DQF-COSY = Double-Quantum Filtered-COrrelated SpectroscopY

Transcription

1 DQF-COSY = Double-Quantum Filtered-COrrelated SpectroscopY The pulse sequence: x - t 2 Consider:, and J I,S [eq.] Ĥ = /2 (Î x + Š x ) 90 x I z and S z [0] -I y and -S y Ĥ = Î z ( ) + Š z ( ) Ĥ = 2Î z Š z (J IS ) -I y cos( ) +I x sin( ) -S y cos( ) +S x sin( )

2 -I y cos( ) +I x sin( ) -S y cos( ) +S x sin( ) -I y cos( )cos( J IS ) +2I x S z cos( )sin( J IS ) +I x sin( )cos( J IS ) Ĥ = 2Î z Š z (J IS ) +2I y S z sin( )sin( J IS ) -S y cos( )cos( J IS ) +2S x I z cos( )sin( J IS ) +S x sin( )cos( J IS ) [ ] +2S y I z sin( )sin( J IS ) Ĥ = /2 (Î x + Š x ) 90 x memo. = cos( /2) = 0, sin( /2) = 1 -I z cos( )cos( J IS ) -2I x S y cos( )sin( J IS ) +I x sin( )cos( J IS ) -2I z S y sin( )sin( J IS ) -S z cos( )cos( J IS ) -2S x I y cos( )sin( J IS ) +S x sin( )cos( J IS ) [,0] -2S z I y sin( )sin( J IS ) memo. I z and S z (z magnetization) I x S y and S x I y (double quant. coherence) I x and S x (single quant. coherence) I z S y and S z I y (single quant. coherence)

3 In DQF-COSY we preserve only double quant. coherences: I x S y and S x I y Therefore only two terms remain: -2I x S y cos( )sin( J IS ) [,0] -2S x I y cos( )sin( J IS ) In reality I x S y and S x I y are still mixtures of zero-quantum and double-quantum coherences memo : I + = I x + ii y I = I x ii y S + = S x + is y S = S x is y consequently: 1/2 [I + + I ]= I x and 1/(2i)[S + - S ]= S y Therefore: -2I x S y = -2{1/2 [I + + I ]1/(2i)[S + -S ]}= -1/(2i) {I + S + - I + S + I + - I } only I + S + and I are double quant. coh. (or coherence order 2), I + S and I + are zero quant. coh. (or coherence order 0) In reality via phase cycling the zero quantum coherences are removed and thus only 1/(2i) {I + S + - I } terms remain.

4 In conclusion term -1/(2i) {(I + S + )-(I )} is as follows: In summary: now 1/(2i) [{(I x + ii y )(S x + is y )} - {(I x - ii y )(S x - is y )}] = 1/(2i) [I x S x + ii y S x + ii x S y y S y x S x + ii y S x + ii x S y + I y S y ] 1/(2i) [ii y S x + ii x S y + ii y S x + ii x S y ] 1/2 [2I y S x +2I x S y ] -2I x S y 1/2 [2I y S x + 2I x S y ] (the 2 true double quant. parts of it) for the same reason: -2S x I y 1/2 [2I x S y + 2I y S x ] -2I x S y cos( )sin( J IS ) 1/2 [2I y S x +2I x S y ] cos( )sin( J IS ) -2S x I y cos( )sin( J IS ) 1/2 [2I x S y +2I y S x ] cos( )sin( J IS ) is set to be short and thus: - no evolution - no coupling I y S x cos( )sin( J IS ) I x S y cos( )sin( J IS ) I x S y cos( )sin( J IS ) I y S x cos( )sin( J IS ) Ĥ = /2 (Î x + Š x ) 90 x I z S x cos( )sin( J IS ) I x S z cos( )sin( J IS ) I x S z cos( )sin( J IS ) I z S x cos( )sin( J IS )

5 I z S x cos( )sin( J IS ) I x S z cos( )sin( J IS ) I x S z cos( )sin( J IS ) I z S x cos( )sin( J IS ) During acquisition (t 2 ): Ĥ = Î z ( t 2 ) + Š z ( t 2 ) and 2Î z Š z (J IS t 2 ) t 2 the I x S z term during ACQ -I x S z cos( )sin( J IS )cos( t 2 )cos( J IS t 2 ) -1/2I y cos( )sin( J IS )cos( t 2 )sin( J IS t 2 ) +I y S z cos( )sin( J IS )sin( t 2 )cos( J IS t 2 ) -1/2I x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) the I z S x term during ACQ -I z S x cos( )sin( J IS )cos( t 2 )cos( J IS t 2 ) -1/2S y cos( )sin( J IS )cos( t 2 )sin( J IS t 2 ) +I z S y cos( )sin( J IS )sin( t 2 )cos( J IS t 2 ) -1/2S x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) the I z S x term during ACQ -I z S x cos( )sin( J IS )cos( t 2 )cos( J IS t 2 ) -1/2S y cos( )sin( J IS )cos( t 2 )sin( J IS t 2 ) +S y I z cos( )sin( J IS )sin( t 2 )cos( J IS t 2 ) -1/2S x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) the I x S z term during ACQ -I x S z cos( )sin( J IS )cos( t 2 )cos( J IS t 2 ) -1/2I y cos( )sin( J IS )cos( t 2 )sin( J IS t 2 ) +S z I y cos( )sin( J IS )sin( t 2 )cos( J IS t 2 ) -1/2I x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 )

