Evolution of chemical shift

The execution of a rf pulse or the evolution of chemical shift or J-scalar coupling is described by an operator. The operation of this operator on the expanded density matrix is exclusively related to the coefficients of the corresponding operator matrix cJexpanded-... 

The Cartesian product operators are the most common operator basis used to understand pulse sequences reduced to one or two phase combinations. This operator formalism is the preferred scheme to describe the effects of hard pulses, the evolution of chemical shift and scalar coupling as well as signal enhancement by polarization transfer. The basic operations can be derived from the expressions in Table 2.4. The evolution due to a rf pulse, chemical shift or scalar coupling can be expressed by equation [2-8]. 

More than a decade ago, Hamond and Winograd used XPS for the study of UPD Ag and Cu on polycrystalline platinum electrodes [11,12]. This study revealed a clear correlation between the amount of UPD metal on the electrode surface after emersion and in the electrolyte under controlled potential before emersion. Thereby, it was demonstrated that ex situ measurements on electrode surfaces provide relevant information about the electrochemical interface, (see Section 2.7). In view of the importance of UPD for electrocatalysis and metal deposition [132,133], knowledge of the oxidation state of the adatom in terms of chemical shifts, of the influence of the adatom on local work functions and knowledge of the distribution of electronic states in the valence band is highly desirable. The results of XPS and UPS studies on UPD metal layers will be discussed in the following chapter. Finally the poisoning effect of UPD on the H2 evolution reaction will be briefly mentioned. 

If the nuclear spin has a Larmor frequency co, then its time evolution under the effect of chemical shift is given by the following rules ... 

The effects of chemical shift and scalar coupling on the time evolution of one spin can be accounted for independently, regardless of the order (the two effects are said to commute). For example ... 

The chemical shift evolution (precession of spins as a result of chemical shift) can be represented as a circle with the rotation rate (in radians per second) written in the center (Fig. 7.6). This is the same as the motion of the net magnetization vector, viewed from the axis. Homonuclear product operators (Ha represented by Ia and Hb represented by Ib) undergo chemical shift evolution in the same way ... 

During the evolution (fi) period, the Ha magnetization rotates with angular frequency I2a in the x -y1 plane, and the doublet components (Hb = a and Hb = f>) separate from this center position with angular frequency /ab/2 in Hz, or jrJab in radians. In contrast to the INEPT experiment, we have no control over these two kinds of evolution and both will happen at the same time. A spin echo will not help because pulses do not distinguish between Ha and I lb both would receive a 180° pulse and we would have no chemical-shift evolution, only /-coupling evolution. Without chemical-shift evolution we cannot create a second dimension ... 

At t = 21 Ja, you are back to the starting magnetization. With product operators we do not need to draw vector diagrams, because we treat the vectors as pure in-phase (Ia, Ib) and antiphase (2IaIb, 2IaIb) components. Now plug these results in wherever you see Ia or Ia as a result of chemical-shift evolution ... 

Figure A.7 shows the time evolution of product operators as a result of chemical shift only. Each wheel represents one full cycle of evolution (rotation in the /-/ plane), starting on the right side and moving to the top (90° or tt/2 rotation counterclockwise), to the left side, and to the bottom. The center of the wheel is the rotation angle in radians is the I-spin offset (distance from the center of the spectral window in radians s-1) and is the S-spin offset. I-spin SQC rotates at a rate 2i S-spin SQC rotates at rate 2s DQC...

The product operator formalism is normally applied only to weakly coupled spin systems, where independent operators for I and S are meaningful. That means that it is permissible to treat evolution under chemical shifts separately from evolution under spin coupling. It also means that a nonselective pulse can be treated as successive selective pulses affecting only one type of spin. To simplify the notation and to facilitate the handling of the transformation of each product operator, such separations are almost always made. 

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