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Theoretica chimica acta

, Volume 58, Issue 2, pp 137–144 | Cite as

Some rules forS(-2k) dipole sums?

  • Jonathan A. Yoffe
  • Gerald M. Maggiora
  • A.Terry Amos
Original Investigations

Abstract

Stieltjes conditions and the ratio test provide necessary but not sufficient conditions onS(-2k) dipole sums. If the dipole sums are accurate the associated [n, n −1] Padé approximant provides a better representation of α (Ω), the frequency-dependent dipole polarizability, than a truncated series expression and, in addition, should bound α(Ω) below. It is shown how constraints on the dipole sums effect the form of the [2,1] Padé approximant and an additional constraint is derived that ensures the analyticity of the approximant on 0≤ Ω < Ω1. There then follows a discussion of the reliability of available literature dipole sum values for small molecules containing H, C, N and O.

Key words

Dipole sums Padé approximants 

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Copyright information

© Springer-Verlag 1981

Authors and Affiliations

  • Jonathan A. Yoffe
    • 1
  • Gerald M. Maggiora
    • 1
  • A.Terry Amos
    • 2
  1. 1.Departments of Biochemistry and ChemistryUniversity of KansasLawrenceUSA
  2. 2.Department of MathematicsUniversity of NottinghamUniversity ParkEngland

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