6 memo 1: receiver on x therefore only the four x term remain -1/2S x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) -1/2S x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) -1/2I x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) -1/2I x cos( )sin( J IS )sin( t 2 )sin( J IS t 2 ) memo 2: cos(a)sin(b ) = 1/2[sin(A+B)-sin(A-B)] sin(a)sin(b ) = 1/2[cos(A-B)-cos(A+B)] therefore +1/8I x [+sin{( + J IS ) } - sin{( J IS ) }] [+cos{( J IS )t 2 }- cos{( +S )t 2 }] +1/8I x [+sin{( + J IS ) }- sin{( - J IS ) }] [+cos{( J IS )t 2 - cos{( + J IS )t 2 }] +1/8S x [+sin{( + J IS ) }-sin{( - J IS ) }] [+cos{( J IS )t 2 }- cos{( + J IS )t 2 }] +1/8S x [+sin{( + J IS ) }- sin{( J IS ) }] [+cos{( J IS )t 2 }-cos{( + J IS )t 2 }]

7 the following terms can be found I x [ ] at, I x [ ] at, S x [ ] at, S x [ ] at, if one sets the phase that sin is absorptive (a) in cos is absorptive (d) in t 2 I x [+a.. -a.. +a.. -a..] at, I x [+a.. -a.. +a.. -a..] at, S x [+a.. -a.. +a.. -a..] at, S x [+a.. -a..+a.. -a..] at, so the diagonals as well as all off-diagonals have absorptive line shape memo: line shapes positive absorptive (+a), negative absorptive (-a), positive dispersive (+d), negative dispersive (-d), t 2

8 Comment: The intensity of the DQF-COSY peaks are half of the appropriate COSY peaks (1/8 -> 1/4) Phase cycled DQF-COSY is 4 time longer than the appropriate COSY. Note: If selection is made not by phase-cycling but by "gradient", then the time requirement of the two experiments are identical. t 2

9 Summary: 1 H- 1 H DQF-COSY the raise of an off-diagonal peak I I z +2I x S z cos( )sin( J IS ) S -I y A DQ tagból a zq tag kiemelését követően: -2S x I y 1/2 [2I x S y +2I y S x ] I z S x cos( )sin( J IS ) -1/2S x cos( )sin( J IS ) sin( t 2 )sin( J IS t 2 ) +1/8S x [+sin{( + J IS ) }- sin{( J IS ) }] [+cos{( J IS )t 2 }- cos{( + J IS )t 2 }] t 2

10 DQF-COSY with bipolar gradient and : Phase: x x x x x x x x x y 1 H t 2 G z a b 2a+b = y= bipolar gradient is taking care of water during evolution: a pair of gradients (typically of low power e.g. 0.5%) of increasing length covering the overall time of evolution ( ). Radiation dumping is minimized since the otherwise bulk water, as well as any other signals, are dephased and rephased in a symmetric manner during evolution. (No uniform (big) water, no radiation dumping occurs.) The 180 pulse of DQF (the one between the second and the third 90s): It is there since a finite (ms!) time is required for the gradient under which time evolution of chemical shift will occur. This unwanted evolution is eliminated by the refocusing effect of the 180 o pulse (see echo) Two step phase cycling (0, ) is required to refocus axial peaks present because of quadrature detection (see phase cycling). The watergate or binominal water suppression is to remove water before acquisition Gradient a dephases a double quantum coherence transferred subsequently to a single quantum coherence. When coherence is refocused by the second gradient before acquisition it has to have a length of 2*a. Gradient b is that of the standard watergate.

11 DQF-COSY-bipolar gradient and : Net magnetization form H 2 O (on resonance) o step phase cycling (0, ) th quadrature detection refocus axial peaks: 1 H =0 y=0 = X x x x x y = X And needs to be refocused Phase: x x x x x x x x x y G z a b 2a+b = y= X x x x x X t 2 A1 B1 I z I y I y I z +I z I y rec.=x I y =disp. Y x x x x Y I z +I y +I y +I z +I z I y rec=x I y =disp. Y x x x x Y A2 B2 I z +I x +I x +I x +I x +I x rec.=y +I x =disp. I z I x I x I x I x I x rec=x I x =disp. The constructive co-adding of A1 and A2 is possible. The constructive co-adding of B1 and B2 is possible.