Probably the most useful NMR experiment for elucidation and the HSQC-INADEQUATE data can be written of the structure of small molecule natural products is the 13 C INADEQUATE. Some of the many experimental modifica-S hsqc0inad (t 1 , t 2 ) tions which have been made to improve the S/N of this low-Å A 2 ns 2 exp(0iv dqc1 t 1 )exp(0iv h1 t 2 )exp(0t 2 /T 2h ) sensitivity experiment include transfer of proton polarization to 13 C (1, 2), the use of 1 H detection (3-6), and composite / B 2 ns 2 exp(0iv dqc2 t 1 )exp(0iv h2 t 2 )exp(0t 2 /T 2h ) refocusing of 13 C multiplets (7). We have recently shown / ns 2 n hsqc0inad (t 2 ),
[2] that some of the problems that are inherent in a protondetected INADEQUATE which displays 1 H along one axis can be addressed by combining a proton-detected singlewhere sq refers to frequencies indirectly observed in the quantum (SQ) HMQC or HSQC data set with the proton-HSQC experiment, dq refers to frequencies indirectly obdetected double-quantum (DQ) HMQC-INADEQUATE or served in the HSQC-INADEQUATE experiment, and T 2h . We refer to these proton-deis the observed decay time of the 1 H free-induction decay. tected experiments which display 13 C along f 2 as CDHMQC-The subscripts 1 and 2 refer to data acquired in the SQ INADEQUATE or CDHSQC-INADEQUATE. Here we and DQ experiments respectively. The numbers of scans have taken a low-molecular-weight natural product and comfor the SQ and DQ experiments ( ns 1 and ns 2 ) are figured pared the typical carbon-detected INADEQUATE acquired in as a linear signal-intensity dependence and a squareon a standard multinuclear probe, with proton-detected INroot noise dependence. A and B are the amplitudes of ADEQUATEs acquired on a standard inverse triple-resothe proton signals corresponding to carbons A and B. In nance probe with and without conversion of the f 2 axis to general, these amplitudes are dependent upon the numbers 13 C. The strengths and weaknesses of each method are of equivalent protons contributing to each signal. Because shown, along with indications of when the methods might of natural-abundance effects, it can be assumed that A 1 / be best applicable.
A 2 and B 1 / B 2 are about 91 ( due to the 1.1% abundance First, we expand on the treatment of the data-processing of 13 C pairs relative to single 13 C's ) . procedure used in the CDHSQC-INADEQUATE. Following
Equations [1] and [2] assume that there are no 1 H-1 H J Ref. ( 8), we consider the combination of a DQ data set with couplings, that 13 C-1 H couplings are removed from t 1 and its SQ complex conjugate. Two CH groups are considered, t 2 , and that the noise contributions (n hsqc and n hsqc0inad ) are labeled A and B, which may have different intensities, but random functions representing the noise present in the proton which lack proton-proton couplings. These data can be con-(t 2 ) dimension. For the conditions discussed here, the RMS sidered to have been generated using the experiment shown values of these two noise functions can be assumed to be in Fig. 1. The phase-modulated HSQC data obtained from equal. For the simplest situation of first-order proton-proton this experiment with t 1 Å 1/(2J CH ) and t 2 Å 1/(2J CC ) can couplings, each term in Eq. [1] and Eq. [2] would be be written multiplied by cos r pJ hh t 2 , where r represents the proton multiplicity and J hh the proton homonuclear coupling. S hsqc (t 1 , t 2 ) Following acquisition of n rows of SQ data and m rows Å A 1 ns 1 exp(0iv sqc1 t 1 )exp(0iv h1 t 2 )exp(0t 2 /T 2h ) of DQ data, the procedure outlined in Fig. 2 is carried out. Elimination of the dependence on the proton frequency v h / B 1 ns 1 exp(0iv sqc2 t 1 )exp(0iv h2 t 2 )exp(0t 2 /T 2h ) is realized by multiplying Eq. [2] by the complex conjugate of Eq. [1], and integrating over t 2 / ns 1 n hsqc (t 2 ),
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