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The suppression of Bloch-Siegert shifts and subtraction artifacts in double-resonance difference spectroscopy
JOURNAL
OF MAGNETIC
RESONANCE
9,289-298
(1982)
The Suppressionof Bloch-Siegert Shifts and Subtraction Artifacts in Double-ResonanceDifference Spectroscopy JOHN D. MERSH AND JEREMY
K. M. SANDERS*
University Chemical Laboratory, Lensfreld Road, Cambridge CB2 IEW, United Kingdom Received June 18. 1982 Several approaches to minimizing the artifacts due to Bloch-Siegert shifts in decoupling difference spectroscopy are presented. In the most effective the shifts are suppressed by computational correction of the decoupled spectrum using interpolation between data points; the resulting difference spectra are much improved, particularly at low-field strengths. Similarly, the familiar dispersion artifacts in NOE dilference spectra can be reduced by small linear shifts of one spectrum relative to the other.
Difference spectroscopy is a powerful method for the selective observation of small changes against a dominant but unchanging background. However, its value is crucially dependent on good subtraction of those background signals. The presence of unwanted signals can so dominate a difference spectrum that the responses of interest are completely obscured, this is particularly true when differences are taken between two separate solutions. In decoupling difference spectroscopy the unwanted signals arise primarily from Bloch-Siegert shifts (1) and are a fundamental property of the experiment. In NOE difference spectroscopy the artifacts are of purely instrumental origin and may vary unpredictably from sample to sample and spectrometer to spectrometer. Differences taken between two solutions also reflect concelntration and shimming, and produce a third category of artifact. We show here that although these various types of artifact arise by quite different m.echanisms, they can be effectively suppressed by similar methods of computational correction, i.e., shifting one spectrum relative to the other before subtraction. These correction methods extend the usefulness of decoupling difference techniques to lower-field strengths, allow more reliable measurements of small NOE values in the presence of large signals and generally should allow more varied application of difference techniques. Many of the results reported here were obtained using the progesterone
* Author to whom correspondence should be addressed.
289
0022-2364/82/140289-10$02.00/0 Copyright Q 1982 by Academic Press, Inc. All rights of reproduction in any form rescned.
290
MERSH AND SANDERS
(c)
A
A
after correction
FIG. 1. Schematic view of the Bloch-Siegcrt (BS) problem and its correction. At the top is a normal spectrum of two mutually coupled doublets and a singlet. In the center are shown the combined effects of BS shift and decoupling. At the bottom is the decoupled spectrum after correction.
whose complete spectroscopic and conformational where (2). BLOCH-SIEGERT
analysis we have reported else-
SUPPRESSION
The Bloch-Siegert (BS) shift has historically been little more than a minor nuisance, and it is useful for calibrating decoupler power. In modern decoupling difference spectroscopy, however, it has become a major problem except at the highest field strengths. A control spectrum with irradiation off resonance is subtracted from a spectrum with irradiation on resonance (L+): the desired responses arise solely from decoupling effects but additional signals arise from the imperfect subtraction of sharp signals which suffer a shift in the decoupled spectrum. This is illustrated schematically in Fig. 1; an experimental example is shown in Fig. 2. For signals near the irradiation the shift A of a proton originally at v. Hz to a new frequency Y, is given by A=v~--v~=~, [II Q-r
-
VO
where K is dependent on the decoupling power Bz according to
K = (vB;)/2.
