Abstract:
A point charge model for the nuclear quadrupole moment tensor (PCNQM) is developed in order to determine accurate electric field gradients (EFG) at the relativistic and correlated levels. The symmetric s contributions arising from the Poisson equation are avoided by using an appropriate point charge distribution in three-dimensional space. It is shown that the PCNQM model yields virtually the same EFGs compared to the conventional method of expectation values, if the point charges are set at small displacements from the nucleus (d<10-13 m) and the SCF energy is converged out to 12 significant figures. We further demonstrate that the choice of the point charge ? is not very critical to the PCNQM perturbation, and that the correlation energy at both the nonrelativistic and relativistic level of theory depends linearly on ?. This suggests that accurate EFG tensors can be obtained by performing only two correlated calculations for each atom and tensor component. The PCNQM model is tested on one-electron atoms and on the Cu and F EFG in CuF Relativistic and correlation effects on EFGs are discussed in detail. A Z-expansion on one-electron systems demonstrates that the relativistic correction scales ?Z5. For the CuF molecule Douglas-Kroll and Dirac-Fock coupled cluster calculations are in good agreement with each other. At the best level of theory (coupled cluster Dirac-Fock plus correction from basis set incompleteness) we obtain a nuclear quadrupole coupling constant for 63Cu of 23 Mhz. This is in very good agreement with the experimental result of 22 MHz considering the large standard deviation of the 63Cu nuclear quadrupole moment applied, 220(10) mb.