Calculation of properties from response theory

Apart from primary structural and energetic data, which can be extracted directly from four-component calculations, molecular properties, which connect measured and calculated quantities, are sought and obtained from response theory. In a pilot study, Visscher et al. (1997) used the four-component random-phase approximation for the calculation of frequency-dependent dipole polarizabilities for water, tin tetrahydride and the mercury atom. They demonstrated that for the mercury atom the frequency-dependent polarizability (in contrast with the static polarizability) cannot be well described by methods which treat relativistic effects as a perturbation. Thus, the varia-tionally stable one-component Douglas-Kroll-Hess method (Hess 1986) works better than perturbation theory, but differences to the four-component approach appear close to spin-forbidden transitions, where spin-orbit coupling, which the four-component approach implicitly takes care of, becomes important. Obviously, the random-phase approximation suffers from the lack of higher-order electron correlation. 

Of particular importance in chemistry is the response of a molecular system to an external magnetic field as applied in routinely performed NMR experiments for the identification of compounds, the analysis of reaction mechanisms, and reaction control. Theoretical tools must provide spin-spin coupling constants and shielding tensors in order to calculate quantities, which can be related to experimental data. Needless to say, coupling constants and chemical shifts calculated from shielding tensors can only be obtained from accurate four-component methods for heavy nuclei. The theory of relativistic calculations of magnetic properties has recently been analysed in great detail (Aucar et al. 1999). 

On the molecular level, magnetic fields arise also from nuclei with nonzero spin resulting in nuclear spin-spin and electronic-spin-nuclear-spin interactions. 

An interaction operator for the interaction of an electron at position r with an external magnetic field Bext and with a nucleus at position Ra ta = r — Ra) is of the form (Quiney et al. 1998b) 

The components of the shielding tensor are defined by (Quiney et al. 1998b) 

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