13. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER)

Transcription

1 94 Prduct Operatr Treatment 3. PO TREATMENT OF DEPT (DISTORTIONLESS ENHANCEMENT POLARIZATION TRANSFER) DEPT is a ne-dimensinal sequence used as a tl fr unambiguus identificatin f the CH, CH, and CH 3 peaks in a prtn decupled 3 C spectrum. It shares with INEPT the advantage f permitting a fast repetitin rate. The recycle time has t be lnger than the prtn relaxatin time but can be fairly shrter than the carbn T. The nnprtnated carbns will nt shw up in a DEPT spectrum. The sequence is shwn in Figure II.8. 90xH 80xH q ± yh H Decuple 90xC 80xC 3 C /J /J /J t d t(0) t() t() t(3) t(4) t(5) t(6) t(7) Figure II.8. The basic (ne-dimensinal) DEPT sequence: 90xH /J 80xH 90xC /J 80xC θ ± yh /J AT(dec ). The initial density matrix is D(0) = λ( p'/ n){ z} q'{ z} (II.7) where l is a recvery factr fr carbn [see (II.53)] 90xH D(0) λ( p'/ n){ z} + q'{ y} (II.7) D()

2 DEPT 95 Fr the evlutin we use the ntatins c= cs Ω / J c' = cs Ω / J C = cs π J / J = cs π / = 0 C H s= sin Ω C / J s' = sin Ω H / J S = sin πj / J = sin π / = (II.73) In treating the evlutin, the shift and cupling may be handled in any rder. Here, because f the particular values f C and S, we are better ff by starting with the cupling. J cupl. () λ( '/ ){ } '{ } D p n z q zx shift H λ( p'/ n){ z} q' c'{ zx} q' s'{ zy} (II.74) D() 80xH () λ( '/ ){ } ' '{ } + ' '{ } D p n z q c zx q s zy 90xC λ( p'/ n){ y} + q' c'{ yx} q' s'{ yy} (II.75) D(3) The multiplet frmalism { } can help us nly s far. It des nt apply t the cupled evlutin f terms like {zx} r {yx} since this cupled evlutin is fllwed by sme mre pulses (cf. Rule #5 in Appendix L). We have t cnsider separately the CH, CH, and CH 3, using the crrespnding subscripts,,3. Fr cmpleteness, we will als cnsider the case f the nnprtnated carbn (subscript zer). D (3) = λ p '[ y ] D (3) = λ p'[ y] + q' c'[ yx] q' s'[ yy] D (3) = λ p'[ y] + q' c'([ yx] + [ y x]) q' s'([ yy] + [ y y]) D (3) = λ p'[ y] + q' c'([ yx] + [ yx] + [ y x]) 3 qs ' '([ yy] + [ yy ] + [ y y]) (II.76)

3 96 Prduct Operatr Treatment The evlutin frm t(3) t t(4) leads t D p c y s x shift C (3) λ '( [ ] [ ]) = D(4) (n cupling) D p xz q c yx s yy J cupl. (3) λ '[ ] + '( '[ ] '[ ]) shift H λ p'[ xz] + q'( c' [ yx] + c' s '[ yy] s ' c'[ yy] + s' [ yx]) = λ p'[ xz] + q'[ yx] shift C + + = λ p '( c[ xz] s[ yz]) q'( c[ yx] s[ xx]) D (4) In prcessing the evlutin f D (3) we have t treat separately the cupling f the carbn with the first and with the secnd prtn. D p xz q c yx xzx q s yy xzy cplax (3) λ '[ ] + ' '([ ] [ ]) ' '([ ] [ ]) cplax + λ p'[ yzz] q' c'( [ xxz] [ xzx]) q' s'([ xyz] [ xzy]) shift H + + λ p'[ yzz] q ' c' ( [ xxz] [ xzx]) q' c' s '( [ xyz] [ xzy]) q ' s ' c'( [ xyz] [ xzy]) q' s ' ([ xxz] + [ xzx] ) = λp yzz q xxz + xzx p c yzz s xzz shift C '[ ] '([ ] [ ]) λ '( [ ] [ ]) q ' c([ xxz] + [ xzx]) q' s([ yxz] + [ yzx]) = D ( 4) We were allwed t handle the evlutin f bth prtns in ne step nly because nne f the POs had x r y fr bth prtns, i.e., nly ne prtn was affected by the evlutin in each PO. Similar calculatins will prduce D 3 (4). Summarizing the results at t(4) we have: D (4) = λ p '( c [ y ] s [ x ]) D (4) = λ p '( c[ xz] s[ yz]) + q' c[ y x] q' s[ xx] (II.77) D (4) = λ p '( c[ yzz] + s[ xzz]) q' c([ xxz] + [ xzx]) q ' s([ yxz] + [ yzx]) D3 (4) = λ p'( c[ xzzz] + s[ yzzz]) q ' c([ yxzz] + [ yzxz] + [ yzzx]) + q' s([ xxzz] + [ xzxz] + [ xzzx])

