Trapped hydrogen atoms in irradiated frozen solutions. Isotope effects

Isotope effects in the yields of H- and D-atoms in acid, neutral and alkaline matrices have been studied by EPR methods. In acid matrices the isotope effect is the same in UV- and X-irradiated matrices, but in neutral and alkaline matrices the effect is larger in UV-irradiated matrices. Furthermore, when the H- and D-atoms are formed by photobleaching of trapped electrons the isotope effect is strongly dependent on the wavelength of the bleaching light, increasing with increasing wavelenghts. The isotope effect in sulphuric acid matrices is dependent on the concentration of the acid. The observation are briefly discussed.     

Introduction of organic/hydro-organic matrices in inductively coupled plasma optical emission spectrometry and mass spectrometry: A tutorial review. Part I. Theoretical considerations

Due to their outstanding analytical performances, inductively coupled plasma optical emission spectrometry (ICP-OES) and mass spectrometry (ICP-MS) are widely used for multi-elemental measurements and also for isotopic characterization in the case of ICP-MS. While most studies are carried out in aqueous matrices, applications involving organic/hydro-organic matrices become increasingly widespread. This kind of matrices is introduced in ICP based instruments when classical “matrix removal” approaches such as acid digestion or extraction procedures cannot be implemented. Due to the physico-chemical properties of organic/hydro-organic matrices and their associated effects on instrumentation and analytical performances, their introduction into ICP sources is particularly challenging and has become a full topic. In this framework, numerous theoretical and phenomenological studies of these effects have been performed in the past, mainly by ICP-OES, while recent literature is more focused on applications and associated instrumental developments. This tutorial review, divided in two parts, explores the rich literature related to the introduction of organic/hydro-organic matrices in ICP-OES and ICP-MS. The present Part I, provides theoretical considerations in connection with the physico-chemical properties of organic/hydro-organic matrices, in order to better understand the induced phenomena. This focal point is divided in four chapters highlighting: (i) the impact of organic/hydro-organic matrices from aerosol generation to atomization/excitation/ionization processes; (ii) the production of carbon molecular constituents and their spatial distribution in the plasma with respect to analytes repartition; (iii) the subsequent modifications of plasma fundamental properties; and (iv) the resulting spectroscopic and non spectroscopic interferences. This first part of this tutorial review is addressed either to beginners or to more experienced scientists who are interested in the analysis of organic/hydro-organic matrices by ICP sources and would like to consider the theoretical background of effects induced by such matrices.     

Introduction of organic/hydro-organic matrices in inductively coupled plasma optical emission spectrometry and mass spectrometry: A tutorial review. Part II. Practical considerations

Inductively coupled plasma optical emission spectrometry (ICP-OES) and mass spectrometry (ICP-MS) are increasingly used to carry out analyses in organic/hydro-organic matrices. The introduction of such matrices into ICP sources is particularly challenging and can be the cause of numerous drawbacks. This tutorial review, divided in two parts, explores the rich literature related to the introduction of organic/hydro-organic matrices in ICP sources. Part I provided theoretical considerations associated with the physico-chemical properties of such matrices, in an attempt to understand the induced phenomena. Part II of this tutorial review is dedicated to more practical considerations on instrumentation, instrumental and operating parameters, as well as analytical strategies for elemental quantification in such matrices.     

Infrared cryogenic studies: Part 14. Chloromethane in various matrices at 10 K

Infrared spectra are reported for chloromethane in argon, krypton, nitrogen, and carbon monoxide matrices at 10 K. No evidence was found for rotation of chloromethane in any of the matrices. In Kr band splitting of the A modes due to intermolecular coupling was observed. In CO, and possibly N₂, minor perturbations of the v₃ mode due to multiple trapping sites were observed. Concentration studies in all matrices show the growth of multimer bands, the predominant species is believed to be an open-chain dimer.     

Localized impurity states in the Hartree-Fock,LCAO approximation. I.

