- Email: [email protected]
Editing of proton-coupled 13C NMR Spectra
JOURNALOFMAGNETICRFSONANCE65,222-238(1985)
Editing of Proton-Coupled13CNMR Spectra* ULLA
B. SORENSEN, HENRIK
BILDS~E,
AND HANS J. JAKOBSEN
Department of Chemistry, University of Aarhus, 8000 Aarhus C, Denmark AND OLE W. SORENSEN Laboratorium fiir Physikalische Chemie, Eidgeniissische Technische Hochschule, 8092 Zurich, Switzerland Received March 26, 1985 Editing of proton-coupled 13CNMR spectra into independent subspectra depending on the number of attached protons is analyzed using the product operator formalism. Pulse sequences which have proven successful for editing of decoupled spectra are shown to be unsuitable for editing in the coupled mode. This is because of poor editing accuracy and because various types of distortions appear in the edited subspectra. These problems are shown, both theoretically and experimentally, to be remedied by two new pulse sequences, SEMUT GL+ and DEPT GLf. 0 1985 Academic press, hc.
Simplification of complex NMR spectra through the application of multipulse experiments has become an indispensable aid in structural elucidation and in assignment of NMR parameters. A variety of one- and two-dimensional NMR pulse sequences has been proposed for this purpose in recent years. Among these, i3C spectral editing constitutes a particular useful method in that it allows decomposition of conventional 13C NMR spectra into four subspectra according to the number of directly attached protons (C, CH, CH2, and CH3). Edited proton-decoupled subspectra can be obtained with an acceptable accuracy using the SEMUT (1) and DEPT (2) pulse sequences provided the range of ‘J-n values is small (i.e., within 10% from the ‘JcH used in tuning the delays) (1). For molecules with large spreads in ‘JcH values often encountered in organic molecules (120 < ‘JcH < 220 Hz), the GL procedure must be incorporated (i.e., yielding SEMUT GL and DEPT CL (3)) to suppress J cross-talk between subspectra. In this paper we evaluate the application of spectral editing techniques for protoncoupled 13C spectra. The purpose of editing coupled 13C spectra is not to determine proton multiplicities, but rather to obtain spectrum simplification. When a 13C spectrum is acquired without proton decoupling, there can be an enormous increase in the number of resonances and the standard spectrum is often too crowded to interpret. Editing into four subspectra is therefore useful for the measurement of 13C-‘H coupling constants. * Presented
in part at the “7th EENC,” Ahavilla Militia, Italy, May 1984.
0022-2364185 $3.00 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved.
222
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
223
The usual pulse sequences for editing decoupled 13C spectra cannot be directly adapted to coupled spectra by simply acquiring the FIDs without proton decoupling. This is because the decoupling removes antiphase product operators which distort the spectral phases and, in contrast to a recent statement by Bendall and Pegg (4), seriously influence the editing accuracy. Therefore the pulse sequences must be extended to include purging techniques. PURGING
TECHNIQUES
FOR ELIMINATION
OF SPECTRAL
DISTORTIONS
A spectrum is defined as distorted if it is impossible to phase all lines to positive absorption, or if the relative line intensities within multiplets deviate from those encountered in a simple 90”-acquisition experiment. In proton-coupled 13CNMR spectra (I$$ spin systems with I = ‘H, and S = 13C)an undistorted 13Cmultiplet is represented by the S, (or S,) operator in the product operator formalism (5, 6). When the 13C chemical shifts are refocused, the spectral distortions are caused by antiphase product operators (e.g., 21i,S,, 411Zl&$, * . . ) (7). Those containing an odd number of 1, operators produce dispersive contributions to the spectrum and have been named phase-anomaly terms (7). The product operators with even numbers of 1, operators have been named multiplet-anomaly terms (7) because they do not disturb the phasing of the spectrum, but only the relative line intensities. Techniques for purging phase and multiplet distortions in coupled 13C spectra, obtained via the polarization transfer methods of DEPT and refocused INEPT (8, 9) were introduced in Ref. (7). One purging scheme applies a proton 180” pulse at the start of acquisition in alternate scans. When introduced into DEPT, i.e., DEPT+ (7), coupled spectra free of phase distortions are obtained because the phase-anomaly terms appear with opposite sign in every second scan. The multiplet distortions, on the other hand, are invariant to this purging method. A second purging scheme (7) inserts a 90” proton pulse immediately prior to acquisition in all scans in order to eliminate both phase and multiplet distortions irrespective of the spread in one-bond or in long-range 13C-‘H couplings. For example a 90” purging pulse can be added to APT (10, II) (using the proton flip version as for example shown in Fig. 1 of Ref. (1 I)) and refocused INEPT to give APT+ and INEPT+ (7) which both yield distortionless coupled spectra. If heteronuclear multiple quantum coherence (MQC) is present, careful attention must be given to the refocusing of ‘H chemical shifts before inserting the 90” purging pulse into a pulse sequence. Thus, for DEPT this “++ purging scheme” requires an additional T period and extra pulses to give DEPT++ (7) or the equivalent condensed pulse sequence, MQDEPT (1.2). The two purging methods discussed can similarly be incorporated into SEMUT resulting in the SEMUT+ and SEMUT++ pulse sequences, also providing coupled spectra free of phase distortions. In SEMUT GL and DEPT GL the heteronuclear multiple-quantum coherences present after the 0 pulse are “stored” along both orthogonal directions in the rotating frame (e.g., 41&.& and 41rJzJJ and a 90” purging pulse would inevitably convert part of this back to antiphase magnetization. Therefore, only the simple “+ purging scheme” with a 180” pulse in every second experiment is applicable for the GL pulse sequences designed to suppress J cross-talk. As mentioned above, this only eliminates the phase anomalies but we should note that the multiplet distortions are unimportant
224
SBRENSEN
ET
AL.
for practical applications because they in no way disturb the measurements of coupling constants. As shall be shown in the next section, the purging is also essential for the suppression of antiphase J cross-talk signals. The new pulse sequences SEMUT GL+ and DEPT GL+ for editing coupled r3C spectra are outlined in Fig. 1. Because the proton 180” purging pulse must be applied at the very start of data acquisition, these sequences employ “delayed coupling” (7r < r3) instead of “delayed acquisition” (7r > r3) as used in the sequences for editing of decoupled spectra (3). From the general analysis of S/N (signal-to-noise ratio) in SEMUT GL and DEPT GL subspectral editing (13) it is clear that the best sensitivity for editing coupled spectra is achieved by using DEPT GL+ to edit CH, CH2, and CH3 resonances and SEMUT GL+ with 8 = 90” to generate the quaternary carbon subspectrum. For the latter sequence the two successive pulses 90,“90,” may be replaced by a single 90; pulse; thus the special quatemary carbon sequence SEMUT GL+(q), shown in Fig. lc, may be used for this experiment.
'H
a 13c
b
90: 13C
, I
-h
1808 t3
- t1
, I
tj+
2
62 ‘c2 7
+ x3
61
'H
C
t3
-h
180' i-; ' '-
90; 13C
t2
l-l
?
+ z3
T2
7
+ t3 b
ELG. 1. Pulse sequences SEMUT GL* (a), DEPT GL+ (b), and SEMUT GL+(q) (c) for editing of protoncoupled “C NMR spectra. The phase-cycling scheme (see experimental section) for the purging sandwich and 8 proton pulses is shown in Table 4. Two series of experiments are coadded, one with the proton 180” pulse prior to acquisition and one without this pulse.
EDITING ANALYSIS
OF PROTON-COUPLED
OF COUPLED
SEMUT
225
CARBON- 13 SPECTRA GL AND DEPT GL SPECTRA
Analysis of pulse sequences based on the product operator formalism (5) allows a convenient step-by-step calculation of the density operator. Although straightforward, product-operator calculations for large systems can be extremely paper- and time-consuming when all transformations are carried out in sequential order and all terms retained throughout. Therefore, a computer programme, SEQUENCE (Z4), which calculates the result of an arbitrary pulse sequence based on product operators, was introduced recently. Another approach (6) exploits the high symmetry of Z,S spin systems to factor the density operator evolutions in a convenient way. The result is that once the response of an ZS spin system is known, it can easily be generalized to Z,S spin systems. This considerably speeds up calculations and also provides better insight into the “mechanism” of the pulse sequences. This procedure is illustrated below for the SEMUT GL and DEPT GL sequences without proton decoupling. For the SEMUT GL sequence (Fig. la) the series of transformations from the point immediately after the 13C 90” pulse, 0, to the end of the delay 73 immediately before the dotted T pulse, point 0, is written as
C uJ(rz/2)2I,zSz -v--u2
z: ; Iti
2 SI,
2 ?rJ732I,S, 111
where the summations are for all Z spins (i = 1, 2, . . . , n). The phase of the first ‘H 90” pulse of the purging sandwich has been set to x and the phase Cpof the 180” refocusing pulse is x. In Eq. [ 1] all chemical-shift evolutions have been neglected because (a) S-spin chemical shifts are refocused, (b) Z-spin chemical-shift evolution during 72 is refocused, (c) chemical-shift evolution is active only for transverse operators (I,, Z,) which are not present for the Z spin during TV, and (d) such terms present during r3 in the forms of MQC’s or Z-spin single-quantum coherence do not influence observable S-spin magnetization. In density operator calculations, refocusing pulses can always be thought of as if they were “applied” at the beginning of the respective free precession periods (5, 6). Therefore the 180,“(S) pulse can be moved in front of all other transformations by changing the signs of all preceding transformations containing S, and has the simple effect of converting -S, into S,. Likewise the TZ, pulse can be moved to the beginning of the 72 delay and condensed with the (r/2)1, pulse. Finally, since operators of different spins commute the transformation of Eq. [ 11 can be rewritten as 7 (-rJr,ZI&
- ; Ii, ?rJr22I&
@I =s,--
-
; Iti 0I,
~J7,21&}
--
-
02.
PI
This implies that for the SEMUT GL sequence the overall transformation for an Z,,S spin system can be decomposed into n identical propagators Ps, one for each Z spin, and represented by the terms within the brackets of Eq. [2]. From this we obtain the recurrence formula PSk
az(L,S)
-
~2UkS)
where Psk is the propagator with respect to the ZcthZ spin.
