Quadrature detection, reduced dimensionality and GFT-NMR

Transcription

1 2/5 Quadrature detection, reduced dimensionalit and GFT-NMR J.m.Chem.Soc. 25, (2003) Measuring time in NMR D: 32 scans: 42 seconds 2D: 52 FIDs, 6 scans: 0650 sec, 3 hours 3D: FIDs, 8 scans: sec, 48 hours 4D: FIDs, 4 scans: sec, 96 hours oder FIDs, scan: sec, 3030 hours, 26 das We are at the sampling limit rather than at the sensitivit limit 3/5 4/5. NMR basics (4-6) asis for NMR spectroscop is the nuclear spin that can be viewed as a combination of magnet and spinning top 2. Fourier transformation (7 2) 3. Quadrature detection (22 34) 4. Reduced dimensionalit (35-37) 5. GFT-NMR (38 49) 5/5 6/5 spinning top has an angular momentum the ais of the angular momentum constant in space magnet orients in the direction of the magnetic field, this is prevented b the fact that its a spinning top precession begins

2 7/5 8/5 When a magnetic field is switched on, this does not change immediatel, but thermal motion drives spins to orient predominantl along the field Without an eternal magnetic field spins are oriented randoml in all possible directions 9/5 0/5...along the main field, resulting in a olzman distribution That builds up a net magnetization... /5 2/5 radio frequnc pulse turns the spins. nd with them the net magnetization Note the difference between an orientation in the, plane and a coherence

3 3/5 4/5 The net magnetization performs a precession M =cosωt ep (-t/t 2 ) M = sin ωt ep (-t/t 2 ) The signal is detected via a coil and then digitized using an DC (analog-digital-converter) M = M + i M M = ep (iωt) ep (-t/t 2 ) 5/5 6/5 To make digitization possible, we subtract the original The reference signal is normall the center of the spectrum signal from the one returned from the sample 7/5 8/5 comple NMR signal has the following form We ignore the phase factor for the time being and appl a Fourier transformation s(t)= ep(iφ) ep(-t/t 2 ) ep(iω 0 t) s( Ω) = s( t) ep( iωt) dt 0 phase of the signal (time independent!) deca of the signal (relaation) oscillation of the signal (the frequenc) s(ω)= (/T 2 ) i(ω Ω 0 )

4 9/5 20/5 We obtain a comple Lorentian line shape, Now we reintroduce the phase factor it consist of an absorbtive and a dispersive part S(Ω) = [(Ω) + i D(Ω) ]ep(iφ) (Ω)= (/T 2 ) (/T 2 ) 2 + (Ω Ω 0 ) 2 S(Ω) = R(Ω) + i I(Ω) Real and imaginar part are mitures of (Ω Ω D(Ω)= 0 ) 2 (/T 2 ) 2 + (Ω Ω 0 ) 2 absorptive and dispersive line shapes R(Ω) = (Ω) cosφ D(Ω) sin φ I(Ω) = D(Ω)cosφ + (Ω) sinφ 2/5 22/5 We appl a zero-order phase correction (Ω) = R(Ω) cosφ + I(Ω) sin φ D(Ω) = I(Ω)cosφ R(Ω) sinφ What if we have onl one of the components either cosine or sine ep(iα) = cosα + i sinα ep(-iα) = cosα isinα cosα =ep(iα) + ep(-iα) sinα = ep(iα) ep(-iα) (the famous Euler formulas) 23/5 24/5 We get two signals each So we have to do a quadrature detection

5 /5 26/5 The first wa to do it is States (or Ruben-States-Haberkorn) Cosine and sine signal are then combined 2 27/5 28/5 second wa to do it is TPPI (time proportional phase increment) One half of the spectrum is then discarded 29/5 30/5 When a continous signal s(t) is sampled at evenl spaced intervals as s(k t), the highest detectable frequenc is the Nquist frequenc: f n = (2 t) That has consequences depending on the tpe of quadrature detection

6 3/5 32/5 liasing and folding The same problem eists for indirect dimensions 33/5 34/5 Quadrature detection in F Methods for quadrature detection.fid: φ =, - 2.FID: φ =, -.FID: φ rec = +, - 2.FID: φ rec = +, - Methode Phase des Präparations pulses Empfängerphase rt der Fouriertransformation Position der ialpeaks Redfield (t + 0* ) reell Zentrum (t + * ) (t + 2* ) - (t + 3* ) - TPPI (t + 0* ) reell Rand (t + * ) - (t + 2* ) - (t + 3* ) SHR (t + 0* ) komple Zentrum (t + 0* ) (t + 2* ) (t + 2* ) TPPI-States (t + 0* ) komple Rand (t + 0* ) - (t + 2* ) - - (t + 2* ) - 35/5 36/5 (H)N(COC)NH and HN(COC)NH (H)N(COC)NH and HN(COC)NH quadrature detection in t quadrature detection in t 2 racken et al. J.iomol. NMR 9 (997) reduced dimensionalit: evolution on H N is recorded concomitantl with the evolution on N but without an scheme for quadrature detection

7 37/5 38/5 (H)N(COC)NH HN(COC)NH reduced dimensionalit: nd information in an (n-)d spectrum δ( 5 N) GFT-NMR: Generalization of the this principle nd information in an (n-k)d spectrum racken et al. J.iomol. NMR 9 (997) /5 40/5 First the target dimensionalit is selected 5D-HCCONHN and (5,2)D-HCCONHN If there is barel Overlap in the 5 N-HSQC the target dimensionalit is 2D 4/5 42/5 (5,2)D HCCONHN Three additional dimensions require 8 basic spectra special modulation scheme, 6 spectra are recorded normal quadrature detection S cos(ω 0 t) cos(ω t) cos(ω 2 t) cos(ω 3 t) S2 cos(ω 0 t) sin(ω t) cos(ω 2 t) cos(ω 3 t) S3 cos(ω 0 t) cos(ω t) sin(ω 2 t) cos(ω 3 t) S4 cos(ω 0 t) sin(ω t) sin(ω 2 t) cos(ω 3 t) S5 cos(ω 0 t) cos(ω t) cos(ω 2 t) sin(ω 3 t) S6 cos(ω 0 t) sin(ω t) cos(ω 2 t) sin(ω 3 t) S7 cos(ω 0 t) cos(ω t) sin(ω 2 t) sin(ω 3 t) S8 cos(ω 0 t) sin(ω t) sin(ω 2 t) sin(ω 3 t)

8 43/5 Proper combination results in spectra with onl one peak FT of S-S8 44/5 That corresponds to a matri operation = 45/5 It is difficult to decide which peak is which, therefore central peaks are recorded S9 cos(ω 0 t) cos(ω t) cos(ω 2 t) S0 cos(ω 0 t) sin(ω t) cos(ω 2 t) S cos(ω 0 t) cos(ω t) sin(ω 2 t) S2 cos(ω 0 t) sin(ω t) sin(ω 2 t) S3 cos(ω 0 t) cos(ω t) S4 cos(ω 0 t) sin(ω t) S5 cos(ω 0 t) 46/5 Thats how it looks 47/5 The result are 5 2Ds 48/5 The G-matri does it all in the time domain

9 49/5 50/5 Comparison of numbers: (5,2)D HCCONHN 5 spectra can be recorded in 34 min and ields a set of two-dimensional spectra Proc. Natl. cad. Sci. US 99, (2002) 5D HCCONHN 0*(t ) *(t 2 ) 22*(t 3 ) 3* (t 4 ) 52*(t 5 ) scan per FID, second per scan 5.83 das 4D spectrum in 94 msec... Processed to the same resolution 68 G 5/5