligible leads to the conclusion that the relative intensities of two lines in the same product are given by the equation (Intensity)i/(Intensity)j =(Ei/Ej)(T~i/T,j)[l-eXp(-T/T~i)][l-eXp(-T/T~j]-l.
[121
Thus the intensity ratio for r > Ti is modified by the ratio ( T1 J Tlj). The expected change with T due to the value of about 7 (i.e., 20/3) for this ratio for C-l/C-2 is within experimental error of that observed: (2.6/0.5). Absolute Enhancement
Factors
Returning to Eq. [8] we find that in the limit where thermal polarization is negligible the accumulated intensity of a single CIDNP line for T < Ti is given simply
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Intensity CCESLO, where SL” is the intensity of the hypothetical unpolarized signal arising from the amount of product formed (or reactant lost) during the portion of the reaction over which CIDNP spectra were accumulated. Thus is a remarkable result: Eq. [13] is independent of both T, and the kinetic behavior of the reaction. If r is set short enough to prevent loss of intensity due to relaxation, and E is large enough to be able to ignore overlap with “unpolarized” product, the value of E is determined from the ratio of the observed accumulated intensity to the intensity associated with the unpolarized product. The latter may in principle be obtained directly from a single spectrum taken at the end of the reaction using the same spectrometer settings as those used to accumulate the CIDNP spectra. If the intensity of the unpolarized signal is too weak to see with a single scan, signal averaging may, of course, be employed, but it is essential that signal saturation and any NOE be suppressed. Alternatively the intensity of the line from an unpolarized product may be estimated using the intensity of a reactant line at the beginning of the reaction and the yield of product. This method of determining E is illustrated here for C-2 in the product 2 (Scheme 1) formed from the peroxide 1 during decomposition at 120°C in ortho-dichlorobenzene (ODCB) (16). The CIDNP spectra obtained in ODCB are similar to those shown in Fig. 3 except that the emission line, C-4, is absent. ODCB was chosen in this case because secondary decomposition of the products seems to occur to some extent in HCA, making reliable estimates of product yields difficult. Sixty transients spaced by 1.2 set were collected over a period beginning 30 set after the sample was placed in the heated probe and ending 72 set later. In separate experiments the sample was quenched by rapidly cooling and product yields were determined by ‘H NMR integration. In this way it was shown that the above 72-set period encompassed greater than 95% of the reaction. The intensity SL” was calculated by scaling down the signal observed from the solvent lines, under nonsaturating conditions and with NOE suppression, at the end of the reaction using the known peroxide concentration (0.5 M) and the yield of 2 (15%). The value of E thus obtained is +5000* 1000. This is comparable to other estimated CIDNP enhancement factors for carbon-13 (19). In the next section we compare this enhancement factor with that obtained for the protons bonded to the same carbon. This value could, of course, also be used to calculate the value of E for other lines using the relative enhancements analogous to those in Table 1. Limitations
of the Progressive Saturation Method
The limitations and possible sources of error in the progressive saturation method as used here are the same as those which pertain when the method is employed for Tl measurements on normal samples (20). These include limitations due both to instrumentation and to the intrinsic properties of the sample. In the former category are effects arising from the fact that the rf field and/or chemical reaction rate may not be distributed uniformly throughout the sample. This
QUANTITATIVE
CIDNP
USING
FI NMR
145
means that the sum in Eq. [8] should be averaged over the entire sample, but in a way which reflects the diffusion of spins with different polarizations into and out of the receiver coil (21). The diffusive properties of the sample and the required distribution functions, however, will generally not be known. It is therefore essential to minimize these effects by restricting the sample size to just fill the receiver coil (20). Another instrumental effect arises from pulses which deviate from 90” (see Experimental). More fundamental limitations of the progressive saturation method may arise from the properties of the sample. These include: (i) distortions due to spin echoes (22) when the spin-spin relaxation time, Tzi, is comparable to 7; (ii) incomplete saturation and distortion due to truncation (22) when the effective spin-spin relaxation time, Tzi, is comparable to T; (iii) distortion of homonuclear CIDNP multiplet effects when 90” pulses are used (9). None of these effects is important for 13C because (i) spin echoes are suppressed by *H broadband decoupling (22); (ii) r3C Tli values, and therefore acceptably short values of T, are usually longer than the Tzi imposed by field inhomogeneity; and (iii) 13C homonuclear spin coupling is usually absent. The significance of this last feature of 13C CIDNP spectra has not always been appreciated and small pulse angles or long waiting times between pulses have often been employed needlessly (23). As we have shown above, however, there is never any reason to use pulse angles less than 90” for 13C CIDNP spectra with, or without, decoupling of protons or other nuclei. Use of smaller pulse angles needlessly reduces the size of the signal. For ‘H CIDNP, on the other hand, the above limitations may all exist simultaneously. This makes the progressive saturation method generally unsuitable for ‘H CIDNP. A pulse sequence which is satisfactory for ‘H CIDNP is described in the following section. SATURATION
RECOVERY
Method
The “saturation-recovery” pulse sequence, (Psat-7-PobbtobS)N, was developed originally to measure T1 by monitoring the intensity at tabsas a function of r (5). The method as applied to CIDNP spectra is philosophically the same as the progressive saturation technique described in the last section. The only difference between the two methods is that in the latter method P,,, = P&s and tabs= r. Figure 4 shows the pulse sequence employed to obtain CIDNP spectra using this technique. The limitations described in the previous section are no longer present with this pulse sequence because (i) echoes are suppressed because PSatdestroys all components Of M, including M, and MY ; (ii) tabsmay be easily made greater than T:, eliminating the effects of truncation; and (iii) P&s is no longer restricted to 90” and may thus be made as small as desired to eliminate distortions in spectra with homonuclear multiplet effects (9). The saturation-recovery method does possess some potential disadvantages over progressive saturation. It is somewhat more difficult to achieve experimentally since
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FIG. 4. Schematic representation of pulse sequence employed for the saturation-recovery minimizing relaxation effects. The time intervals shown are those used in Eq. [13].
method of
the spectrum must be fully saturated in a short time (see, however, the Experimental section for a simple way to achieve this with commercial spectrometers equipped for broadband ‘H decoupling). Furthermore, the overall signal/noise is lower than for progressive saturation for continuously reacting samples because the chemical polarization which occurs during r&s (which might be considerably longer than 7) is destroyed by the next P,,, pulse and is therefore wasted. For photolysis, however, this waste is avoided by turning the light off during fobs. Finally, the restriction of PObsto small angles when multiplet effects are present decreases the size of the signal. If one requires only net effects, however, in spin systems without intensity borrowing (9), 90” pulses may again be used. Applications
An analysis of the saturation-recovery technique similar to that leading to Eq. [8] for progressive saturation leads to the following relationship between the accumulated CIDNP intensities obtained using the two techniques with the same value of 7 over a total reaction time which is very long compared to the time for one (Psat+-Pobs-tabs)
cycle.
(Intensity)sn = (Intensity)ps[T/T,]
sin 6&,
[I41
where 7, = 7 + T,,~+ t&s. The quantity T,,~ is the length of PSat(typically 0.8 set) and &bs is the angle of Pobs. The ratio 7/rc is simply the ratio of the number of spectra accumulated in the SR and PS modes, respectively. Aside from this factor, and the overall reduction of intensity via sin 6&s, the intensities for a given 7 are the same. In particular, the short-7 condition for obtaining “unrelaxed” spectra is the same in the two methods. Relative Enhancements
in ‘H CIDNP
In Fig. 5 are shown spectra obtained from the methylene group quartet, Q, of 4, obtained by decomposition of 0.5 M propionyl-m chlorobenzoyl peroxide (3) in 3 : 2 HCA-ODCB at 140°C. The relevant chemical reactions leading to this product are shown in Scheme 2 (24). This multiplet provides a classic example of the frequent observation that the multiplet effect in a CIDNP spectrum relaxes faster than the net effect for the same set of nuclei (13, 14). In both m -chloroethylbenzene,
QUANTITATIVE
CIDNP USING FT NMR
147
FIG. 5. CIDNP spectra of the methylene quartet (Q) of ethylbenzene formed according to Scheme 2 in a 3:2 mixture of HCA and ODCB at 140°C. (a) Pob,= 20”, number of spectra=4, time between spectra = 10 set; accumulation started 110 set after the sample was placed in the heated probe. (b) Same conditions as (a) except that a 2-W, 0.8-set broadband decoupler pulse, P,,, was applied at time r = 4 set before Pobs. (c) Theoretically predicted spectrum. The frequency scale employed in (c) is about 30% narrower than that in (a) and (b).
spectra a pulse angle of 20” has been employed to avoid distortions of the multiplet effect; yet the multiplet effect has relaxed away from the spectrum obtained without presaturation. When relaxation is avoided using the SR method, however, the relative intensities are in excellent agreement wi.th those predicted theoretically (24). In this case the overlap with unpolarized signals is negligible. R’C0202CR
(3) --) [R’C02.
.R]
[R’COr. .R] -+ COr+R’-CI&-CHs Q R’ = m-ClC6H4,
(4)
R = CH&Hs
SCHEME 2
Absolute Enhancement Using Eq. [14] in the limit of short T we have by analogy with Eqs. [13] and [lOc] (Intensity)snoc:{SL’[E
+ E]+N(L’)(~/T~)}(~/~,)
sin dabs.
[I51
We will illustrate the use of this equation to determine E for the emission line, H-2, for protons bonded to the carbon atom, C-l, in ester 2 produced by thermal decomposition of the peroxide 1 (Scheme 1) in ODCB. The spectrum is very similar to that shown in Fig. 1 except that the signal H-4 is not observed in this case. Since the signal of interest is a singlet it is permissible to use a value of cobs= 90” to optimize the sensitivity. It is found that 2 is formed in an approximately first-order reaction with rate constant, ki, about 3 x 10e2 set-‘. The spectrum of the reaction mixture was accumulated as 50 scans over the first 220 set of reaction using values of T = 1 set and 7c = 4.4 sec. From Eq. [l la] we find that the last term in Eq. [15] above has the value
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where T max= NT, = 220 sec.