I31
226
S0RENSEN
ET AL.
For an IS spin system, the following two relevant transformations for the SEMUT GL sequence may easily be derived using Eq. [2] (only observable terms are included) PSI WI 8, -
+
(clc2c3
where ck, Sk= cos(rJTk), sin(r&)
Thus, the transformations
-
hs3d&
(cIc2s3
-
WI
W3d2~dx
and co, se = cos 19,sin 19.To save space we abbreviate A =
ClC2C3 +
SIS~C~
PaI
B =
~1~2~3
slC3Ce.
[W
-
[4a] and [4b] become PSI
S, - AS, + B21,&,
bl
PSI
S,, -+ AS, - B2I,&
WI
which are of form similar to the basic equations for J-coupling evolution, (e.g., Eqs. [ 171 and [ 181 in Ref. (5)). The reverse transformations (analogues of the transformations describing refocusing of antiphase magnetization, Eqs. [ 191 and [20] in Ref. (5)) have coefficients different from A and B. However, only [6a] and [6b] are of interest in the present context and the density operator for an IS system at point 0 may be written ~~~(1s)= AS, - B2Z,,S,. [71 The transformation and [71)
for an 12Sspin system now takes the form (using [3], [6al, [6bl,
AS,, - B2I,&
2 A(AS,, - B212&)
- B2I,,(AS,
+ B21,&)
i.e., a2(12S) = A2S,, - AB2(Z1, + 12dSx - B24~ddy.
PI
Before we derive the response of an I,S system, it is convenient to introduce a number of operator abbreviations: F; = E;
FJ = 5 Ii,;
FZ = i Ii,Ij,;
i=l
Fz =
c
Iiz4jzlkz, etc.
i
iJ
and s-, = -s,;
s-, = -s,.
The operator F$’ is the sum of the 6) different products of p I, operators in I,$ groups, where n = ii?! (n - p)!p! * 0P Due to the equivalence of Eq. [ 31 to a cascade of J couplings it is easy to determine the coefficient of the general product operator 2*F$Sti+p,2j: Starting from u1 = S,, p of the couplings must dephase (meaning introduction of IJ yielding a factor BP, and the remaining (n - p) couplings must not cause dephasing yielding a factor A”-*. The
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
227
(;) combinations, which fulfil this requirement, reflect the number of products in F$‘, and we may write the coefficient and the operator
PI
A”-PBP2PFPS 2 cy+prrm*
It follows that the response for an I,S spin system undergoing the SEMUT GL sequence without proton decoupling is a&S)
= i A”-PBP2PF$!3y+m,2j. p=o
1101
For the case I = ‘H, S = 13C (1,s systems with IZ = 0, 1,2, and 3) only the first four terms of the summation in Eq. [lo] need consideration. For clarity these four terms have been written out in the usual nomenclature of product operators in Table 1. For the decoupled SEMUT GL pulse sequence only the first term in the summation of Eq. [9] is retained (3). TABLE 1 Intensity Expressions Based on the Product Operator Formalism for the Response of a General Z,,SSpin System Subjected to SEMUT GL and DEPT GL without Z-Spin (‘H) Decoupling” SEMUT GL z,s: (C&S, - s,c3c&“(c~c*c3+ s,s&s,
DEPT GL ZJ: ns,s3s,(c,c*s3 +
- s,c,c~)o(c*c2c3+ -
[-s‘c3s~c~c~s3
+ (n -
+
s,c3&c,c~c3
1)S,S3S&,C2S3
-
s,s3ce~-‘Sx s,s,c,)“-’
S,C&&CzC~
+ S,S3C&-‘]2
i zils, i=l
+ [2s,c3s.&,c2s3- slc3ce)‘(c1qc3 t sls3c,)“-2 - (Tl +
2)S,S3S,(C&S3
[3s,c3s&,czs3
- (Tl -
-
-
SIC~C,)~(C&#~
+
s,c3c,y(c,c*c3
3)S$S3S@(ClC#3
-
+
S,S&)“-‘]4i
i
z&&
s*s3c,)“-3
SlC3C#)3(ClC$3
+
S,S3C~)“4]8
i
ZizZjzZhSy
kjck +
.
a Abbreviations: ci = cos(r.Z~J, si = sin(7FJ73, c, = cos 0 and se = sin 8.
228
S0RENSEN
ET
AL.
For the coupled DEPT GL sequence (Fig. lb) it is noted that, because of the modification (TV> or) required as compared to normal decoupled DEPT GL (3), an interval (r3 - 7,) has been inserted between the 90,“(S) pulse and point 0. With this interval centered around the 180,“(I) pulse, it ensures S-spin chemical shift refocusing at the point of data acquisition and also suppresses JIs coupling during r3 - 71 . The calculation of the response of an I,$ system to a polarization transfer pulse sequence can be simplified by noting that each of the y1equivalent I spins gives rise to the same amount of polarization transfer to the S spin. Therefore, the transfer from one of them, say I,, can be calculated and the total result obtained by multiplication by a factor n. We introduce a propagator PO, = PD1(rl, 72, 73, 0) which denotes the complete set of transformations affecting only II and S in an I,S system for the pulse sequence in Fig. l(b). Using standard product operator theory, the following transformation can easily be derived (we show only observable terms): PDI I,, - S~S3S& - s,c+s~21&l. [Ill Because there are no interactions between the protons, the remaining y1- 1 protons first influence the magnetization arising from II after the 90,“(S) pulse, i.e., they undergo a SEMUT CL pulse sequence in this case. Therefore, the fate of the magnetization starting on II may be derived from the series of transformations: Pm Ps2 P,
I lz--+3+...-...--+*
PSi
PSI
WI
The total response of an I,S system is obtained by summing the results of the series of y1transformations of the type [ 121. This may formally be written
[I31 Using the abbreviations, c =
WI [14bl
SIS3S9
D = sIc3s8 for the coefficients in the result of the PO, transformation a2(lS) for an IS system is given by u&Y) = I,, 2 C’s, - D2I&,
[ 111, the density operator
= u2(Is).
[I51
For an I$ system the transformation of I,, and IzZ into the two separate terms a$(12S) and &12S) yields the following results (using [ 151 and [6a, b]) u;(12S) = C(AS, + B212,Sy) - D2I,,(AS,
- B212&)
[164
a$(Z2S) = C(AS, + B2Id,)
- B2Z&)
116bl
- D2I&AS,,
and the total response a2 = CT:+ as for an I$ spin system may be written a2(12S) = 2ACS, + (BC - AD)2FfS,, + 2BD4F;Sp
[I71
Again we derive the general response by calculating the coefficient of the product operator 2pF$S~x+m~2~.With reference to ~7~in Eq. [ 151, where all transformations
EDITING
OF
PROTON-COUPLED
CARBON-l
229
3 SPECTRA
involving I, have been carried out, the first term (CS,) requires dephasing with respect to p of the remaining (n - 1) I spins and thus introduces a factor of BP. The remaining (n - p - 1) 1 spins must not cause dephasing thereby contributing a factor of ARep-‘. The p I spins can be taken as (” ; I) combinations. Because each of the n I spins contribute the same amount, we obtain a total of n X (” ; l) terms. F$ contains (;) of these terms, leaving a resulting factor of (n - a). Thus, the total contribution from the first term in [ 151 amounts to (n - p) X CAnPpPIBp. The second term in the transformation [ 151 already contains one 1, operator. Introducing the remaining (p - 1) 1, operators gives a factor BP-’ and the remaining (n - p) I spins contribute a factor of AneP. This represents (; I f ) different terms. Polarization is transferred from each of the n I spins giving a total of y1X (; I 1) terms. Taking the G) terms in F{ into account we obtain a resulting numerical factor p. Hence the total contribution from the second term in ~2 of Eq. [ 151 is given by -pDA”dPBP-l. In conclusion the term containing p 1, operators gives a response proportional to -pDAnPPBP-’ + (n - p)CAnPP-‘BP.
[I81
The general response for DEPT GL without proton decoupling can now be written in the condensed form c2(I,J) = c { -PDA”-~B~-’
+ (n - p)CA”-P-‘BP}2pF$5’cx+m,2j.
