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Analysis with Single Determinant Methods

The analysis starts with a restricted open-shell Kohn-Sham (ROKS) calculation on the HS state. If necessary, the magnetic orbitals are transformed to the representation with local orthogonal orbitals a and b, as shown in the first column of Fig. 5.11. Staying within the spin-restricted formalism makes that for each a orbital a orbital can be found which has the same spatial part. In the first step, the direct exchange is estimated from the energy difference of the HS(ROKS) and a BS determinant in which only the spin of one of the unpaired electrons is inverted, but neither the core nor the magnetic orbitals are optimized. [Pg.157]

With the help of Yamaguchi s expression (Eq.4.65), one can define the direct exchange contribution (Jde) to the total magnetic coupling as [Pg.157]

Step 2 consists in the optimization of the magnetic orbitals of the BS determinant in the fixed field of fhe doubly occupied orbitals, a so-called frozen core (FC). The magnetic orbitals become more delocalized and, more specifically, gain some amplitude on the other magnetic center. This means that the unpaired electrons can move from one center to the other and activate the kinetic exchange mechanism. The contribution to J is [Pg.158]

To a very good approximation, the spatial part of the new magnetic BS orbitals a and b can be written as a weighted sum of the ROKS orbitals [Pg.158]

9 Calculate the overlap of the spatial part of the relaxed magnetic orbitals [Pg.158]


D.G. Themelis, A. Economou, A. Tsiomlektsis, P.D. Tzanavaras, Direct determination of phosphate in urine by sequential-injection analysis with single on-line dilution-calibration method and photometric detection, Anal. Biochem. 330 (2004) 193. [Pg.288]

Ballew, R. M. and Demas, J. N. (1991). Error analysis of the rapid lifetime determination method for single exponential decays with a nonzero base-line. Anal. Chim. Acta 245, 121-7. [Pg.144]

Many of the published methods for the determination of metals in seawater are concerned with the determination of a single element. Single-element methods are discussed firstly in Sects. 5.2-5.73. However, much of the published work is concerned not only with the determination of a single element but with the determination of groups of elements (Sect. 5.74). This is particularly so in the case of techniques such as graphite furnace atomic absorption spectrometry, Zeeman background-corrected atomic absorption spectrometry, and inductively coupled plasma spectrometry. This also applies to other techniques, such as voltammetry, polarography, neutron activation analysis, X-ray fluroescence spectroscopy, and isotope dilution techniques. [Pg.128]

When a single crystal of a solid can be produced. X-ray diffraction provides an accurate, definitive structure, with bond lengths determined to tenths of a picometre. In recent years, the technique has been transformed from a very slow method reserved only for the most special structures, to a method of almost routine analysis with modern machines, suites of computer programs and fast computers are used to solve several crystal structures per week. [Pg.113]

In individual compound analysis with the FID, analyte identification relies solely on retention time. As a result, single compound determinations (for example, individual phenols or PAHs) are usually gravely affected by interferences that often render the results unreliable or unusable. Because the FID methods for individual compound analysis are so susceptible to false positive results, they should be used with caution and only for interference-free matrices. [Pg.218]

Various alkyl and aryltin compounds were determined in aquatic matrices, namely sediments, biota and water by means of gas chromatographic methods. In this work, comparisons of single or dual flame photometric detectors and electron capture detectors were reported (Tolosa et al., 1991). Sample preparations included acid digestion, extraction, formation of methyl derivatives and clean-up with alumina prior to gas chromatographic analysis. With the electron capture detector, cold on-column injection of organo-tin chlorides was studied. The conclusion was that a single or dual flame photometric detector equipped with a 600 nm interference filter yielded the best performance for determinations of tin species as methyl derivatives. Detection limits for the method using flame... [Pg.429]

In 1944, about the time Sanger determined the primary structure of insulin, two-dimensional paper chromatography became available for analyzing amino acids of protein samples.32 This method allowed Sanger to analyze 20 amino acids in a single run with considerably less sample and time compared to the previous methods. The development of an automated amino acid analyzer in 1958 by Spackman, Stein and Moore had made further progress.33 This first amino acid analyzer performed an analysis with 1 pmol of sample in 20 hours. Due to the continuous improvements made on amino acid analyzers,... [Pg.26]


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