Inverted direct response

The Inverted Direct Response (IDR)-HSQC-TOCSY pulse sequence is shown in Fig. 18 [58]. The experiment begins with an HSQC segment... 

Fig. 10.18. IDR (Inverted Direct Response)—HSQC-TOCSY pulse sequence. The experiment first uses an HSQC sequence to label protons with the chemical shift of their directly bound carbons, followed by an isotropic mixing period that propagates magnetization to vicinal neighbor and more distant protons. The extent to which magnetization is propagated in the experiment is a function of both the size of the intervening vicinal coupling constants and the duration of the mixing period. After isotropic mixing, direct responses are inverted by the experiment and proton detection begins.

Fig. 8.31 Pulse sequence schematic for the inverted direct response GHSQC-TOCSY experiment. After labeling protons with the respective, directly bound carbon chemical shifts, magnetization is propagated from a given pro-...

The applicability of the HSQC experiment in natural product structure elucidation studies remains to be evaluated. To the best of our knowledge, no natural product structure elucidation studies have been reported using HSQC rather than HMQC to establish direct proton-carbon chemical shift correlations. This will undoubtedly change in time. A modification of the HSQC experiment, inverted direct response HSQC-TOCSY, has, however, been reported using strychnine as a model compound (Domke 1991). In the case of congested proton spectra, there may be advantages inherent to the use of HSQC instead of HMQC. 

Fig. 11. A Pulse sequence to invert direct (one-bond) responses based on HSQC-TOCSY (Domke 1991). B Pulse sequence to invert direct responses based on HMQC-TOCSY (Martin et al. 1992). When the adjustable pulse, P, is set to 180°, the direct responses are inverted as in the original work of Domke (1991). In contrast, when p = 90°, direct responses will be canceled in a manner analogous to the procedure used to calibrate decoupler pulses (Thomas et al. 1981 Bax 1983b). In experiments when the direct response is to be canceled, there is no need of broadband heteronuclear decoupling during acquisition, allowing higher levels of digital resolution in F2 than would otherwise be possible...

Fig. 12A-C. HMQC-TOCSY contour plots recorded for the alkaloid quindoline (3) using the pulse sequence shown in Fig. IIB. The spectrum was recorded with a mixing time of 24 ms. A Contour plot showing all responses. B Contour plot in which only negative contours from inverted direct responses are plotted. C Contour plot in which only the positive TOCSY responses appear...

Fig. 10.19. IDR-HSQC-TOCSY spectrum of the complex marine polyether toxin brevetoxin-2 (7). The data were recorded overnight using a 500 pg sample of the toxin (MW = 895) dissolved in 30 pi of d6-benzene. The data were recorded at 600 MHz using an instrument equipped with a Nalorac 1.7 mm SMIDG probe. Direct responses are inverted and identified by red contours relayed responses are plotted in black. The IDR-HSQC-TOCSY data shown allows large contiguous protonated segments of the brevetoxin-2 structure to be assembled, with ether linkages established from either long-range connectivities in the HMBC spectrum and/or a homonuclear ROESY spectrum.

Martin GE, Spitzer TD, Crouch RC, Luo J-K, Castle RN (1992) Inverted and suppressed direct response HMQC-TOCSY spectra - a convenient method of spectral editing. J Heterocycl Chem 29 577-582... 

We could go through the Laplace domain by approximating and then inverting. However, there is a direct conversion V. V. Solodovnilcov, Introduction to Statistical Dynamics of Autoinatic Control, Dover, 1960). Suppose we want to find the impulse response of a stable system (defined as g,), given the system s frequency response. Since the Laplace transformation of the impulse input is unity,... 

Exactly like its classical analog Eq. (94), Eq. (125) allows one to express the displacement response function in terms of the time-dependent diffusion coefficient. However, contrary to the classical case in which Xxx( 0 is directly proportional to D(t — t ), in the quantum formulation Xxv( 0 is a convolution product, for the value t — t of the argument, of the functions D(t ) and logcoth(7i fi /2 h). Inverting the convolution equation (125) yields an expression for D(t) in terms of the dissipative part of the displacement response function ... 

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