Simultaneous multi-element analysis of trace elements in soil samples by means of high-resolution inductively coupled plasma sector field mass spectrometry (SF-ICP-MS)

The potential of SF-ICP-MS for trace element analysis in complex environmental matrices such as soil solutions was investigated. Spectral interferences found in mass spectra of soil matrices are presented in detail. Furthermore, the influences of single components of the soil matrix on the signal intensity of selected elements were studied. Detection limits of different elements are presented with respect to the composition of the matrix. A fast and accurate method for quasi-simultaneous determination of Al, Si, P, V, Cr, Mn, Fe, Ni, Co, Cu, Zn, As, Se, Sr, Mo, Cd, Sn, Hg and Pb in aqueous soil extracts was established. Received: 3 January 2000 / Revised: 28 March 2000 / Accepted: 31 March 2000     

对称群标准表示矩阵计算新方法

在多体问题的对称群方法中,群表示矩阵的计算是关键性问题。Young-Yamanouchi规则给出了标准正交表示的计算方法,然而该法相当繁琐,颇难使用,本文将2列Young表标准表示的计算方法[1]推广到任意不可约表示,给出对称群标准表示矩阵计算新方法.     

Elements of irreducible tensorial matrices generated by finite groups with applications to ligand field Hamiltonians

Using symmetry to determine Hamiltonian matrix elements for quantum systems with finite group symmetry is a special case of obtaining group-generated irreducible tensorial matrices. A group-generated irreducible tensorial matrix transforms irreducibly under the group and is a linear combination of group transformations on a reference matrix. The reference matrix elements may be appropriate integrals or parameters. The methods of normalized irreducible tensorial matrices (NITM) are employed to express elements of the generated matrix in terms of those of the reference matrix without performing the actual transformations. Only NTTM components of the reference matrix with the same transformation properties as the group-generated matrix will contribute to its elements. The elements of invariant symmetry-generated matrices are proportional to simple averages of certain elements of the reference matrix. This relation is substantially more efficient than previous techniques for evaluating matrix elements of octahedral and tetragonal d-type ligand-field Hamiltonians.     

Integrals and derivatives for correlated Gaussian functions using matrix differential calculus

The matrix differential calculus is applied for the first time to a quantum chemical problem via new matrix derivations of integral formulas and gradients for Hamiltonian matrix elements in a basis of correlated Gaussian functions. Requisite mathematical background material on Kronecker products, Hadamard products, the vec and vech operators, linear structures, and matrix differential calculus is presented. New matrix forms for the kinetic and potential energy operators are presented. Integrals for overlap, kinetic energy, and potential energy matrix elements are derived in matrix form using matrix calculus. The gradient of the energy functional with respect to the correlated Gaussian exponent matrices is derived. Burdensome summation notation is entirely replaced with a compact matrix notation that is both theoretically and computationally insightful. © 1996 John Wiley & Sons, Inc.     

Efficient method for computation of representation matrices of the unitary group generators

The representation matrices of the unitary group generators E_k1 are equivalent to the representation matrices of cyclic permutations (k, k ± l, …, l ? 1, l). A method is presented for simultaneous computation of matrices corresponding to all different generators at a cost of less than one multiplication per nonzero element. The number of operations necessary for calculation of individual matrices for single generators or for products of two generators is at most proportional to the number of matrix elements of the final matrix. This approach eliminates the need to store the representation matrices in CI calculations.     

Representations of the symmetric group generated by projected spin functions: A graphical approach

The representation matrices generated by the projected spin functions have some very interesting properties. All the matrix elements are integers and they are quite sparse. A very efficient algorithm is presented for the calculation of these representation matrices based on a graphical approach and a new indexing scheme for representation of primitive spin functions is introduced. Test calculations show that the method is very fast and suited for calculations on vector computers. © 1996 John Wiley & Sons, Inc.     

High-resolution spectra of selected rare earth elements and spectral interferences studied by inductively coupled plasma-atomic emission spectroscopy (ICP-AES)

The rare earth elements (REEs) play very important roles in industrial manufacturing, technology development and biological processes. Due to their complex emission spectra, trace levels of REEs are difficult to analyze by conventional ICP-AES techniques. The present study investigates possible spectral interferences of matrices (rare earth oxides of Ce, Pr, Nd, Sm and Dy) on the analytical lines (± 0.1 nm) of a target REE. Detailed and well-resolved spectra for selected REEs are presented, and procedures used to rectify the problem of spectral interferences caused by REE matrices are discussed. A computer-assisted system (CAS) for spectral recognition has been developed and used to assist in the study of matrix interference. To determine directly trace rare earth elements in REE matrices without sample pre-separation, the application potential is demonstrated with a one meter sequential instrument retrofitted with a 3600 grooves/mm grating.     

