Sensitivity optimization in subspectral editing

JOURNAL

OF MAGNETIC

57, 506-512

RESONANCE

(1984)

Sensitivity Optimization

in Subspectral Editing

OLE W. SORENSEN Laboratorium ftir Physikalische Chemie, Eidgeniissische Technische Hochschule, 8092 Zurich, Switzerland Received

December

20, 1983;

revised

February

6, 1984

During the last few years considerable attention has been given to the development of techniques for retrieving proton multiplicities from decoupled 13C NMR spectra (Z-13). Whereas earlier attempts were mainly concerned with the distinction of 13C resonances according to the number of attached protons being odd or even (Z-9), later papers have demonstrated the feasibility of distinguishing according to the exact multiplicity (10-23). Since all these techniques rely on one-bond J cu coupling constants, the editing accuracy is influenced by the width of the J range present in the sample under investigation. Analysis of J cross-talk has shown (I I) that DEPT (10) as well as SEMUT (I I) can provide edited spectra of acceptable accuracy for a range of Jo f O.lJ,, where Jo is the coupling constant used in setting the delays in the pulse sequences. However, only with the introduction of the GL procedure (13) could the region of accurate editing be extended to the whole range of coupling constants encountered in organic molecules. In this communication we address the problem of optimizing the sensitivity of the SEMUT GL and DEPT GL experiments in terms of signal-to-noise ratios in the edited subspectra. The pulse sequences for the two experiments (13) are shown in Fig. 1. For simplicity we assume exact time matching T, = 72 = 73 = (2J)-‘. This gives the following intensity expressions for a CH, (n = 0, 1, 2, 3) group (10-14) as a function of the 0 pulse angles: SEMUT GL: Z(CH,) = cos” 6’ DEPT GL: Z(CH,) = n sin 6 co&‘-‘) 6.

Cl1 PI

The subspectra are generated by combining experiments obtained with different 8 flip angles. The carbons with odd and even numbers of attached protons, respectively, are easily separated by an appropriate 180” phase shift of a proton u/2 pulse (23). This is equivalent to saying that only 8 pulse angles between 0 and ?r/2 need be considered. Thus for both experiments two different 8 angles suffice, namely [0] and an as yet unknown optimum angle [/3s] for SEMUT GL and [fin] and [7r/2] for DEPT GL. We are interested in determining the optimum setting of the variable pulse angle and the relative number of scans for the subexperiments of the two pulse sequences. For this purpose it is convenient to introduce a parameter tl which is the number of scans recorded with 0 = /3s,b divided by the number of scans recorded with 8 = 0 0022-2364184

$3.00

Copyri&t Q 1984 by Academic Ress, Inc. All rights of reproduction in any form reserved.

506

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507

180:

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90:

8,

90;

6,

180$

13C

go&

180:

180:

b

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FIG. spectra.

I. Pulse

sequences

SEMUT

180%

GL

(a) and

DEPT

GL

(b) (13) for subspectral

editing

of 13C NMR

(r/2). It is also convenient to normalize the total number of scans to 1; i.e., 11 ( 1 + Q) scans are recorded for 0 = 0 (7r/2) and q/( 1 + q) for B = &,o. In practice, to get integer numbers of scans, multiples of these numbers are recorded. Starting with SEMUT GL we note that the task of the editing procedure is reduced to separating CH, and CH,,, resonances. The noise and signal levels in a single scan experiment are arbitrarily set to 1. The editing procedure and the signal-to-noise ratios (S/N) are listed in Table 1. The S/N ratios are functions of two variables (v and &), but it is relatively easy to show that the maximum with respect to q is given by q = (cosw*) 6))’ and T = (cos” 0)’ for the CH, and CH,,, subspectm, respectively. It can also be shown that the optimum flip angle /3s is the same for CH, and CHn+*, and can be determined numerically from the equation: 2 co2 &( 1 + cos” &) - n sin* & = 0.

