Calculation of Magnetic Properties

The nuclear spin-spin coupling constants of are given in Table 8.4 

Even better agreement with experiment can be obtained by vibrational averaging. 

The relative importance of the various contributions to the spin-spin coupling constants varies greatly from system to system, and it appears absolutely necessary to compute them all. In Table 8.6 the results for at the equi- 

The difference between the HRPA and the SOPPAl approximations is primarily the inclusion of the so-called 2particle-2hole correction in SOPPAl. It is generally observed that the Fermi contact (fc) contribution exhibits the strongest dependence on internuclear separation. 

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The IGLO method, an important breakthrough for the calculation of magnetic properties, was developed in the mid-1980s by Kutzelnigg et al.2 After some... 

The difficulties encountered in the calculation of magnetic properties are illustrated by a series of Hartree-Fock calculations of the indirect spin-spin coupling constant of the molecule at the experimental geometry... 

From the above discussion it becomes clear that in order to eliminate the spin-orbit interaction in four-component relativistic calculations of magnetic properties one must delete the quaternion imaginary parts from the regular Fock matrix and not from other quantities appearing in the response function (35). It is also possible to delete all spin interactions from magnetic properties, but this requires the use of the Sternheim approximation [57,73], that is calculating the diamagnetic contribution as an expectation value. 

T. Helgaker, P. Jorgensen, An electronic hamiltonian for origin independent calculations of magnetic properties, J. Chem. Phys. 95 (1991) 2595. 

While the chemical interpretation of the e parameters is a matter of real concern to us, there are also several other difficulties which are, however, more apparent than real. Consider the question of the calculation of magnetic properties in transition metal complexes - paramagnetic susceptibilities and e.s.r. g values. In contrast to the study of eigenvalues for optical transition energies, these require descriptions of the wavefunc-tions after the perturbation by the ligand field, interelectron repulsion and spin-orbit coupling effects. In susceptibility calculations it is customary to use Stevens orbital reduction factor k in the magnetic moment operator... 

There are two factors which make the calculation of magnetic properties somewhat... 

S.P.A. Sauer, 1. Paidarov J. Oddershede, Correlated and Gauge Origin Independent Calculations of Magnetic Properties. 1. Triply Bonded Molecules, Mol. Phys. 81 (1994) 87. 

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). 

Expressions for the calculation of magnetic properties at the relativistic level of theory can be derived by replacing the momentum operator p in the Dirac equation (1) with the generalized momentum operator n... 

While this chapter has focused on the area of our expertise—the treatment of electron correlation in NMR calculations via MP and CC theories—it should also be mentioned that DFT-based calculations of magnetic properties offer great promise for the treatment of large molecules. However, there are formal problems associated with the way that these calculations are currently carried out, and further theoretical developments in this area are needed. In its present state, errors in NMR shielding constants obtained in DFT calculations can be quite substantial (see again Fig. 6.12) and render definitive interpretation of experimental spectra in some, though not all cases difficult. 

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