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Evolutionary algorithms to solve complicated NMR spectra
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Image of FIG. 1.
FIG. 1.

The all trans conformer of pentane showing the labeling of the protons.

Image of FIG. 2.
FIG. 2.

NMR spectrum of pentane dissolved in 1132. The experimental spectrum (a) is compared with the final fit obtained by varying 11 dipolar couplings, 9 indirect spin-spin couplings, and 3 chemical shieldings (b); in the next frames the spectrum is enlarged to show the experimental spectrum (d) and the same fit as above (c). All horizontal scales are in Hz. The 11 indirect spin-spin couplings were varied only in the final fitting procedure; in earlier iterations they were given their isotropic values.

Image of FIG. 3.
FIG. 3.

The first four generations of an ES: (1) an initial population is generated, and the best offspring is used as the next parent. (2) The offspring is spread over a larger area in the second generation due to the relatively large step made in the previous generation. The vector from the parent to the best offspring (dashed line) is combined with the (shortened) mutation vector of the last generation (dotted line) to generate the new parent (solid line). (3) Due to the correlation between the past two mutations the search range has been extended again in the general direction of both mutations while it has been limited in the perpendicular direction. The best offspring is now a local minimum. The memory effect of the EA, which incorporates past mutation vectors into the calculation of the next parent, helps to overcome the local minimum and the next parent is still closer to the global minimum. (4) The barrier between the local and global minima has been overcome, and the optimization is progressing toward the global minimum.

Image of FIG. 4.
FIG. 4.

A small part of the NMR spectrum of pentane dissolved in magic mixture. This shows the effect of the background removal method discussed in the text. (a) The upper and lower traces show the experimental spectra without and with background removal, respectively. (b) The noise-free trace is the calculated spectrum and the other the experimental spectrum after removal of background. All horizontal scales are in Hz.


Generic image for table
Table I.

Dipolar couplings (in Hz) for pentane. The indirect couplings are equal within experimental error in the two experiments. The values (in Hz) determined from the magic mixture and 1132 spectra are, respectively, , ; , ; , ; , ; , ; , ; , ; , ; and , . The values and [estimated from the Karplus relationship (Ref. 30) using the GAUSSIAN 03 conformer structures and the conformer probabilities reported in this table] agree with the experimental values.

Generic image for table
Table II.

Fitted parameters for pentane. Numbers in parentheses indicate uncertainties in least significant digits. The parameters and reported here correspond to the original definitions in Ref. 7. Note that the values reported in Ref. 5 should be multiplied by a factor in order to compare them to the theory of Ref. 7.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Evolutionary algorithms to solve complicated NMR spectra