[V

From Table 1 we see that S/N is always more favorable in the CH, spectrum and that the optimum S/N in a subspectrum in general decreases as the number of attached protons increases. Since any editing scheme is only as useful as its weakest point, a good guess for the optimum SEMUT GL parameters corresponds to those giving the best S/N ratio in the methyl subspectrum. This turns out to be correct and Table 2

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TABLE

1

DERIVATION OFGENERAL SIGNAL-TO-NOISE (S/N) EXPRESSIONSFOR SEMUT GL EDITINGOFCH,ANDCH.+~ GROUPS"

Subspectrum generation

Wsl- llc”‘Wl

W”P1 - Wsl

Signal intensity

m

Noise level

SIN s2c” 1 + c”+2

SJN optimized with respect to ?j

?c” 1 + c”

(9=.$ 1

1 v=c”+z

( )

’ The number of scans for the 0 = 0 ([0]) and B = & ([&I) experiments are I/( 1 + v) and q/( 1 + v), respectively. Abbreviations: s = sin 0s; c = cos Is,.

lists all S/N ratios together with the parameters which optimize S/N in individual subspectra. The conclusion is that the best performance is obtained by recording twice as many scans for 0 = u/3 as for 8 = 0 (a procedure applied in our original development of SEMUT (II)) and that an average penalty of 63% loss in sensitivity has to be paid for the editing in comparison to a standard experiment. TABLE 2 SIGNAL-TC~NOISE RATI~~FOR~NLWIDUAL SEMUT GL SUBSP~RA” Subspectrum

Optimized multiplicity c:& = u/2, t) = w CH.& = ~13, 7 = 8 CH2$s = u/2, I] = 1 cH,:& = n/3, 9 = 2

C

CH

CHz

CH3

1 0.58 0.71 0.58

0 0.33 0 0.30

0 0.24 0.50 0.35

0 0.20 0 0.25

“~istheratioofthenumberofscansrecordedwithB=~stothenumberrecordedwith~=O.Fora standard experiment S/N = 1 for all carbons.

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We now turn to the DEPT GL scheme for editing of CH, CH2 and CHs resonances. Because of the elimination of quaternary carbons, the editing procedure is simpler than for SEMUT GL. The signal-to-noise considerations are summarized in Table 3. Again the S/N of individual subspectra can be optimized or a smooth distribution can be pursued. Table 4 gives the details. First it is seen that optimized parameters for the weakest subspectrum (CHs) give a 14% sensitivity improvement compared to the equivalent of the parameters proposed by Doddrell et al. (10). This means a 23% time saving. The optimum parameters were deduced by demanding equal S/N ratios in all subspectra, leading to 81 v = 4(1 + 56)

’

7-i-z 9

sin2 fin = ~

[41

The closest practical numbers result in the following regimen: 8 experiments with fl = 37.90”, 8 also with ti = 37.90” but with phase inversion of the second proton 7r/2 pulse, and 17 experiments with 6 = 7r/2. The possibly more convenient 1:1:2 ratio and &, = 38.33” degrades the S/N of the CH2 and CH3 subspectra by 1.1% and improves the S/N of the CH subspectrum by 1.6%. Close inspection of the optimum parameters in Tables 2 and 4 reveals a deeper significance for some of the procedures. In SEMUT GL as well as in DEPT GL the optimum parameters for the CH2 subspectrum correspond to selecting the proton double-quantum coherence present during TV. In full analogy the optimum parameter~ for the CHs subspectra correspond to filtering out the proton triple-quantum coherence existing in the 72 period. Unfortunately the quatemary and CH parameters do not

TABLE 3 DERIVATION

OF THE SIGNAL-TO-NOISE (S/N) EXPREWONS OF THE DEFT CL EXPERIMENT”

CH Subspectrum generation

FOR THE THREE

SIJB~PECTRA

CfL

CH,

1*/21

lBD1

lPo1- &*/21

1

2sc

3sc* 1+s

(tl = 0)

(9 = a)

(q = SC’)

Signal intensity Noise level

SfN optimized with respect to q

a The number of scans for the 0 = rr/2 ([x/2]) and B = B. ([&J) s&experiments and q/(1 + T), respectively. Abbreviations: s = sin &, and c = cos &,.

are I/( 1 + q)

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TABLE 4 SIGNAL-ho-NOISE

RATIOS

FOR INDIVIDUAL

DEPT

CH

GL

SUBSPECTRA’

(3%

CH3

Standard (no editing) Maximum intensity for a given multiplicity (no editing)

0.82

0.94

0.82

1 (e = r/2)

