Breit corrections, computing, relativistic

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]. 

Computational procedures such as those illustrated in Table 2 are easy to apply to simple atomic systems but need to be modified for complex calculations when expansions explode as the orbital set increases. The current grasp2K code encounters convergence problems when two correlation orbitals of the same symmetry are varied simultaneously. A practical and stable procedure in this case is to introduce only one new orbital of each symmetry and optimize only the new orbitals. These orbitals are sometimes referred to as a layer [2]. In this way, a basis of relativistic orbitals is built for a final calculation that includes other effects such as Breit and QED corrections. Such a procedure was used in the determination of transitions probabilities for Fe + [19]. 

As described previously, in practical computational schemes of relativistic quantum chemistry the Dirac-Coulomb Hamiltonian is frequently preferred. The use of this Hamiltonian, which retains only the Coulomb interaction between the electrons, omitting the Breit term and higher-order corrections, is justified by the argument that these terms are small and the effect on most properties of chemical interest is insignificant. The validity of this argument appears to be supported by actual applications. Saue and Helgaker (2002) have shown that when this Hamiltonian is used in the... 

A number of static perturbations arise from internal interactions or fields, which are neglected in the nonrelativistic Born-Oppenheimer electronic Hamiltonian. The relativistic correction terms of the Breit-Pauli Hamiltonian are considered as perturbations in nonrelativistic quantum chemistry, including Darwin corrections, the mass-velocity correction, and spin-orbit and spin-spin interactions. Some properties, such as nuclear magnetic resonance shielding tensors and shielding polarizabilities, are computed from perturbation operators that involve both internal and external fields. 

Besides the computational savings, ECPs have the advantage that they allow for the implicit inclusion of relativistic effects, even of the Breit interaction or quantum electrodynamic (QED) corrections, by simple parametrizations to relativistic AE data. Furthermore, ECPs permit the usage of smaller basis sets and thus the basis set superposition error is less significant compared to AE calculations. Even the difficulties due to open shells may be avoided by applying ECPs, if these open shells are included in the core system as it is the case for the 4f-in-core [7-9] and 5f-in-core [10-12] pseudopotentials (PP) for lanthanides and actinides, respectively. However, these PPs can only be applied, if the f orbitals do not participate significantly in chemical bonding (see Section 6.3.1). 

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