One-electron energies and wave functions for deep trap impurity electrons in a crystal are calculated by the Hartree-Fock, single determinant method. The interactions arising from a many-electron single determinant crystal wave function, with automatic inclusion of exchange effects, are those which determine the one-electron functions and energies. The crystal plus impurity system has no translational symmetry and hence the Bloch theorem is not applicable for the solution of the essentially infinite Hartree-Fock eigenvalue matrix. Thus we develop a technique in which the Hamiltonian and overlap matrices are written in terms of bordered matrices, with the interaction of the impurity functions with the rest of the crystal environment contained in the bordering rows and columns. The resulting secular equation explicitly includes the effects of orthogonalization of the entire basis set, including the impurity functions. This technique could be used in an iterative calculation of the electronic structure of a small number of electrons, assuming that the rest of the electrons in the environment are fixed according to an initial estimate.     

Ab initio electron propagator theory of molecular wires. II. Multiorbital terminal description

Correlated, ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical formalism is developed for the calculation of retarded and advanced Green functions in terms of the electron propagator matrix for a bridge molecule. The calculation of the current requires integration in a complex half-plane for a trace that involves terminal and Green function matrices that may have any rank. Because the latter arrays have poles represented by matrices, an alternative expression is developed in terms of ordinary poles which are (n-1)-fold degenerate or nondegenerate. For an arbitrary number of terminal orbitals, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator, i.e., the parameters that are found in the output of numerical calculations.     

Algebraic structure of fermion density matrices. II

The properties of the algebraic structure of fermion density matrices are studied. The algebraic structure of a density matrix leads to a more varied and detailed classification scheme than that offered by the usual shell structure approach. Investigation of the algebraic structure of fermion density matrices by the methods of algebraic topology leads to a classification scheme based on Betti numbers.     

On the characterization of DNA primary sequences by triplet of nucleic acid bases.

We consider construction of a set of smaller 4 x 4 matrices to represent DNA primary sequences which are based on enumeration of all 64 triplets of nucleic acids bases. The leading eigenvalue from the constructed matrices has been selected as an invariant for construction of a vector to characterize DNA. Additional invariants considered of the derived condensed matrices of DNA include a 64-component vector, the components of which consist of ordered triplets XYZ, with X, Y, Z = A, C, G, T. Construction of similarity/dissimilarity tables based on different invariants for a set of sequences of DNA belonging to the first exon of the beta-globin gene of eight species illustrates the utility of newly formulated invariants for DNA.     

Techniques for gas chromatography of volatile terpenoids from a range of matrices.

The commercial importance of the volatile mono- and sesqui-terpenoids has resulted in a wide range of techiques being used for extraction, concentration, chromatography, and characterisation of constituents. The major chromatographic technique is gas chromatography, and tandem techniques of chromatography linked to further chromatography and spectroscopy, allow much increased resolution, and greater ease of characterisation of terpenes. A wide range of extraction techniques are discussed, and suitability for particular matrices and sample sizes outlined. Chromatography operating conditions and stationary phases, and techniques for solute identification are laid out. A number of applications of terpene analysis in many different matrices are discussed.     

Solvated electron in liquid methanol. An example of a statistical species in chemistry

The methods of analysis of the statistical ensembles of trapping sites, before and after electron localization, for electrons in disordered media are surveyed. The review covers the computer-search methods for pre-existing traps in polar matrices, random field theory of disordered polar matrices and the path integral simulations of solvated electron. The common picture provided by all these methods is emphasized: the solvated electron is a unique in chemistry statistical species characterized by statistical distributions of the structural parameters, energy states, reactivity, etc. The numerical examples are provided by the simulations of the trapping sites and the solvated electron in liquid methanol.     