4 DEPT 97 The θ ± y pulse is mathematically equivalent t a ± θ y pulse. Therefre, we will treat it as a rtatin abut the y-axis with alternate signs f q. We take als int accunt that cs( θ ) = cs θ ; sin( θ) = sinθ cs( ± θ ) = cs θ ; sin( ± θ) =± sinθ 80xC D (4) λ p'( c[ y] s[ x]) = D (5) (the prtn pulse has n effect). D p c xz s yz q c yx q s xx 80xC (4) λ '( [ ] + [ ]) ' [ ] ' [ ] ± θ yh λp'cs θ( c[ xz] + s[ yz]) ± q'sin θ( c[ yz] + q' s[ xz] + NOT = D (5) In the last calculatin we have retained nly the bservable terms ([x],[y])and the ptentially bservable terms ([xz],[yz]). We have relegated terms as [xx], [xy], [yx], [yy] t the NOT bunch (nnbservable terms), as described in Appendix K. In prcessing D (4) we have t calculate the effect f the prtn pulse, which is neither 90 nr 80, separately n the tw prtns (see end f Sectin II.6). (4) 80xC D λ p'( c[ yzz] + s[ xzz]) q' c([ xxz] + [ xzx]) + q' s([ yxz] + [ yzx]) ± θ yx λ θ + + θ + p'cs ( c[ yzz] s[ xzz]) q'cs ( c[ xzx] s[ yzx]) ± q'sin θ ( c[ xzz] s[ yzz]) + NOT ± θ yx λ θ + ± θ θ p'cs ( cyzz [ ] sxzz [ ]) q'cs sin ( cxzz [ ] syzz [ ]) ± q'sinθcs θ( c[ xzz] s[ yzz]) + NOT = λp θ c yzz + s xzz ± q θ θ c xzz s yzz + 'cs ([ ] [ ]) 'cs sin ([ ] [ ]) NOT = D (5)

5 98 Prduct Operatr Treatment Similar calculatins have t be perfrmed n D 3 (4) and the situatin at t(5) is D (5) = λ p '( c [ y ] s [ x ]) D (5) = λ p'cs θ ( c[ xz] + s[ yz]) ± q'sin θ ( c[ yz] + q' s[ xz] + NOT D p c yzz s xzz (5) = λ 'cs θ( [ ] + [ ]) ± q'csθsin θ( c[ xzz] s[ yzz]) + NOT (II.78) D lp q c xzzz s yzzz 3 3(5) = 'cs ( [ ] [ ]) ± 3 q'csqsin q( c[ yzzz] s[ xzzz]) + NOT Fllws nw the last /J cupled evlutin. We will retain nly the bservable terms, having x r y fr carbn and fr all prtns. shift C D (5) λp'( c [ y] + cs[ x] sc[ x] s [ y]) = λp'[ y] = λ p'[ y] = D (6) D p c y s x q c x s y cupl. (5) λ 'cs θ ( [ ] [ ]) ± 'sin θ ( [ ] + [ ] + NOT shift C λp 'cs θ( c [ y] + cs[ x] sc[ x] s [ y]) ± q c x cs y + sc y s x + 'sin θ ( [ ] [ ] [ ] [ ]) NOT = λp'cs θ[ y] ( ± q'sin θ[ x]) + NOT= D (6) After perfrming similar calculatns fr D (5) and D 3 (5), we can summarize the results at t(6) as fllws D (6) = λ p'[ y] D (6) = ( λ p 'cs θ [ y ] ± q 'sin θ [ x ]) + NOT (II.79) D p y q x (6) = ( λ 'cs θ [ ] ± 'sin θ cs θ [ ]) + NOT D p y q x 3 3 (6) = ( λ 'cs θ [ ] ± 3 'sin θ cs θ [ ]) + NOT As a remarkable achievement f the DEPT sequence, we ntice that n chemical shift (prtn r carbn) is expressed in the density matrix at time t(6), when the acquisitin begins. We will nt have any frequency dependent phase shift. This alne can justify the "distrtinless" claim in the name f the sequence.