In an independent experiment, an upper limit to the magnitude of this term was estimated by accumulating 50 scans of the product mixture using the same values of 7, doss, and 7, as those employed in collecting the CIDNP spectrum. The intensity of the line H-2 thus obtained was about 10% of the absolute intensity of that line in the CIDNP spectrum. It follows therefore that the ratio of the two terms in Eq. [15] was about 10 to 1. To estimate the value of SL’(r/r,) the intensity of a single scan of H-2 at equilibrium in the product mixture was determined and reduced by the ratio T/T,. By combining the CIDNP intensity and the two estimates of SL” one obtains a value of E = - 590 f 60 for the line H-2 and an estimate of Tl greater than about 4 set for these protons. The latter value is consistent with estimates derived from preliminary experiments using different r values. It is of interest to compare the above values of E for H-2 with the value + 5000* 1000 reported above for the corresponding carbon-13. In the limit where the CIDNP intensity is proportional to the hyperfine splitting (Table 1, footnote b) we expect the ratio of enhancement factors in the same molecule to be U%IEHLI~=
(&/AH)(~H/~c)
-(+40/-20)(4)-
-8
and we find (EC/EH)obs = -8’.5 zt 2,
in excellent agreement with the theory. PRACTICAL
CONSIDERATIONS
The analysis and examples presented up to now have been based on several assumptions about the ability of the NMR spectrometer to produce ideal 90” pulses or complete saturation and about the constancy of parameters describing CIDNP during the reaction. We describe here some of the consequences of simple, small deviations from this ideal behavior and also discuss the optimal choice of 7 and T,,,,, required to minimize errors due to relaxation and maximize signal/noise. Unless otherwise indicated, for purposes of illustration it will be assumed that the CIDNP line of interest is in the product of a first-order reaction, and contributions of thermal polarization to the intensity will be ignored. Choice of T
CIDNP spectra acquired by either the PS or the SR method exhibit loss of intensity due to relaxation unless 7 <>Tli, i.e., for steady-state spectra. For intermediate values of T it is convenient to define an error, E=,in intensity I due to relaxation.
Er= [I(O)- ~(~)l/~Ko,
[17al
QUANTITATIVE
CIDNP USING F-I NMR
149
which, from Eq. [8] or Eq. [14], becomes er= 1 -(TI/7)[1
-exp(
-7/TI>]
=$(T/T’)-;(T/Tl)*+.
[17bl
**.
Thus if less than 10% loss of intensity is desired, a value of r I 0.2Ti is required. For the case of relative enhancements, the error, E!, is conveniently defined as
EZ= [(li/J)O- (lilIj)rll(lil~)O ~1-(T~~/T~j)[l-exp(-7/T~i)l[l-~x~(-~/~~j)l~1 =&[T;;
-yyi’]+.
...
I381
This is a rather less restrictive condition on r since it involves the difference in relaxation rate constants. It is instructive to demonstrate experimentally the validity of Eq. [8] in describing the dependence of accumulated intensity on r. In Fig. 6 is shown a plot of the accumulated intensity of the emission line, C-4, in Fig. 3 vs the value of T relative to Tl for this line using the PR method over a constant total accumulation time, Tmax. The value of Tl = 6.3 set was obtained from least-squares fitting of the intensity to T using Eq. [8]. The calculated intensity error, E,, for this line for different values of T/ Tl is also shown.
-.-.-.a._ 0.1 .-,’ k 0
1 0.5
I 1.0
1 1.5
I 2.0
I 2.5
I 3.0
T/T,
FIG. 6. Comparison of calculated (-) and observed s/n (Cl) and summed intensity (0) for line C-4 of Fig. 3 as a function of r. The total accumulation time, T,,, was fixed at 120 set and the data points correspond to the summation of N = 6, 12, 20, 40, and 60 spectra, reading from long 7 to short. The measured value of Ti, 6.3 set, was obtained by least-squares fitting of the summed intensity to r using Eq. [g] in the limit where the thermal polarization is negligible. The calculated s/n curve was obtained using Eq. [19] and scaled to pass through the point r/ ri = 1. The fractional error due to relaxation, E, (- - -), was calculated from Eq. [17]. The relative noise level (- . -) varies simply as 7-l” and was arbitrarily set to the value 0.25 for T/T, = 1.
I so
LAWLER
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Optimal Signal/Noise
A straightforward approach to the removal of distortion due to relaxation would be to use as short a T value as achievable and accumulate as many scans as possible before the reaction is over. The drawback of this seemingly obvious approach becomes apparent if we consider the way in which the signal/noise (s/n) varies with the total number of scans. s/n ocI/N’j2, where, as before, I is the accumulated CIDNP intensity. Using Eq. [S] we have s/nOCELo(CO)(T~/T,,,)1’2[1-exp(-klT,,,)][1-exp(-~/T~)](~/T1)-”2.
[I91 This function is plotted in Fig. 6 and compared with the experimentally observed variation of s/n with 7 for line C-4. It is thus found that the optimum s/n in a PS sequence of fixed total duration occurs when r = 1.3 T1. The intensity error, E, under these conditions is, however, about 40%. It is therefore clearly necessary to reach a compromise between intensity error and loss of s/n. Figure 6 shows, however, that using 7 = 0.2T1 leads to a reduction in s/n of less than a factor of 2. Thus, except in cases of extremely low intensity, it should be possible to use a T sufficiently short to introduce less than 10% intensity error. It should be noted that the expression for s/n given in Eq. [19] depends on the rate constant, ki, as well as other parameters. In many cases it may be possible to use the reaction rate as a variable to be manipulated so as to optimize s/n, e.g., by changing temperature, concentration, or light intensity. If we keep the fraction of reaction fixed, e.g., let klT,,, be constant, to avoid excessive overlap with the unpolarized product line, Eq. [19] may be written s/n ccEL’(co)( T1/7 “*)k:‘*[l-exp(-r/Ti)][l-exp(-kiT,,)].
PO1
Therefore the s/n increases with k :‘*, demonstrating the desirability of making k1 as large as experimentally feasible. It should be borne in mind, however, that Eq. [20] and previous equations are based on the assumption that k1 is small enough that variation of dL’/dt during the r epoch is negligible. For very fast reactions and very small numbers of spectra, however, the accumulated intensity will be very sensitive to the exact times at which spectra were taken with Fobs; i.e., the intensity will become very sensitive to the reaction kinetics, a situation we have tried to avoid up to now. Nonideal rf Pulses
The rf pulses employed in FT NMR are susceptible to several types of imperfections (20) including inaccuracy or jitter in the pulse length, rf field inhomogeneity at the sample, variation of Hi during the pulse (commonly in the form of “droop” near the end of the pulse if the amplifier cannot sustain its output), or nonuniform power density across the spectrum arising from weak pulses. For the progressive saturation method described above most of these effects mean that some of the lines in a spectrum and/or a region of the sample are subject to rf pulses different from the
QUANTITATIVE
CIDNP
USING
F’l- NMR
151
90” desired. The analogous effect in the saturation-recovery method is incomplete saturation of the signal by P,,,. It is convenient to express the effects of nonideal pulses as an error, Ed, in the observed accumulated intensity, I,, relative to its value, I90 for an ideal pulse. &p =
(190
-
L)/190.
To estimate cp we consider here only the effects of deviation of the pulse from 90” by the angle 6 in a [(Y - ~1~ progressive saturation sequence, where LY= 90 - 6. The first task in the analysis is to find the intensity L(n) due to the nth a-degree pulse in the sequence. Simple geometry gives L(n) = sin a&(n), where Lo(n) is the intensity which would be observed at time t, with a 90” pulse. If (Y is not 90”, however, Lo(n) will have a contribution from L(n - l), the line intensity actually observed with the (n - 1)st pulse. L(n) = (cos a)L(n - 1) exp( - r/ Ti) +(sin (~)EL~(co)Ic~Ti[l -exp(-T/Ti)]exp(-klt,).
Vll
Solutions to this recursive relationship have been derived by Sojka and co-workers (25) for the purpose of determining kinetic parameters from CIDNP spectra. Their estimates of enhancement factors, however, were based on steady-state spectra. The accumulated intensity is given, as in Eq. [8], by Intensity (Y f L(n). n=l
The evaluation of the sum in the present case, however, is complicated by the fact that each value of L(n) in Eq. [21] depends on previous values (25). If the rate of reaction is slow, however, the line intensities observed with two adjacent pulses will be nearly the same. With that approximation (26) we have L(n)=(sin
a)EL”(~)klT1[l
-exp(-7/T1)]exp(-klt,)[l
-(cos (Y)exp(-T/T1)]-*.
L=l This result has also been derived by Grant and co-workers (27) and applied to the problem of optimizing the sensitivity for T1 measurements in reacting samples. The sum is performed only over the exponential decaying with kl. It therefore follows immediately that the error in accumulated intensity due to deviations from 90” by the angle 5 is ep = 1 - (cos t)[l - (sin 4) exp( - T/ T,)]-‘.
[231
For small deviations from 90”, Eqs. [22] and [23] lead to the surprising conclusion that the intensity increases as the pulse angle decreases. This effect depends, however, on the value of exp( - T/ T1) and disappears when 7 > T1, i.e., when a steady state is reached between pulses. It therefore originates in “saturation” of the polarized signal when large angle pulses and short recovery times are used. This is quite analogous to saturation effects observed in ordinary FT NMR (26,B). While
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in principle it could be exploited to optimize the sensitivity for CIDNP detection (27), in practice its use would lead to spectra distorted to at least some degree by relaxation, but in a way difficult to assess because of the complicated way in which T,, T, and cy interact in Eq. [22]. The above effect of incomplete saturation can be put in somewhat better perspective by considering the consequences for estimation of the enhancement factor E. We may define an experimentally determined value of E’ which would be determined using the same pulse angle cx for both accumulation of CIDNP spectra and determination of the intensity proportional to Lo(~) at the end of the reaction. E’ = [C L(n)]/[(sin
a)L’(co)].
1241
Substituting for L(n) from Eq. [21] and defining the “true” value of E as that determined using exact 90” pulses, we have for the error in E, &E = (E - E’)/E
= 1 - [ 1 - (sin 5) exp( - T/ ri)]-‘.
