Relativistic Theory and Applications

Perspective: Relativistic effects

“…59 Although the DCB Hamiltonian is in general not Lorentz-invariant, it has been said to provide "an excellent approximation to the full theory." 46 There are, however, important conceptual issues connected with the DCB Hamiltonian and the role of the vacuum in correlated relativistic quantum chemical methods that need to be addressed in future work. 23,49 Effects beyond DCB lie in the realm of QED which are discussed at some length in a recent review.…”

Relativistic calculations of magnetic resonance parameters: background and some recent developments

“…In order to account for effects due to the Breit term on atomic and molecular properties other than total energies and orbital energies, a variational treatment would be preferred over a perturbative scheme [113]. The DCB Hamiltonian is in general not Lorentz-invariant, but it has been said to provide an excellent approximation to the full theory [22].…”

Recent Advances in Nuclear Shielding Calculations

“…Finally, Kutzelnigg and Liu 21 consider various approximations previously proposed which do not give the exact results in the limit of a complete basis, for example, see Xiao et al 22 All of these approximations are based on methods which give the correct non-relativistic limit and use a pseudo sum-over-states formulation with the restriction of the intermediate eigenstates to those with positive energy. Along the way, various commonly used approximations such as the Douglass-Kroll-Hess approximation 23 and the Zeroth-Order Regular Approximation (ZORA) 24 are discussed in context. Cheng et al showed that these variants of approaches using magnetic balance can all be recast into one unified form.…”

“…208 This softness is achieved at the cost of relaxing the property of norm conservation and so the pseudo-wavefunctions obey a generalized orthonormality condition. GIPAW with ultrasoft pseudopotentials has been applied to elements in various parts of the Periodic Table : in minerals such as kaolinite, 209 perovskites, 210 molecular crystals, 211, 212, 213, 214 organic single crystals, 215 inorganic solids, for example, 95 Mo shielding in solid state molybdenum compounds, 216 Br in alkaline earth bromides, 217 glasses, e.g., 73 Ge correlation with Ge-O-Ge bond angle in vitreous GeO 2 , 218 19 F, 29 Si, 31 P and 23 Na in bioactive glasses, 219 biomolecules in the solid state, e.g., peptides. 220 Truflandier et al 221 have designed ultrasoft pseudopotentials for 3d transition elements in GIPAW.…”

“…the same for both glasses) simple linear dependence. 253 The subsequent example of the analysis of how 29 Si, 17 O, and 23 Na shieldings depend on the environment in sodium silicate glasses is another good one. 254 The mean values and also the distributions of structural parameters can be obtained by the GIPAW -MD approach to glasses.…”