PI
There are several approaches to minimizing the effects of Eq. [I]. The first is to keep decoupler power (and hence K) as low as possible consistent with retaining some decoupling. This has the advantage of improving frequency selectivity in the irradiation, but sign&ant shifts are still observed at low-field strengths. The second approach (3) is to minimize relative shifts by placing the control irradiation as close as possible to the decoupling position, yirr. This can be quite effective but is time-consuming when many different irradiations are necessary, and it may become impossible in complex spectra which lack clear regions to accommodate the control. Our new approach is to measure K in the decoupling experiment and then to correct the decoupled spectrum before subtraction by restoring the original shifts.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
291
By comparing the chemical shifts of intense singlets (e.g., CH3 groups, solvent, TMS) in control and decoupled spectra, we can measure their Bloch-Siegert shifts (A); K can then be evaluated from a linear regression analysis of A as a function of offset from the decoupling irradiation. This is straightforward if the control spectrum is acquired with irradiation several kilohertz off resonance (in contrast to the second approach above). Even more effective is to evaluate K by comparing two control spectra, with irradiation close to the spectrum and several kilohertz off resonance; in this case the entire spectrum can be used to evaluate K. The regression actually fits Eq. [3], where the small constant a takes account of residual shifts from the control irradiation:
a
I 2
I
I 1
I
FIG. 2. Partial 25~MHz spin-decoupling difference spectra of progesterone 1 in C&, solution. (a) Control spectrum; (b) an uncorrected difference spectrum obtained on decoupling H7,; (c) the same data set after correction for the BS shift.
292
MERSH AND SANDERS
The next stage is to calculate for each data point v. a value of u,. Thus the value of the decoupled spectrum at v. + A = Y, must be the true value at uo. This is obtained from a simple linear interpolation of the decoupled spectrum. This step is repeated for all the data points to generate a corrected spectrum from which the control can now be subtracted. The effect of this treatment is shown in Figs. 2 and 3.95% suppression of unwanted responses is achieved near the decoupling frequency allowing easy identification of true decoupling responses. In Fig. 2 note particularly the absence of “noise” in the region 1.O to 1.5 6 in the corrected spectrum. Similarly in Fig. 3 the solvent and aromatic signal artifacts virtually disappear. The efficiency of suppression falls further away from the irradiation (as the simple Eq. [l] fails) but this is of little consequence as the effects are far smaller. What are the theoretical limits of the technique? As v. - qrr approaches zero the BS shift tends to infinity so there is a region close to the irradiation within which no useful spectroscopic information is present (see Fig. 4). The turnaround occurs at K ‘I2 Hz. The region just outside this boundary contains substantial amounts of information from within the “dead” region. In general the area within approximately
b.
a.
+
I
i/ll------/\
m+
.I
H
Ii
,?.
_-t----
I 7-J
I 7-O
Cc&H
FIG. 3. Partial 250-MHz spin-decoupling difference spectra of twwcinnamic acid in CDCIs solution. (a) Control spectrum with irradiation at d 6.97; (b) uncorrected difference spectrum obtained on irradiating proton indicated; (c) the same data set after correction.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
293
128
A=Bloeh-Slegert
shift
188
6a
FIG. 4. Plot of q, vs Y,,+ A for the progesterone experiment in Fig. 2. Units are Hz.
Intensity Of
response I%1
0
0.02
0.84
0.96 0.06 8.10 in Hz FIG. 5. Plots of the peak-to-peak intensity (as a percentage of one proton) resulting from the subtraction of a singlet from an identical singlet with variable frequency offsets between them. Results from three different digitization simulations are shown. Tt was 0.5 sec. Offset
294
MERSH AND SANDERS
+3K I’* Hz is unreliable; in the example above (Figs. 2 and 4) this corresponds to just 25 Hz either side of the irradiation. There are also practical limits to the efficiency of correction. Clearly some BS shifts must be large enough to measure, i.e., at least one data point: at 400 MHz we have been forced to use unrealistically high decoupler power levels to generate such shifts. This is not a problem at lower-field strengths; indeed too large shifts are not efficiently corrected for reasons that are most apparent from the simulation experiments summarized in Figs. 5-7. We chose to simulate a singlet with a Tf of 0.5 set (i.e., a linewidth of 0.64 Hz) at digital resolutions of 0.061, 0.244, and 0.98 Hz/point. This singlet was subtracted from an identical singlet as the frequency or phase shift between them was varied. The resulting peak-to-peak intensity was plotted against the frequency shift (Figs. 5,7) or phase shift (Fig. 6). When the digitization is good, the intensity increases very fast indeed, reaching 40% of one proton at 0.1 Hz. For poor digitization the effect is not surprisingly much smaller. Figure 7 shows the intensity behavior as spectrum offset increases to 3 Hz. The lumpy shape of these curves arises from the errors associated with inadequate digitization, and leads to the amusing conclusion that partial correction of offset can actually increase the artifact intensity under certain circumstances. This does not occur very often in practice, but what does happen is that correction of 90% of a large induced shift barely improves the artifact intensity. Only when the shift is reduced to below the effective linewidth is the correction effective.