p=o
[I91
Equation [ 191 has been written out explicitly for the cases relevant to 13C NMR in Table 1. Finally, incorporation of the “+ purging scheme” into the SEMUT GL and DEPT GL pulse sequences, i.e., a proton 180” pulse applied at the start of acquisition in every second experiment, eliminates product operators containing odd numbers of 1, operators. Therefore, in discussions of SEMUT GL+ and DEPT GL+ to the cases relevant for editing of coupled 13C NMR spectra (i.e., n < 3) only terms with zero and two I, operators need consideration. J CROSS-TALK
IN
SUBSPECTRAL
EDITING
OF
COUPLED
“C
SPECTRA
For the ideal conditions 71 = r2 = 73 = (25)-l (i.e., cl = c;! = c3 = 0 and s1 = s3 = 1) the general intensity expressions for SEMUT GL and DEPT GL (Table 1 or Eqs. [ lo] and [ 191) reduce to SEMUT GL: az(Z,S) = c& DEPT GL: f12(1$$) = ns&‘S,
[201 PII
i.e., the intensities for the S-spin NMR signals in an I,$ spin system are proportional to cos”B and n sin 0 COS”~‘6’for SEMUT GL and DEPT GL, respectively. Thus, for both sequences proper linear combinations of spectra obtained with different B flip angles allow a separation of the NMR resonances into subspectra according to the number of I spins (subspectral editing (1-3, 13). In practical applications the non-
230
S0RENSEN
ET
AL,
ideal conditions pi f (2J)-’ prevail and COS(rJTi) f 0 in Table 1 and Eqs. [lo] and [ 191. Thus part of the responses of the in-phase and antiphase terms for a coupled I,S group will be proportional to cos’? for SEMUT GL and sin 19cos”-‘0 for DEPT GL. These contributions from the I,S spin system mimic the behaviour of an Z,S group and give rise to unwanted “spurious” resonances in the I,,$’ subspectrum. This phenomenon has been dubbed J cross-talk and analyzed for decoupled SEMUT/DEPT (1) and SEMUT GL/DEPT GL (3). With proton (I-spin) decoupling, only the inphase terms contribute and Jcross-talk for SEMUT (GL) and DEPT (GL) is identical (I, 3) and can only take place in the “downward direction” (m < n); e.g., from CH3 to CHp but not from CH2 to CH3. It has been demonstrated that the GL procedure effectively suppresses J cross-talk in editing of decoupled 13C spectra (3). In the coupled mode serious cross-talk contributions from the antiphase terms similarly occur in the “downward direction.” In addition, for an I,$ system antiphase terms with proper flip angle factors co03 for SEMUT (GL) and sin 0 co?‘0 for DEPT(GL) may give severe distortions of the genuine multiplets. Application of the 180” purging pulse suppresses this J cross-talk and phase anomalies in editing of coupled spectra quite effectively (vide infra) . In the following we derive explicit general expressions for the Jcross-talk in coupled SEMUT GL and DEPT GL spectra. It is instructive to define the Jcross-talk intensity from an I,$’ spin system to the 1,s subspectrum relative to the ideal response of the I,$ group (7i = 72 = 73 = (2J)-‘). From the general intensity expressions (Table 1 or Eqs. [lo] and [ 191) it follows that the J cross-talk (I,$ - I,$?) for the in-phase terms is the same as for the decoupled case and identical for SEMUT GL and DEPT GL (3), i.e.,
t221 The general J cross-talk expressions (Ins + 1,s) for coupled SEMUT GL and DEPT GL are easily calculated from the general intensity expressions (cf. Table 1) as the coefficients of cosV and m sin 0 cos”-’ 13,respectively. Rearrangement of the expressions for SEMUT GL in Table 1 and collecting terms proportional to COSY gives for the J cross-talk intensity in coupled SEMUT GL(I,S - Z,S):
-K +
;
>(c1c2~3)2(-%c3)o clc2s3)L(-sIc3)’
(C~C*C3)n-m-2(S1S3)m
(C,C2C3)n-m-1(S1S3)m-1
“-m(s,s3)“2]4F~Sy
+ - - -}
[23]
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
231
In a general condensed form this becomes: (c,c#‘-~c;-~-~+~~s~s~+~-~~(-
1
l)k 2pF~S~,+p,,2, . [24]
The summation over k extends only for values k i m and k >, m + p - n. In a similar way the intensity expression for the coupled DEPT GL (cf. Table 1 and Eq. [ 191) sequence may be rearranged. The general condensed form for the terms involving m sin 0 cos*-‘0 in coupled DEPT GL, which are proportional to the J crosstalk intensity, is given by:
mw8-‘i,;
[j.
(; ~~)~)(C’,)“-mc;-m-p+2k~~~~+p-2k~
(-I)k]2pF,,+m,2~}
[25]
with k < m and k 2 m + p - n. Comparison of Eqs. [24] and [25] shows that the J cross-talk signals are identical for all terms in coupled SEMUT GL and DEPT GL. For clarity the rearrangements of the expressions in Table 1 represented by the Eqs. [24] and [25] are written in an explicit form in Table 2 for I,,S spin systems relevant for editing coupled 13C spectra (n < 3). Only the terms appropriate for the SEMUT GLf and DEPT GLf sequences, i.e., terms containing an even number (zero and two) of 1, operators, are given. TABLE 2 SEMUT GL+ and DEPT GL’ Responses of Coupled CH, Group&
c:
xos,
CH:
~0~1~2~3~y
a For SEMUT GL+, x,,, = cos”8 and for DEPT GL+, x, = m sin 6’ cos”% For other abbreviations see Table 1. b Without practical consequences the DEPT GLC responses have been phase shifted by 90”.
232
SILIRENSEN ET AL.
For a comparison of experimental results (vide infra) obtained from the ordinary SEMUT and DEPT pulse sequences with those of their GL+ versions, Table 3 contains explicit SEMUT and DEPT responses of I,Sgroups with n i 3. Here the substitutions sI = s3 = s = sin ~JT, cl = c3 = c = cos rJr, and c2 = 1 have been introduced and all antiphase terms retained. EXPERIMENTAL
13C NMR experiments were performed on a Varian XL-300 spectrometer (10 mm probe) at 75.45 MHz with appropriate programming of the pulse sequence codes and phase cycling schemes for the DEPT GL+, SEMUT GL+(q), DEPT, and SEMUT sequences. The editing of coupled r3C spectra was achieved using DEPT GL+ for generating the separate subspectra for the CH, CH2, and CH3 resonances and SEMUT GL+(q) to obtain the quaternary carbon subspectrum. For an experimental demonstration of the advantages achieved using the GLf purging scheme similar subspectra were also generated using ordinary DEPT and SEMUT. The delays 71, 72, and ~(7, < rs), generated within the sequence codes for the GL+ versions, were calculated
TABLE 3 Ordinary SEMUT and DEPT Responses of Coupled Responses for CH ” Groupsngb c:
x&’
CH2:
xo[&%, + x,[cs(2csS, + x,[s*(s*s,
CH3:
- cs2(Z,, + I,,)& - s24Z,,Z&)] - (2s'
- 1)2(11,+
Z&T,
+ cs2(Z,,
+ Z,,)S,
- c*4z,,z&l
x,,[c3(c3SY- c’sZ(Z,, + Zzz+ -
cs24tZ1zZ2z
+ x,[c*s(3cw,
+
Z1zZ3z
+ x3[s3(s3Sy
+ I,J3z
+ (3c2s - s)2(Z,,
+ (3cs2 - c)4(Z,zZ,, + cs22(Z,,
Z,,)S,
+ s38Z,U3zU
Z,r,z)s,
- (3csZ - c)2(Z,,
+ (3~~s - s)4(Z&r + x,[cf~(3cs?$'
+
+ 2cs4Z,,Z&)J
+ Z& + z3&Y, + ZzJ3r)sy
- ~c~~%M~&~I
+ z, f Z33&
+ Z,zZ32 + IzX3Sy
+ 3c*~~~,zl,zl,z&~1
+ z-2, + Z,,)S,
- c2MZA + ZlzZ3r + Zd&% - c~~ZI~Z~~Z&)I n For SEMUT, x,,, = cos”l and for DEPT, x, = m sin 19cos”-‘8. c = cos(?rJT) and s = sin(?rk). b Without practical consequences the DEPT responses have ken phase shifted by 90”.
EDITING
OF PROTON-COUPLED
CARBON- I3 SPECTRA
233
according to the J range to be covered (Jmin < J < Jmax) as described elsewhere (3). The single 7 delay applied for DEPT and SEMUT was taken from the mean of the J range, T = (2J,,,,)-‘, for the sample under study. For the DEPT GLf proton pulses the 16 step phase cycling scheme, shown in Table 4 for the purging sandwich and fl pulses, was supplemented by independent exorcycling (15) of the first 180” ‘H pulse giving a total of 64 steps. The 180” ‘H purging pulse was a 90,” 180; 90,” composite pulse (16). The 180” 13Cpulse was phase cycled according to EXORCYCLE (15) and finally the 90” and 180 a 13C pulses were taken through a CYCLOPS cycling (17). The phase cycling scheme for SEMUT GL+(q) is similar to the one described earlier for SEMUT GL (3). For ordinary DEPT and SEMUT the pulses were run through a scheme equivalent to their GL versions. For the DEPT GL’/DEPT experiments the optimum 0 flip angle values (0 = 38, 90, and 142”) and 7 = 1 (13) were applied. However, the DEPT GL’ experiment corresponding to 0 = 142” was obtained employing 0 = 38” and a simultaneous 180” phase shift between the two 90” ‘H pulses of the purging sandwich (3). This minimizes the effect of rf inhomogeneity on the 0 pulse. The CH, CHZ, and CH3 subspectrum generation was fully automated using a least-squares analysis (program ADEPT (18)). Alternatively, the mixing coefficients for the different subexperiments may be entered manually using a program MANDEP implemented on the XL-300 computer system. RESULTS
AND DISCUSSION
The various aspects of the GL+ and standard DEPT/SEMUT schemes for editing of coupled 13C spectra are clearly apparent from the spectra in Figs. 2-5. To illustrate the effect of GLf editing of a complex spectrum, Fig. 2 shows the result for a sample of cholesterol (a molecule with a moderate spread in ‘JCH couplings) obtained with ordinary SEMUT and DEPT. Figure 3 shows the corresponding edited spectra obtained TABLE 4 16-Step Phase-Cycling Scheme Applied for the Proton Purging Sandwich and 0 Pulses in DEPT GL+” 90” X
+X
X
*Y tx +Y
-x -X
-X -X
180”
X
‘tX
X
+Y fX *Y
90” X -X --x X X -X -X X
0 Y -Y Y -Y -Y Y -Y Y
’ For the experiments with 0 > 90” one of the 90” pulses is phase shifted by 180” throughout. The phase cycling of the proton pulses was supplemented by independent EXORCYCLING (15) of the first 180” ‘H pulse in DEPT GL+.
234
I
S0RENSEN
I
140
ET AL.
,
120
80
100
I
60
40
20
ppm
0
FIG. 2. Edited proton-coupled 13C NMR spectra of cholesterol (0.015 M in CDC13) obtained using the standard DEPT and SEMUT sequences for the protonated and quaternary carbon spectra, respectively. The delay 7 has been optimized corresponding to an average value of ‘.Icu = 135 Hz. The CH, spectrum, which contains ah protonated carbons, is the 0 = 38” DEPT subexperiment.
CH3
CH2
CH .-” C
A. ,
140
/
I
120
I
/
100
I
I
80
I
60
40
,
I
20
I
ppm
1
0
FIG. 3. Edited proton-coupled 13CNMR spectra of cholesterol (0.015 Min CDC13) obtained on a Varian XL-300 spectrometer using the DEPT GL+ and SEMUT GL+(q) pulse sequences for the protonated and quatemary carbon spectra, respectively. The 7 delays have been adjusted according to Jmi. = 125 Hz and J = 160 Hz (3). The signals marked with an asterisk (*) are caused by residual CHCI, (1%) of the dE$eratcd solvent. The CHCI, molecules cause J cross-talk signals (negative, cf. Table 2) in the quatemary carbon subspectrum, because ‘JcH (=2 13 Hz) is outside the optimized J range. The CH. spectrum is the 8 = 38” DEPT GL+ s&experiment.
