Molecular density functional ZORA EFG calculations

Density functional theory (DFT) provides an accurate and inexpensive access to molecular electronic structure and properties and was already used for scalar relativistic EFG calculations for example on Fe in solids [145] or in molecules [146,147]. We will not report on nonrela-tivistic DFT EFG calculations here but focus on the ZORA [148-151] and especially ZORA-4 methods, the latter including the density from the small component. Since the ZORA method is a two-component method sizable picture change effects will occur when calculating a core property like the EFG. In order to briefly illustrate this method a few of the fundamental equations will be given. A concise treatment of the ZORA formalism and its applications can be found in [152]. 

The principle idea is to find an expansion being regular also in spatial regions very close to the nucleus where the potential V = 1/r becomes very large. One immediately sees that in the classical case where the energy of a particle can be written as 

Since the ZORA eigenfunctions are approximations to the FW wave functions generated by a unitary transformation the usual way of cal- 

4 First-principles moleculsir Dirac-Hartree-Fock EFG calculations 

At the moment the number of true four-component molecular EFG calculations is still rather limited due to the considerable computational effort especially in the post-DHF steps. Just five years ago Pj kko expressed the need for fully relativistic benchmark calculations in order to abandon perturbative corrections for considerable relativistic effects and to establish reference results. Furthermore spin-orbit effects can cause an EFG e.g. in atoms with Z 0 and half-filled shells where according to nonrelativistic theory the EFG should vanish. This is the case for e.g. a system leading to a Pij2P f2 spin-orbit-split configuration. Also in closed-shell molecules with heavy halogen nuclei the spin-orbit effect is not completely quenched [88]. 

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