Intensity ze I
0 0
1.0
FIG.
3.0
2.0
Phase
4.0
5.0
shift
6. As for Fig. 5 but with simulated phase shifts (in degrees) instead of frequency sh;fts.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
295
Intensity
Offset in
Hz
FXG. 7. The same simulation as Fig. 5 extended to much larger offsets. SUPPRESSION OF SUBTRACTION
ARTIFACTS
Many NOE difference spectra show small apparent dispersion signals where sharp intense signals are imperfectly subtracted. (See Fig. 8). In favorable cases these signals can be adequately reduced by judicious use of line broadening but when severe they cannot be removed without severe loss of resolution in the resonances of interest. Since these artifact signals have the same dispersion appearance as in the BlochSicgert case but are of similar intensity across the whole spectrum, we investigated whether they could be removed by a simple linear shift of one spectrum relative to the other. As Fig. 8 shows, this technique can be remarkably effective and allows us to see confidently small enhancements in signals which are otherwise dominated by artifact. In the case shown a shift of 0.005 Hz was employed. The sample was the corrin cobester (4); the NOE values are a little less than 1%. Repetition of the simulation of Fig. 5 but incorporating a 1% NOE into the positive signal gives the results shown in Fig. 9: in the high-digitization case, corresponding to the sharp lines encountered in small organic molecules of less than 1000 MW it is necessary to adjust the two spectra with a precision of approximately 1 mHz. In principle Fig. 5 acts as a calibration curve for the required shift if Tif can be estimated: it would be completely general if both digitization and offset were expressed in units of linewidth. However, in practice, judgment and guesswork are likely to be more useful tools for achieving good correction. Note that these artifacts are not a problem for broad lines such as those encountered in proteins. The source of the artifacts remains obscure. It is not even clear to us whether they are phase shifts or frequency shifts. They do not appear to be correlated with field strength, drift, solvent, decoupler properties, or any other obvious factor. They
296
MERSH AND SANDERS
A
I 2.4
I 2.2
FIG. 8. Control, and NOE difference displays of a small portion of a spectrum of cobester (4). (A) Control spectrum; (B) uncomected difference spectrum; (C) the corrected difference spectrum obtained after a 0.005-Hz relative shift of the two spectra.
certainly vary from spectrometer to spectrometer, and from day to day on any given instrument. They are sufficiently random that, like more familiar noise, they decrease in intensity relative to real signal with the square root of the number of transients acquired. They are also reduced significantly by acquiring two control spectra at the beginning and middle of an automated sequence of several irradiations, and averaging the two controls before subtraction. The linear shift correction method described here may also be valuable in removing subtraction artifacts arising from subtractions between different solutions. IMPLEMENTATION
AND CONCLUSIONS
All the spectra and simulations were processed on an IBM 370/165 mainframe computer. Raw FIDs were transferred by cassette or magnetic tape from ASPECT 2000 computers attached to Bruker spectrometers. The complete IBM package of one- and two-dimensional NMR software is home-written and is based on an early prototype by R. G. Brereton in this laboratory (5). Simple linear interpolations between data points was used reasonably successfully; more sophisticated methods are unlikely to produce more than marginal improvements. The regression and interpolation routines used in this work are straightforward and could readily be implemented on standard NMR-dedicated minicomputers. They could also be incorporated into commercial NMR software. Our motives for using mainframe pro-
JOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
297
Intensity
Offset
FIG.
9.