P51
Thus depending on the sign of the deviation, 6, from 90”, E may be either over- or underestimated using this procedure. For 7 < T,, as would normally be used to remove relaxation effects, deviations of f 5” from perfect 90” pulses would lead to about a 10% error in the estimate of E. Variation of E and T1 during Spectrum Accumulation
Many samples which exhibit CIDNP change their composition, temperature, or other chemical and physical properties during the course of the reaction. We describe briefly a simple interpretation which may be given to the enhancement factor E obtained from spectra accumulated under such changing conditions. It seems reasonable to assume in any case that variation of E and Tl during an individual 7 epoch is small. For simplicity we also consider the case 7 < T,(t) for all t and ignore the contribution from thermal polarization, E. In this limit Eq. [8] becomes Utn) -L”(t,-*)[7/T~(t,-l)l
+[~“(tn) -~“k-dlE(tn-d.
WI
Since the first term will usually be small compared to the second, any time dependence of Ti will usually be inconsequential for evaluation of E. To describe the effects of a time-dependent enhancement factor, E, we may define E(t,-1)
= E,,+S(t,-1).
Ignoring the first term in Eq. 1261 we then have Utn) -[L”(t,)-Lo(t,-~)lCEo+S(t,-~)l. If we choose E. and the set of values S(t,-1) such that the second term vanishes when we take the sum over all pulses, we thus redefine the Eo, determined in the usual manner from accumulated spectra, as a weighted average. Eo = {C [Lo(&) -L”(t,-l)]E(t,-l)}/So,
[271
QUANTITATIVE
CIDNP
USING
F-l- NMR
153
where 6L” is defined by Eq. [gal. In principle the variation of E with time could be detected by accumulating spectra over several portions of the reaction and calculating a value of E for each. In extreme cases (29) where more than one CIDNPproducing reaction may occur simultaneously, the sign of E may even change with time. Clearly under these conditions simple accumulation of the spectrum over the total reaction time would lead to an erroneous estimate of E. An Afterthought
The above treatment of FT NMR applied to samples exhibiting CIDNP obviously ignores situations in which the spectrometer sensitivity varies with time. It is clear, however, that this is a potential problem whenever the conditions for chemical reaction affect the detection system of the spectrometer. The most dramatic such effect occurs when the sample, either by design or by accident, leaves the spectrometer during accumulation! EXPERIMENTAL
Saturation-Recovery
: ‘H CIDNP
CIDNP spectra were acquired on a Bruker WP-60 NMR spectrometer with internal ‘H field/frequency lock. Saturation pulses were generated with the ‘H (60 MHz) broadband decoupler that is standard equipment with the WP-60. The decoupler and analytical channel frequencies were set equal. Two modifications were made, however, to reduce the amount of decoupler noise leaking into the analytical channel during the data-acquisition period with the decoupler nominally gated OFF. The gating of the decoupler was improved by about 15 db by the addition of opposing series diodes at the decoupler rf output. In addition, decoupler leakage was converted to a dc signal during the gated OFF period by turning off the noise modulation (setting the decoupler to cw mode), and taking advantage of the fact that the center frequency of the decoupler channel was set equal to the analytical carrier frequency. These modifications effectively removed any background signal due to rf leakage. The effectiveness of the rf noise pulses (power = 2 W, length = 0.8 set) in saturating the NMR signals was determined by detecting the residual unsaturated signal immediately after the saturation pulse was gated OFF. In all cases the residual signal was found to be less than the background noise in the spectrum from a single FID, typically at least a 20-fold decrease in signal. Progressive Saturation : 13C CIDNP
The WP-60 was used in its unmodified form for the progressive saturation (r3C CIDNP) experiments, i.e., 13C at 15.08 MHz with broadband decoupling at 60 MHz. Special care was taken, however, to reduce errors due to nonideal rf pulses by limiting rf field inhomogeneity and accurately adjusting the rf pulse length. The former was accomplished (20) by adjusting the height of the sample to be less than or
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equal to the height of the receiver/transmitter coil. The 360” null method was used to find the 90” rf pulse length. For the 13C CIDNP spectra it was assumed that the observed lienwidths were dominated by the numerical filter constant (2-3 Hz), and, therefore, that signal heights directly reflected the integrated areas. Sample Preparation
Diacyl peroxides were synthesized in the usual manner (30) and purified by treating the reaction mixtures briefly with anhydrous potassium carbonate and then rapidly passing the solutions through a short column of anhydrous silica. Bulk solutions of the peroxides were prepared at room temperature and samples were placed in the preheated probe of the spectrometer in either of two sample holders. 2H Lock for Reacting Samples
The sample holder for the 13C CIDNP experiments was a coaxial arrangement of a 5-mm-o.d. inner tube containing DMSO-d6 for the 2H field/frequency lock and a lo-mm-o.d. outer tube. The peroxide solution occupied the space between the tubes. A similar arrangement, but with a 5-mm-o.d. outer tube and a correspondingly smaller inner tube, was employed in the ‘H CIDNP experiments described in Fig. 5. The remaining ‘H CIDNP experiments used a sample holder of similar design, but the contents of the inner and outer tubes were exchanged. This allowed containment of the peroxide solution in a sealed inner tube. This substantially reduced bubbling due to CO2 produced during the decomposition. The smaller-diameter sample tube also exhibited less line broadening due to magnetic field inhomogeneity. In fact, for most samples the linewidth was not significantly reduced by sample spinning. ACKNOWLEDGMENTS We gratefully acknowledge financial support from the National Science Foundation under Grants CHE 76-10987 and CHE 78-24171. R.G.L. acknowledges the hospitality of Argonne National Laboratory during preparation of substantial portions of the manuscript.
REFERENCES 1. L. T. Muus, P. W. ATKINS, K. A. MCLAUCHLAN, AND J. B. PEDERSEN (Eds.), “Chemically Induced Magnetic Polarization”, Reidel, Dordrecht, 1977. 2. J. BARGON AND H. FISCHER, Z. Nuturforsch. A 22, 1556 (1967). 3. L. G. WERBELOW AND D. M. GRANT, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 9, p, 189, Academic Press, New York, 1977; R. L. VOLD AND R. R. VOLD, in “Progress in Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.), Vol. 12, p. 79, Pergamon, Elmsford, N.Y., 1978. 4. R. FREEMAN AND H. D. W. HILL, J. Chem. Phys. 54,3367 (1971). 5. J. L. MARKLEY, W. J. HORSLEY, AND M. P. KLEIN, J. Chem. Phys. 55, 3604 (1971); G. C. MCDONALD AND J. S. LEIGH, JR., J. Magn. Reson. 9,358 (1973). 6. A. L. BUCHACHENKO AND SH. A. MARKARIAN, Znt. J. Chem. Kinet. 4,513 (1972). 7. S. SCHKUBLIN, A. WOKAUN, AND R. R. ERNST, J. Magn. Reson. 27,273 (1977); G. L. CLOSS AND R. J. MILLER, J. Am. Chem. Sot. 101,1639 (1979).
QUANTITATIVE
CIDNP
USING
FT NMR
1SS
8. S. SCH,&UBLIN, A. WOKAUN, AND R. R. ERNST, Chem. Phys. 14,285 (1976). 9. S. SCHKUBLIN, A. H~HENER, AND R. R. ERNST, J. Magn. Reson. 13,196 (1974); R. R. ERNST, W. P. AUE, E. BARTHOLDI, A. H~HENER, AND S. SCHKUBLIN, Pure Appl. Chem. 37, 47 (1974). 10. G. L. CLOSS, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 7, p. 157, Academic Press, New York, 1974. 11. R. G. LAWLER AND H. R. WARD, in “Determination of Organic Structures by Physical Methods” (F. C. Nachod and J. J. Zuckerman, Eds.), Vol. 5, p. 99, Academic Press, New York, 1973. 12. A. ABRAGAM, “Principles of Nuclear Magnetism,” p. 522, Oxford Univ. Press, London, 1961; B. W. GOODWIN AND R. WALLACE, J. Magn. Reson. 32,325 (1978). 13. R. G. LAWLER, in “Progress in Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.), Vol. 9, p. 145, Pergamon, Elmsford, N.Y., 1973. 14. K. MILLER AND G. L. CLOSS, J. Am. Chem. Sot. 94,1002 (1972). 15. G. L. CLOSS AND M. S. CZEROPSKI;Chem. Phys. Lett. 45,115 (1977); F. J. J. DE KANTER AND R. KAPTEIN, Chem. Phys. Lett. 62,421 (1979). 16. R. G. LAWLER, P. F. BARBARA, AND D. JACOBS, J. Am. Chem. Sot. loo,4912 (1978). 17. R. W. FESSENDEN, J. Phys. Chem. 71,74 (1970). 18. N. J. KARCH, E. T. KOH, B. L. WHITSEL, AND J. M. MCBRIDE, J. Am. Chem. Sot. 97,6729 (1974); see, however, the criticism of this structure by M. B. YIM, 0. KIKUCHI, AND D. E. WOOD, J. Am. Chem. Sot. 100,1869 (1978). 19. E. LIPPMAA, T. SALUVERE, AND M. MAGI, Org. Magn. Reson. 5,429 (1973); E. LIPPMAA, T. PEHK, A. L. BUCHACHENKO, AND S. V. RYKOV, Chem. Phys. Lett. 5,521 (1970). 20. G. C. LEVY AND I. R. PEAT, J. Magn. Reson. 18,500 (1975). 21. M. HALFON, Ph.D. dissertation, Brown University, 1974. 22. R. FREEMAN AND H. D. W. HILL, J. Magn. Resort. 4,366 (1971). 23. R. KAPTEIN, R. FREEMAN, H. D. W. HILL, AND J. BARGON, Chem. Commun., 953 (1973); C. BROWN, R. F. HUDSON, AND A. J. LAWSON, J. Am. Chem. Sot. 95,650O (1973); H. IWAMURA, M. IWAMURA, M. IMANARI, AND M. TAKEUCHI, Tetrahedron Lett., 2325 (1973); R. KAPTEIN, R. FREEMAN, AND H. D. W. HILL, Chem. Phys. Lett. 26, 104 (1974); W. B. MONIZ, C. F. PORANSKI, JR., AND S. A. SOJKA, J. Org. Chem. 40,2946 (1975); K. ALBERT, K-M. DANGEL, A. RIEKER, H. IWAMURA, AND Y. IMAHASHI, Bull. Chem. Sot. Jpn. 49,2537 (1976). 24. R. E. SCHWERZEL, R. G. LAWLER, AND G. T. EVANS, Chem. Phys. Lett. 29,106 (1974). 25. C. F. PORANSKI, JR., S. A. SOJKA, AND W. B. MONIZ, J. Am. Chem. Sot. 98,1337 (1976); C. F. PORANSKI, JR., W. B. MONIZ, AND S. A. SOJKA, J. Am. Chem. Sot. 97,4275 (1975). 26. J. S. WAUGH, J. Mol. Spectrosc. 35, 298 (1970). 27 K. A. CHRISTENSEN, D. M. GRANT, E. M. SCHULMAN, AND C. WALLING, J. Phys. Chem. 75, 1971 (1974). 28. R. R. ERNST, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 2, p. 1, Academic Press, New York, 1966. 29. M. L. MANION-SCHILLING, R. S. HURON, AND H. D. ROTH, J. Am. Chem. Sot. 99,7792 (1977); G. L. CLOSS AND R. J. MILLER, J. Am. Chem. Sot. loo,3483 (1978); S. M. ROSENFELD, Ph.D. dissertation, Brown University, 1973. 30. W. H. URRY AND M. S. KHARASCH, J. Am. Chem. Sot. 66,1438 (1944).
