Two-component relativistic density functional

C. van Wiillen. Spin densities in two-component relativistic density functional calculations Noncollinear versus coUinear approach. /. Comput. Chem., 23 (2002) 779-785. 

D. Peng, W. liu, Y. Xiao, L. Cheng. Making four- and two-component relativistic density functional methods fully equivalent based on the idea of "from atoms to molecule". J. Chem. Phys., 127 (2007) 104106. 

Mitin, A.V., van Wiillen, C. Two-component relativistic density-functional calculations of the dimers of the halogens from bromide through element 117 using effective core potential and all-electron methods. J. Chem. Phys. 124, 064305(7) (2006)... 

Zaitsevski, A., van Wiillen, C., Rykova, E.A. Two-component relativistic density functional modeling of the adsorption of element 114 (eka-led) on gold. Phys. Chem. Chem. Phys. 12, 4152 156 (2010)... 

Aquino F, Govind N and Autschbach J 2010 Electric field gradients calculated from two-component relativistic density functional theory inclnding spin-orbit coupling. J. Chem. Theory Comput. 6, 2669-2686. 

We review the Douglas-Kroll-Hess (DKH) approach to relativistic density functional calculations for molecular systems, also in comparison with other two-component approaches and four-component relativistic quantum chemistry methods. The scalar relativistic variant of the DKH method of solving the Dirac-Kohn-Sham problem is an efficient procedure for treating compounds of heavy elements including such complex systems as transition metal clusters, adsorption complexes, and solvated actinide compounds. This method allows routine ad-electron density functional calculations on heavy-element compounds and provides a reliable alternative to the popular approximate strategy based on relativistic effective core potentials. We discuss recent method development aimed at an efficient treatment of spin-orbit interaction in the DKH approach as well as calculations of g tensors. Comparison with results of four-component methods for small molecules reveals that, for many application problems, a two-component treatment of spin-orbit interaction can be competitive with these more precise procedures. 

J. Autschbach. Two-component relativistic hybrid density functional computations of nuclear spin-spin coupling tensors using Slater-type basis sets and density-fitting techniques. /. Chem. Phys., 129 (2008) 094105. 

We have updated the material considering the latest developments in the field over the past five years. These developments comprise both computational and more fundamental advances such as exact two-component approaches and the study of explicitly correlated two-electron wave functions in the context of the Brown-Ravenhall disease, respectively. Other topics, such as relativistic density functional theory and its relation to nonrelativistic spin-... 

As well as the chemical shift, indirect nuclear spin-spin coupling constant (SSCC) is one of the most important molecular properties measured routinely in NMR experiments. Much effort has been devorted until now to the development of theoretical tools to compute SSCCs from first-principles theory. For SSCCs in heavy element compounds, a relativistic theory is needed. Moreover, SSCCs are sensive to electron correlation. Therefore, in the computation of SSCCs for heavy-atom included systems, density functional theory (DFT) employing two-component relativistic methods plays a major role because of its applicability to relatively large molecules. 

Wang F, Ziegler T (2005) Theoretical study of the electronic spectra of square-planar platinum (II) complexes based on the two-component relativistic time-dependent density-functional theory. J Qiem Phys 123... 

In this paper we present the first application of the ZORA (Zeroth Order Regular Approximation of the Dirac Fock equation) formalism in Ab Initio electronic structure calculations. The ZORA method, which has been tested previously in the context of Density Functional Theory, has been implemented in the GAMESS-UK package. As was shown earlier we can split off a scalar part from the two component ZORA Hamiltonian. In the present work only the one component part is considered. We introduce a separate internal basis to represent the extra matrix elements, needed for the ZORA corrections. This leads to different options for the computation of the Coulomb matrix in this internal basis. The performance of this Hamiltonian and the effect of the different Coulomb matrix alternatives is tested in calculations on the radon en xenon atoms and the AuH molecule. In the atomic cases we compare with numerical Dirac Fock and numerical ZORA methods and with non relativistic and full Dirac basis set calculations. It is shown that ZORA recovers the bulk of the relativistic effect and that ZORA and Dirac Fock perform equally well in medium size basis set calculations. For AuH we have calculated the equilibrium bond length with the non relativistic Hartree Fock and ZORA methods and compare with the Dirac Fock result and the experimental value. Again the ZORA and Dirac Fock errors are of the same order of magnitude. 

Accounting for relativistic effects in computational organotin studies becomes complicated, because Hartree-Fock (HF), density functional theory (DFT), and post-HF methods such as n-th order Mpller-Plesset perturbation (MPn), coupled cluster (CC), and quadratic configuration interaction (QCI) methods are non-relativistic. Relativistic effects can be incorporated in quantum chemical methods with Dirac-Hartree-Fock theory, which is based on the four-component Dirac equation. " Unformnately the four-component Flamiltonian in the all-electron relativistic Dirac-Fock method makes calculations time consuming, with calculations becoming 100 times more expensive. The four-component Dirac equation can be approximated by a two-component form, as seen in the Douglas-Kroll (DK) Hamiltonian or by the zero-order regular approximation To address the electron cor-... 

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... 

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