Relativistic Spin-DFT

In relativistic current-density funtional theory discussed above, the noninteracting reference system is chosen such that it possesses the same 4-current 

it is possible to develop a relativistic density-only d ) KS-DFT, which will resemble the nonrelativistic spin-restricted KS-DFT formalism, by only requiring that the noninteracting reference system possesses the same density as the interacting system. Then, the total (relativistic) energy functional can be decomposed as 

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E l)[p,Mz] and E p, m ] [394], For these choices, for which in addition to the electron density one further quantity is to be reproduced by the KS system, the resulting exchange-correlation potential has two components. This is in close analogy to the case of nonrelativistic unrestricted KS-DFT formulated for a- and /5-spin densities, j0 and pp. For this reason, approximate exchange-correlation functionals developed for nonrelativistic DFT are simply employed in actual relativistic spin-DFT calculations. However, the exchange-correlation potential is defined differently in nonrelativistic unrestricted KS-DFT and in the relativistic collinear and noncollinear cases. Consequently, different exact conditions also apply to the exchange-correlation functional [394]. 

It is instructive to see how the nonrelativistic unrestricted KS-DFT formalism emerges from relativistic spin-DFT. This is most easily seen for the collinear approach, although the noncollinear one also reduces to the same nonrela-... 

Fig. 7 One-bond metal-ligand reduced nudear spin-spin coupling constants (absolute values) for 5d metal complexes. Scalar relativistic ZORA DFT results (VWN functional) versus experimental values. A few data points for Pb are also included. Data taken from Refs. [45,123]. The line is not a fit but indicates where Ka c = Kexp. The different markers indicate the different metals. For not octahedrally or not tetrahedrally coordinated metal centers, the first coordination shell was completed with solvent molecules, as described in Ref. [124]...

Autschbach and Ziegler presented relativistic spin-spin coupling constants based on the two-component ZORA formulation. They published four papers. In the first paper of their series, only the scalar relativistic part was included, and a full inclusion of the ZORA effects was implemented in the second paper. They used the density functional theory (DFT) approach. The first paper showed that scalar relativistic calculations are able to reproduce major parts of the relativistic effects on the one-bond metal-ligand couplings of systems containing Pt, Hg and Pb. It was found that the... 

Bryce and Autschbach performed the accurate calculation of the isotropic and anisotropic (AT) parts of indirect nuclear spin spin coupling tensors for diatomic alkali metal halides (MX M = Li, Na, K, Rb, Cs X = F, Cl, Br, I) with the relativistic hybrid DFT approach. The calculated coupling tensor components were compared with experimental values obtained from molecular-beam measurements on diatomic molecules in the gas phase. Molecular-beam experiments offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects. The hyperfine Hamiltonian used in analyzing molecular-beam data contains Hc IkDIi and //C4/a /l terms. The relationships between the parameters C3 and C4, used in molecular-beam experiments, and Rdd, A/, and used in NMR spectroscopy, are summarized in the following equations ... 

Computations of indirect spin-spin couplings using two-component relativistic hybrid DFT with a hybrid functional has been reported by Autschbach. In particular, for the isotropic coupling and the coupling anisotropy of Tl-X (X = F, Cl, Br, I), the PBEO hybrid functional yielded considerably improved agreement with experiment. 

Forgeron el calculated one-bond P, P indirect nuclear spin-spin coupling tensors, /( P, P), using nonrelativistic DFT and relativistic ZORA DFT methods. Thousands of solution and solid-state P NMR studies have been carried out, and many one-bond P, P isotropic SSCCs, V( P, P)iso, have been measured." The dependence of /( P, P)wo on parameters such as oxidation state, coordination number, substituent electronegativity, the presence or absence of localized electron lone pairs, and stereochemistry is somewhat known, and values of P)wo may be... 

On the other hand, high-level computational methods are limited, for obvious reasons, to very simple systems.122 Calculations are likely to have limited accuracy due to basis set effects, relativistic contributions, and spin orbit corrections, especially in the case of tin hydrides, but these concerns can be addressed. Given the computational economy of density functional theories and the excellent behavior of the hybrid-DFT B3LYP123 already demonstrated for calculations of radical energies,124 we anticipate good progress in the theoretical approach. We hope that this collection serves as a reference for computational work that we are certain will be forthcoming. 

The calculation of NMR shielding tensors based on DFT and the GIAO approach has been implemented into the Amsterdam Density Functional code ADF (27,25-27). The non-relativistic as well as scalar relativistic (Pauli) implementations are the work of Schreckenbach and Ziegler (5-7) whereas the spin-orbit (Pauli) and ZORA NMR approaches were implemented by Wolff et al. (9,10). For the mathematical and technical details, the reader is referred to the literature. 

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