OF
MAGNETIC
RESONANCE
40, 135-1.55
(1980)
Practical Aspects of Quantitative CIDNP Using FT NMR RONALD G. LAWLER AND PAUL Department
of Chemistry,
Brown
University,
Providence,
F. BARBARA Rhode
Island
02912
Received October 26, 1979 Two procedures have been devised for minimizing the distorting effects of relaxation on NMR spectra obtained from continuously reacting samples which exhibit CIDNP. The techniques employ (90-7)~ or (Pu,<-POt,S- tob.)Npulse sequences. These record the chemically driven component of the spectrum which develops a short time after the signal has been saturated by one or more rf pulses. The theory of the method is developed for several models of reaction kinetics and illustrated with experimental determinations of the absolute and relative CIDNP enhancement factors for ‘H and 13C spectra obtained from two thermally decomposing organic peroxides. It is found that the enhancement factors obtained from relaxation-free CIDNP spectra are in excellent agreement with predictions of the high-field radical pair theory. Errors arising from incomplete saturation are estimated and the compromise between signal/noise and removal of relaxation effects is discussed. INTRODUCTION
Since its discovery in 1967, chemically induced dynamic nuclear polarization (CIDNP) has become an important tool for the study of free radical reactions (1). The phenomenon is manifested by greatly enhanced NMR signals, in absorption (A) or emission (E), observed in molecules formed from radical intermediates. Most applications of CIDNP to data have employed only the sign of enhancement of NMR lines (A or E) rather than the magnitude. More quantitative determination of CIDNP enhancements is difficult because the observed intensity depends not only on the intrinsic enhancement due to the chemical reaction but also on the competition between the “chemical pumping” of the spin system and nuclear relaxation (2). Although cw NMR has been employed in most recent CIDNP investigations, it is inevitable that the ubiquitous FTNMR spectrometer will inherit the bulk of the future CIDNP workload. Nearly all CIDNP spectra published so far using either method, however, are of the “steady state” (SS) variety, recorded by using either low cw rf power or long waiting periods between rf pulses and small pulse angles. To extract intrinsic CIDNP intensities from SS spectra it is necessary to determine accurately both the rate of the reaction and the relaxation times of the nuclei of interest (2), a tedious undertaking even for simple NMR spectra. Furthermore, the complex kinetic behavior of many reactions and nonexponential relaxation in any but the simplest spin systems present added complications (3). We report here the use of two FT pulse sequences to record CIDNP spectra in which the intensity distortions arising from spin-lattice relaxation are greatly 135
0022-2364/80/100135-21$02.00/0 Copyright @ 1980 by Academic Press, Inc. All rights of reproduction in any form reserved Printed in Great Britain
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reduced. We also describe a protocol by which one may extract relative and absolute enhancement factors from such spectra without knowing the detailed kinetics of the reaction. The methods are variants of the “progressive saturation” (PS) (4) and “saturation-recovery” (SR) (5) techniques used to determine T1 values in normal spectra. In our case, however, we take advantage of the principle, first stated by Buchachenko and Markarian (6), that the magnetization of an initially saturated spin system depends at short times primarily on the rate of CIDNP production, i.e., is independent of Ti. A similar approach was employed recently (7) for samples excited by intermittent irradiation. We are concerned here, however, with applications to the commonly occurring cases in which the reaction rate cannot be easily controlled, e.g., continuous thermolysis, bimolecular redox reactions, continuous irradiation, etc.
THEORY
OF STEADY-STATE
CIDNP SPECTRA
In the absence of an rf field the magnetization of a chemically pumped spin system is affected by both the chemical reaction, r(t), which converts a reactant (R) into a “polarized” product (P*), and by relaxation, w(t), via transitions within the nuclear spin system. Relaxation redistributes and eventually destroys the polarization to give the “unpolarized” product (PO) R -
r(t)
P* w(t? PO.
[II
During a reaction the changing chemical and physical properties of the sample will generally impart a time dependence to both r and w. Furthermore, only in idealized cases will these two processes be adequately described by first-order kinetics. In what follows we ignore complicating effects of CIDNP on pulsed NMR spectra which may arise in homonuclear spin systems at very short times (8) or when large pulse angles are employed (9). The first effect is seen only in experiments where the chemical and rf excitations of the sample are phase coherent. It is absent when chemical excitation is continuous, is reduced when several nuclei are present, or may be eliminated by jitter in the timing of light and rf pulses. The second effect is easily circumvented, but with some loss of sensitivity, by employing pulse angles less than 30” or so. In the absence of the above effects the observed intensity,’ Li, of a line i extracted from a free-induction decay taken at time t is proportional to the population difference between two energy levels of the nuclear spin system. For such a “simple line” (12) in a spectrum exhibiting CIDNP we may write (13) dLi/dt = EidLP/dt+EidLP/dt-
T;: (Li-Lp)-r
Aik(Lk -Li). k
I21
’ We prefer to discuss the experimentally observed line intensities rather than population differences (10) or magnetizations (11). In doing so we assume that degeneracy factors and “intensity borrowing” effects in spin-coupled systems have been properly included in the definitions of Li and the relaxation parameters in Eq. [2].
QUANTITATIVE
If the transition
CIDNP USING FT NMR
137
i is between nuclear spin states a and b
T;; = 2 Aik
=
wab
(!i>(
+ ($1 c”
c
Wac
-
(wac
+
wbc),
I31 WI
wbc).
A superscript zero denotes thermal equilibrium, Ei (with a value between 0 and 1) determines the contribution to Li from thermal polarization in the reactant,2 and Ei is the (possibly time dependent) enhancement factor arising from CIDNP. The fourth term on the right-hand side of Eq. [2] arises from coupling between line i and other lines which share state a or state b. This term may become important either if the differential relaxation probability, Aik, is especially large (14) or if Ek is much larger than Ei (15). Such effects probably contribute to nearly all steady-state spectra, but we ignore them for simplicity in what follows. They are removed along with other relaxation effects by use of the pulse sequences described in later sections. The steady-state solution of Eq. [2] in the limit where coupled relaxation is negligible becomes (L~)ss = Lp + Tli(Ei + Ei)(dLP/dt).
[41
The observed intensity under these conditions thus follows the intensity of the unpolarized spectrum dLP/dt, i.e., the rate of reaction. A typical series of spectra obtained under steady-state conditions is shown in Fig. 1. Rearranging Eq. [4] we obtain the following expression for Ei. Ei = T;: [Li(t)ss-LLP(t)][dLP/dt];‘-&i.
[51
We see that even in the absence of the complicating effects of coupled relaxation, a determination of Ei from a steady-state spectrum requires knowing, in addition to
H-4,
0
50
100 150 SEC
200
4
II
3
2 km
1
0
FIG. 1. Typical steady-state spectra obtained during thermolysis of peroxide (1) in hexachloroacetone at 120°C. H-2 and H-4 are methylene Each spectrum was obtained from a single 20” pulse taken at intervals moment the sample was placed in the heated probe. The time dependence
t-butylacetyl-m-chlorobenzoyl protons identified in Scheme 1. of 20 set and beginning at the of peak H-4 is shown at the left.
* The contribution to L arising from the reactant and described by E will in general depend on the relaxation time of the reactant, TR, as well as on r and Tl. Thus E will take on the values 1 or 0 if T, is much shorter or much larger than Tl, respectively. The value of E for intermediate cases is given by E = I- T,( TR - TJ’[exp( - T/ TR) -exp( - r;/Tr)][l - exp( - T/T,)]-‘. It is assumed that both the reactant and product lines are initially fully saturated.
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the observed intensity, (Li)ss, three other quantities: Lp, Tri, and the reaction rate, dL?/dt, all at the time of measurement of (Li)ss. If the CIDNP intensity is large the corrections for Lp and ei will be unimportant. Furthermore, since dL’/dt will differ at most by a constant factor for each line in the spectrum of a given reaction product the relative enhancement factors of two such lines will be given by
[61
(EiIEj) -(T1jlT,i)[(Li)ss-LPI[(Lj)ss-LPI-’.
However, even in this case an accurate determination of the ratio of the Tl values is required. It is thus not surprising that little use of the magnitudes of enhancement factors has been made. Steady-state CIDNP spectra are of qualitative value only. A series of such spectra may be used, however, as in Fig. 1, to obtain an estimate of the time span during which data should be collected when the pulse schemes described below are applied. PROGRESSIVE
SATURATION
Theory
The key to minimizing relaxation effects in CIDNP spectra lies in making all but the second term in Eq. [2] as small as possible. In strongly enhanced spectra the contributions of ei and Lp are small. The relaxation terms may therefore be made small by recording the spectrum only when Li is small, e.g., before significant relaxation has taken place following a 90” pulse or saturating pulse sequence. Equation [2] may be integrated over the range of time 7=t,-tn-1
between application of a saturation pulse at tnel and observation of an FID at t,. The intensity, L, of the line obtained from the FID is
L(L) -L”(tn-dl -exp(-~/T~)l+[L”(t,)-Lo(t,-~)l xi1 + (TI/T)(~- 1X1-exp( - 4 Tdl) +[L”(~n)-Lo(t,-~)l(T~I~)E[l--xp(-~/T~)l.
