By Gheorghe D. Mateescu, Adrian Valeriu
In contrast to such a lot really good books in this topic that emphasize the mathematical foundations of second NMR, this booklet deals an experimentally-based, transparent rationalization of the density-matrix and product operator remedies hence permitting non-experts to see sequences of various levels of complexity.
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Extra info for 2D Nmr: Density Matrix and Product Operator Treatment
89)]. They can be discriminated by cycling F and properly choosing the receiver phase Y [the detected signal S = MT exp(-iY)]. The table below shows that two cycles are sufficient to eliminate MT(ncpl). Cycle F Y 1 2 (1+2) 0 90o 0 -90o ncpl -------------expi(F-Y) 1 -1 0 cpl -------------expi(-F-Y) 1 1 2 Even small imperfections of the rf pulse will allow leakage of the strong undesired signal into the resultant spectrum. This makes it necessary to apply one of several cycling patterns consisting of up to INADEQUATE 43 256 steps, which attempt to cancel the effects of too long, too short, or incorrectly phased, pulses.
The general expression of the 90ΦAX operator is given in Appendix C [see(C39)]. 83) where a = iexp( − iF) and F is the angle between the x-axis and the direction of B1. When F takes the value 0, 90o, 180o or 270o, the pulse is applied on axis x, y, − x, or − y, respectively. For clarity we will discuss the coupled and the noncoupled (isolated) carbon situations separately. 82)] the populations are equalized and all information is contained in the w elements. 85) G = ( w − w*) / 4 = −(1/ 2)(−1)k cos Ω14 ∆ D(7) shows that the newly created single quantum coherences contain the double quantum coherence information, W14.
70) INADEQUATE 37 The z-magnetization is still zero (relaxation effects are neglected). 72) We see that there are four vectors rotating with four different angular velocities in the equatorial (xy) plane. 74) ⎥ 1 ⎥⎦ Two important changes have been induced by the 180o pulse. First, all single quantum coherences were conjugated and changed sign. 38 Density Matrix Treatment This means that all x-components changed sign while the y-components remained unchanged: M T = M x + iM y − M T* = − M x + iM y This shows, indeed, that all four vectors rotated 180o around the yaxis.
2D Nmr: Density Matrix and Product Operator Treatment by Gheorghe D. Mateescu, Adrian Valeriu