Douglas electron density

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. 

R. Mastalerz, R. Lindh, M. Reiher. The Douglas-Kroll-Hess Electron Density at an Atomic Nucleus. Chem. Phys. Lett., 465 (2008) 157-164. 

Bioinorganic systems often contain heavy elements that need to be treated with an explicit relativistic method. It is now possible to carry out an explicit relativistic electronic structure calculation on the fly (152). The scalar-relativistic Douglas - Kroll - Hess method was implemented by us recently in the BOMD simulation framework (152). To use the relativistic densities in a non-relativistic gradient calculations turned out to be a valid approximation of relativistic gradients. An excellent agreement between optimized structures and geometries obtained from numerical gradients was observed with an error smaller than 0.02 pm. 

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-... 

The Douglas-Kroll approach to relativistic electronic structure theory in the framework of density functional theory was reviewed focussing on recent method developments and illustrative applications which demonstrate the capabilities of this approach. Compared to other relativistic methods, which often are only applied to small molecules for demonstration purposes, the DK approach has been used in a variety of fields. Besides the very popular pseudopotential approach, which accounts for relativistic effects by means of a potential replacing the core electrons, until now the scalar relativistic variant of the second-... 

J. C. Boettger. Approximate two-electron spin-orbit coupling term for density-functional-theory DFT calculations using the Douglas-Kroll-Hess transformation. Phys. Rev. B, 62(12) (2000) 7809-7815. 

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