Computed Coupling Constants

Bally and Rablen ° followed up their important study of the appropriate basis sets and density functional needed to compute NMR chemical shifts with an examination of procedures for computing proton-proton coupling constants. They performed a comparison of 165 experimental with computed proton-proton coupling constants from 66 small, rigid molecules. They tested a variety of basis sets and functionals, along with questioning whether all four components that lead to nuclear-nuclear spin coupling constants are required, or if just the Fermi contact term would suffice. 

Their recommended method, one that is compntationally very efficient, provides excellent agreement with the experimental conpUng constants. The steps are as follows  

This methodology provides coupling constants with a mean error of 0.51 Hz, and when applied to a probe set of 61 conpUng constants from 37 different molecules (including a few that require a number of conformers and thus a Boltzmann-weighted averaging of the coupling constants), the mean error is only 

TABLE 2.10 RMS Deviation (Hz) from Experiment of Computed Proton-Proton Coupiing Constants 

Bally and Rablen supply a set of scripts to automate the computation of the coupling constants according to this prescription using GAUSSIAN-09 these scripts are available in the supporting materials of the paper and also on the Cheshire Web site.  

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Computed coupling constants show moderate to large sensitivity to basis set, and accurate predictions require very llexible bases (see, for example, the hydrogen fluoride (HF) data in Table 9.7). In addition, DFT is much more robust than HF theory for predicting coupling constants, and the latter level of theory simply should not be used for this purpose. 

Structure 21 was subsequently synthesized by Porco, " its X-ray structure obtained, and its NMR spectra was found to be completely consistent with the original hexacyclinol compound reported by Grafe. In addition, Bagno recomputed the and chemical shifts of 17 and 21 at B97-2/cc-pVTZ/B3LYP/6-31G(d,p). The mean absolute error between the experimental and computed stractures is half that for 21 than for the originally proposed structure 17. The computed coupling constants also are in much better agreement with 21. 

The present authors own initial studies have focused on the J(P-P) coupling constants in a series of cis and tmns bis-phosphane complexes M(CO)4(PH3)2 (M = Cr, Mo, W). As shown in Figure 5, the computed coupling constants are rather sensitive to the nature of the local or gradient-corrected exchange-correlation functional employed. This is due to the above-mentioned sensitivity of the FC term, which dominates the couplings. The trends are reasonably well reproduced by... 

Gaussian computes isotropic hyperfine coupling constants as part of the population analysis, given in the section labeled "Fermi contact analysis the values are in atomic-units. It is necessary to convert these values to other units in order to compare with experiment we will be converting from atomic units to MHz, using the following expressions ri6ltYg ... 

Compute the isotropic hyperfine coupling constant for each of the atoms in HNCN with the HF, MP2, MP4(SDQ) and QCISD methods, using the D95(d,p) basis set Make sure that the population analysis for each job uses the proper electron density by including the Density=Current keyword in the route section. Also, include the 5D keyword in each job s route sectionfas was done in the original study). 

Consequently, structures 85b and 85c must be considered resonance structures rather than valence isomers. Hyperfine coupling constants were computed for a series of dithiazolyl radicals and related compounds [96MRC913]. An absolute mean deviation of 0.12 mT with respect to experimental data is reported for 10 sulfur hyperfine coupling constants obtained from UB3-LYP/TZVP calculations. 

In addition to the obvious structural information, vibrational spectra can also be obtained from both semi-empirical and ab initio calculations. Computer-generated IR and Raman spectra from ab initio calculations have already proved useful in the analysis of chloroaluminate ionic liquids [19]. Other useful information derived from quantum mechanical calculations include and chemical shifts, quadru-pole coupling constants, thermochemical properties, electron densities, bond energies, ionization potentials and electron affinities. As semiempirical and ab initio methods are improved over time, it is likely that investigators will come to consider theoretical calculations to be a routine procedure. 

Hyperfine coupling constants provide a direct experimental measure of the distribution of unpaired spin density in paramagnetic molecules and can serve as a critical benchmark for electronic wave functions [1,2], Conversely, given an accurate theoretical model, one can obtain considerable information on the equilibrium stmcture of a free radical from the computed hyperfine coupling constants and from their dependenee on temperature. In this scenario, proper account of vibrational modulation effects is not less important than the use of a high quality electronic wave function. 

Figure 3. (a) The computer-simulated spectrum of the olefinic protons using chemical shifts of 6.3 and 6.1 ppm and a coupling constant (J) of 15 Hz. (b) The olefinic region of the 100 MHz H-NMR spectrum of the originally isolated xenognosin A. The marked resonances correspond exactly with the resonances of the simulated spectrum. 

Fig. 9. — (a) H-N.m.r. Spectrum (270 MHz, Resolution-enhanced) of Beef-lung Heparin in D20 (40%, w/v) at 90° (b) Computer-simulated Spectrum, with Calculated, Interproton Coupling-Constants (/, at 35°) for the Amino Sugar (A) and L-Iduronic acid (I) Residues.84... 

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