Repeat of Fig. 5 simulation incorporating
a 1% NOE in the positive peak.
cessing are several, but they are not related to the particular applications described in the paper. In conclusion, we have shown that subtraction artifacts and Bloch-Siegert shift artifacts can be dealt with in a variety of ways, the most powerful of which include computational correction of the spectra. In view of the way this correction method cleans up difference spectra by removing the unsightly stains, we propose for it the name SUDSY (Splendidly Uncluttered Difference SpectroscopY). EXPERIMENTAL
METHODS
The progesterone 1 was a gift from Professor D. N. Kirk (Westfield College, London). It was examined as an approximately 0.02 M solution in undegassed & benzene. The 400-MHz FIDs of cobester used to generate the spectra in Fig. 8 were kindly provided by Professor A. R. Battersby; experimental details are given elsewhere (4). The 250-MHz decoupling experiments were carried out on Bruker WM250 instruments in Cambridge and London (Imperial College), using previously described microprograms (3, 6). The FIDs were stored on disk and transferred to the Cambridge University IBM 370/ 165 by cassette or magnetic tape via ASPECT 2000 computers attached to Cambridge spectrometers. The IBM data processing software (written by J.D.M.) is as yet unpublished. ACKNOWLEDGMENTS We gratefully acknowledge the time and generosity of H. Rzepa and D. Neuhaus (Imperial College, L.ondon) in obtaining data during the early stages of this work, the FIDs supplied by Professor A. R.
298 Battersby, financial
MERSH illuminating support from
conversations the SERC.
with
AND Drs.
SANDERS
J. C. Waterton
(ICI)
and
W.
E. Hull
(Bruker),
and
REFERENCES 1. R. FREEMAN AND W. A. ANDERSON, J. Chem. Phys. 37, 85 (1962). 2. M. W. BARRE-IT, R. D. FARRANT, D. N. KIRK, J. D. MERSH, J. K. M. SANDERS, AND W. L. DUAX, J. Chem. Sot. Perkin Trans. 2, 105 (1982). 3. L. D. HALL AND J. K. M. SANDERS, J. Am. Chem. Sot. 102, 5703 (1980). 4. A. R. BATTERSBY, C. EDINGTON, C. J. R. FOOKES, AND J. M. HOOK, J. Chem. Sot. Perkin Trans. 2, in press. 5. R. G. BRERETON, submitted. 6. L. D. HALL AND J. K. M. SANDERS, J. Org. Chem. 46, 1132 (1981).
OF MAGNETIC
RESONANCE
9,289-298
(1982)
The Suppressionof Bloch-Siegert Shifts and Subtraction Artifacts in Double-ResonanceDifference Spectroscopy JOHN D. MERSH AND JEREMY
K. M. SANDERS*
University Chemical Laboratory, Lensfreld Road, Cambridge CB2 IEW, United Kingdom Received June 18. 1982 Several approaches to minimizing the artifacts due to Bloch-Siegert shifts in decoupling difference spectroscopy are presented. In the most effective the shifts are suppressed by computational correction of the decoupled spectrum using interpolation between data points; the resulting difference spectra are much improved, particularly at low-field strengths. Similarly, the familiar dispersion artifacts in NOE dilference spectra can be reduced by small linear shifts of one spectrum relative to the other.
Difference spectroscopy is a powerful method for the selective observation of small changes against a dominant but unchanging background. However, its value is crucially dependent on good subtraction of those background signals. The presence of unwanted signals can so dominate a difference spectrum that the responses of interest are completely obscured, this is particularly true when differences are taken between two separate solutions. In decoupling difference spectroscopy the unwanted signals arise primarily from Bloch-Siegert shifts (1) and are a fundamental property of the experiment. In NOE difference spectroscopy the artifacts are of purely instrumental origin and may vary unpredictably from sample to sample and spectrometer to spectrometer. Differences taken between two solutions also reflect concelntration and shimming, and produce a third category of artifact. We show here that although these various types of artifact arise by quite different m.echanisms, they can be effectively suppressed by similar methods of computational correction, i.e., shifting one spectrum relative to the other before subtraction. These correction methods extend the usefulness of decoupling difference techniques to lower-field strengths, allow more reliable measurements of small NOE values in the presence of large signals and generally should allow more varied application of difference techniques. Many of the results reported here were obtained using the progesterone
* Author to whom correspondence should be addressed.
289
0022-2364/82/140289-10$02.00/0 Copyright Q 1982 by Academic Press, Inc. All rights of reproduction in any form rescned.
