Double -quantum filtered COSY
Product operators: same treatment as before, identical to the COSY up to the third pulse:
the third pulse converts double quantum coherences back into single quantum for observation.
(Results from COSY before precession:) -Iz, 2IzSy, Ix, -2IxSy
Third 90x pulse in DQF COSY :-Iy, 2IySz, Ix, 2IxSz
in principle all observable, or can evolve into observable components.
Phase cycling: These four terms will respond differently to changes in the pulse direction (the phase of the pulse) = allows us to systematically vary pulse angles between repetitions of the same FID, which will lead to cancellation of some coherences, while others will be additive and survive. = “DQ filter”
DQF- phase cycle: ? = 0 1 2 3 observe direction 0 3 2 1
x, y, -x, -y x, -y, -x, y
Phase cycling in this experiments filters out the -Iy, Ix and 2IySz component (after the third COSY pulse), and only leaves the magnetization from 2IxSz (which is the DQ component converted back) as observable magnetization.
Product operator description of double zero quantum during 90 ?/ and phase cycle:
Notes:
(cos ? Isin?) 90 ? coupling(sin?) precession () only component in obs.dir
-2Ix Sy 2IxSz Iy Ix sin?I detect. in x: I
-2IzSy Sx -Sy sin?S -y: S
-2IxSz -Iy -Ix sin?I -x: I
Result for 4 transients: - [ 1/2 Icos ?Isin? sin ?Isin ?
+1/2Scos ?Isin?sin ?Ssin ? ]
Compared to the COSY, the DQF COSY has only half the sensitivity. However, cross peaks and diagonal have the same modulation, and can be concurrently phased to adsorptive line shape! Also, peaks without couplings are removed from the spectra, simplifying diagonals. Both leads t better recognition of signals close to the diagonal, which in practice more than compensates for the sensitivity loss.