[71
We have continued to ignore Aik and it is assumed that E, T,, and dL’/dt are varying slowly enough that they may be considered constant during the 7 epoch. For convenience the subscript i has been dropped here and in what follows. The variation of L during a string of 90” pulses is shown in Fig. 2a for two different values of 7 and is compared with the corresponding changes under steady-state conditions for a first-order reaction. Equation [7] may be summed over a series of N equally spaced FIDs collected between times tl and tN following 90” pulses applied at to through tN-l. Intensity cc f L(t,,) = SL”+SLo[l
-exp(-T/TI)]
?I=1
x {[E.+ (E - ~)](T,/T)
+ N(L”)(SLo)-‘},
l-81
QUANTITATIVE
139
CIDNP USING PTNMR HALF-LIVES
4
I
2
3
t/T,
FIG. 2. (a) Calculated time dependence of CIDNP intensity during a string of 90” pulses applied to a first-order reaction with rate constant k. Times are given in units of 7’i. Values of KT,, E, E,and r/T1 used in Eq. [6] are as shown. The evaluation of intensity under steady-state conditions, i.e., using a very small pulse angle, is shown by the dashed line. (b) Summed intensity of lines in (a) using Eq. [7].
where
SLO = E, [LO(a) -LO@,-l)] =Lo&v)-LOOo),
N(LO>= c” LO(t,-l), n=l
Pal Pbl
and we have assumed that E and T1 do not change during the reaction. For large N,
N(LO) = 7-l I
c-1 fo
Lo(t) dt.
[9cl
It is useful to consider four practical limiting situations in which Eq. [8] would apply.
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Stable Sample L’)(t,)
= I/(?to)
for all n,
Intensity a N[ 1 - exp( - T/ T,)]LO( to),
[loal
which is simply the expression employed to determine T, by the saturation-recovery method using perfect 90” pulses (5). No CIDNP E = 0,
Intensity aSLo{
+ (E - l)(T,/~)[l
-exp( - ~/Ti)l} +N(L’)[l
-exp(r/Ti)].
[lob1
It is interesting to compare Eqs. [lOa] and [lob] for the case r < Ti. In this limit Eq. [lob] becomes Intensity a N(L’)(r/
7’i) + e&5’.
The first term is analogous to Eq. [lOa] except for the replacement of L” by its average value. The second term represents the contribution to Lo from polarization in the reactant and might persist even at values of r short enough to make the first term negligible, provided that the reactant molecule is either not saturated or recovers rapidly from saturation.* Overlapping CIDNP and Thermal Polarization LO(t&
in the Product
LO(thr).
If we restrict ourselves to the case r < Ti, we have approximately Intensity a EL”(tN) + eL”(tN) + N(L0)(7/ T,).
[1Ocl
The first term is the one of usual interest in CIDNP studies, but we see that no matter how short r is, the second term will also contribute to the accumulated signal. Since E is typically several hundred, however, but E is not expected to exceed unity, the second term may usually be ignored. The third term represents overlap of the polarized spectrum with “unpolarized” product. Although it would appear from the form of this term that it could be reduced to arbitrarily small size by using a very small value of r, the situation is complicated. This term will continue to grow in size with increasing number of scans once the reaction is over. For a large number of scans the magnitude of this term may be determined by evaluating the integral in Eq. [SC] for various kinetic models. First-order formation: Lo(t) = L”(oO)[l -exp( - kit)],
N(L”>(dTd= (Tmax/TdLo(~){l-[l-exp(-klT,,,)l(klT,,)-‘}, where T,,, = NT.
[lla
QUANTITATIVE
CIDNP
USING
FT NMR
141
Second-order formation: LO(t) = L0(00)t[T2 + t]-.l,
N(L0)(~/T~)=(T,,,/~~)L'(~){l-(~2/~max)ln[l+(~,,,/~~)l}r
[lib
where 7T1 = k2R(0); k2 is the second-order rate constant and R(0) is the initial concentration of reactant. We see from Eqs. [ 11 a] and [ 11 b] that, as predicted, the overlap term continues to grow in magnitude with increasing number of scans beyond the time that the reaction is over, i.e., for T,,,,, greater than k;’ or 72 for the above models. Thus it is obviously desirable to stop the accumulation once the reaction is over (see Practical Considerations below for further discussion of the optimum number of scans). Overlapping CIDNP and Thermal Polarization
in the Reactant3
LO(to) >>LO(t&
In this case dL’/dt in Eq. [2] is negative. When allowance is made for this, Eq. [8] becomes, in the short T limit, Intensity ccL”(tO)[e + E] + N(L”>(7/ T,).
[10dl
This differs from Eq. [lOc] only in the interpretation given to the last term. Here again this overlap term may be evaluated for specific kinetic models. First-order decay: Lo(t) = Lo(O) exp( - klt),
N(L’)(d Td = CT,,,/ TI)L~(O)II~ - exp(- kl T,,,)l(kl T,,J’. In this case the overlapping term of scans but approaches a limiting will decrease in magnitude for Reactions other than first-order
[llcl
does not continue to grow with increasing number value, L’(O)(k, TJ’ for T,,, > k;‘. Thus this term either a fast reaction or a long relaxation time. should produce qualitatively similar results. Applications
Relative Intensities
The usefulness of the progressive saturation method is illustrated by comparing the two carbon-13 spectra shown in Fig. 3. The chemical reaction is the decomposition of 0.5 M t-butyl-acetyl-m-chlorobenzoyl peroxide, 1, in hexachloroacetone (HCA) at 120°C (Id). The reaction products and assignments of carbon-13 lines are given in Scheme 1. Both spectra were obtained over a total reaction time, 3 We ignore the possibility that a line from an unreactive compound, e.g., solvent, may overlap the line exhibiting CIDNP. This situation is best avoided, of course, since N(L’) can become very large. If this is not possible, the overlapping spectrum may in principle be subtracted since its intensity is related to the number of scans via Eq. [lOa]. In practice, however, the widths and positions of lines in reacting and nonreacting samples are seldom identical. Incomplete cancellation of slightly shifted lines can also introduce line distortions which might be incorrectly interpreted as arising from lines exhibiting CIDNP.
142
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I
I60
I
I
I
1
+
t30
120
110
C-7
I
150 t40
AND BARBARA
I ’ c-4
I 00
1 70
1
1 60
I 50 pm
I 40
I 30
J 20
FIG. 3. Carbon-13 CIDNP spectrum of sample whose ‘H spectrum is shown in Fig. 1. The spectrum was obtained using N successive 90” pulses separated by r, as indicated. Note that the lower spectrum has been attenuated four-fold relative to the upper. Assignments of lines are given in Scheme 1. Broadband ‘H decoupling was employed.
NT, of 120 sec. The upper spectrum comes close to that expected under steady-state conditions since the 20 set between pulses is comparable to the longest relaxation time in the spectrum (ca. 20 set for C-l), whereas the lower spectrum has employed a value of T shorter than the shortest TI (ca. 3 set for C-2) and should be close to an “unrelaxed” spectrum. The intensities of unpolarized lines are lower than the noise R’COaO&R
(1) + [R’C02. .R]
[R’C02. .R] -+ R’-C02-m-C-(CH,), C-l c-2 c-3 H-2
Pair formation (2)
Coupling
[R’C02. .R] + CO2 + R’-CH&-(CH& C-6 C-l
Coupling
[R’COc. .R] + R’COI.+.R
Cage escape
HCA+.R
-a Cl-CH2-C-(CH& c-4 c-5 H-4 R’ = m -CICbHd,
Scavenging
R = CHPC(CH3), SCHEME
1
QUANTITATIVE
EFFECT
CIDNP
USING
TABLE 1 ON RELATIVE CIDNP INTENSITIES OF VARYING PROGRESSIVE SATURATION METHODS
Intensity ratio Calculatedi’ “Unrelaxed”’ “Steady state”e
C-l/C-2 0.5 0.5 *Old 2.6~tO.5
143
F-l- NMR
(C-3 + C-7)/(C-2 + C-6) -0.34 -0.41 f 0.08 -1.60+0.13
7 USING
THE
c-5/c-4 -0.34 -0.35 i 0.03 -0.60 + 0.10
a Experimental data are derived from carbon-13 spectra similar to those shown in Fig. 3. The pertinent reactions are shown in Scheme 1. b It is assumed that the CIDNP intensity is proportional to the hyperfine-coupling constant of the nucleus in the intermediate radical pair. This approximation (13, 18) is valid for net polarization when Ag& is greater than the hyperfine-coupling constant of the polarized nucleus. Since the 13C hyperfine-coupling constants have not been determined by EPR for neopentyl or benzoyloxy radicals, these parameters were estimated. It was assumed that the 13C hyperfine-coupling constants for the ethyl radical (A, = +40 G and A, = -13.5 G) (17) are a reasonable estimate to those for neopentyl radical. For the carbonyl carbon (C-l) in the benzoyloxy radical, the estimated value was -20 G. This is the theoretical estimate (18) based on the assumption tha: benzoyloxy is a planar r radical. ’ 7 = 1.2 set; N = 100 scans. d Average of ratios obtained from spectra of three samples. Error estimate is one standard deviation. e T = 20 set; N = 6 scans.
level in these spectra and may be ignored. As expected, the noise level in the lower spectrum is 4 times that of the upper since nearly 16 times as many spectra were averaged in the former case. The actual signal intensity, however, is substantially lower in the upper spectrum for all but C-l. This reflects the loss of intensity due to relaxation when r > T1. Table 1 summarizes the ratios obtained for three groups of lines in the spectra under “unrelaxed” and “steady-state” conditions. As expected, the relative intensities obtained using a small value of r are in much better agreement with theoretical predictions than are those obtained under steady-state conditions. The differences are especially large for the ratio C-l/C-2 because the values of r1 differ by nearly an order of magnitude. Indeed, examination of Eq. [8] in the limit where thermal polarization is negligible leads to the conclusion that the relative intensities of two lines in the same product are given by the equation (Intensity)i/(Intensity)j =(Ei/Ej)(T~i/T,j)[l-eXp(-T/T~i)][l-eXp(-T/T~j]-l.
