Fast inversion algorithms of Toeplitz-plus-Hankel matrices

Summary The paper deals with the problems of fast inversion of matricesA=T+H, whereT is Toeplitz andH is Hankel. Several algorithms are presented and compared, among them algorithms working for arbitrary strongly nonsingular matricesA=T+H.     

The energy dependence of fusion in the 9Be+28Si system

The angular distributions of the energy spectra of the light charged particles (p, d and α) from the ⁹Be + ²⁸Si reaction have been measured in the energy range 12 ≦ E_lab ≦ 30 MeV. The particle evaporation spectra and the angular distributions were analyzed with a spin dependent statistical model. Angular distributions of ⁹Be ions elastically scattered on ²⁸Si have been measured at the energies 12 MeV, 17 MeV, 23 MeV and 30 MeV and were analysed, together with previously measured cross sections, with the optical model. The fusion cut-off angular momentum l_fus(E), the fusion cross section σ_fus(E) and the ratio σ_fus/σ_R^OM(E) were deduced. The excitation function for fusion was analyzed with the Glas and Mosel model. The parameters obtained from the fusion excitation function were compared with the corresponding ones from the ⁹Be + ²⁸Si optical-model interaction potential.     

On the Presumptive Similarity of Kohn–Sham and Brueckner Orbitals

For states of many-electron systems disclosing various degrees of quasidegeneracy, we have carried out comparative studies of Kohn–Sham orbitals (KSO) generated for several xc-potentials, Brueckner orbitals (BO) represented by the Brueckner-coupled cluster orbitals, and Hartree–Fock (HF) orbitals by means of criteria directly related to the orbital structure which are based on relative distance indices for various pairs of equidimensional subspaces defined by the KSO and BO basis sets. We have found that both for weak and strong quasidegeneracy there are systems for which the KSO–BO distances are larger than the BO–HF ones. For strongly quasidegenerate states it is found that the distance indices are the largest for hybrid potentials, and that the subspaces spanned by KSOs are closer to those spanned by HF orbitals than by BOs. Hence, our results do not support the recently formulated expectations concerning the similarity of Brueckner orbitals and Kohn–Sham orbitals, including those corresponding to purely local exchange-correlation potentials.     

On the mechanism of the gif system for the oxidation of saturated hydrocarbons

The high selectivity of the Gif system for hydrocarbon oxidation is shown to depend upon the capture of $\text{tert.}$ radicals by pyridine; the mechanism for the secondary oxidation products has only a minor radical component as judged by competitive trapping.     

Kinetic isotope effects of nitrogen and hydrogen in reaction of N-tert-butyl-P-phenylphosphonamidothioic acid with alcohols

Nitrogen and hydrogen isotope effects for the reaction of N-tert-butyl-P-phenylphosphonamidothioic acid 1 with alcohols (methanol, butanol, iso-propanol, tert-butanol) were measured in dichloromethane at 30 °C. The observed nitrogen isotope effect k₁₄/k₁₅ is only slightly sensitive to a steric hindrance of the alcohol [1.0070 ± 0.0002 (MeOH), 1.0074 ± 0.0004 (BuOH), 1.0062 ± 0.0004 (PrⁱOH), 1.0087 ± 0.0007 (Bu^tOH)]. The pre-equilibrium step, with proton transfer from oxygen to nitrogen was proved by the inverse hydrogen effect k_ROH/k_ROD[0.778 ± 0.052 (MeOH), 0.863 ± 0.063 (BuOH), 0.883 ± 0.080 (PrⁱOH), 0.746 ± 0.084 (Bu^tOH)]. The experimental values are consistent with theoretical results of semiempirical calculations on PM3 level for an elimination-addition mechanism and metathiophosphonate PhPSO intermediacy. For the reaction with methanol the addition-elimination mechanism is also possible.     

Applicability of coupled-pair theories to quasidegenerate electronic states: A model study

The coupled-pair many-electron theory, its linear approximation, and various other approximate coupled-pair approaches based on the orthogonally spin-adapted coupled-pair theory are applied to simple model systems in which the degree of quasidegeneracy can be continuously varied over a wide range. The four-electron models studied are three ab initio minimum basis set models involving four hydrogen atoms in various spatial arrangements as well as the semiempirical Pariser–Parr–Pople π-electron model of cis-butadiene. The results are compared with the exact full configuration interaction results as well as with those obtained with other approximate limited configuration interaction approaches and Davidson's formula estimate, and the effect of quasidegeneracy on various approaches is discussed. We also examine the difference between the correlation energies obtained with the coupled-pair many-electron theory and its linear version and discuss the source of these differences and of the breakdown of the latter approximation in the case of very strong quasidegeneracies.     

Detection of protease activities with the mass-spectrometry-assisted enzyme-screening (MES) system

The MALDI-MES provides a rapid, sensitive and reproducible alternative approach to existing analytical techniques for the detection of enzymatic activities that does not require a chromophore or radiolabeling. An improved method is presented, by which enzymes with defined substrate specificities can be detected with a MALDI mass spectrometer in complex protein fractions. In order to demonstrate the utility of the new method, in this study we describe the use of MALDI-MES to detect proteolytic activities in a protein extract from porcine renal tissue, which contained several thousand proteins as visualized by 2D electrophoresis. The analytical procedure is based on covalent immobilization of proteins to beads. By immobilizing proteins, autolytic and proteolytic degradation is prevented and the removal of those molecules from the protein fraction is achieved, which otherwise would interfere with the mass spectrometric detection of the enzymatic reaction products. The enzymatic activity is determined by incubating the immobilized proteins with a reaction-specific probe, followed by the analysis of the reaction mixture with the MALDI-MS after defined incubation times. The presence of the target enzyme is validated by locating a signal, which fits the molecular mass of the expected reaction product in the mass spectrum. To demonstrate how to detect proteolytic activities in this system, the reactions catalyzed by endopeptidase, angiotensin-converting enzyme, kallikrein, renin, and urotensin-converting enzyme were monitored. The experiments showed that the MALDI-MES method is sufficient according the quantification to investigate the effects of inhibitors. This is demonstrated using a specific renin inhibitor to inhibit an angiotensin-I generating enzyme activity in a renal protein extract.Abbreviations MALDI-MS matrix-assisted mass spectrometry - MES mass-spectrometry-assisted enzyme-screening system     

Multiple solutions of the single-reference coupled-cluster equations. I. H4 model revisited

Single-reference coupled-cluster methods corresponding to various approximate forms of the cluster operator including up to four-electron operators are applied to the simple H 4 model system with the aim of numerically studying the attainability and properties of multiple solutions of the systems of nonlinear equations for the cluster amplitudes. Various solutions have been obtained for the excited states 2¹ A₁ and 5¹ A₁. It is documented that there exist nonphysical nonstandard solutions that yield energies very close to the physical ones. A simple way of selecting the physically meaningful solutions is proposed. It is demonstrated that the attainability of nonstandard solutions describing a state of H4 within the framework of a given SE -CC method strongly depends on the cluster structure of that state. © 1994 John Wiley & Sons, Inc.     

Applicability of the Galerkin—Petrov method in quantum chemistry. The quartic oscillator problem

The use of a scheme based on the Galerkin—Petrov method for quantum chemical calculations is suggested.The results of its application to the calculation of the ground and excited states of the quartic oscillator are presented.