Correlations of13C chemical shifts and geometry modifications

The effect of geometry modifications of¹³C chemical shifts has been investigated in a small subset of molecules using both LO-INDO and Gaussian 70 (4–31) calculations. The Gaussian calculations, while known to give poor absolute shifts, compare well to the reparameterized semi-empirical INDO determinations in calculated shift changes. In virtually all cases the signs of the shift changes were found to be opposite to that of the changes in the calculated electronic energy.     

A comparative quantum mechanical study of bond separation energies as a measure of cyclic conjugation

Restricted Hartree-Fock (RHF), second-order Møller-Plesset (MP2), and density functional calculations [using the Becke/Lee-Yang-Parr (B-LYP) exchange/correlation gradient-corrected functionals] employing the 6-311G(d, p) and 6-311 + + G(d, p) basis sets have been carried out to calculate isodesmic bond separation energies for reactions involving a number of representative five- and six-membered ring organic compounds. The MP2 and density functional approaches yield reasonably good energies; the density functional method agrees particularly well with experiment, exhibiting a root-mean-square error of only 2.5 kcal/mol. Ring geometries are calculated satisfactorily in all approaches but are given particularly accurately by the MP2 approach. A comparison of the B-LYP bond separation energies with several other definitions of resonance energy shows that these different approaches correlate with each other in a reasonable fashion. © 1995 John Wiley & Sons, Inc.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

An electron localization function investigation of bonding in some simple four‐coordinate nitrogen and phosphorus compounds

The bonding in some simple four‐coordinate species involving nitrogen and phosphorus has been studied by the electron localization function (ELF) approach and compared to that in their conventionally singly and doubly bonded counterparts. Despite evidence suggesting the presence of a conventional multiple bond in certain cases of the four‐coordinate species, the ELF study shows this not to be the case. Rather, the situation is better pictured as, for example, in the case of H₃PCH₂as where both ionic and covalent interactions are present, a type of bond we term cov‐ionic. While the ionic interaction is generally strong, the covalent part can be weak, as in the case of the four‐coordinate nitrogen compounds, or strong, as in the case of the four‐coordinate phosphorus species. The quantum mechanically determined properties of the cov‐ionic bonded compounds are consistent with this picture. © 2000 John Wiley & Sons, Inc. Heteroatom Chem 11:341–352, 2000     

Bonding in the Si2H2 isomers: A topographical study

Chemical bonding in the isomers of the formally triply bonded Si₂H₂ system are studied from the point of view of electron localization function (ELF) bond basin populations and atoms‐inmolecules (AIM) delocalization indices. Calculation carried out at the B3LYP/6‐31 + G(d,p) and MP2 (FC)/6‐31 + G(d,p) level leads to ELF topographies and basin populations that are in good agreement with our intuitive chemical pictures of bonding in these molecules. One single, two double, and one triple silicon silicon bonds are found in the four isomers. It is shown that, with one AIM exception, ratios of basin populations and delocalization indices are consistent and useful in characterizing the nature of the chemical bonding involved. © 2002 John Wiley & Sons, Inc. Heteroatom Chem 13:53–62, 2002; DOI 10.1002/hc.1106     

Use of locally dense basis sets for nuclear magnetic resonance shielding calculations

The locally dense basis set approach to the calculation of nuclear magnetic resonance shieldings is one in which a sufficiently large or dense set of basis functions is used for an atom or molecular fragment containing the resonant nucleus or nuclei of interest and fewer or attenuated sets of basis functions employed elsewhere. Provided the dense set is of sufficient size, this approach is capable of determining chemical shieldings nearly as well as a calculation with a balanced basis set of quality equal to the locally dense set, but with considerable savings of CPU time. Detailed comparisons are provided of locally dense and balanced calculations in the gauge including atomic orbital (GIAO) method for the individual principal values, the isotropic shieldings, and the tensor orientations for hydrogen, carbon, nitrogen, oxygen, fluorine, and phosphorus nuclei. It is seen that chemical functional groups can often define the appropriate molecular fragment to be taken locally dense. While the present test cases are for the most part small molecules, the value of the method is that it will allow calculations on systems that would otherwise presently be computationally expensive or inaccessible. © John Wiley & Sons, Inc.     

Analysis of coefficient identification problems associated to the inverse Euler-Bernoulli beam theory

A rigorous investigation of the identification of a heterogeneousflexural rigidity coefficient in the Euler-Bernoulli steady-statebeam theory in the presence of a prescribed load is presented.Mathematically, this study is an extension to higher-order differentialequations of the coefficient identification problem analysedby Marcellini (1982) for the one-dimensional Poisson equation.In addition, various types of boundary conditions are discussed.Conditions for the well-posedness of these inverse problemsare established and, furthermore, numerical results obtainedusing a regularization algorithm are presented.     

A critical investigation of the effects of the radio frequency potential on the trapping of externally injected ions in ion trap mass spectrometry

The sensitivity of all ion trap mass spectrometry (ITMS) methods is dependent on the trapping efficiency of the instrument. For ITMS instruments utilizing external ion sources, such as laser desorption, trapping efficiency is known to depend on the phase and amplitude of the radio frequency (RF) potential applied to the ring electrode at the time of ion introduction. It is remarkable that, in a considerable body of literature, no consensus exists regarding the effects of these parameters on the efficacy of trapping externally generated ions. In this paper, a summary of the literature is presented in order to highlight significant discrepancies. New laser desorption ion trap mass spectrometry (LD-ITMS) data are also presented, from which conclusions are drawn in our effort to clarify some of the confusion. Copyright 1999 John Wiley & Sons, Ltd.