Atom-match matrix

Assume that the molecule A contains N(A) nonhydrogen atoms. The distance matrix for A, DA is then an N(A) x N(A) matrix such that the I th element, DA(I, J), contains the distance between the /th and Jth atoms in A (and similarly for the matrix DB representing the N(B)-atom molecule B). The first stage of the procedure compares each atom from A with each atom from B. Consider the /th atom in A, A(I) then the /th row of the distance matrix DA contains the distances from / to all of the other atoms in A. This set of distances is compared with each of the rows, J, from the distance matrix DB to identify the matching distances. These common distances are used to calculate a Tani-moto coefficient, S(I, J), that measures the similarity between A(I) and B(J). S(I, J) is the //th element of an N(A) x N(B) atom-match matrix, S, that contains the similarities between all pairs of atoms, A(I) and B(J), from A and B. The... 

Once the atom match matrix has been created, the interatomic similarities contained within it are used to determine that atom from B which is most similar to each atom from A, i.e., the matrix is used to estabUsh a set of equivalences of the form A(J) = B(J) where B J) is that atom in B that hes at the centre of the most similar area of 3-D space, as defined by the atoms surrounding it, as does the atom A(7). The basic matching algorithm that is used to estabUsh these equivalences is as foUows ... 

Scan the atom match matrix to find the pair of atoms that have the largest calculated value for T(/,J). 

Description of Method. Salt substitutes, which are used in place of table salt for individuals on a low-sodium diet, contain KCI. Depending on the brand, fumaric acid, calcium hydrogen phosphate, or potassium tartrate also may be present. Typically, the concentration of sodium in a salt substitute is about 100 ppm. The concentration of sodium is easily determined by flame atomic emission. Because it is difficult to match the matrix of the standards to that of the sample, the analysis is accomplished by the method of standard additions. 

Brenner et al. [ 169] applied inductively coupled plasma atomic emission spectrometry to the determination of calcium (and sulfate) in brines. The principal advantage of the technique was that it avoided tedious matrix matching of calibration standards when sulfate was determined indirectly by flame techniques. It also avoided time-consuming sample handling when the samples were processed by the gravimetric method. The detection limit was 70 ig/l and a linear dynamic range of 1 g/1 was obtained for sulfate. 

The actual calculation consists of minimizing the intramolecular potential energy, or steric energy, as a function of the nuclear coordinates. The potential-energy expressions derive from the force-field concept that features in vibrational spectroscopic analysis according to the G-F-matrix formalism [111]. The G-matrix contains as elements atomic masses suitably reduced to match the internal displacement coordinates (matrix D) in defining the vibrational kinetic energy T of a molecule ... 

Interferences in atomic absorption measurements can arise from spectral, chemical and physical sources. Spectral interference resulting from the overlap of absorption lines is rare because of the simplicity of the absorption spectrum and the sharpness of the lines. However, broad band absorption by molecular species can lead to significant background interference. Correction for this may be made by matrix matching of samples and standards, or by use of a standard addition method (p. 30 et seq.). 

ICP offers good detection limits and a wide linear range for most elements. With a direct reading instrument multi-element analysis is extremely fast. Chemical and ionization interferences frequently found in atomic absorption spectroscopy are suppressed in ICP analysis. Since all samples are converted to simple aqueous or organic matrices prior to analysis, the need for standards matched to the matrix of the original sample is eliminated. 

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