EDITING
OF
PROTON-COUPLED
CARBON-
13 SPECTRA
235
using the GL+ sequences. In Figs. 4 and 5 the same set of experiments has been performed on a mixture of two molecules (menthol and 3-methylpyridine) which have a spread in ‘Jon from 125 to 185 Hz. The spectra clearly demonstrates the necessity of using the CL’ pulse sequences for editing of coupled spectra with wide ‘Jcn ranges. The severe distortions and J cross-talk resonances observed (especially in the Fig. 4 subspectra) for the standard SEMUT/DEPT editing experiments are easily accounted for theoretically using the intensity expressions in Table 3. From these expressions it is seen that the dominating distortions in all SEMUT/DEPT edited subspectra arise from the p = 1 antiphase terms (i.e., product operators involving one Z, operator, 2 Cy==,Zi,s,) because the coefficients for these terms contain only one cos(rJr) factor. Thus, two types of serious anomalies (both purged using the GL+ sequences) may occur for SEMUT/DEPT edited spectra: (1) Phase distortions of the genuine signals themselves from the dispersion mode p = 1 antiphase term, and (2) J cross-talk of dispersion mode antiphase contributions from CH, multiplets to the CH,-i subspectrum. Distortions of the first type (phase anomalies within the genuine multiplets) are clearly observed for the spectra in Fig. 4 but also for the doublet at lowest shielding in the cholesterol spectrum (Fig. 2). Under the experimental conditions used for the Fig. 4 spectra these distortions result from a mixing of up to 25% of the intensity originating from antiphase dispersion mode terms. For example, inspection of the CH3 subspectrum (Fig. 4) shows that phase anomalies may prevent accurate measurement of 13C-‘H coupling constants. The second type of serious distortions in edited SEMUT/DEPT coupled spectra (i.e., Jcross-talk of antiphase dispersion-mode CH, multiplets into CH,-i subspectra) occur, as for all other J cross-talk terms and for the decoupled case, only in a “downward” direction (Table 3). These distortions are also clearly apparent in the Fig. 4 spectra. For samples \;ith wide ‘JcH ranges and heavily overlapping coupled multiplets, the J cross-talk of dispersion mode multiplets may mask genuine multiplets. This is illustrated in the Fig. 4 CH2 subspectrum, where the CH2 triplet at highest shielding is severely distorted by J cross-talk from the CH, spectrum and appears more like a “doublet.” In addition the usual in-phase (S,,) Jcross-talk observed in SEMUT/DEPT editing (I) also seriously contributes to the distortions observed in Fig. 4. As shown earlier (I) the S, J cross-talk has its largest contribution from CHs groups to the CH2 subspectrum (3 c2s4S, term) for a given AJ deviation in setting the T delay. For the experimental conditions in Fig. 4 the cross-talk from in-phase CHs magnetization is of the order of 20% while the three CH3 antiphase J cross-talk terms contribute from 5 to 25% (increasing percentage with decreasing numberp ofZz operators). The extensive downward J cross-talk distortions observed experimentally in edited SEMUT/DEPT CH and C subspectra (Fig. 4) are similarly dominated by antiphase dispersion mode terms from CH2 and CH multiplets, respectively (Table 3). Finally, it should be noted that the sign change observed for all antiphase dispersion mode terms with only one cos(a’JcH7) factor, depending upon ‘JCH < Jo -c ‘J&T = (~Jo))‘), is clearly reflected in the Fig. 4 spectra. Compare, for example, the CH dispersion mode cross-talk resonances in the C subspectrum at high and low shielding. The problems discussed above and associated with SEMUT/DEPT editing ofcoupled i3C spectra are absent when the SEMUT GL+(q)/DEPT GL+ pulse sequences are
236
WRENSEN
ET AL.
CHn
CH3 CH2
CH
I
I
I
I
I
I
140
120
100
80
60
40
I 20
ppm
0
FIG. 4. Edited proton-coupled 13CNMR spectra of a mixture of menthol (0.025 M) and 3-methylpyridine (0.030 M) in CDCI, obtained on a Varian XL-300 spectrometer using the standard DEPT and SEMUT sequences for the protonated and quatemary carbon spectra, respectively. The r delay has been optimized corresponding to an average value of ‘J cH = I55 Hz. Note the enormous J cross-talk signals and also the illustration of the fact that J cross-talk only takes place in the “downward direction.” The CH, spectrum is the 19= 38” DEPT subexperiment.
applied. The reason is that the GL+ editing procedure purges the antiphase terms with odd numbers (a = 1 and 3) of I, operators and introduces an additional cosine factor, cos(~I~~), into all J cross-talk terms. Thus, these sequences yield edited spectra free of phase anomalies and with negligible multiplet distortions arising from product operators containing two I, operators (p = 2). The effects of the GL+ procedure in cleaning edited coupled 13Cspectra are nicely illustrated experimentally by the spectra in Figs. 3 and 5. CONCLUSION
A factoring procedure for the density operator evolutions has been proven to be very useful in the analysis of coupled SEMUT/SEMUT GL and DEPT/DEPT GL spectra. Theoretical and experimental results prove that spectral editing of coupled 13C spectra em p lo y’m g the standard SEMUT/DEPT pulse sequences may be accompanied by severe distortions of the observed subspectra. Thus, for simplification of complex coupled 13Cspectra we suggest the DEPT GL+ and SEMUT GL+(q) sequences for editing coupled 13C spectra of protonated and quaternary carbons, respectively. The experimental results and analysis of J cross-talk show that the GLf procedure purges all phase anomalies and suppresses J cross-talk between subspectra. For mol-
EDITING
OF PROTON-COUPLED
CARBON-l 3 SPECTRA
237
** I QcH:CH3Q-[3 OH
3 CH2
C I
/
I
140
120
100
/
80
/
I
1
60
LO
20
I
ppm
0
FIG. 5. Edited proton-coupled “C NMR spectra, of the same sample as used in Fig. 4, obtained on a Varian XL300 spectrometer using the DEPT GL+ and SEMUT GL+(q) pulse sequences for the protonated and quaternary carbon spectra, respectively. The 7 delays have been adjusted according to Jmr. = 125 Hz and J,, = 185 Hz (3). The signals marked with an asterisk (* ) are caused by residual CHQ (1%) of the deuterated solvent. Note that the negative CHC& J cross-talk signals in the quatemary carbon subspectrum are suppressed in this case (cf. Fig. 3). The CH, spectrum is the 0 = 38” DEPT GL’ subexperiment.
ecules or mixtures of molecules with wide ‘JcH ranges we conclude that the “+purging scheme” and GL procedure are not merely cosmetics (4) for the standard pulse sequences. ACKNOWLEDGMENTS This research was supported by the Danish Natural Science Research Council (J. No. 5 1 I-15041 and 1 l3933). The use of the facilities at the University of Aarhus NMR Laboratory sponsored by the Danish Reseach Councils (SNF and STVF) and Carlsbergfondet is acknowledged. The support of a scholarstipend to UBS by Carlsbergfondet is also acknowledged. OWS thanks Professor R. R. Ernst for support and encouragement. REFERENCES 1. 2. 3. 4. 5.
H. D. 0. M. 0.
BILDS~E, S. D~NsTR~~, H. J. JAKOBSEN, AND 0. W. SORENSEN, J. Magn. Reson. 53, 154 (1983). T. PEoo, D. M. DODDRELL, AND M. R. BENDALL, .I. Chem. Phys. 77,2745 (1982). W. SC~RENSEN, S. D~NSTRUP, H. BILDS~E, AND H. J. JAKOBSEN, J. Magn. Reson. 55, 347 (1983). R. BENDALL AND D. T. F%GG, J. Mugn. Reson. 59,237 (1984). W. S&ENSEN, G. EICH, M. H. LEVITT, G. BODENHAUSEN, AND R. R. ERNST, in “Progress in
Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.) Vol. 16, p. 163, Pergamon, Oxford, 1983.
238
S0RENSEN
ET
AL.
6. 0. W. S&ENSEN, “Modem Pulse Techniques in Liquid State Nuclear Magnetic Resonance Spectroscopy”, ETH, Diss. No. 7658, 1984. 7. 0. W. S&ENSEN AND R. R. ERNST, J. Magn. Reson. 51,477 (1983). 8. G. A. MORRIS AND R. FREEMAN, J. Am. Chem. Sot. 101, 760 (1979). 9. D. P. BURIJM AND R. R. ERNST, J. Magn. Reson. 39, 163 (I 980). 10. S. L. PATT AND J. N. SHOOLERY, .I. Magn. Reson. 46,535 (1982). II. H. J. JAKOBSEN, 0. W. S&ENSEN, W. S. BREY, AND P. KANYHA, J. Magn. Reson. 48,328 (1982). 12. U. B. SORENSEN, H. BILDS~E, AND H. J. JAKOBSEN, J. Magn. Reson. 58, 5 17 (1984). 13. 0. W. S&ENSEN, J. Magn. Reson. 57,506 (1984). 14. S. D@NSTRUP, H. BILDSIZIE, AND H. J. JAKOBSEN, presented at the “7th European Experimental NMR Conference,” Altavilla Militia, Italy, May 1984. 15. G. BODENHAUSEN, R. FREEMAN, AND D. L. TURNER, .I. Magn. Reson. 27,51 I (1977). 16. M. H. LEVITT, J. Mugn. Reson. 48,234 (1982); 50,95 (1982). 17. D. I. HOULT AND R. E. RICHARDS, Proc. R. Sot. (London) Ser. A 344, 3 11 (1975). 18. R. RICHARZ, W. AMMANN, AND T. WIRTHLIN, “Varian Nuclear Magnetic Resonance Application Note: DEPT,” No. Z-15, August 1982.
