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

Based on the work ofRebane ³ andStaemmler ⁴, 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.     

Eichinvariante Berechnung des Diamagnetismus und der chemischen Verschiebung

The procedure derived in^1–4 was used to calculate the magnetic susceptibilities of a series of unsaturated hydrocarbons (propene, isobutene, 1-butene, cyclohexene, butadiene,trans-1,3,5-hexatriene). The difference between the measured and computed susceptibilities of these molecules is discussed. The discussion shows, that there is no correlation existing between the difference and the presumed delocalisation effects.

Die Ergebnisse sind Bestandteil einer der letzten Arbeiten, die von dem von uns hochverehrten, leider zu früh verstorbenen, Prof. Dr.W. Haberditzl betreut wurden.     

A game-theoretical model for the determination of charge and configuration of a metal in complex compounds

A model is presented permitting a one-step calculation of the required effective charge number q and the configuration 3d^a 4s^b 4p^c at the central metal ion, using the mathematical method of zero-sum two-person games.     

Eichinvariante Berechnung des Diamagnetismus und der chemischen Verschiebung

The procedure described in^1,2 was used to calculate the magnetic susceptibility contributions of C-H bonds to the diamagnetism of various hydrocarbons. It was found a correlation between these C-H-bond contributions and the bond lengths. The transferability of the evaluated C-H-bond susceptibilities from one molecule to another is discussed.