Douglas scalar approximation

Bauschlicher [48] compared a number of approximate approaches for scalar relativistic effects to Douglas-Kroll quasirelativistic CCSD(T) calculations. He found that the ACPF/MTsmall level of theory faithfully reproduces his more rigorous calculations, while the use of non-size extensive approaches like CISD leads to serious errors. For third-row main group systems, studies by the same author [49] indicate that more rigorous approaches may be in order. 

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. 

Equilibrium distances r, vibrational constants (Og and dissociation energies Dg for the ground state of molecular iodine, fium Ref. [102], All-electron (AE) calculations are obtained from either the scalar-relativistic Douglas-Kroll-HeB (DKH) approximation or 4-component Dirac-Hartree-Fock (DHF) correlated calculation taken from Ref [103]. 

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. 

A self-consistent scalar-relativistic (SR) version of the LCGTO-DF method has also been developed recently." "The SR variant employs a unitary second-order Douglas-Kroll-Hess (DKH) "" transformation for decoupling large and small components of the full four-component spinor solutions to the Dirac-Kohn-Sham equation. The approximate DKH transformation, very appropriate and efficient for molecular calculations, has been implemented this variant utilizes nuclear potential-based projectors and leaves the electron-electron interaction untransformed. 

The scalar relativistic (SR) corrections were calculated by the second-order Douglas-Kroll-Hess (DKH2) method [53-57] at the (U/R)CCSD(T) or MRCI level of theory in conjunction with the all-electron aug-cc-pVQZ-DK2 basis sets that had been recently developed for iodine [58]. The SR contributions, as computed here, account for the scalar relativistic effects on carbon as well as corrections for the PP approximation for iodine. Note, however, that the Stuttgart-Koln PPs that are used in this work include Breit corrections that are absent in the Douglas-Kroll-Hess approach [58]. 

We may substitute f p for Sp in the kinematic factors in both the Douglas-Kroll and the Barysz-Sadlej-Snijders approximations. To separate out the zeroth-order Fiamiltonian from the perturbation, we follow an analogous procedure to that used for the scalar potential. We will concern ourselves only with the terms linear in the vector potential, but extension to other terms is straightforward, if tedious. 

In the MCP, or more advanced AIMP, approximations [72, 73], is represented by an adjustable local potential and a projection operator. This potential is constructed so that the inner nodal stmcture of the pseudo-valence orbitals is conserved, thus closely approximating all-electron valence AOs. Scalar relativistic effects are directly taken into account by relativistic operators such as Douglas-Kroll (DK) one. SO effects can be included with the use of the SO operator,... 

Scalar relativistic corrections at the levels of Douglas-Kroll, ZORA, and the infinite-order relativistic approximation (lORA) (Dyall and van Lenthe 1999). 

---