Editing of Proton-Coupled13CNMR Spectra* ULLA
B. SORENSEN, HENRIK
BILDS~E,
AND HANS J. JAKOBSEN
Department of Chemistry, University of Aarhus, 8000 Aarhus C, Denmark AND OLE W. SORENSEN Laboratorium fiir Physikalische Chemie, Eidgeniissische Technische Hochschule, 8092 Zurich, Switzerland Received March 26, 1985 Editing of proton-coupled 13CNMR spectra into independent subspectra depending on the number of attached protons is analyzed using the product operator formalism. Pulse sequences which have proven successful for editing of decoupled spectra are shown to be unsuitable for editing in the coupled mode. This is because of poor editing accuracy and because various types of distortions appear in the edited subspectra. These problems are shown, both theoretically and experimentally, to be remedied by two new pulse sequences, SEMUT GL+ and DEPT GLf. 0 1985 Academic press, hc.
Simplification of complex NMR spectra through the application of multipulse experiments has become an indispensable aid in structural elucidation and in assignment of NMR parameters. A variety of one- and two-dimensional NMR pulse sequences has been proposed for this purpose in recent years. Among these, i3C spectral editing constitutes a particular useful method in that it allows decomposition of conventional 13C NMR spectra into four subspectra according to the number of directly attached protons (C, CH, CH2, and CH3). Edited proton-decoupled subspectra can be obtained with an acceptable accuracy using the SEMUT (1) and DEPT (2) pulse sequences provided the range of ‘J-n values is small (i.e., within 10% from the ‘JcH used in tuning the delays) (1). For molecules with large spreads in ‘JcH values often encountered in organic molecules (120 < ‘JcH < 220 Hz), the GL procedure must be incorporated (i.e., yielding SEMUT GL and DEPT CL (3)) to suppress J cross-talk between subspectra. In this paper we evaluate the application of spectral editing techniques for protoncoupled 13C spectra. The purpose of editing coupled 13C spectra is not to determine proton multiplicities, but rather to obtain spectrum simplification. When a 13C spectrum is acquired without proton decoupling, there can be an enormous increase in the number of resonances and the standard spectrum is often too crowded to interpret. Editing into four subspectra is therefore useful for the measurement of 13C-‘H coupling constants. * Presented
in part at the “7th EENC,” Ahavilla Militia, Italy, May 1984.
0022-2364185 $3.00 Copyright 0 1985 by Academic Press, Inc. All rights of reproduction in any form reserved.
222
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
223
The usual pulse sequences for editing decoupled 13C spectra cannot be directly adapted to coupled spectra by simply acquiring the FIDs without proton decoupling. This is because the decoupling removes antiphase product operators which distort the spectral phases and, in contrast to a recent statement by Bendall and Pegg (4), seriously influence the editing accuracy. Therefore the pulse sequences must be extended to include purging techniques. PURGING
TECHNIQUES
FOR ELIMINATION
OF SPECTRAL
DISTORTIONS
A spectrum is defined as distorted if it is impossible to phase all lines to positive absorption, or if the relative line intensities within multiplets deviate from those encountered in a simple 90”-acquisition experiment. In proton-coupled 13CNMR spectra (I$$ spin systems with I = ‘H, and S = 13C)an undistorted 13Cmultiplet is represented by the S, (or S,) operator in the product operator formalism (5, 6). When the 13C chemical shifts are refocused, the spectral distortions are caused by antiphase product operators (e.g., 21i,S,, 411Zl&$, * . . ) (7). Those containing an odd number of 1, operators produce dispersive contributions to the spectrum and have been named phase-anomaly terms (7). The product operators with even numbers of 1, operators have been named multiplet-anomaly terms (7) because they do not disturb the phasing of the spectrum, but only the relative line intensities. Techniques for purging phase and multiplet distortions in coupled 13C spectra, obtained via the polarization transfer methods of DEPT and refocused INEPT (8, 9) were introduced in Ref. (7). One purging scheme applies a proton 180” pulse at the start of acquisition in alternate scans. When introduced into DEPT, i.e., DEPT+ (7), coupled spectra free of phase distortions are obtained because the phase-anomaly terms appear with opposite sign in every second scan. The multiplet distortions, on the other hand, are invariant to this purging method. A second purging scheme (7) inserts a 90” proton pulse immediately prior to acquisition in all scans in order to eliminate both phase and multiplet distortions irrespective of the spread in one-bond or in long-range 13C-‘H couplings. For example a 90” purging pulse can be added to APT (10, II) (using the proton flip version as for example shown in Fig. 1 of Ref. (1 I)) and refocused INEPT to give APT+ and INEPT+ (7) which both yield distortionless coupled spectra. If heteronuclear multiple quantum coherence (MQC) is present, careful attention must be given to the refocusing of ‘H chemical shifts before inserting the 90” purging pulse into a pulse sequence. Thus, for DEPT this “++ purging scheme” requires an additional T period and extra pulses to give DEPT++ (7) or the equivalent condensed pulse sequence, MQDEPT (1.2). The two purging methods discussed can similarly be incorporated into SEMUT resulting in the SEMUT+ and SEMUT++ pulse sequences, also providing coupled spectra free of phase distortions. In SEMUT GL and DEPT GL the heteronuclear multiple-quantum coherences present after the 0 pulse are “stored” along both orthogonal directions in the rotating frame (e.g., 41&.& and 41rJzJJ and a 90” purging pulse would inevitably convert part of this back to antiphase magnetization. Therefore, only the simple “+ purging scheme” with a 180” pulse in every second experiment is applicable for the GL pulse sequences designed to suppress J cross-talk. As mentioned above, this only eliminates the phase anomalies but we should note that the multiplet distortions are unimportant
224
SBRENSEN
ET
AL.
for practical applications because they in no way disturb the measurements of coupling constants. As shall be shown in the next section, the purging is also essential for the suppression of antiphase J cross-talk signals. The new pulse sequences SEMUT GL+ and DEPT GL+ for editing coupled r3C spectra are outlined in Fig. 1. Because the proton 180” purging pulse must be applied at the very start of data acquisition, these sequences employ “delayed coupling” (7r < r3) instead of “delayed acquisition” (7r > r3) as used in the sequences for editing of decoupled spectra (3). From the general analysis of S/N (signal-to-noise ratio) in SEMUT GL and DEPT GL subspectral editing (13) it is clear that the best sensitivity for editing coupled spectra is achieved by using DEPT GL+ to edit CH, CH2, and CH3 resonances and SEMUT GL+ with 8 = 90” to generate the quaternary carbon subspectrum. For the latter sequence the two successive pulses 90,“90,” may be replaced by a single 90; pulse; thus the special quatemary carbon sequence SEMUT GL+(q), shown in Fig. lc, may be used for this experiment.
'H
a 13c
b
90: 13C
, I
-h
1808 t3
- t1
, I
tj+
2
62 ‘c2 7
+ x3
61
'H
C
t3
-h
180' i-; ' '-
90; 13C
t2
l-l
?
+ z3
T2
7
+ t3 b
ELG. 1. Pulse sequences SEMUT GL* (a), DEPT GL+ (b), and SEMUT GL+(q) (c) for editing of protoncoupled “C NMR spectra. The phase-cycling scheme (see experimental section) for the purging sandwich and 8 proton pulses is shown in Table 4. Two series of experiments are coadded, one with the proton 180” pulse prior to acquisition and one without this pulse.
EDITING ANALYSIS
OF PROTON-COUPLED
OF COUPLED
SEMUT
225
CARBON- 13 SPECTRA GL AND DEPT GL SPECTRA
Analysis of pulse sequences based on the product operator formalism (5) allows a convenient step-by-step calculation of the density operator. Although straightforward, product-operator calculations for large systems can be extremely paper- and time-consuming when all transformations are carried out in sequential order and all terms retained throughout. Therefore, a computer programme, SEQUENCE (Z4), which calculates the result of an arbitrary pulse sequence based on product operators, was introduced recently. Another approach (6) exploits the high symmetry of Z,S spin systems to factor the density operator evolutions in a convenient way. The result is that once the response of an ZS spin system is known, it can easily be generalized to Z,S spin systems. This considerably speeds up calculations and also provides better insight into the “mechanism” of the pulse sequences. This procedure is illustrated below for the SEMUT GL and DEPT GL sequences without proton decoupling. For the SEMUT GL sequence (Fig. la) the series of transformations from the point immediately after the 13C 90” pulse, 0, to the end of the delay 73 immediately before the dotted T pulse, point 0, is written as
C uJ(rz/2)2I,zSz -v--u2
z: ; Iti
2 SI,
2 ?rJ732I,S, 111
where the summations are for all Z spins (i = 1, 2, . . . , n). The phase of the first ‘H 90” pulse of the purging sandwich has been set to x and the phase Cpof the 180” refocusing pulse is x. In Eq. [ 1] all chemical-shift evolutions have been neglected because (a) S-spin chemical shifts are refocused, (b) Z-spin chemical-shift evolution during 72 is refocused, (c) chemical-shift evolution is active only for transverse operators (I,, Z,) which are not present for the Z spin during TV, and (d) such terms present during r3 in the forms of MQC’s or Z-spin single-quantum coherence do not influence observable S-spin magnetization. In density operator calculations, refocusing pulses can always be thought of as if they were “applied” at the beginning of the respective free precession periods (5, 6). Therefore the 180,“(S) pulse can be moved in front of all other transformations by changing the signs of all preceding transformations containing S, and has the simple effect of converting -S, into S,. Likewise the TZ, pulse can be moved to the beginning of the 72 delay and condensed with the (r/2)1, pulse. Finally, since operators of different spins commute the transformation of Eq. [ 11 can be rewritten as 7 (-rJr,ZI&
- ; Ii, ?rJr22I&
@I =s,--
-
; Iti 0I,
~J7,21&}
--
-
02.
PI
This implies that for the SEMUT GL sequence the overall transformation for an Z,,S spin system can be decomposed into n identical propagators Ps, one for each Z spin, and represented by the terms within the brackets of Eq. [2]. From this we obtain the recurrence formula PSk
az(L,S)
-
~2UkS)
where Psk is the propagator with respect to the ZcthZ spin.