Direct flame atomic absorption spectrophotometric determination of Mn in rocks, nodules, soils and related materials using tartaric acidKClSrCl(2) mixture

A mixture of tartaric acid-potassium chloride and strontium chloride has been used for accurate and precise estimation of manganese in various international reference rocks, nodules, soil and related samples by flame atomic absorption spectrophotometry (FAAS). The method is fairly rapid and involves no separation of the analyte from the matrix elements. Sample decomposition is straight-forward (2:1 mixture of hydrogen fluoride and perchloric acid). Forty-seven well characterized standard reference samples of diverse matrices have been analysed and the results are compared with the reported data.     

Determination of arsenic in plant samples by inductively coupled plasma atomic emission spectrometry with ultrasonic nebulization: a complex problem

Under well-defined conditions, the analysis of most trace elements by inductively coupled plasma atomic emission spectrometry with ultrasonic nebulization (ICP-AES-USN) leads to accurate results for environmental matrices usually studied. Due to differences in matrix composition between standards and samples, ICP-AES-USN determinations of arsenic are interfered with by changes that take place mainly within the desolvation stage of the USN device. In this work, effects of plant matrices on the determination of As in six arsenic species have been investigated. Firstly, interferences were simulated by measuring analyte (species) signals in solutions containing variable concentrations of the main matrix elements encountered in mineralized plant samples (K, Ca, Mg, P and Na). Secondly, the influence of real plant matrices on emission signals of arsenic species was also studied. In this case, the observed effects were different than for individual matrix elements considered separately: Ca and Mg always present in real samples efficiently compensate the undesirable effects. Validation of this statement has been performed using mineralized plant reference materials. In addition, ICP-AES-USN results have been compared with those obtained by Zeeman electrothermal atomic absorption spectrometry.     

Investigation of plasma-related matrix effects in inductively coupled plasma-atomic emission spectrometry caused by matrices with low second ionization potentials—identification of the secondary factor

Plasma-related matrix effects induced by a comprehensive list of matrix elements (a total of fifty-one matrices) in inductively coupled plasma-atomic emission spectrometry were investigated and used to confirm that matrix effects caused by elements with a low second ionization potential are more severe than those from matrix elements having a low first ionization potential. Although the matrix effect is correlated unambiguously with the second ionization potential of a matrix, the correlation is not monotonic, which suggests that at least one other factor is operative. Through study of a large pool of matrix elements, it becomes possible to identify another critical parameter that defines the magnitude of the matrix effect; namely the presence of low-lying energy levels in the doubly charged matrix ion. Penning ionization by Ar excited states is proposed as the dominant mechanism for both analyte ionization/excitation and matrix effects; matrices with a low second ionization potential can effectively quench the population of Ar excited states through successive Penning ionization followed by ion-electron recombination and lead to more severe matrix effects.     

Explicit formulas for the Hamiltonian matrix elements

The explicit formulas for the evaluation of the Hamiltonian matrix elements are presented. The calculation of the integral coefficients is independent of both the nature of the orbitals and th spin coupling schemes. It is fully automatic and only dependent on the number of doubly and singly occupied orbitals. Further-more, the symmetric group representation matrices are not needed, and the N! problem can be avoided.     

Tomography and elemental analysis using neutrons in transmission

Expressions for the calculation of minimum detectable mass and length fractions of elements, compounds and mixtures in a sample using neutron attenuation coefficients are derived, based on previous work done with photon attenuation coefficients. These expression allow quantitative information about elemental concentration to be extracted from neutron transmission measurements and neutron transmission tomography. Calculations are carried out for the detectable mass fraction of hydrogen in a number of sample matrices of industrial interest and of elements in a water matrix highlighting the differences with photon attenuation measurements. Results are presented for three neutron energies, cold (0.001 eV), thermal (0.025 eV) and fast (14 MeV).     

ALIGN_MTX—An optimal pairwise textual sequence alignment program,adapted for using in sequence-structure alignment

The presented program ALIGN_MTX makes alignment of two textual sequences with an opportunity to use any several characters for the designation of sequence elements and arbitrary user substitution matrices. It can be used not only for the alignment of amino acid and nucleotide sequences but also for sequence-structure alignment used in threading, amino acid sequence alignment, using preliminary known PSSM matrix, and in other cases when alignment of biological or non-biological textual sequences is required. This distinguishes it from the majority of similar alignment programs that make, as a rule, alignment only of amino acid or nucleotide sequences represented as a sequence of single alphabetic characters. ALIGN_MTX is presented as downloadable zip archive at http://www.imbbp.org/software/ALIGN_MTX/ and available for free use.As application of using the program, the results of comparison of different types of substitution matrix for alignment quality in distantly related protein pair sets were presented. Threading matrix SORDIS, based on side-chain orientation in relation to hydrophobic core centers with evolutionary change-based substitution matrix BLOSUM and using multiple sequence alignment information position-specific score matrices (PSSM) were taken for test alignment accuracy. The best performance shows PSSM matrix, but in the reduced set with lower sequence similarity threading matrix SORDIS shows the same performance and it was shown that combined potential with SORDIS and PSSM can improve alignment quality in evolutionary distantly related protein pairs.     

