Monatshefte für Chemie / Chemical Monthly

, Volume 106, Issue 3, pp 701–714 | Cite as

Eichinvariante Berechnung des Diamagnetismus und der chemischen Verschiebung, 1. Mitt.: Ableitungeiner eichin varianten Theorie und ihre Anwendung auf zweiatomige Moleküle und lokalisierte Orbitale

  • U. Sternberg
  • W. Haberditzl
Anorganische, Struktur- und Physikalische Chemie

Gauge-invariant calculation of diamagnetism and chemical shift, I.: Derivation of a gauge-invariant theory and its application to diatomic molecules and localized orbitals


Based on the work ofRebane3 andStaemmler4, a general method has been developed for the approximation of theVan-Vleck-term χ P and theRamsey-term σ P (high frequency contribution of the susceptibility and the chemical shift). An advantage of the method is its complete independence of the coordinate origin. This feature does not depend on approximations in the wave function. Furthermore it is not necessary to construct the perturbated wave function for the calculation of . As these terms are obtained from a power series, only the knowledge of the following one-electron-integrals is necessary:
$$\begin{gathered} \left\langle {\varphi a\left| {X^i Y^j Z^k } \right|\varphi _b } \right\rangle for \chi ^P and \hfill \\ \left\langle {\varphi a\left| {(X^i Y^i Z^k )r^{ - 3} } \right|\varphi b} \right\rangle for \sigma ^P \hfill \\ \end{gathered} $$
(a,b-Slater-type orbitals).

To demonstrate the efficiency and convergence of the procedure a calculation on the H2-molecule has been made. The results resemble in accuracy theHartree—Fock perturbation theory.

Furthermore it is shown that the proposed method is applicable to localized orbitals, the susceptibility being divided into incrementary contributions. The calculations carried out on the LiH and N2 molecules serve as an example of this procedure.

Moreover it is demonstrated that both the total susceptibility and χP can be displayed in terms of incrementary contributions if the translatory parts of theVan-Vleck-paramagnetism are explicitly taken into account. Comparison of experimental and calculated rotationalg-factors permits assessment of the accuracy of the σP-calculation.


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Copyright information

© Springer-Verlag 1975

Authors and Affiliations

  • U. Sternberg
    • 1
  • W. Haberditzl
    • 1
  1. 1.Arbeitsgruppe MagnetochemieSektion Chemie der Humboldt-Universität zu Berlin (DDR)BerlinDeutschland

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