Empirical and DFT GIAO quantum‐mechanical methods of 13C chemical shifts prediction: competitors or collaborators?

The accuracy of ¹³C chemical shift prediction by both DFT GIAO quantum‐mechanical (QM) and empirical methods was compared using 205 structures for which experimental and QM‐calculated chemical shifts were published in the literature. For these structures, ¹³C chemical shifts were calculated using HOSE code and neural network (NN) algorithms developed within our laboratory. In total, 2531 chemical shifts were analyzed and statistically processed. It has been shown that, in general, QM methods are capable of providing similar but inferior accuracy to the empirical approaches, but quite frequently they give larger mean average error values. For the structural set examined in this work, the following mean absolute errors (MAEs) were found: MAE(HOSE) = 1.58 ppm, MAE(NN) = 1.91 ppm and MAE(QM) = 3.29 ppm. A strategy of combined application of both the empirical and DFT GIAO approaches is suggested. The strategy could provide a synergistic effect if the advantages intrinsic to each method are exploited. Copyright © 2010 John Wiley & Sons, Ltd.     

Differentiation between [1,2,4]triazolo[1,5‐a] pyrimidine and [1,2,4]triazolo[4,3‐a]‐ pyrimidine regioisomers by 1H?15N HMBC experiments

The condensation of malonoaldehyde derivatives with either a 3‐amino‐[1,2,4]‐triazole or a 3,5‐diamino‐[1,2,4]‐triazole precursor was studied. In agreement with previous reports, two different bicycles, namely, bearing the regioisomeric [1,2,4]triazolo[1,5‐a]pyrimidine ( 1 ) or[1,2,4] triazolo [4,3‐a]pyrimidine ( 2 ) structural surrogates, could be obtained. We found that, depending on the triazole precursor, only one regioisomer resulted, either of the 1 or 2 series. We also observed that these two structural surrogates could be unambiguously differentiated by indirectly measuring their ¹⁵N chemical shifts by ¹H? ¹⁵N HMBC experiments. The occasional conversion of [1,2,4]triazolo[4,3‐a]pyrimidines to the [1,2,4]triazolo[1,5‐a]pyrimidine counterparts could be unequivocally determined by ¹⁵N NMR data. Copyright © 2010 John Wiley & Sons, Ltd.     

Study of conformations and hydrogen bonds in the configurational isomers of pyrrole‐2‐carbaldehyde oxime by 1H, 13C and 15N NMR spectroscopy combined with MP2 and DFT calculations and NBO analysis

The ¹H, ¹³C and ¹⁵N NMR studies have shown that the E and Z isomers of pyrrole‐2‐carbaldehyde oxime adopt preferable conformation with the syn orientation of the oxime group with respect to the pyrrole ring. The syn conformation of E and Z isomers of pyrrole‐2‐carbaldehyde oxime is stabilized by the N? H···N and N? H···O intramolecular hydrogen bonds, respectively. The N? H···N hydrogen bond in the E isomer causes the high‐frequency shift of the bridge proton signal by about 1 ppm and increase the ¹J(N, H) coupling by ～3 Hz. The bridge proton shows further deshielding and higher increase of the ¹J(N, H) coupling constant due to the strengthening of the N? H···O hydrogen bond in the Z isomer. The MP2 calculations indicate that the syn conformation of E and Z isomers is by ～3.5 kcal/mol energetically less favorable than the anti conformation. The calculations of ¹H shielding and ¹J(N, H) coupling in the syn and anti conformations allow the contribution to these constants from the N? H···N and N? H···O hydrogen bondings to be estimated. The NBO analysis suggests that the N? H···N hydrogen bond in the E isomer is a pure electrostatic interaction while the charge transfer from the oxygen lone pair to the antibonding orbital of the N? H bond through the N? H···O hydrogen bond occurs in the Z isomer. Copyright © 2010 John Wiley & Sons, Ltd.     

Reachability problems for a class of integro-differential equations

We study control problems for some integro-differential equations using the Hilbert Uniqueness Method. To do that we follow a harmonic analysis approach. Our results can be applied to concrete examples in viscoelasticity theory.     

On lovely pairs of geometric structures

We study the theory of lovely pairs of geometric structures, in particular o-minimal structures. We use the pairs to isolate a class of geometric structures called weakly locally modular which generalizes the class of linear structures in the settings of SU-rank one theories and o-minimal theories. For o-minimal theories, we use the Peterzil-Starchenko trichotomy theorem to characterize for a sufficiently general point, the local geometry around it in terms of the thorn U-rank of its type inside a lovely pair.