290
MERSH AND SANDERS
(c)
A
A
after correction
FIG. 1. Schematic view of the Bloch-Siegcrt (BS) problem and its correction. At the top is a normal spectrum of two mutually coupled doublets and a singlet. In the center are shown the combined effects of BS shift and decoupling. At the bottom is the decoupled spectrum after correction.
whose complete spectroscopic and conformational where (2). BLOCH-SIEGERT
analysis we have reported else-
SUPPRESSION
The Bloch-Siegert (BS) shift has historically been little more than a minor nuisance, and it is useful for calibrating decoupler power. In modern decoupling difference spectroscopy, however, it has become a major problem except at the highest field strengths. A control spectrum with irradiation off resonance is subtracted from a spectrum with irradiation on resonance (L+): the desired responses arise solely from decoupling effects but additional signals arise from the imperfect subtraction of sharp signals which suffer a shift in the decoupled spectrum. This is illustrated schematically in Fig. 1; an experimental example is shown in Fig. 2. For signals near the irradiation the shift A of a proton originally at v. Hz to a new frequency Y, is given by A=v~--v~=~, [II Q-r
-
VO
where K is dependent on the decoupling power Bz according to
K = (vB;)/2.
PI
There are several approaches to minimizing the effects of Eq. [I]. The first is to keep decoupler power (and hence K) as low as possible consistent with retaining some decoupling. This has the advantage of improving frequency selectivity in the irradiation, but sign&ant shifts are still observed at low-field strengths. The second approach (3) is to minimize relative shifts by placing the control irradiation as close as possible to the decoupling position, yirr. This can be quite effective but is time-consuming when many different irradiations are necessary, and it may become impossible in complex spectra which lack clear regions to accommodate the control. Our new approach is to measure K in the decoupling experiment and then to correct the decoupled spectrum before subtraction by restoring the original shifts.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
291
By comparing the chemical shifts of intense singlets (e.g., CH3 groups, solvent, TMS) in control and decoupled spectra, we can measure their Bloch-Siegert shifts (A); K can then be evaluated from a linear regression analysis of A as a function of offset from the decoupling irradiation. This is straightforward if the control spectrum is acquired with irradiation several kilohertz off resonance (in contrast to the second approach above). Even more effective is to evaluate K by comparing two control spectra, with irradiation close to the spectrum and several kilohertz off resonance; in this case the entire spectrum can be used to evaluate K. The regression actually fits Eq. [3], where the small constant a takes account of residual shifts from the control irradiation:
a
I 2
I
I 1
I
FIG. 2. Partial 25~MHz spin-decoupling difference spectra of progesterone 1 in C&, solution. (a) Control spectrum; (b) an uncorrected difference spectrum obtained on decoupling H7,; (c) the same data set after correction for the BS shift.
292
MERSH AND SANDERS
The next stage is to calculate for each data point v. a value of u,. Thus the value of the decoupled spectrum at v. + A = Y, must be the true value at uo. This is obtained from a simple linear interpolation of the decoupled spectrum. This step is repeated for all the data points to generate a corrected spectrum from which the control can now be subtracted. The effect of this treatment is shown in Figs. 2 and 3.95% suppression of unwanted responses is achieved near the decoupling frequency allowing easy identification of true decoupling responses. In Fig. 2 note particularly the absence of “noise” in the region 1.O to 1.5 6 in the corrected spectrum. Similarly in Fig. 3 the solvent and aromatic signal artifacts virtually disappear. The efficiency of suppression falls further away from the irradiation (as the simple Eq. [l] fails) but this is of little consequence as the effects are far smaller. What are the theoretical limits of the technique? As v. - qrr approaches zero the BS shift tends to infinity so there is a region close to the irradiation within which no useful spectroscopic information is present (see Fig. 4). The turnaround occurs at K ‘I2 Hz. The region just outside this boundary contains substantial amounts of information from within the “dead” region. In general the area within approximately
b.
a.
+
I
i/ll------/\
m+
.I
H
Ii
,?.