1 (l9 = 7r/4)

1.15 (0 = 35.26”)

TJ= 0 (optimum for CH) l) = aI,& = K/4 (optimum for CH& 9 = 2, &, = u/6 (optimum for CHs) ?j= I,&=*/4 (Doddrell et al. (10)) q = 17116, &, = 37.90” q = I, &, = 38.33”

1

0

0

-

-

1

0.58

0.71

0.75

0.71 0.70 0.7 1

0.71 0.70 0.69

0.61 0.70 0.69

a 9 is the ratio of the number of scans recorded with ~9= j3n to the number recorded with 0 = u/2. A single experiment with 0 set to the magic angle (54.74”) has been chosen as standard.

fit into a multiple-quantum cycle. However, one general statement can be made about all the optimum pro&lures; namely that the best S/N for a given subspectrum is obtained when the mixing coefficient is equal to one. For example, the scaling factor on the 0 = 0 experiment required to generate the CH, and CHn+Z subspectra in Table 1, is equal to 1 for the optimum 7. This means that instead of scaling a spectrum by a certain factor for linear combination with another spectrum, it is more favorable to achieve the required signal intensity by changing the number of scans to fit a scaling factor of 1. An important feature of the DEPT GL editing scheme is that on the average only 19% sensitivity is lost compared to the standard nonedited polarization transfer spectrum (6 = 54.74’). For completeness a special case of SEMUT GL (13) can be used to generate an accurate quaternary subspectrum as a supplement to the three obtained with DEPT GL. If we record one scan of this experiment and a total of 1 + TJDEPT GL spectra and assume the NOE and polarization transfer (PT) enhancements to be equal we arrive at an S/N of 1 in all subspectra. A number 2 + q of SEMUT GL experiments would give S/N’s of 1.01,0.53, 0.62, and 0.44 for the C, CH, CH2, and CH3 subspectra, respectively. This is on the average 35% and for the weakest subspectrum 56% less than using DEPT GL. In comparing NOE and PT enhancements one has to be cautious. Ideally NOE yields a factor 3 and PT a factor 4, but applying DEPT GL to a system of one carbon with II directly bonded as well as m - n passive protons scales the PT for the genuine signals (13) down by a factor fj#

COS

(2KJliT1)

COS”

(?TJliTz)

151

i=n+l

because of homonuclear couplings. Heteronuclear long-range couplings also attenuate the PT enhancement in a similar manner, but since this is also true for SEMUT GL

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these factors have been left out of expression [5]. Long-range couplings can also iead to cross-talk between subspectra, but this is beyond the scope of the present paper. Together with the more pulses in DEPT GL and the fact that the sequence is longer than SEMUT GL we believe the equality of NOE and PT enhancements to be reasonable for many cases of 13C NMR. For other applications, such as editing of “N NMR spectra, polarization transfer can be substantially superior to NOE. A point which is definitely in favor of the NOE based scheme in 13C NMR concerns the repetition rate of the experiment when proton decoupling is applied during acqui&ion. Relying on polarization transfer, one must include a relaxation delay to re-estabhsh proton magnetization after switching off the decoupler. However, relying on NOE, one obtains the optimum S/N within a given time without a relaxation delay (15, 16) and by adjusting the flip angle of the first carbon pulse of SEMUT GL according to Table 1 of Ref. (16). Referring to that table, 90” should be added to o! because of the refocusing rr pulse in SEMUT GL. Using this scheme the sensitivity of SEMUT GL is improved. However, only when long acquisition times are used will the performance be comparable to that of DEPT GL.

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FIG. 2. Refined versions of the SEMUT GL (a) and DEPT GL (b) pulse seqtaences. As sbihowa in the text two consecutive. pulses(r/2)& have the Same effect as a single n/2 pulse of phaseB.Thesever&ns are less sensitive to pulse imperfections than those of Fig. 1.