I31
226
S0RENSEN
ET AL.
For an IS spin system, the following two relevant transformations for the SEMUT GL sequence may easily be derived using Eq. [2] (only observable terms are included) PSI WI 8, -
+
(clc2c3
where ck, Sk= cos(rJTk), sin(r&)
Thus, the transformations
-
hs3d&
(cIc2s3
-
WI
W3d2~dx
and co, se = cos 19,sin 19.To save space we abbreviate A =
ClC2C3 +
SIS~C~
PaI
B =
~1~2~3
slC3Ce.
[W
-
[4a] and [4b] become PSI
S, - AS, + B21,&,
bl
PSI
S,, -+ AS, - B2I,&
WI
which are of form similar to the basic equations for J-coupling evolution, (e.g., Eqs. [ 171 and [ 181 in Ref. (5)). The reverse transformations (analogues of the transformations describing refocusing of antiphase magnetization, Eqs. [ 191 and [20] in Ref. (5)) have coefficients different from A and B. However, only [6a] and [6b] are of interest in the present context and the density operator for an IS system at point 0 may be written ~~~(1s)= AS, - B2Z,,S,. [71 The transformation and [71)
for an 12Sspin system now takes the form (using [3], [6al, [6bl,
AS,, - B2I,&
2 A(AS,, - B212&)
- B2I,,(AS,
+ B21,&)
i.e., a2(12S) = A2S,, - AB2(Z1, + 12dSx - B24~ddy.
PI
Before we derive the response of an I,S system, it is convenient to introduce a number of operator abbreviations: F; = E;
FJ = 5 Ii,;
FZ = i Ii,Ij,;
i=l
Fz =
c
Iiz4jzlkz, etc.
i
iJ
and s-, = -s,;
s-, = -s,.
The operator F$’ is the sum of the 6) different products of p I, operators in I,$ groups, where n = ii?! (n - p)!p! * 0P Due to the equivalence of Eq. [ 31 to a cascade of J couplings it is easy to determine the coefficient of the general product operator 2*F$Sti+p,2j: Starting from u1 = S,, p of the couplings must dephase (meaning introduction of IJ yielding a factor BP, and the remaining (n - p) couplings must not cause dephasing yielding a factor A”-*. The
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
227
(;) combinations, which fulfil this requirement, reflect the number of products in F$‘, and we may write the coefficient and the operator
PI
A”-PBP2PFPS 2 cy+prrm*
It follows that the response for an I,S spin system undergoing the SEMUT GL sequence without proton decoupling is a&S)
= i A”-PBP2PF$!3y+m,2j. p=o
1101
For the case I = ‘H, S = 13C (1,s systems with IZ = 0, 1,2, and 3) only the first four terms of the summation in Eq. [lo] need consideration. For clarity these four terms have been written out in the usual nomenclature of product operators in Table 1. For the decoupled SEMUT GL pulse sequence only the first term in the summation of Eq. [9] is retained (3). TABLE 1 Intensity Expressions Based on the Product Operator Formalism for the Response of a General Z,,SSpin System Subjected to SEMUT GL and DEPT GL without Z-Spin (‘H) Decoupling” SEMUT GL z,s: (C&S, - s,c3c&“(c~c*c3+ s,s&s,
DEPT GL ZJ: ns,s3s,(c,c*s3 +
- s,c,c~)o(c*c2c3+ -
[-s‘c3s~c~c~s3
+ (n -
+
s,c3&c,c~c3
1)S,S3S&,C2S3
-
s,s3ce~-‘Sx s,s,c,)“-’
S,C&&CzC~
+ S,S3C&-‘]2
i zils, i=l
+ [2s,c3s.&,c2s3- slc3ce)‘(c1qc3 t sls3c,)“-2 - (Tl +
2)S,S3S,(C&S3
[3s,c3s&,czs3
- (Tl -
-
-
SIC~C,)~(C&#~
+
s,c3c,y(c,c*c3
3)S$S3S@(ClC#3
-
+
S,S&)“-‘]4i
i
z&&
s*s3c,)“-3
SlC3C#)3(ClC$3
+
S,S3C~)“4]8
i
ZizZjzZhSy
kjck +
.
a Abbreviations: ci = cos(r.Z~J, si = sin(7FJ73, c, = cos 0 and se = sin 8.
228
S0RENSEN
ET
AL.
For the coupled DEPT GL sequence (Fig. lb) it is noted that, because of the modification (TV> or) required as compared to normal decoupled DEPT GL (3), an interval (r3 - 7,) has been inserted between the 90,“(S) pulse and point 0. With this interval centered around the 180,“(I) pulse, it ensures S-spin chemical shift refocusing at the point of data acquisition and also suppresses JIs coupling during r3 - 71 . The calculation of the response of an I,$ system to a polarization transfer pulse sequence can be simplified by noting that each of the y1equivalent I spins gives rise to the same amount of polarization transfer to the S spin. Therefore, the transfer from one of them, say I,, can be calculated and the total result obtained by multiplication by a factor n. We introduce a propagator PO, = PD1(rl, 72, 73, 0) which denotes the complete set of transformations affecting only II and S in an I,S system for the pulse sequence in Fig. l(b). Using standard product operator theory, the following transformation can easily be derived (we show only observable terms): PDI I,, - S~S3S& - s,c+s~21&l. [Ill Because there are no interactions between the protons, the remaining y1- 1 protons first influence the magnetization arising from II after the 90,“(S) pulse, i.e., they undergo a SEMUT CL pulse sequence in this case. Therefore, the fate of the magnetization starting on II may be derived from the series of transformations: Pm Ps2 P,
I lz--+3+...-...--+*
PSi
PSI
WI
The total response of an I,S system is obtained by summing the results of the series of y1transformations of the type [ 121. This may formally be written
[I31 Using the abbreviations, c =
WI [14bl
SIS3S9
D = sIc3s8 for the coefficients in the result of the PO, transformation a2(lS) for an IS system is given by u&Y) = I,, 2 C’s, - D2I&,
[ 111, the density operator
= u2(Is).
[I51
For an I$ system the transformation of I,, and IzZ into the two separate terms a$(12S) and &12S) yields the following results (using [ 151 and [6a, b]) u;(12S) = C(AS, + B212,Sy) - D2I,,(AS,
- B212&)
[164
a$(Z2S) = C(AS, + B2Id,)
- B2Z&)
116bl
- D2I&AS,,
and the total response a2 = CT:+ as for an I$ spin system may be written a2(12S) = 2ACS, + (BC - AD)2FfS,, + 2BD4F;Sp
[I71
Again we derive the general response by calculating the coefficient of the product operator 2pF$S~x+m~2~.With reference to ~7~in Eq. [ 151, where all transformations
EDITING
OF
PROTON-COUPLED
CARBON-l
229
3 SPECTRA
involving I, have been carried out, the first term (CS,) requires dephasing with respect to p of the remaining (n - 1) I spins and thus introduces a factor of BP. The remaining (n - p - 1) 1 spins must not cause dephasing thereby contributing a factor of ARep-‘. The p I spins can be taken as (” ; I) combinations. Because each of the n I spins contribute the same amount, we obtain a total of n X (” ; l) terms. F$ contains (;) of these terms, leaving a resulting factor of (n - a). Thus, the total contribution from the first term in [ 151 amounts to (n - p) X CAnPpPIBp. The second term in the transformation [ 151 already contains one 1, operator. Introducing the remaining (p - 1) 1, operators gives a factor BP-’ and the remaining (n - p) I spins contribute a factor of AneP. This represents (; I f ) different terms. Polarization is transferred from each of the n I spins giving a total of y1X (; I 1) terms. Taking the G) terms in F{ into account we obtain a resulting numerical factor p. Hence the total contribution from the second term in ~2 of Eq. [ 151 is given by -pDA”dPBP-l. In conclusion the term containing p 1, operators gives a response proportional to -pDAnPPBP-’ + (n - p)CAnPP-‘BP.
[I81
The general response for DEPT GL without proton decoupling can now be written in the condensed form c2(I,J) = c { -PDA”-~B~-’
+ (n - p)CA”-P-‘BP}2pF$5’cx+m,2j.