_-t----
I 7-J
I 7-O
Cc&H
FIG. 3. Partial 250-MHz spin-decoupling difference spectra of twwcinnamic acid in CDCIs solution. (a) Control spectrum with irradiation at d 6.97; (b) uncorrected difference spectrum obtained on irradiating proton indicated; (c) the same data set after correction.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
293
128
A=Bloeh-Slegert
shift
188
6a
FIG. 4. Plot of q, vs Y,,+ A for the progesterone experiment in Fig. 2. Units are Hz.
Intensity Of
response I%1
0
0.02
0.84
0.96 0.06 8.10 in Hz FIG. 5. Plots of the peak-to-peak intensity (as a percentage of one proton) resulting from the subtraction of a singlet from an identical singlet with variable frequency offsets between them. Results from three different digitization simulations are shown. Tt was 0.5 sec. Offset
294
MERSH AND SANDERS
+3K I’* Hz is unreliable; in the example above (Figs. 2 and 4) this corresponds to just 25 Hz either side of the irradiation. There are also practical limits to the efficiency of correction. Clearly some BS shifts must be large enough to measure, i.e., at least one data point: at 400 MHz we have been forced to use unrealistically high decoupler power levels to generate such shifts. This is not a problem at lower-field strengths; indeed too large shifts are not efficiently corrected for reasons that are most apparent from the simulation experiments summarized in Figs. 5-7. We chose to simulate a singlet with a Tf of 0.5 set (i.e., a linewidth of 0.64 Hz) at digital resolutions of 0.061, 0.244, and 0.98 Hz/point. This singlet was subtracted from an identical singlet as the frequency or phase shift between them was varied. The resulting peak-to-peak intensity was plotted against the frequency shift (Figs. 5,7) or phase shift (Fig. 6). When the digitization is good, the intensity increases very fast indeed, reaching 40% of one proton at 0.1 Hz. For poor digitization the effect is not surprisingly much smaller. Figure 7 shows the intensity behavior as spectrum offset increases to 3 Hz. The lumpy shape of these curves arises from the errors associated with inadequate digitization, and leads to the amusing conclusion that partial correction of offset can actually increase the artifact intensity under certain circumstances. This does not occur very often in practice, but what does happen is that correction of 90% of a large induced shift barely improves the artifact intensity. Only when the shift is reduced to below the effective linewidth is the correction effective.
Intensity ze I
0 0
1.0
FIG.
3.0
2.0
Phase
4.0
5.0
shift
6. As for Fig. 5 but with simulated phase shifts (in degrees) instead of frequency sh;fts.
DOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
295
Intensity
Offset in
Hz
FXG. 7. The same simulation as Fig. 5 extended to much larger offsets. SUPPRESSION OF SUBTRACTION
ARTIFACTS
Many NOE difference spectra show small apparent dispersion signals where sharp intense signals are imperfectly subtracted. (See Fig. 8). In favorable cases these signals can be adequately reduced by judicious use of line broadening but when severe they cannot be removed without severe loss of resolution in the resonances of interest. Since these artifact signals have the same dispersion appearance as in the BlochSicgert case but are of similar intensity across the whole spectrum, we investigated whether they could be removed by a simple linear shift of one spectrum relative to the other. As Fig. 8 shows, this technique can be remarkably effective and allows us to see confidently small enhancements in signals which are otherwise dominated by artifact. In the case shown a shift of 0.005 Hz was employed. The sample was the corrin cobester (4); the NOE values are a little less than 1%. Repetition of the simulation of Fig. 5 but incorporating a 1% NOE into the positive signal gives the results shown in Fig. 9: in the high-digitization case, corresponding to the sharp lines encountered in small organic molecules of less than 1000 MW it is necessary to adjust the two spectra with a precision of approximately 1 mHz. In principle Fig. 5 acts as a calibration curve for the required shift if Tif can be estimated: it would be completely general if both digitization and offset were expressed in units of linewidth. However, in practice, judgment and guesswork are likely to be more useful tools for achieving good correction. Note that these artifacts are not a problem for broad lines such as those encountered in proteins. The source of the artifacts remains obscure. It is not even clear to us whether they are phase shifts or frequency shifts. They do not appear to be correlated with field strength, drift, solvent, decoupler properties, or any other obvious factor. They
296
MERSH AND SANDERS
A
I 2.4
I 2.2
FIG. 8. Control, and NOE difference displays of a small portion of a spectrum of cobester (4). (A) Control spectrum; (B) uncomected difference spectrum; (C) the corrected difference spectrum obtained after a 0.005-Hz relative shift of the two spectra.
