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Journal of Mathematical Chemistry

, Volume 48, Issue 3, pp 601–616 | Cite as

Integrals of the paramagnetic contribution in the relativistic calculation of the shielding tensor

  • Hassan Safouhi
Original Paper

Abstract

Of the nuclear magnetic resonance (MMR), the nuclear shielding tensor is of a great interest. The relativistic calculation of the nuclear shielding tensor involves extremely challenging integrals of first and second order. Among the first order integrals are paramagnetic contribution integrals, which are extremely difficult to evaluate analytically and numerically, especially when using exponential type functions (ETFs). The main difficulty in the analytical development arises from the presence of 1/r 5 in the operators. In the present contribution, we developed the Fourier transform of the operators of the paramagnetic contribution and we used the Fourier integral transformation to derive analytic expressions for the integrals under consideration over ETFs. The main difficulty in the numerical treatment of the obtained analytic expressions arises from the presence of highly oscillatory spherical Bessel integrals. Extrapolation methods and nonlinear transformations are used to develop highly accurate algorithms for the numerical evaluation of the integrals of the paramagnetic contribution in the relativistic calculation of the shielding tensor.

Keywords

Magnetic properties of molecules Nuclear shielding tensor Fourier integral transformations Extrapolation methods Nonlinear transformations Numerical integration 

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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Mathematical Section, Campus Saint-JeanUniversity of AlbertaEdmontonCanada

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