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  • Matrix element  (1)
  • derivative spectrophotometry  (1)
  • Springer  (2)
  • 1
    ISSN: 1436-5073
    Keywords: neodymium ; erbium ; 5,7-dibromo-8-hydroxyquinoline ; rare earths determination ; derivative spectrophotometry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract The absorption spectra of 4f electron transitions of the complexes of neodymium and erbium with 5,7-dibromo-8-hydroxyquinoline in the presence of octylphenol poly(ethyleneglycol)ether have been studied by normal and third-derivative spectrophotometry. The proposed method is free of interference of other rare earths. The calibration graphs were linear up to 18 μg/ml of neodymium and 21 μg/ml of erbium (in the final solution). The derivative molar absorptivities are 395 l.mol–1.cm−1 for neodymium and 3421.mol−1.cm−1 for erbium. The corresponding values of Sandell's sensitivity were 0.36 and 0.49 μg.cm−1, respectively. The relative standard deviations evaluated from ten independent determinations of 2.5 μg/ml of neodymium and erbium are 1.5 and 3.8% for neodymium and 1.8 and 4.1% for erbium in absence and presence of 70 μg of lanthanum, respectively. The detection limits (signal to noise ratio=2) are 0.23 μg/ml for neodymium and 0.30 μg/ml for erbium. The method has been used for the determination of neodymium and erbium in mixed rare earths with satisfactory results.
    Type of Medium: Electronic Resource
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Theoretical chemistry accounts 96 (1997), S. 135-139 
    ISSN: 1432-2234
    Keywords: Key words: Irreducible tensor operator ; Matrix element ; Real basis ; Symmetry
    Source: Springer Online Journal Archives 1860-2000
    Topics: Chemistry and Pharmacology
    Notes: Abstract . Molecular matrix elements of a physical operator are expanded in terms of polycentric matrix elements in the atomic basis by multiplying each by a geometrical factor. The number of terms in the expansion can be minimized by using molecular symmetry. We have shown that irreducible tensor operators can be used to imitate the actual physical operators. The matrix elements of irreducible tensor operators are easily computed by choosing rational irreducible tensor operators and irreducible bases. A set of geometrical factors generated from the expansion of the matrix elements of irreducible tensor operator can be transferred to the expansion of the matrix elements of the physical operator to compute the molecular matrix elements of the physical operator. Two scalar product operators are employed to simulate molecular two-particle operators. Thus two equivalent approaches to generating the geometrical factors are provided, where real irreducible tensor sets with real bases are used.
    Type of Medium: Electronic Resource
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