[121
Thus the intensity ratio for r > Ti is modified by the ratio ( T1 J Tlj). The expected change with T due to the value of about 7 (i.e., 20/3) for this ratio for C-l/C-2 is within experimental error of that observed: (2.6/0.5). Absolute Enhancement
Factors
Returning to Eq. [8] we find that in the limit where thermal polarization is negligible the accumulated intensity of a single CIDNP line for T < Ti is given simply
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Intensity CCESLO, where SL” is the intensity of the hypothetical unpolarized signal arising from the amount of product formed (or reactant lost) during the portion of the reaction over which CIDNP spectra were accumulated. Thus is a remarkable result: Eq. [13] is independent of both T, and the kinetic behavior of the reaction. If r is set short enough to prevent loss of intensity due to relaxation, and E is large enough to be able to ignore overlap with “unpolarized” product, the value of E is determined from the ratio of the observed accumulated intensity to the intensity associated with the unpolarized product. The latter may in principle be obtained directly from a single spectrum taken at the end of the reaction using the same spectrometer settings as those used to accumulate the CIDNP spectra. If the intensity of the unpolarized signal is too weak to see with a single scan, signal averaging may, of course, be employed, but it is essential that signal saturation and any NOE be suppressed. Alternatively the intensity of the line from an unpolarized product may be estimated using the intensity of a reactant line at the beginning of the reaction and the yield of product. This method of determining E is illustrated here for C-2 in the product 2 (Scheme 1) formed from the peroxide 1 during decomposition at 120°C in ortho-dichlorobenzene (ODCB) (16). The CIDNP spectra obtained in ODCB are similar to those shown in Fig. 3 except that the emission line, C-4, is absent. ODCB was chosen in this case because secondary decomposition of the products seems to occur to some extent in HCA, making reliable estimates of product yields difficult. Sixty transients spaced by 1.2 set were collected over a period beginning 30 set after the sample was placed in the heated probe and ending 72 set later. In separate experiments the sample was quenched by rapidly cooling and product yields were determined by ‘H NMR integration. In this way it was shown that the above 72-set period encompassed greater than 95% of the reaction. The intensity SL” was calculated by scaling down the signal observed from the solvent lines, under nonsaturating conditions and with NOE suppression, at the end of the reaction using the known peroxide concentration (0.5 M) and the yield of 2 (15%). The value of E thus obtained is +5000* 1000. This is comparable to other estimated CIDNP enhancement factors for carbon-13 (19). In the next section we compare this enhancement factor with that obtained for the protons bonded to the same carbon. This value could, of course, also be used to calculate the value of E for other lines using the relative enhancements analogous to those in Table 1. Limitations
of the Progressive Saturation Method
The limitations and possible sources of error in the progressive saturation method as used here are the same as those which pertain when the method is employed for Tl measurements on normal samples (20). These include limitations due both to instrumentation and to the intrinsic properties of the sample. In the former category are effects arising from the fact that the rf field and/or chemical reaction rate may not be distributed uniformly throughout the sample. This
QUANTITATIVE
CIDNP
USING
FI NMR
145
means that the sum in Eq. [8] should be averaged over the entire sample, but in a way which reflects the diffusion of spins with different polarizations into and out of the receiver coil (21). The diffusive properties of the sample and the required distribution functions, however, will generally not be known. It is therefore essential to minimize these effects by restricting the sample size to just fill the receiver coil (20). Another instrumental effect arises from pulses which deviate from 90” (see Experimental). More fundamental limitations of the progressive saturation method may arise from the properties of the sample. These include: (i) distortions due to spin echoes (22) when the spin-spin relaxation time, Tzi, is comparable to 7; (ii) incomplete saturation and distortion due to truncation (22) when the effective spin-spin relaxation time, Tzi, is comparable to T; (iii) distortion of homonuclear CIDNP multiplet effects when 90” pulses are used (9). None of these effects is important for 13C because (i) spin echoes are suppressed by *H broadband decoupling (22); (ii) r3C Tli values, and therefore acceptably short values of T, are usually longer than the Tzi imposed by field inhomogeneity; and (iii) 13C homonuclear spin coupling is usually absent. The significance of this last feature of 13C CIDNP spectra has not always been appreciated and small pulse angles or long waiting times between pulses have often been employed needlessly (23). As we have shown above, however, there is never any reason to use pulse angles less than 90” for 13C CIDNP spectra with, or without, decoupling of protons or other nuclei. Use of smaller pulse angles needlessly reduces the size of the signal. For ‘H CIDNP, on the other hand, the above limitations may all exist simultaneously. This makes the progressive saturation method generally unsuitable for ‘H CIDNP. A pulse sequence which is satisfactory for ‘H CIDNP is described in the following section. SATURATION
RECOVERY
Method
The “saturation-recovery” pulse sequence, (Psat-7-PobbtobS)N, was developed originally to measure T1 by monitoring the intensity at tabsas a function of r (5). The method as applied to CIDNP spectra is philosophically the same as the progressive saturation technique described in the last section. The only difference between the two methods is that in the latter method P,,, = P&s and tabs= r. Figure 4 shows the pulse sequence employed to obtain CIDNP spectra using this technique. The limitations described in the previous section are no longer present with this pulse sequence because (i) echoes are suppressed because PSatdestroys all components Of M, including M, and MY ; (ii) tabsmay be easily made greater than T:, eliminating the effects of truncation; and (iii) P&s is no longer restricted to 90” and may thus be made as small as desired to eliminate distortions in spectra with homonuclear multiplet effects (9). The saturation-recovery method does possess some potential disadvantages over progressive saturation. It is somewhat more difficult to achieve experimentally since
LAWLER
146
AND BARBARA
FIG. 4. Schematic representation of pulse sequence employed for the saturation-recovery minimizing relaxation effects. The time intervals shown are those used in Eq. [13].
method of
the spectrum must be fully saturated in a short time (see, however, the Experimental section for a simple way to achieve this with commercial spectrometers equipped for broadband ‘H decoupling). Furthermore, the overall signal/noise is lower than for progressive saturation for continuously reacting samples because the chemical polarization which occurs during r&s (which might be considerably longer than 7) is destroyed by the next P,,, pulse and is therefore wasted. For photolysis, however, this waste is avoided by turning the light off during fobs. Finally, the restriction of PObsto small angles when multiplet effects are present decreases the size of the signal. If one requires only net effects, however, in spin systems without intensity borrowing (9), 90” pulses may again be used. Applications
An analysis of the saturation-recovery technique similar to that leading to Eq. [8] for progressive saturation leads to the following relationship between the accumulated CIDNP intensities obtained using the two techniques with the same value of 7 over a total reaction time which is very long compared to the time for one (Psat+-Pobs-tabs)
cycle.
(Intensity)sn = (Intensity)ps[T/T,]
sin 6&,
[I41
where 7, = 7 + T,,~+ t&s. The quantity T,,~ is the length of PSat(typically 0.8 set) and &bs is the angle of Pobs. The ratio 7/rc is simply the ratio of the number of spectra accumulated in the SR and PS modes, respectively. Aside from this factor, and the overall reduction of intensity via sin 6&s, the intensities for a given 7 are the same. In particular, the short-7 condition for obtaining “unrelaxed” spectra is the same in the two methods. Relative Enhancements
in ‘H CIDNP
In Fig. 5 are shown spectra obtained from the methylene group quartet, Q, of 4, obtained by decomposition of 0.5 M propionyl-m chlorobenzoyl peroxide (3) in 3 : 2 HCA-ODCB at 140°C. The relevant chemical reactions leading to this product are shown in Scheme 2 (24). This multiplet provides a classic example of the frequent observation that the multiplet effect in a CIDNP spectrum relaxes faster than the net effect for the same set of nuclei (13, 14). In both m -chloroethylbenzene,
QUANTITATIVE
CIDNP USING FT NMR
147
FIG. 5. CIDNP spectra of the methylene quartet (Q) of ethylbenzene formed according to Scheme 2 in a 3:2 mixture of HCA and ODCB at 140°C. (a) Pob,= 20”, number of spectra=4, time between spectra = 10 set; accumulation started 110 set after the sample was placed in the heated probe. (b) Same conditions as (a) except that a 2-W, 0.8-set broadband decoupler pulse, P,,, was applied at time r = 4 set before Pobs. (c) Theoretically predicted spectrum. The frequency scale employed in (c) is about 30% narrower than that in (a) and (b).
spectra a pulse angle of 20” has been employed to avoid distortions of the multiplet effect; yet the multiplet effect has relaxed away from the spectrum obtained without presaturation. When relaxation is avoided using the SR method, however, the relative intensities are in excellent agreement wi.th those predicted theoretically (24). In this case the overlap with unpolarized signals is negligible. R’C0202CR
(3) --) [R’C02.
.R]
[R’COr. .R] -+ COr+R’-CI&-CHs Q R’ = m-ClC6H4,
(4)
R = CH&Hs
SCHEME 2
Absolute Enhancement Using Eq. [14] in the limit of short T we have by analogy with Eqs. [13] and [lOc] (Intensity)snoc:{SL’[E
+ E]+N(L’)(~/T~)}(~/~,)
sin dabs.
[I51
We will illustrate the use of this equation to determine E for the emission line, H-2, for protons bonded to the carbon atom, C-l, in ester 2 produced by thermal decomposition of the peroxide 1 (Scheme 1) in ODCB. The spectrum is very similar to that shown in Fig. 1 except that the signal H-4 is not observed in this case. Since the signal of interest is a singlet it is permissible to use a value of cobs= 90” to optimize the sensitivity. It is found that 2 is formed in an approximately first-order reaction with rate constant, ki, about 3 x 10e2 set-‘. The spectrum of the reaction mixture was accumulated as 50 scans over the first 220 set of reaction using values of T = 1 set and 7c = 4.4 sec. From Eq. [l la] we find that the last term in Eq. [15] above has the value
[161
14x
LAWLER
AND BARBARA
where T max= NT, = 220 sec.