Ab initio electron propagator theory of molecular wires. I. Formalism

Ab initio electron propagator methodology may be applied to the calculation of electrical current through a molecular wire. A new theoretical approach is developed for the calculation of the retarded and advanced Green functions in terms of the electron propagator matrix for the bridge molecule. The calculation of the current requires integration in a complex half plane for a trace that involves terminal and Green's-function matrices. Because the Green's-function matrices have complex poles represented by matrices, a special scheme is developed to express these "matrix poles" in terms of ordinary poles. An expression for the current is derived for a terminal matrix of arbitrary rank. For a single terminal orbital, the analytical expression for the current is given in terms of pole strengths, poles, and terminal matrix elements of the electron propagator. It is shown that Dyson orbitals with high pole strengths and overlaps with terminal orbitals are most responsible for the conduction of electrical current.     

Analytical pyrolysis of carbohydrates: I. Chemical interpretation of matrix influences on pyrolysis-mass spectra of amylose using pyrolysis-gas chromatography-mass spectrometry

Inorganic additives, viz. Na₂CO₃, NaOH, HCl, ZnC₂, NaH₂PO₄, Na₂HPO₄, NaCl. MgSO₄ and sea salt, to the pyrolysis matrix change the pyrolysis-mass spectrum of amylose significantly. Carbonyl compounds, acids and their lactones, furans, pyranones anhydrosugars and aromatic substances are found in different ratios under the various conditions, as determined by pyrolysis-gas chromatography-mass spectrometry (Py-GC-MS).Carbonyl compounds, acids and lactones are released from alkaline and neutral matrices. Furans and anhydrohexoses are particularly formed under neutral and acidic conditions. Pyranones are specific for phosphate matrices. Unsaturated hydrocarbons and aromatic substances arise from strongly alkaline or dehydrating matrices. Degradation pathways are proposed for various compound categories.The results of pyrolysis-mass spectrometry and Py-GC-MS are highly compatible.     

Extrapolation of real-space quantum chemical calculations from finite-size super cells to the ideal infinite system. I. Theory

A method is proposed how to calculate the correct density matrix of an infinite polymeric chain from that of a standard finite supercell calculation. The density matrix of the finite supercell is transformed into k-space for all k-values allowed by the periodic boundary conditions. The k-dependent matrices are then unitarily transformed, with each unitary matrix being represented by a set of complex rotation matrices. It is shown that the corresponding angles can be interpolated and extrapolated toward the zone boundaries in a straghtforward manner and that this extrapolation can be done from any finite supercell with reasonable accuracy. This gives rise to an infinite system density matrix for which all fundamental properties are guaranteed by construction. This infinite system density matrix may be used to construct a corrected density matrix for the finite supercell calculation. © 1994 John Wiley & Sons, Inc.     

Macroreticular redox polymers. III. Characterization of some hydroquinone–quinone redox polymers

A series of hydroquinone–quinone redox polymers on highly and lightly crosslinked macroreticular styrene–divinylbenzene matrices was characterized for redox capacity, reactivity, equilibria, and redox potential. The effects of cerium(IV), iron(III), and oxygen on determinations of redox capacity are described.     

Evaluation of the mode of binding of immunoglobulin to activated agarose.

Determining the orientation of the immobilization of proteins to solid-phase matrices is of critical importance in the development of systems that employ immobilized proteins. Among these are enzyme-linked immunoassays, immobilized enzymes and affinity chromatography matrices. To determine the orientation of immunoglobulin G (IgG) on activated agaroses, we coupled the immunoglobulin covalently to various activated matrices. The IgG was then cleaved with papain and the liberated fragments collected and analyzed using high-performance liquid chromatography. Only Fab fragments could be detected regardless of the activation method used. This implies that IgG binds to these matrices predominantly via the Fc domain. In order to develop a quantitative method of measuring the Fab and Fc fragments, we compared the binding of IgG and its papain cleavage fragments to S-Zephyr columns and Mono-S columns. Comparison between these columns showed that IgG is bound more tightly to the S-Zephyr column and, in contrast, its retention on Q-Zephyr is less than on a comparable Mono-Q column. The resolution of IgG and its fragments was better in all cases on S-Zephyr than on Mono-S under the conditions employed.     

Chromatographic analysis of alpha-tocopherol and related compounds in various matrices.

