Continuous symmetry analysis of NMR chemical shielding anisotropy

Molecular symmetry is a key parameter which dictates the NMR chemical shielding anisotropy (CSA). Whereas correlations between specific geometrical features of molecules and the CSA are known, the quantitative correlation with symmetry--a global structural feature--has been unknown. Here we demonstrate a CSA/symmetry quantitative relation for the first time: We study how continuous deviation from exact symmetry around a nucleus affects its shielding. To achieve this we employed the continuous symmetry measures methodology, which allows one to quantify the degree of content of a given symmetry. The model case we use for this purpose is a population of distorted SiH(4) structures, for which we follow the (29)Si CSA as a function of the degree of tetrahedral symmetry and of square-planar symmetry. Quantitative correlations between the degree of these symmetries and the NMR shielding parameters emerge.     

Left counital Hopf algebras on free Nijenhuis algebras

Factorization in algebra is an important problem. In this paper, we first obtain a unique factorization in free Nijenhuis algebras. By using of this unique factorization, we then define a coproduct and a left counital bialgebraic structure on a free Nijenhuis algebra. Finally, we prove that this left counital bialgebra is connected and hence obtain a left counital Hopf algebra on a free Nijenhuis algebra.     

A r (Ω)-Weighted Imbedding Inequalities for A-Harmonic Tensors

We prove the basic A _r ()-weighted imbedding inequalities for A-harmonic tensors. These results can be used to estimate the integrals for A-harmonic tensors and to study the integrability of A-harmonic tensors and the properties of the homotopy operator T: C (D, ^l )C (D, ^l–1).     

Some Non-trivial Symmetry Classes of Tensors Associated with Certain Characters

Let G be a finite group and a set of n elements. Assume that G acts faithfully on and let V be a vector space over the complex field , with dim V = m 2. It is shown that for each irreducible constituent of permutation character of G, the symmetry class of tensors associated with G and is non-trivial. This extends a result of Merris and Rashid (see [6, Theorem 2]).1995 AMS subject classification primary 20C30 secondary 15A69This research was in part supported by a grant from IPM.     

Crystal structure and single crystal EPR of (NH4)2(15-crown-5)3[Cu(mnt)2] and (NH4)2(benzo-15-crown-5)4[Cu(mnt)2]·0.5H2O

The X-ray crystal structures of (NH4)2(15-crown-5)3[Cu(mnt)2] (1) and (NH4)2(benzo-15-crown-5)4- [Cu(mnt)2]·0.5H2O (2) were determined. Two single crystals are composed of distinct structures of ammonium-crown ether supramolecular cation and [Cu(mnt)2]2- anion. The triple-decker dication in complex 1 and a sandwich dimmer in complex 2 were observed. X-Band EPR studies on the single crystals of both complex 1 and complex 2 have been carried out at room temperature, which revealed that complex 2 showed a perfect hyperfine structure of Cu whereas that of complex 1 could not be observed. The principal values and direction cosines of the principal axes of the g and A tensors were computed by a least-squares fitting procedure. The spin density of Cu(Ⅱ) was estimated according to the principal values of the A tensors and compared well with the results calculated based on DFT method.     

Theoretical study of the in-plane components of the 13C shielding tensors in condensed aromatic hydrocarbons

The Pople model for chemical shielding is applied to calculate the in-plane components of the ¹³C shielding tensors of condensed aromatic hydrocarbons. The wave functions are evaluated using the MNDO method and the calculated results are supported by the very good agreement with the experimental results in the few cases in which experimental information is available.The relationship found between the calculated bond orders and the in-plane components of the ¹³C shielding tensors suggest that the experimental study of the ¹³C shielding tensors in these compounds may provide a powerful technique for studying aromaticity. The in-plane components are found to be directly affected by the degree of delocalization of the -electrons in the adjacent bonds. Rules are given for estimating the orientation of the two in-plane components of the shielding tensor.     

Computations of the Raman optical activity via the sum‐over‐states expansions

A computationally convenient and reasonably accurate scheme of computation of the Raman Optical Activity (ROA) is presented and tested on model examples. Electromagnetic tensors were obtained using the sum‐over‐states (SOS) methodology, while their nuclear derivatives were estimated through numerical differentiation. An origin dependence of the results was overcome by a distributed origin gauge transformation. Becke‐3LYP functional and corresponding Kohn–Sham orbitals are used for the excited states. The method was compared to a benchmark coupled‐perturbed (CP) calculation on formamide and a standard ROA spectral simulation and experiment for α‐pinene. Spectra of four standard peptide conformations (α‐helix, 3₁₀‐helix, coil, and β‐sheet) were simulated with smaller fragments and compared to previous experimental observations. © 2001 John Wiley & Sons, Inc. J Comput Chem 22: 426–435, 2001