A provenance study of coffee by photon activation analysis

Photon activation analysis (PAA) is a multi-elemental radioanalytical technique in trace elements analysis with high accuracy and precision. Researchers at the Idaho accelerator center performed PAA analysis on coffee samples from several locations around the world as an initial step in assessing the relationship between trace elements in illicit drugs and the soils in which they were grown. The preliminary results show coffees from different locations have different concentrations of trace elements. In the three cases where we have soil samples, the matrices of elements in the coffee samples are closely related to the matrices of the elements of the local soil samples. The majority of trace elemental content is similar to that of the local soil sample in which the coffee is planted. It may be that coffee assimilates numerous elements from the soil where it is grown in similar ratios as is found in the soil. Thus, it is conceivable that the elemental content could serve as “fingerprint” to trace the origins of the coffee. To verify our analytical results we applied X-ray fluorescence (XRF) methods as well. Our PAA results are consistent with XRF experimental data. The future of tracing the origin of illicit drugs with the PAA technique is promising.     

On-line coupled supercritical fluid extraction and chromatography for the determination of thiolcarbamate herbicides in soil matrix

Supercritical fluid extraction (SFE) was on-line coupled with supercritical fluid chromatography (SFC) for the determination of thiolcarbamate herbicides in soil matrix. Inert ODS-silica gel packings were used as a trap column for an interface between SFE and SFC and as an analytical column for the satisfactory separation of extracts. Thiolcarbamate herbicides could be extracted satisfactorily from the soil matrix, which had different characteristics. The results indicated that the proposed system was useful for the rapid determination of thiolcarbamate herbicides in soil matrices.     

Formulation of the vibrational theory in terms of redundant internal coordinates

Using the generalized inverse of matrices and the method of canonical matrices, this paper develops an unambiguous formulation of the theory of small vibrations of molecules which is valid when redundant internal coordinates are used. Such treatment includes the attainment of unambiguous relationships relating the compliance matrix (the generalized inverse of the canonical force constants matrix) with experimental data (vibrational frequencies, Coriolis coupling constants, centrifugal distortion constants and mean-square amplitudes). Moreover, expressions for the elements of the Jacobian matrices of the above magnitudes with respect to the compliance constants have been also obtained as well as some sum rule relationships.     

Statistical correlation between configuration-dependent properties of polymer chains

A new methodology for formulating the averages of elements of generator matrices is presented. Incorporation of this technique to the Rotational Isomeric State (RIS) model allows the efficient generation of the higher and mixed moments of any conformation-dependent physical property of a polymer chain. The computational technique is based on symbolic manipulation of the generator matrix elements which are treated as character strings. Successful application of the technique is demonstrated by calculating the correlation coefficient between the dipole moment and the end-to-end distance of polymer chains with symmetric rotation potentials and in the independent bond rotation approximation. It is shown that the correlation heavily depends on the orientation of the bond dipole moment vector orientation.     

Semigroups and the density matrix formulation of quantum mechanics

A formulation of quantum mechanics is presented based on the theory of semigroups and the associated enveloping algebras of functions defined on countable subsemigroups. The existence of a unique *-involution is not assumed. The fundamental elements of a semigroup are identified with experimental precedures for the separation of subensembles from a given ensemble of experimental systems. Observables are represented as elements of enveloping algebras, and ensembles as density matrices within an enveloping algebra. The statistical properties of ensembles are expressed in terms of traces defined on the semigroup and its enveloping algebras. The elements and generators of the Poincaré group can be defined and interpreted in the usual way. A variety of applications is described, in which the theory of the density matrix plays an essential or effective role. Advantages associated with the resulting freedom from the limitations of Hilbert space are illustrated.     

Determination of gold in sludge and soil by sequential ICP-AES after preconcentration and separation with thiol-cotton fibre

Summary A method is presented for the determination of gold in sludge and soil samples by sequential ICP-AES after preconcentration and separation from the common alkali and alkaline-earth metals, as well as other matrix components, e.g. iron, by a thiol-cotton fibre column. The cotton fibre, impregnated with thioacetic acid, quantitatively adsorbs gold, thus eliminating the severe spectral interferences encountered by direct ICP-AES analysis. After preconcentration and separation the results obtained at Au 242.795 nm and Au 267.595 nm agree with each other. A quantitative recovery for added spikes was obtained. The method allows the determination of gold in complex matrices such as soil or sludge samples that have been proven to be impossible by conventional ICP-AES without separation from the matrix.On leave from Shanghai Institute of Metallurgy, Academia Sinica, Shanghai 2000 50, China     

LINCS: A linear constraint solver for molecular simulations

In this article, we present a new LINear Constraint Solver (LINCS) for molecular simulations with bond constraints. The algorithm is inherently stable, as the constraints themselves are reset instead of derivatives of the constraints, thereby eliminating drift. Although the derivation of the algorithm is presented in terms of matrices, no matrix matrix multiplications are needed and only the nonzero matrix elements have to be stored, making the method useful for very large molecules. At the same accuracy, the LINCS algorithm is three to four times faster than the SHAKE algorithm. Parallelization of the algorithm is straightforward. © 1997 John Wiley & Sons, Inc. J Comput Chem 18 : 1463–1472, 1997