Tocopherols and tocotrienols (Vitamin E) are part of a group of "minor components" of main interest, present in the unsaponifiable fraction of many samples. Their importance in biological, metabolical and nutritional studies makes determination of tocopherols and related compounds of major interest. Present work critically reviews the different ways to perform sample pre-treatment and analysis of these compounds, related to the matrices, other analytes to be measured, sensitivity, and simplicity. The review includes well referenced tables that provide in-depth summaries of methodology for the chromatographic analysis of alpha-tocopherol and related compounds in foods, pharmaceuticals, plants, animal tissues and other matrices.     

Molecular symmetry. IV. The coupled perturbed Hartree–Fock method

Symmetry methods employed in the ab initio polyatomic program HONDO are extended to the coupled perturbed Hartree–Fock (CPHF) formalism, a key step in the analytical computation of energy first derivatives for configuration interaction (CI) wavefunctions, and energy second derivatives for Hartree–Fock (HF) wavefunctions. One possible computational strategy is to construct Fock-like matrices for each nuclear coordinate in which the one- and two-electron integrals of the usual Fock matrix are replaced by the integral first derivatives. “Skeleton” matrices are constructed from the unique blocks of electron-repulsion integral derivatives. The correct matrices are generated by applying a symmetrization operator. The analysis is valid for many wavefunctions, including closed- or open-shell spin-restricted and spin-unrestricted HF wavefunctions. To illustrate the method, we compare the computer time required for setting up the coupled perturbed HF equations for eclipsed ethane using D_3h symmetry point group and various subgroups of D_3h. Computational times are roughly inversely proportional to the order of the point group.     

Toward high-performance computational chemistry: I. Scalable Fock matrix construction algorithms

Several parallel algorithms for Fock matrix construction are described. The algorithms calculate only the unique integrals, distribute the Fock and density matrices over the processors of a massively parallel computer, use blocking techniques to construct the distributed data structures, and use clustering techniques on each processor to maximize data reuse. Algorithms based on both square and row-blocked distributions of the Fock and density matrices are described and evaluated. Variants of the algorithms are discussed that use either triple-sort or canonical ordering of integrals, and dynamic or static task clustering schemes. The algorithms are shown to adapt to screening, with communication volume scaling down with computation costs. Modeling techniques are used to characterize algorithm performance. Given the characteristics of existing massively parallel computers, all the algorithms are shown to be highly efficient for problems of moderate size. The algorithms using the row-blocked data distribution are the most efficient. © 1996 by John Wiley & Sons, Inc.     

Error matrices in gas-electron diffraction: II. Influence of weight matrix

The properties of three different forms of error matrices in electron diffraction are investigated, assuming the presence of stationary, Gaussian, Markovian noise in the primary data. The error matrices studied are M_x^p based on the optimum weight matrix P the bona fide error matrix M_x^w based on the nonoptimum weight matrix W, and the false error matrix M_x^o commonly calculated by diffractionists using the formula for the optimum error matrix while incorporating a nonoptimum weighting. Simple formulae relating the elements of the various matrices are derived in the case where W is the best diagonal weight matrix and where geometric constraints are not imposed on parameters. The influence of geometric constraints is tested. Calculations indicate that diagonal weight matrices in ordinary circumstances give results imperceptibly inferior to the results obtained with the best nondiagonal weight matrices. Elements of M_x^w closely approach those of M_x^p whereas elements of the false error matrix, taken alone, may be very misleading.     

Symmetric group approach to relativistic CI. I. General formalism

General formulas for matrix elements of spin-dependent operators in a basis of spin-adapted antisymmetrized products of orthonormal orbitals are derived. The resulting formalism may be applied to construction of the Hamiltonian matrices both for Pauli and for projected no-pair relativistic configuration interaction methods. From a formal point of view, it is a generalization of the symmetric group approach to the CI method for the case of spin-dependent Hamiltonians. © 1997 John Wiley & Sons, Inc.