6 DEPT 99 The term cntaining l can be relatively small when a high repetitin rate is used. We are interested in the secnd term, which des nt cntain the factr l and is als plarizatin enhanced (has q' rather than p'). The first term can be edited ut by phase cycling. The ± sinq factr in the expressin f the density matrix crrespnds t the last prtn pulse (see Figure II.8) being applied alng the +y and y axis, respectively. If we take a scan with the phase +y and subtract it frm the ne with phase y, the first term is cancelled and we are left with D (6) = q 'sin θ [ x ] + NOT D (6) = q 'sin θ cs θ [ x ] + NOT (II.80) 3 (6) = 3 'sin θ cs θ [ ] + NOT D q x The subtractin is perfrmed by a 80 shift in the receiver phase. Theretically, a tw-step phase cycling is enugh, in which the phase f the last prtn pulse is y +y and the receiver phase is 0 80 Additinal phase cycling is cmmnly used t cancel radi-frequency interferences and the effect f pulse imperfectins. The nnprtnated carbns d nt appear in the phase-cycled spectrum. The discriminatin between CH, CH, and CH 3 is dne by running the sequence three times, with different values f the flip angle q, namely 90, 45 and 35. When q = 90, then csq = 0, sinq = and (II.80) becmes D (6) = q'[x]) + NOT D (6) = NOT D 3 (6) = NOT This is a 3 C spectrum in which nly the CH lines appear. When q is slightly larger r smaller than 90, a CH will appear as a small singlet, negative r psitive, respectively. That is why DEPT is a gd methd fr calibrating the 90 prtn pulse in a spectrmeter cnfigured fr bserving carbn.

7 00 Prduct Operatr Treatment When q = 45, csq = /, sinq = / and (II.80) becmes D (6) = (/ )q'[x]) + NOT D (6) = q'[x] + NOT D 3 (6) = (3/ ) q'[x]) + NOT All CH, CH, and CH 3 appear as psitive singlets. When q = 35, then csq = -/, sinq = / and (II.80) becmes D (6) = (/ )q'[x]) + NOT D (6) = q'[x] + NOT D 3 (6) = (3/ ) q'[x]) + NOT This is the same situatin as fr 45, but CH peaks appear negative. We have discussed all the features f DEPT using the expressin f the density matrix at time t(6), when the acquisitin begins. The 3 C magnetizatin, which is riented alng x at t(6), will precess during the acquisitin with the Larmr frequency crrespnding t the respective line and will appear as a singlet. In principle nly the 90 and the 35 runs are sufficient fr an unambigus identificatin f the CH, CH, and CH 3 peaks. The 45 run is necessary when ne wants t d spectral editing. Fr the nnprtnated carbns, a nrmal run is needed with a lng recycle time. Mdern instruments ffer the pssibility t edit DEPT spectra in rder t select nly the peaks f ne grup (e.g., CH) while eliminating the peaks f the ther tw grups (CH and CH 3 ). This is theretically based n linear cmbinatins f the spectra btained with different values f q (45, 90, 35 ). Table II. cntains the relative amplitudes f CH, CH, and CH 3 peaks fr each f the three angles.

8 DEPT 0 Table II.. Relative peak amplitudes in the raw DEPT spectra. Spectrum θ CH CH CH 3 A 45 3 ( ) (0.707) (.06) B C 35 (0.707) - 3 ( ) (.06) Table II.3 shws the peratins necessary t btain spectrs f nly ne f the three grups r all f them tgether (nte that the spectrum taken at 45 als shws the peaks f all grups, but nt their true amplitudes). Table II.3. Linear cmbinatins f the raw DEPT spectra, necessary in rder t btain nly ne f the three grups r all f them tgether. Cmbinatin CH CH CH 3 B 0 0 (A C)/ 0 0 (A+C -.4B)/. 0 0 Sum f the abve Sme instrument sftwares make it pssible t alter the theretical cefficients in rder t cmpensate fr hardware imperfectins.