In an independent experiment, an upper limit to the magnitude of this term was estimated by accumulating 50 scans of the product mixture using the same values of 7, doss, and 7, as those employed in collecting the CIDNP spectrum. The intensity of the line H-2 thus obtained was about 10% of the absolute intensity of that line in the CIDNP spectrum. It follows therefore that the ratio of the two terms in Eq. [15] was about 10 to 1. To estimate the value of SL’(r/r,) the intensity of a single scan of H-2 at equilibrium in the product mixture was determined and reduced by the ratio T/T,. By combining the CIDNP intensity and the two estimates of SL” one obtains a value of E = - 590 f 60 for the line H-2 and an estimate of Tl greater than about 4 set for these protons. The latter value is consistent with estimates derived from preliminary experiments using different r values. It is of interest to compare the above values of E for H-2 with the value + 5000* 1000 reported above for the corresponding carbon-13. In the limit where the CIDNP intensity is proportional to the hyperfine splitting (Table 1, footnote b) we expect the ratio of enhancement factors in the same molecule to be U%IEHLI~=
(&/AH)(~H/~c)
-(+40/-20)(4)-
-8
and we find (EC/EH)obs = -8’.5 zt 2,
in excellent agreement with the theory. PRACTICAL
CONSIDERATIONS
The analysis and examples presented up to now have been based on several assumptions about the ability of the NMR spectrometer to produce ideal 90” pulses or complete saturation and about the constancy of parameters describing CIDNP during the reaction. We describe here some of the consequences of simple, small deviations from this ideal behavior and also discuss the optimal choice of 7 and T,,,,, required to minimize errors due to relaxation and maximize signal/noise. Unless otherwise indicated, for purposes of illustration it will be assumed that the CIDNP line of interest is in the product of a first-order reaction, and contributions of thermal polarization to the intensity will be ignored. Choice of T
CIDNP spectra acquired by either the PS or the SR method exhibit loss of intensity due to relaxation unless 7 <
Er= [I(O)- ~(~)l/~Ko,
[17al
QUANTITATIVE
CIDNP USING F-I NMR
149
which, from Eq. [8] or Eq. [14], becomes er= 1 -(TI/7)[1
-exp(
-7/TI>]
=$(T/T’)-;(T/Tl)*+.
[17bl
**.
Thus if less than 10% loss of intensity is desired, a value of r I 0.2Ti is required. For the case of relative enhancements, the error, E!, is conveniently defined as
EZ= [(li/J)O- (lilIj)rll(lil~)O ~1-(T~~/T~j)[l-exp(-7/T~i)l[l-~x~(-~/~~j)l~1 =&[T;;
-yyi’]+.
...
I381
This is a rather less restrictive condition on r since it involves the difference in relaxation rate constants. It is instructive to demonstrate experimentally the validity of Eq. [8] in describing the dependence of accumulated intensity on r. In Fig. 6 is shown a plot of the accumulated intensity of the emission line, C-4, in Fig. 3 vs the value of T relative to Tl for this line using the PR method over a constant total accumulation time, Tmax. The value of Tl = 6.3 set was obtained from least-squares fitting of the intensity to T using Eq. [8]. The calculated intensity error, E,, for this line for different values of T/ Tl is also shown.
-.-.-.a._ 0.1 .-,’ k 0
1 0.5
I 1.0
1 1.5
I 2.0
I 2.5
I 3.0
T/T,
FIG. 6. Comparison of calculated (-) and observed s/n (Cl) and summed intensity (0) for line C-4 of Fig. 3 as a function of r. The total accumulation time, T,,, was fixed at 120 set and the data points correspond to the summation of N = 6, 12, 20, 40, and 60 spectra, reading from long 7 to short. The measured value of Ti, 6.3 set, was obtained by least-squares fitting of the summed intensity to r using Eq. [g] in the limit where the thermal polarization is negligible. The calculated s/n curve was obtained using Eq. [19] and scaled to pass through the point r/ ri = 1. The fractional error due to relaxation, E, (- - -), was calculated from Eq. [17]. The relative noise level (- . -) varies simply as 7-l” and was arbitrarily set to the value 0.25 for T/T, = 1.
I so
LAWLER
AND
BARBARA
Optimal Signal/Noise
A straightforward approach to the removal of distortion due to relaxation would be to use as short a T value as achievable and accumulate as many scans as possible before the reaction is over. The drawback of this seemingly obvious approach becomes apparent if we consider the way in which the signal/noise (s/n) varies with the total number of scans. s/n ocI/N’j2, where, as before, I is the accumulated CIDNP intensity. Using Eq. [S] we have s/nOCELo(CO)(T~/T,,,)1’2[1-exp(-klT,,,)][1-exp(-~/T~)](~/T1)-”2.
[I91 This function is plotted in Fig. 6 and compared with the experimentally observed variation of s/n with 7 for line C-4. It is thus found that the optimum s/n in a PS sequence of fixed total duration occurs when r = 1.3 T1. The intensity error, E, under these conditions is, however, about 40%. It is therefore clearly necessary to reach a compromise between intensity error and loss of s/n. Figure 6 shows, however, that using 7 = 0.2T1 leads to a reduction in s/n of less than a factor of 2. Thus, except in cases of extremely low intensity, it should be possible to use a T sufficiently short to introduce less than 10% intensity error. It should be noted that the expression for s/n given in Eq. [19] depends on the rate constant, ki, as well as other parameters. In many cases it may be possible to use the reaction rate as a variable to be manipulated so as to optimize s/n, e.g., by changing temperature, concentration, or light intensity. If we keep the fraction of reaction fixed, e.g., let klT,,, be constant, to avoid excessive overlap with the unpolarized product line, Eq. [19] may be written s/n ccEL’(co)( T1/7 “*)k:‘*[l-exp(-r/Ti)][l-exp(-kiT,,)].
PO1
Therefore the s/n increases with k :‘*, demonstrating the desirability of making k1 as large as experimentally feasible. It should be borne in mind, however, that Eq. [20] and previous equations are based on the assumption that k1 is small enough that variation of dL’/dt during the r epoch is negligible. For very fast reactions and very small numbers of spectra, however, the accumulated intensity will be very sensitive to the exact times at which spectra were taken with Fobs; i.e., the intensity will become very sensitive to the reaction kinetics, a situation we have tried to avoid up to now. Nonideal rf Pulses
The rf pulses employed in FT NMR are susceptible to several types of imperfections (20) including inaccuracy or jitter in the pulse length, rf field inhomogeneity at the sample, variation of Hi during the pulse (commonly in the form of “droop” near the end of the pulse if the amplifier cannot sustain its output), or nonuniform power density across the spectrum arising from weak pulses. For the progressive saturation method described above most of these effects mean that some of the lines in a spectrum and/or a region of the sample are subject to rf pulses different from the
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151
90” desired. The analogous effect in the saturation-recovery method is incomplete saturation of the signal by P,,,. It is convenient to express the effects of nonideal pulses as an error, Ed, in the observed accumulated intensity, I,, relative to its value, I90 for an ideal pulse. &p =
(190
-
L)/190.
To estimate cp we consider here only the effects of deviation of the pulse from 90” by the angle 6 in a [(Y - ~1~ progressive saturation sequence, where LY= 90 - 6. The first task in the analysis is to find the intensity L(n) due to the nth a-degree pulse in the sequence. Simple geometry gives L(n) = sin a&(n), where Lo(n) is the intensity which would be observed at time t, with a 90” pulse. If (Y is not 90”, however, Lo(n) will have a contribution from L(n - l), the line intensity actually observed with the (n - 1)st pulse. L(n) = (cos a)L(n - 1) exp( - r/ Ti) +(sin (~)EL~(co)Ic~Ti[l -exp(-T/Ti)]exp(-klt,).
Vll
Solutions to this recursive relationship have been derived by Sojka and co-workers (25) for the purpose of determining kinetic parameters from CIDNP spectra. Their estimates of enhancement factors, however, were based on steady-state spectra. The accumulated intensity is given, as in Eq. [8], by Intensity (Y f L(n). n=l
The evaluation of the sum in the present case, however, is complicated by the fact that each value of L(n) in Eq. [21] depends on previous values (25). If the rate of reaction is slow, however, the line intensities observed with two adjacent pulses will be nearly the same. With that approximation (26) we have L(n)=(sin
a)EL”(~)klT1[l
-exp(-7/T1)]exp(-klt,)[l
-(cos (Y)exp(-T/T1)]-*.
L=l This result has also been derived by Grant and co-workers (27) and applied to the problem of optimizing the sensitivity for T1 measurements in reacting samples. The sum is performed only over the exponential decaying with kl. It therefore follows immediately that the error in accumulated intensity due to deviations from 90” by the angle 5 is ep = 1 - (cos t)[l - (sin 4) exp( - T/ T,)]-‘.
[231
For small deviations from 90”, Eqs. [22] and [23] lead to the surprising conclusion that the intensity increases as the pulse angle decreases. This effect depends, however, on the value of exp( - T/ T1) and disappears when 7 > T1, i.e., when a steady state is reached between pulses. It therefore originates in “saturation” of the polarized signal when large angle pulses and short recovery times are used. This is quite analogous to saturation effects observed in ordinary FT NMR (26,B). While
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in principle it could be exploited to optimize the sensitivity for CIDNP detection (27), in practice its use would lead to spectra distorted to at least some degree by relaxation, but in a way difficult to assess because of the complicated way in which T,, T, and cy interact in Eq. [22]. The above effect of incomplete saturation can be put in somewhat better perspective by considering the consequences for estimation of the enhancement factor E. We may define an experimentally determined value of E’ which would be determined using the same pulse angle cx for both accumulation of CIDNP spectra and determination of the intensity proportional to Lo(~) at the end of the reaction. E’ = [C L(n)]/[(sin
a)L’(co)].
1241
Substituting for L(n) from Eq. [21] and defining the “true” value of E as that determined using exact 90” pulses, we have for the error in E, &E = (E - E’)/E
= 1 - [ 1 - (sin 5) exp( - T/ ri)]-‘.
P51
Thus depending on the sign of the deviation, 6, from 90”, E may be either over- or underestimated using this procedure. For 7 < T,, as would normally be used to remove relaxation effects, deviations of f 5” from perfect 90” pulses would lead to about a 10% error in the estimate of E. Variation of E and T1 during Spectrum Accumulation
Many samples which exhibit CIDNP change their composition, temperature, or other chemical and physical properties during the course of the reaction. We describe briefly a simple interpretation which may be given to the enhancement factor E obtained from spectra accumulated under such changing conditions. It seems reasonable to assume in any case that variation of E and Tl during an individual 7 epoch is small. For simplicity we also consider the case 7 < T,(t) for all t and ignore the contribution from thermal polarization, E. In this limit Eq. [8] becomes Utn) -L”(t,-*)[7/T~(t,-l)l
+[~“(tn) -~“k-dlE(tn-d.
WI
Since the first term will usually be small compared to the second, any time dependence of Ti will usually be inconsequential for evaluation of E. To describe the effects of a time-dependent enhancement factor, E, we may define E(t,-1)
= E,,+S(t,-1).