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Finally we want to discuss briefly an obvious refinement of the two pulse sequences discussed above. Since the pulse 13,immediately follows a 742 pulse, better performance is expected by merging the two into a single pulse. Thus (7r/2)& combine as follows (17, 18): e i(*/2)Ixe

it&

=

ei(*/2)lxe-r(r/2)Ixe-iEI~~;(~/2)I~

=

e-irYtzei(r/2)lx

[61

The effect of the resulting L’-, pulse is to phase shift all preceding pulses by -0. In the present context this is equivalent to phase shifting the following (r/2), pulse by 0 and leaving the phases of the preceding pulses unchanged. Thus (7r/2)4, is equivalent to (7r/2)0 and the refined sequences, shown in Fig. 2, also obey Eqs. [I] and [2]. Whereas 8 flip angles larger than u/2 were undesirable in the versions shown in Fig. 1 because of rfinhomogeneity, extended phase cycling using 0 phase shifts larger than ?r/2 is feasible in the sequences of Fig. 2. If, for example, only 15o phase shifts are possible, only the optimized SEMUT GL procedure (0 = a/3) is convertible by combining pulses. For DEPT GL reasonable performance (CH, CH2, and CH3 S/N ratios of 0.67, 0.68, and 0.67, respectively, instead of the optimum value 0.70 for ail multiplicities) is obtained by combining two sets of experiments, one with 17= 2, 0 = 1F/6 and one with q = 314, 0 = ~14. To conclude, this communication has shown how to optimize signal-to-noise ratios in individual subspectra of two editing methods of equal accuracy, SEMUT GL and DEPT GL. In comparing the two, DEPT GL is in general superior to SEMUT GL. Using optimized editing parameters in DEPT GL as little as 19% sensitivity is lost compared to a standard polarization transfer experiment and equal noise levels are obtained in all subspectra. The latter point should be important for quantitative measurements. ACKNOWLEDGMENTS This research was supported by the Danish Natural Science Research Council (J.nr. 1l-3933) and the Swiss National Science Foundation. Professor R. R. Ernst provided a valuable critique during the preparation of this manuscript. Dr. H. J. Jakobsen gave further helpful advice. REFERENCES 1. D. P. BURUM AND R. R. ERNST, J. Mu@. Reson. 39, 163 ( 1980). 2. D. M. DoDDRELL AND D. T. F%GG, 1. Am. Chem. Sot. 102,6388 (1980). 3. C. LE Cocq AND J.-Y. LALLEMAND, J. Chem. Sot. Chem. Commun., 150 ( 198 1). 4. D. J. COOKSON AND B. E. SMIITH, Org. Mogn. Reson. 16, 111 (1981). 5. D. W. BROWN, T. T. NAKASHIMA, AND D. L. RABENSTEIN, J. Magpl. Reson. 45, 302 ( 198 1). 6. M. R. BENDALL, D. M. D~DDRELL, AND D. T. PEGC, J. Am. Chem. Sot. 103,4603 (1981). 7. S. L. PATT AND J. N. SHOOLERY, .I. Mugn. Reson. 46, 535 (1982). 8. FENGKUI PEI AND R. FREEMAN, J. Magn. Reson. 48, 318 (1982). 9. H. J. JAKOBSEN, 0. W. S~ENSEN, W. S. BREY, AND P. KANYHA, J. Magm. Reson. 48, 328 (1982). 10. D. M. D~DDRELL, D. T. PEGG, AND M. R. BENDALL, J. Mugn. Reson. 48, 323 (1982). II. H. BILD&E, S. D~~N~TRuP, H. J. JAKOBSEN, AND 0. W. S&ENSEN, J. Magn. Reson. 53, 154 (1983). 12. M. R. BENDALL AND D. T. PFXX, J. Mugn. Reson. 53,272 (1983). 13. 0. W. S~ENSEN, S. ~NsT~UJP, H. B-E, ANLI H. J. JAK~B~EN, J. Mugn. Reson. 55, 347 (1983). 14. 0. W. S~~RENSEN AND R. R. ERNST, J. Mugn. Reson. 51, 477 (1983). IS. R. R. ERNST AND W. ANDERSON, Rev. Sci. Instrum. 37,93 (1966). 16. J. S. WAUGH, J. Mol. S&ctrosc. 35, 298 (1970). 17. R. FREEMAN, T. F~ENKIEL, AND M. H. L~~rrr, .I Magn. Reson. 44,409 (1981). 18. 0. W. WRENSEN, G. W. EICH, M. H. LEVI=, G. B~DENHAUSEN, AND R. R ERNST, Prog. NMR

Spectrosc. 16, 163 (1983).