Douglas-Kroll calculations of EFGs excluding the PCE

The first striking feature in figure 3 is the enormous PCE in AuCl reflecting the gold maximum of relativistic effects also with respect to property calculations. The absolute amount of the EFG PCE is larger than the relativistic contribution ( ) to the property and nearly as large as the correlation contribution underlining the importance of PCE-free calculations. In copper and silver the PCE is also comparable to the 

CCSD(T) calculations on three different gallium halides [139] finally gave 171 2 mb for the Ga NQM corroborating the atomic MCDHF value. The deviation can be attributed to basis set deficiencies caused by a neccessary reduction of the basis for the DHF-CCSD(T) calculations. Furthermore, additivity for the smaller contributions like SO, CCSD(T)/SO and vibrational averaging was assumed, but as these effects become larger the assumption of additivity certainly becomes a more serious source of errors due to the inconsistent theoretical framework the individual contributions were obtained in. 

A breakthrough in the combination of PCE-free EFG calculations and the application of the efficient DK method was achieved by Malkin et al. [144] now explicitly performing the DK transformation of the EFG operator. In contrast to the numerical finite field calculations this method is now free from possible numerical errors and it was implemented as a scalar-relativistic version up to second order. The transformed EFG operator q is hereby split in the first and second-order contributions 

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