certainly vary from spectrometer to spectrometer, and from day to day on any given instrument. They are sufficiently random that, like more familiar noise, they decrease in intensity relative to real signal with the square root of the number of transients acquired. They are also reduced significantly by acquiring two control spectra at the beginning and middle of an automated sequence of several irradiations, and averaging the two controls before subtraction. The linear shift correction method described here may also be valuable in removing subtraction artifacts arising from subtractions between different solutions. IMPLEMENTATION
AND CONCLUSIONS
All the spectra and simulations were processed on an IBM 370/165 mainframe computer. Raw FIDs were transferred by cassette or magnetic tape from ASPECT 2000 computers attached to Bruker spectrometers. The complete IBM package of one- and two-dimensional NMR software is home-written and is based on an early prototype by R. G. Brereton in this laboratory (5). Simple linear interpolations between data points was used reasonably successfully; more sophisticated methods are unlikely to produce more than marginal improvements. The regression and interpolation routines used in this work are straightforward and could readily be implemented on standard NMR-dedicated minicomputers. They could also be incorporated into commercial NMR software. Our motives for using mainframe pro-
JOUBLE-RESONANCE
DIFFERENCE
SPECTROSCOPY
297
Intensity
Offset
FIG.
9.
Repeat of Fig. 5 simulation incorporating
a 1% NOE in the positive peak.
cessing are several, but they are not related to the particular applications described in the paper. In conclusion, we have shown that subtraction artifacts and Bloch-Siegert shift artifacts can be dealt with in a variety of ways, the most powerful of which include computational correction of the spectra. In view of the way this correction method cleans up difference spectra by removing the unsightly stains, we propose for it the name SUDSY (Splendidly Uncluttered Difference SpectroscopY). EXPERIMENTAL
METHODS
The progesterone 1 was a gift from Professor D. N. Kirk (Westfield College, London). It was examined as an approximately 0.02 M solution in undegassed & benzene. The 400-MHz FIDs of cobester used to generate the spectra in Fig. 8 were kindly provided by Professor A. R. Battersby; experimental details are given elsewhere (4). The 250-MHz decoupling experiments were carried out on Bruker WM250 instruments in Cambridge and London (Imperial College), using previously described microprograms (3, 6). The FIDs were stored on disk and transferred to the Cambridge University IBM 370/ 165 by cassette or magnetic tape via ASPECT 2000 computers attached to Cambridge spectrometers. The IBM data processing software (written by J.D.M.) is as yet unpublished. ACKNOWLEDGMENTS We gratefully acknowledge the time and generosity of H. Rzepa and D. Neuhaus (Imperial College, L.ondon) in obtaining data during the early stages of this work, the FIDs supplied by Professor A. R.
298 Battersby, financial
MERSH illuminating support from
conversations the SERC.
with
AND Drs.
SANDERS
J. C. Waterton
(ICI)
and
W.
E. Hull
(Bruker),
and
REFERENCES 1. R. FREEMAN AND W. A. ANDERSON, J. Chem. Phys. 37, 85 (1962). 2. M. W. BARRE-IT, R. D. FARRANT, D. N. KIRK, J. D. MERSH, J. K. M. SANDERS, AND W. L. DUAX, J. Chem. Sot. Perkin Trans. 2, 105 (1982). 3. L. D. HALL AND J. K. M. SANDERS, J. Am. Chem. Sot. 102, 5703 (1980). 4. A. R. BATTERSBY, C. EDINGTON, C. J. R. FOOKES, AND J. M. HOOK, J. Chem. Sot. Perkin Trans. 2, in press. 5. R. G. BRERETON, submitted. 6. L. D. HALL AND J. K. M. SANDERS, J. Org. Chem. 46, 1132 (1981).