p=o
[I91
Equation [ 191 has been written out explicitly for the cases relevant to 13C NMR in Table 1. Finally, incorporation of the “+ purging scheme” into the SEMUT GL and DEPT GL pulse sequences, i.e., a proton 180” pulse applied at the start of acquisition in every second experiment, eliminates product operators containing odd numbers of 1, operators. Therefore, in discussions of SEMUT GL+ and DEPT GL+ to the cases relevant for editing of coupled 13C NMR spectra (i.e., n < 3) only terms with zero and two I, operators need consideration. J CROSS-TALK
IN
SUBSPECTRAL
EDITING
OF
COUPLED
“C
SPECTRA
For the ideal conditions 71 = r2 = 73 = (25)-l (i.e., cl = c;! = c3 = 0 and s1 = s3 = 1) the general intensity expressions for SEMUT GL and DEPT GL (Table 1 or Eqs. [ lo] and [ 191) reduce to SEMUT GL: az(Z,S) = c& DEPT GL: f12(1$$) = ns&‘S,
[201 PII
i.e., the intensities for the S-spin NMR signals in an I,$ spin system are proportional to cos”B and n sin 0 COS”~‘6’for SEMUT GL and DEPT GL, respectively. Thus, for both sequences proper linear combinations of spectra obtained with different B flip angles allow a separation of the NMR resonances into subspectra according to the number of I spins (subspectral editing (1-3, 13). In practical applications the non-
230
S0RENSEN
ET
AL,
ideal conditions pi f (2J)-’ prevail and COS(rJTi) f 0 in Table 1 and Eqs. [lo] and [ 191. Thus part of the responses of the in-phase and antiphase terms for a coupled I,S group will be proportional to cos’? for SEMUT GL and sin 19cos”-‘0 for DEPT GL. These contributions from the I,S spin system mimic the behaviour of an Z,S group and give rise to unwanted “spurious” resonances in the I,,$’ subspectrum. This phenomenon has been dubbed J cross-talk and analyzed for decoupled SEMUT/DEPT (1) and SEMUT GL/DEPT GL (3). With proton (I-spin) decoupling, only the inphase terms contribute and Jcross-talk for SEMUT (GL) and DEPT (GL) is identical (I, 3) and can only take place in the “downward direction” (m < n); e.g., from CH3 to CHp but not from CH2 to CH3. It has been demonstrated that the GL procedure effectively suppresses J cross-talk in editing of decoupled 13C spectra (3). In the coupled mode serious cross-talk contributions from the antiphase terms similarly occur in the “downward direction.” In addition, for an I,$ system antiphase terms with proper flip angle factors co03 for SEMUT (GL) and sin 0 co?‘0 for DEPT(GL) may give severe distortions of the genuine multiplets. Application of the 180” purging pulse suppresses this J cross-talk and phase anomalies in editing of coupled spectra quite effectively (vide infra) . In the following we derive explicit general expressions for the Jcross-talk in coupled SEMUT GL and DEPT GL spectra. It is instructive to define the Jcross-talk intensity from an I,$’ spin system to the 1,s subspectrum relative to the ideal response of the I,$ group (7i = 72 = 73 = (2J)-‘). From the general intensity expressions (Table 1 or Eqs. [lo] and [ 191) it follows that the J cross-talk (I,$ - I,$?) for the in-phase terms is the same as for the decoupled case and identical for SEMUT GL and DEPT GL (3), i.e.,
t221 The general J cross-talk expressions (Ins + 1,s) for coupled SEMUT GL and DEPT GL are easily calculated from the general intensity expressions (cf. Table 1) as the coefficients of cosV and m sin 0 cos”-’ 13,respectively. Rearrangement of the expressions for SEMUT GL in Table 1 and collecting terms proportional to COSY gives for the J cross-talk intensity in coupled SEMUT GL(I,S - Z,S):
-K +
;
>(c1c2~3)2(-%c3)o clc2s3)L(-sIc3)’
(C~C*C3)n-m-2(S1S3)m
(C,C2C3)n-m-1(S1S3)m-1
“-m(s,s3)“2]4F~Sy
+ - - -}
[23]
EDITING
OF PROTON-COUPLED
CARBON- 13 SPECTRA
231
In a general condensed form this becomes: (c,c#‘-~c;-~-~+~~s~s~+~-~~(-
1
l)k 2pF~S~,+p,,2, . [24]
The summation over k extends only for values k i m and k >, m + p - n. In a similar way the intensity expression for the coupled DEPT GL (cf. Table 1 and Eq. [ 191) sequence may be rearranged. The general condensed form for the terms involving m sin 0 cos*-‘0 in coupled DEPT GL, which are proportional to the J crosstalk intensity, is given by:
mw8-‘i,;
[j.
(; ~~)~)(C’,)“-mc;-m-p+2k~~~~+p-2k~
(-I)k]2pF,,+m,2~}
[25]
with k < m and k 2 m + p - n. Comparison of Eqs. [24] and [25] shows that the J cross-talk signals are identical for all terms in coupled SEMUT GL and DEPT GL. For clarity the rearrangements of the expressions in Table 1 represented by the Eqs. [24] and [25] are written in an explicit form in Table 2 for I,,S spin systems relevant for editing coupled 13C spectra (n < 3). Only the terms appropriate for the SEMUT GLf and DEPT GLf sequences, i.e., terms containing an even number (zero and two) of 1, operators, are given. TABLE 2 SEMUT GL+ and DEPT GL’ Responses of Coupled CH, Group&
c:
xos,
CH:
~0~1~2~3~y
a For SEMUT GL+, x,,, = cos”8 and for DEPT GL+, x, = m sin 6’ cos”% For other abbreviations see Table 1. b Without practical consequences the DEPT GLC responses have been phase shifted by 90”.
232
SILIRENSEN ET AL.
For a comparison of experimental results (vide infra) obtained from the ordinary SEMUT and DEPT pulse sequences with those of their GL+ versions, Table 3 contains explicit SEMUT and DEPT responses of I,Sgroups with n i 3. Here the substitutions sI = s3 = s = sin ~JT, cl = c3 = c = cos rJr, and c2 = 1 have been introduced and all antiphase terms retained. EXPERIMENTAL
13C NMR experiments were performed on a Varian XL-300 spectrometer (10 mm probe) at 75.45 MHz with appropriate programming of the pulse sequence codes and phase cycling schemes for the DEPT GL+, SEMUT GL+(q), DEPT, and SEMUT sequences. The editing of coupled r3C spectra was achieved using DEPT GL+ for generating the separate subspectra for the CH, CH2, and CH3 resonances and SEMUT GL+(q) to obtain the quaternary carbon subspectrum. For an experimental demonstration of the advantages achieved using the GLf purging scheme similar subspectra were also generated using ordinary DEPT and SEMUT. The delays 71, 72, and ~(7, < rs), generated within the sequence codes for the GL+ versions, were calculated
TABLE 3 Ordinary SEMUT and DEPT Responses of Coupled Responses for CH ” Groupsngb c:
x&’
CH2:
xo[&%, + x,[cs(2csS, + x,[s*(s*s,
CH3:
- cs2(Z,, + I,,)& - s24Z,,Z&)] - (2s'
- 1)2(11,+
Z&T,
+ cs2(Z,,
+ Z,,)S,
- c*4z,,z&l
x,,[c3(c3SY- c’sZ(Z,, + Zzz+ -
cs24tZ1zZ2z
+ x,[c*s(3cw,
+
Z1zZ3z
+ x3[s3(s3Sy
+ I,J3z
+ (3c2s - s)2(Z,,
+ (3cs2 - c)4(Z,zZ,, + cs22(Z,,
Z,,)S,
+ s38Z,U3zU
Z,r,z)s,
- (3csZ - c)2(Z,,
+ (3~~s - s)4(Z&r + x,[cf~(3cs?$'
+
+ 2cs4Z,,Z&)J
+ Z& + z3&Y, + ZzJ3r)sy
- ~c~~%M~&~I
+ z, f Z33&
+ Z,zZ32 + IzX3Sy
+ 3c*~~~,zl,zl,z&~1
+ z-2, + Z,,)S,
- c2MZA + ZlzZ3r + Zd&% - c~~ZI~Z~~Z&)I n For SEMUT, x,,, = cos”l and for DEPT, x, = m sin 19cos”-‘8. c = cos(?rJT) and s = sin(?rk). b Without practical consequences the DEPT responses have ken phase shifted by 90”.
EDITING
OF PROTON-COUPLED
CARBON- I3 SPECTRA
233
according to the J range to be covered (Jmin < J < Jmax) as described elsewhere (3). The single 7 delay applied for DEPT and SEMUT was taken from the mean of the J range, T = (2J,,,,)-‘, for the sample under study. For the DEPT GLf proton pulses the 16 step phase cycling scheme, shown in Table 4 for the purging sandwich and fl pulses, was supplemented by independent exorcycling (15) of the first 180” ‘H pulse giving a total of 64 steps. The 180” ‘H purging pulse was a 90,” 180; 90,” composite pulse (16). The 180” 13Cpulse was phase cycled according to EXORCYCLE (15) and finally the 90” and 180 a 13C pulses were taken through a CYCLOPS cycling (17). The phase cycling scheme for SEMUT GL+(q) is similar to the one described earlier for SEMUT GL (3). For ordinary DEPT and SEMUT the pulses were run through a scheme equivalent to their GL versions. For the DEPT GL’/DEPT experiments the optimum 0 flip angle values (0 = 38, 90, and 142”) and 7 = 1 (13) were applied. However, the DEPT GL’ experiment corresponding to 0 = 142” was obtained employing 0 = 38” and a simultaneous 180” phase shift between the two 90” ‘H pulses of the purging sandwich (3). This minimizes the effect of rf inhomogeneity on the 0 pulse. The CH, CHZ, and CH3 subspectrum generation was fully automated using a least-squares analysis (program ADEPT (18)). Alternatively, the mixing coefficients for the different subexperiments may be entered manually using a program MANDEP implemented on the XL-300 computer system. RESULTS
AND DISCUSSION
The various aspects of the GL+ and standard DEPT/SEMUT schemes for editing of coupled 13C spectra are clearly apparent from the spectra in Figs. 2-5. To illustrate the effect of GLf editing of a complex spectrum, Fig. 2 shows the result for a sample of cholesterol (a molecule with a moderate spread in ‘JCH couplings) obtained with ordinary SEMUT and DEPT. Figure 3 shows the corresponding edited spectra obtained TABLE 4 16-Step Phase-Cycling Scheme Applied for the Proton Purging Sandwich and 0 Pulses in DEPT GL+” 90” X
+X
X
*Y tx +Y
-x -X
-X -X
180”
X
‘tX
X
+Y fX *Y
90” X -X --x X X -X -X X
0 Y -Y Y -Y -Y Y -Y Y
’ For the experiments with 0 > 90” one of the 90” pulses is phase shifted by 180” throughout. The phase cycling of the proton pulses was supplemented by independent EXORCYCLING (15) of the first 180” ‘H pulse in DEPT GL+.
234
I
S0RENSEN
I
140
ET AL.
,
120
80
100
I
60
40
20
ppm
0
FIG. 2. Edited proton-coupled 13C NMR spectra of cholesterol (0.015 M in CDC13) obtained using the standard DEPT and SEMUT sequences for the protonated and quaternary carbon spectra, respectively. The delay 7 has been optimized corresponding to an average value of ‘.Icu = 135 Hz. The CH, spectrum, which contains ah protonated carbons, is the 0 = 38” DEPT subexperiment.
CH3
CH2
CH .-” C
A. ,
140
/
I
120
I
/
100
I
I
80
I
60
40
,
I
20
I
ppm
1
0
FIG. 3. Edited proton-coupled 13CNMR spectra of cholesterol (0.015 Min CDC13) obtained on a Varian XL-300 spectrometer using the DEPT GL+ and SEMUT GL+(q) pulse sequences for the protonated and quatemary carbon spectra, respectively. The 7 delays have been adjusted according to Jmi. = 125 Hz and J = 160 Hz (3). The signals marked with an asterisk (*) are caused by residual CHCI, (1%) of the dE$eratcd solvent. The CHCI, molecules cause J cross-talk signals (negative, cf. Table 2) in the quatemary carbon subspectrum, because ‘JcH (=2 13 Hz) is outside the optimized J range. The CH. spectrum is the 8 = 38” DEPT GL+ s&experiment.