Ignoring the first term in Eq. 1261 we then have Utn) -[L”(t,)-Lo(t,-~)lCEo+S(t,-~)l. If we choose E. and the set of values S(t,-1) such that the second term vanishes when we take the sum over all pulses, we thus redefine the Eo, determined in the usual manner from accumulated spectra, as a weighted average. Eo = {C [Lo(&) -L”(t,-l)]E(t,-l)}/So,
[271
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153
where 6L” is defined by Eq. [gal. In principle the variation of E with time could be detected by accumulating spectra over several portions of the reaction and calculating a value of E for each. In extreme cases (29) where more than one CIDNPproducing reaction may occur simultaneously, the sign of E may even change with time. Clearly under these conditions simple accumulation of the spectrum over the total reaction time would lead to an erroneous estimate of E. An Afterthought
The above treatment of FT NMR applied to samples exhibiting CIDNP obviously ignores situations in which the spectrometer sensitivity varies with time. It is clear, however, that this is a potential problem whenever the conditions for chemical reaction affect the detection system of the spectrometer. The most dramatic such effect occurs when the sample, either by design or by accident, leaves the spectrometer during accumulation! EXPERIMENTAL
Saturation-Recovery
: ‘H CIDNP
CIDNP spectra were acquired on a Bruker WP-60 NMR spectrometer with internal ‘H field/frequency lock. Saturation pulses were generated with the ‘H (60 MHz) broadband decoupler that is standard equipment with the WP-60. The decoupler and analytical channel frequencies were set equal. Two modifications were made, however, to reduce the amount of decoupler noise leaking into the analytical channel during the data-acquisition period with the decoupler nominally gated OFF. The gating of the decoupler was improved by about 15 db by the addition of opposing series diodes at the decoupler rf output. In addition, decoupler leakage was converted to a dc signal during the gated OFF period by turning off the noise modulation (setting the decoupler to cw mode), and taking advantage of the fact that the center frequency of the decoupler channel was set equal to the analytical carrier frequency. These modifications effectively removed any background signal due to rf leakage. The effectiveness of the rf noise pulses (power = 2 W, length = 0.8 set) in saturating the NMR signals was determined by detecting the residual unsaturated signal immediately after the saturation pulse was gated OFF. In all cases the residual signal was found to be less than the background noise in the spectrum from a single FID, typically at least a 20-fold decrease in signal. Progressive Saturation : 13C CIDNP
The WP-60 was used in its unmodified form for the progressive saturation (r3C CIDNP) experiments, i.e., 13C at 15.08 MHz with broadband decoupling at 60 MHz. Special care was taken, however, to reduce errors due to nonideal rf pulses by limiting rf field inhomogeneity and accurately adjusting the rf pulse length. The former was accomplished (20) by adjusting the height of the sample to be less than or
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equal to the height of the receiver/transmitter coil. The 360” null method was used to find the 90” rf pulse length. For the 13C CIDNP spectra it was assumed that the observed lienwidths were dominated by the numerical filter constant (2-3 Hz), and, therefore, that signal heights directly reflected the integrated areas. Sample Preparation
Diacyl peroxides were synthesized in the usual manner (30) and purified by treating the reaction mixtures briefly with anhydrous potassium carbonate and then rapidly passing the solutions through a short column of anhydrous silica. Bulk solutions of the peroxides were prepared at room temperature and samples were placed in the preheated probe of the spectrometer in either of two sample holders. 2H Lock for Reacting Samples
The sample holder for the 13C CIDNP experiments was a coaxial arrangement of a 5-mm-o.d. inner tube containing DMSO-d6 for the 2H field/frequency lock and a lo-mm-o.d. outer tube. The peroxide solution occupied the space between the tubes. A similar arrangement, but with a 5-mm-o.d. outer tube and a correspondingly smaller inner tube, was employed in the ‘H CIDNP experiments described in Fig. 5. The remaining ‘H CIDNP experiments used a sample holder of similar design, but the contents of the inner and outer tubes were exchanged. This allowed containment of the peroxide solution in a sealed inner tube. This substantially reduced bubbling due to CO2 produced during the decomposition. The smaller-diameter sample tube also exhibited less line broadening due to magnetic field inhomogeneity. In fact, for most samples the linewidth was not significantly reduced by sample spinning. ACKNOWLEDGMENTS We gratefully acknowledge financial support from the National Science Foundation under Grants CHE 76-10987 and CHE 78-24171. R.G.L. acknowledges the hospitality of Argonne National Laboratory during preparation of substantial portions of the manuscript.
REFERENCES 1. L. T. Muus, P. W. ATKINS, K. A. MCLAUCHLAN, AND J. B. PEDERSEN (Eds.), “Chemically Induced Magnetic Polarization”, Reidel, Dordrecht, 1977. 2. J. BARGON AND H. FISCHER, Z. Nuturforsch. A 22, 1556 (1967). 3. L. G. WERBELOW AND D. M. GRANT, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 9, p, 189, Academic Press, New York, 1977; R. L. VOLD AND R. R. VOLD, in “Progress in Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.), Vol. 12, p. 79, Pergamon, Elmsford, N.Y., 1978. 4. R. FREEMAN AND H. D. W. HILL, J. Chem. Phys. 54,3367 (1971). 5. J. L. MARKLEY, W. J. HORSLEY, AND M. P. KLEIN, J. Chem. Phys. 55, 3604 (1971); G. C. MCDONALD AND J. S. LEIGH, JR., J. Magn. Reson. 9,358 (1973). 6. A. L. BUCHACHENKO AND SH. A. MARKARIAN, Znt. J. Chem. Kinet. 4,513 (1972). 7. S. SCHKUBLIN, A. WOKAUN, AND R. R. ERNST, J. Magn. Reson. 27,273 (1977); G. L. CLOSS AND R. J. MILLER, J. Am. Chem. Sot. 101,1639 (1979).
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USING
FT NMR
1SS
8. S. SCH,&UBLIN, A. WOKAUN, AND R. R. ERNST, Chem. Phys. 14,285 (1976). 9. S. SCHKUBLIN, A. H~HENER, AND R. R. ERNST, J. Magn. Reson. 13,196 (1974); R. R. ERNST, W. P. AUE, E. BARTHOLDI, A. H~HENER, AND S. SCHKUBLIN, Pure Appl. Chem. 37, 47 (1974). 10. G. L. CLOSS, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 7, p. 157, Academic Press, New York, 1974. 11. R. G. LAWLER AND H. R. WARD, in “Determination of Organic Structures by Physical Methods” (F. C. Nachod and J. J. Zuckerman, Eds.), Vol. 5, p. 99, Academic Press, New York, 1973. 12. A. ABRAGAM, “Principles of Nuclear Magnetism,” p. 522, Oxford Univ. Press, London, 1961; B. W. GOODWIN AND R. WALLACE, J. Magn. Reson. 32,325 (1978). 13. R. G. LAWLER, in “Progress in Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.), Vol. 9, p. 145, Pergamon, Elmsford, N.Y., 1973. 14. K. MILLER AND G. L. CLOSS, J. Am. Chem. Sot. 94,1002 (1972). 15. G. L. CLOSS AND M. S. CZEROPSKI;Chem. Phys. Lett. 45,115 (1977); F. J. J. DE KANTER AND R. KAPTEIN, Chem. Phys. Lett. 62,421 (1979). 16. R. G. LAWLER, P. F. BARBARA, AND D. JACOBS, J. Am. Chem. Sot. loo,4912 (1978). 17. R. W. FESSENDEN, J. Phys. Chem. 71,74 (1970). 18. N. J. KARCH, E. T. KOH, B. L. WHITSEL, AND J. M. MCBRIDE, J. Am. Chem. Sot. 97,6729 (1974); see, however, the criticism of this structure by M. B. YIM, 0. KIKUCHI, AND D. E. WOOD, J. Am. Chem. Sot. 100,1869 (1978). 19. E. LIPPMAA, T. SALUVERE, AND M. MAGI, Org. Magn. Reson. 5,429 (1973); E. LIPPMAA, T. PEHK, A. L. BUCHACHENKO, AND S. V. RYKOV, Chem. Phys. Lett. 5,521 (1970). 20. G. C. LEVY AND I. R. PEAT, J. Magn. Reson. 18,500 (1975). 21. M. HALFON, Ph.D. dissertation, Brown University, 1974. 22. R. FREEMAN AND H. D. W. HILL, J. Magn. Resort. 4,366 (1971). 23. R. KAPTEIN, R. FREEMAN, H. D. W. HILL, AND J. BARGON, Chem. Commun., 953 (1973); C. BROWN, R. F. HUDSON, AND A. J. LAWSON, J. Am. Chem. Sot. 95,650O (1973); H. IWAMURA, M. IWAMURA, M. IMANARI, AND M. TAKEUCHI, Tetrahedron Lett., 2325 (1973); R. KAPTEIN, R. FREEMAN, AND H. D. W. HILL, Chem. Phys. Lett. 26, 104 (1974); W. B. MONIZ, C. F. PORANSKI, JR., AND S. A. SOJKA, J. Org. Chem. 40,2946 (1975); K. ALBERT, K-M. DANGEL, A. RIEKER, H. IWAMURA, AND Y. IMAHASHI, Bull. Chem. Sot. Jpn. 49,2537 (1976). 24. R. E. SCHWERZEL, R. G. LAWLER, AND G. T. EVANS, Chem. Phys. Lett. 29,106 (1974). 25. C. F. PORANSKI, JR., S. A. SOJKA, AND W. B. MONIZ, J. Am. Chem. Sot. 98,1337 (1976); C. F. PORANSKI, JR., W. B. MONIZ, AND S. A. SOJKA, J. Am. Chem. Sot. 97,4275 (1975). 26. J. S. WAUGH, J. Mol. Spectrosc. 35, 298 (1970). 27 K. A. CHRISTENSEN, D. M. GRANT, E. M. SCHULMAN, AND C. WALLING, J. Phys. Chem. 75, 1971 (1974). 28. R. R. ERNST, in “Advances in Magnetic Resonance” (J. S. Waugh, Ed.), Vol. 2, p. 1, Academic Press, New York, 1966. 29. M. L. MANION-SCHILLING, R. S. HURON, AND H. D. ROTH, J. Am. Chem. Sot. 99,7792 (1977); G. L. CLOSS AND R. J. MILLER, J. Am. Chem. Sot. loo,3483 (1978); S. M. ROSENFELD, Ph.D. dissertation, Brown University, 1973. 30. W. H. URRY AND M. S. KHARASCH, J. Am. Chem. Sot. 66,1438 (1944).