EDITING
OF
PROTON-COUPLED
CARBON-
13 SPECTRA
235
using the GL+ sequences. In Figs. 4 and 5 the same set of experiments has been performed on a mixture of two molecules (menthol and 3-methylpyridine) which have a spread in ‘Jon from 125 to 185 Hz. The spectra clearly demonstrates the necessity of using the CL’ pulse sequences for editing of coupled spectra with wide ‘Jcn ranges. The severe distortions and J cross-talk resonances observed (especially in the Fig. 4 subspectra) for the standard SEMUT/DEPT editing experiments are easily accounted for theoretically using the intensity expressions in Table 3. From these expressions it is seen that the dominating distortions in all SEMUT/DEPT edited subspectra arise from the p = 1 antiphase terms (i.e., product operators involving one Z, operator, 2 Cy==,Zi,s,) because the coefficients for these terms contain only one cos(rJr) factor. Thus, two types of serious anomalies (both purged using the GL+ sequences) may occur for SEMUT/DEPT edited spectra: (1) Phase distortions of the genuine signals themselves from the dispersion mode p = 1 antiphase term, and (2) J cross-talk of dispersion mode antiphase contributions from CH, multiplets to the CH,-i subspectrum. Distortions of the first type (phase anomalies within the genuine multiplets) are clearly observed for the spectra in Fig. 4 but also for the doublet at lowest shielding in the cholesterol spectrum (Fig. 2). Under the experimental conditions used for the Fig. 4 spectra these distortions result from a mixing of up to 25% of the intensity originating from antiphase dispersion mode terms. For example, inspection of the CH3 subspectrum (Fig. 4) shows that phase anomalies may prevent accurate measurement of 13C-‘H coupling constants. The second type of serious distortions in edited SEMUT/DEPT coupled spectra (i.e., Jcross-talk of antiphase dispersion-mode CH, multiplets into CH,-i subspectra) occur, as for all other J cross-talk terms and for the decoupled case, only in a “downward” direction (Table 3). These distortions are also clearly apparent in the Fig. 4 spectra. For samples \;ith wide ‘JcH ranges and heavily overlapping coupled multiplets, the J cross-talk of dispersion mode multiplets may mask genuine multiplets. This is illustrated in the Fig. 4 CH2 subspectrum, where the CH2 triplet at highest shielding is severely distorted by J cross-talk from the CH, spectrum and appears more like a “doublet.” In addition the usual in-phase (S,,) Jcross-talk observed in SEMUT/DEPT editing (I) also seriously contributes to the distortions observed in Fig. 4. As shown earlier (I) the S, J cross-talk has its largest contribution from CHs groups to the CH2 subspectrum (3 c2s4S, term) for a given AJ deviation in setting the T delay. For the experimental conditions in Fig. 4 the cross-talk from in-phase CHs magnetization is of the order of 20% while the three CH3 antiphase J cross-talk terms contribute from 5 to 25% (increasing percentage with decreasing numberp ofZz operators). The extensive downward J cross-talk distortions observed experimentally in edited SEMUT/DEPT CH and C subspectra (Fig. 4) are similarly dominated by antiphase dispersion mode terms from CH2 and CH multiplets, respectively (Table 3). Finally, it should be noted that the sign change observed for all antiphase dispersion mode terms with only one cos(a’JcH7) factor, depending upon ‘JCH < Jo -c ‘J&T = (~Jo))‘), is clearly reflected in the Fig. 4 spectra. Compare, for example, the CH dispersion mode cross-talk resonances in the C subspectrum at high and low shielding. The problems discussed above and associated with SEMUT/DEPT editing ofcoupled i3C spectra are absent when the SEMUT GL+(q)/DEPT GL+ pulse sequences are
236
WRENSEN
ET AL.
CHn
CH3 CH2
CH
I
I
I
I
I
I
140
120
100
80
60
40
I 20
ppm
0
FIG. 4. Edited proton-coupled 13CNMR spectra of a mixture of menthol (0.025 M) and 3-methylpyridine (0.030 M) in CDCI, obtained on a Varian XL-300 spectrometer using the standard DEPT and SEMUT sequences for the protonated and quatemary carbon spectra, respectively. The r delay has been optimized corresponding to an average value of ‘J cH = I55 Hz. Note the enormous J cross-talk signals and also the illustration of the fact that J cross-talk only takes place in the “downward direction.” The CH, spectrum is the 19= 38” DEPT subexperiment.
applied. The reason is that the GL+ editing procedure purges the antiphase terms with odd numbers (a = 1 and 3) of I, operators and introduces an additional cosine factor, cos(~I~~), into all J cross-talk terms. Thus, these sequences yield edited spectra free of phase anomalies and with negligible multiplet distortions arising from product operators containing two I, operators (p = 2). The effects of the GL+ procedure in cleaning edited coupled 13Cspectra are nicely illustrated experimentally by the spectra in Figs. 3 and 5. CONCLUSION
A factoring procedure for the density operator evolutions has been proven to be very useful in the analysis of coupled SEMUT/SEMUT GL and DEPT/DEPT GL spectra. Theoretical and experimental results prove that spectral editing of coupled 13C spectra em p lo y’m g the standard SEMUT/DEPT pulse sequences may be accompanied by severe distortions of the observed subspectra. Thus, for simplification of complex coupled 13Cspectra we suggest the DEPT GL+ and SEMUT GL+(q) sequences for editing coupled 13C spectra of protonated and quaternary carbons, respectively. The experimental results and analysis of J cross-talk show that the GLf procedure purges all phase anomalies and suppresses J cross-talk between subspectra. For mol-
EDITING
OF PROTON-COUPLED
CARBON-l 3 SPECTRA
237
** I QcH:CH3Q-[3 OH
3 CH2
C I
/
I
140
120
100
/
80
/
I
1
60
LO
20
I
ppm
0
FIG. 5. Edited proton-coupled “C NMR spectra, of the same sample as used in Fig. 4, obtained on a Varian XL300 spectrometer using the DEPT GL+ and SEMUT GL+(q) pulse sequences for the protonated and quaternary carbon spectra, respectively. The 7 delays have been adjusted according to Jmr. = 125 Hz and J,, = 185 Hz (3). The signals marked with an asterisk (* ) are caused by residual CHQ (1%) of the deuterated solvent. Note that the negative CHC& J cross-talk signals in the quatemary carbon subspectrum are suppressed in this case (cf. Fig. 3). The CH, spectrum is the 0 = 38” DEPT GL’ subexperiment.
ecules or mixtures of molecules with wide ‘JcH ranges we conclude that the “+purging scheme” and GL procedure are not merely cosmetics (4) for the standard pulse sequences. ACKNOWLEDGMENTS This research was supported by the Danish Natural Science Research Council (J. No. 5 1 I-15041 and 1 l3933). The use of the facilities at the University of Aarhus NMR Laboratory sponsored by the Danish Reseach Councils (SNF and STVF) and Carlsbergfondet is acknowledged. The support of a scholarstipend to UBS by Carlsbergfondet is also acknowledged. OWS thanks Professor R. R. Ernst for support and encouragement. REFERENCES 1. 2. 3. 4. 5.
H. D. 0. M. 0.
BILDS~E, S. D~NsTR~~, H. J. JAKOBSEN, AND 0. W. SORENSEN, J. Magn. Reson. 53, 154 (1983). T. PEoo, D. M. DODDRELL, AND M. R. BENDALL, .I. Chem. Phys. 77,2745 (1982). W. SC~RENSEN, S. D~NSTRUP, H. BILDS~E, AND H. J. JAKOBSEN, J. Magn. Reson. 55, 347 (1983). R. BENDALL AND D. T. F%GG, J. Mugn. Reson. 59,237 (1984). W. S&ENSEN, G. EICH, M. H. LEVITT, G. BODENHAUSEN, AND R. R. ERNST, in “Progress in
Nuclear Magnetic Resonance Spectroscopy” (J. W. Emsley, J. Feeney, and L. H. Sutcliffe, Eds.) Vol. 16, p. 163, Pergamon, Oxford, 1983.
238
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ET
AL.
6. 0. W. S&ENSEN, “Modem Pulse Techniques in Liquid State Nuclear Magnetic Resonance Spectroscopy”, ETH, Diss. No. 7658, 1984. 7. 0. W. S&ENSEN AND R. R. ERNST, J. Magn. Reson. 51,477 (1983). 8. G. A. MORRIS AND R. FREEMAN, J. Am. Chem. Sot. 101, 760 (1979). 9. D. P. BURIJM AND R. R. ERNST, J. Magn. Reson. 39, 163 (I 980). 10. S. L. PATT AND J. N. SHOOLERY, .I. Magn. Reson. 46,535 (1982). II. H. J. JAKOBSEN, 0. W. S&ENSEN, W. S. BREY, AND P. KANYHA, J. Magn. Reson. 48,328 (1982). 12. U. B. SORENSEN, H. BILDS~E, AND H. J. JAKOBSEN, J. Magn. Reson. 58, 5 17 (1984). 13. 0. W. S&ENSEN, J. Magn. Reson. 57,506 (1984). 14. S. D@NSTRUP, H. BILDSIZIE, AND H. J. JAKOBSEN, presented at the “7th European Experimental NMR Conference,” Altavilla Militia, Italy, May 1984. 15. G. BODENHAUSEN, R. FREEMAN, AND D. L. TURNER, .I. Magn. Reson. 27,51 I (1977). 16. M. H. LEVITT, J. Mugn. Reson. 48,234 (1982); 50,95 (1982). 17. D. I. HOULT AND R. E. RICHARDS, Proc. R. Sot. (London) Ser. A 344, 3 11 (1975). 18. R. RICHARZ, W. AMMANN, AND T. WIRTHLIN, “Varian Nuclear Magnetic Resonance Application Note: DEPT,” No. Z-15, August 1982.