Relativistic Hamiltonians for Chemistry: A Primer

Saue, Trond

doi:10.1002/cphc.201100682

Cited by 448 publications

(483 citation statements)

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“…Therefore, it can lead to large differences in calculations of properties in a two-component framework. It is noted that the difference between ρ + and ρ 2c is significant mainly deep in the atomic cores and to some extent in the outer atomic core shells of heavy atoms [5,75,76]. In the valence regions of light and heavy atoms, the four-component and the two-component densities are very similar.…”

Section: Picture Changementioning

confidence: 94%

“…The eigenfunction of the (still four-component) FW Hamiltonian is 5) where the goal is to produce a wave function of the form…”

Section: From Four To Two Componentsmentioning

confidence: 99%

“…The FW transformation U can then be written as a product of a decoupling step U d and a renormalization step U N , as [5,47,48]…”

Section: From Four To Two Componentsmentioning

confidence: 99%

“…Thus, the operators are directly constructed in matrix form. The following simplified description has been adapted from [67]; an algorithmic recipe has been given by Saue [5]. The notation for matrices used in this section is as follows.…”

Section: From Four To Two Componentsmentioning

confidence: 99%

“…Recent works [6,72,73] have demonstrated that an atomic and nearest-neighbour (NN) partitioning of decoupling transformations is feasible, for the reason that the regions in space where the Dirac lower component differs significantly from (1/2c)σ · pψ U are confined to the deep atomic cores, close to the nuclei. See also a review by Saue for an illustration [5]. Therefore, the memory-intensive parts of a decoupling transformation can be carried out in a reduced basis, accumulating contributions from different parts of a molecule.…”

Section: From Four To Two Componentsmentioning

confidence: 99%

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

Autschbach

2014

Phil. Trans. R. Soc. A.

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This article outlines some basic concepts of relativistic quantum chemistry and recent developments of relativistic methods for the calculation of the molecular properties that define the basic parameters of magnetic resonance spectroscopic techniques, i.e. nuclear magnetic resonance shielding, indirect nuclear spin-spin coupling and electric field gradients (nuclear quadrupole coupling), as well as with electron paramagnetic resonance g-factors and electron-nucleus hyperfine coupling. Density functional theory (DFT) has been very successful in molecular property calculations, despite a number of problems related to approximations in the functionals. In particular, for heavy-element systems, the large electron count and the need for a relativistic treatment often render the application of correlated wave function ab initio methods impracticable. Selected applications of DFT in relativistic calculation of magnetic resonance parameters are reviewed.

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Section: Picture Changementioning

confidence: 94%

“…The eigenfunction of the (still four-component) FW Hamiltonian is 5) where the goal is to produce a wave function of the form…”

Section: From Four To Two Componentsmentioning

confidence: 99%

“…The FW transformation U can then be written as a product of a decoupling step U d and a renormalization step U N , as [5,47,48]…”

Section: From Four To Two Componentsmentioning

confidence: 99%

Section: From Four To Two Componentsmentioning

confidence: 99%

Section: From Four To Two Componentsmentioning

confidence: 99%

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

Autschbach

2014

Phil. Trans. R. Soc. A.

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CalculatingNMRChemical Shifts andJ‐Couplings for Heavy Element Compounds

Autschbach

2014

Encyclopedia of Analytical Chemistry

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Ab initio calculations of NMR parameters for compounds with heavy elements require a relativistic theoretical framework. Such calculations are able to reproduce experimentally observed ‘heavy atom’ effects in NMR spectroscopy quantitatively. Electron spin‐orbit (SO) coupling is a relativistic effect that leads to the ‘normal halogen dependence’ of light atom chemical shifts in the vicinity of heavy halogens. Similar effects exist for light atoms bound to heavy transition metals or f ‐block elements or heavy main group elements other than halogens. J ‐coupling constants involving heavy elements may increase by several hundred percent because of relativistic effects. The tensor properties of NMR shielding and J ‐coupling, observed routinely in solid‐state NMR, can be impacted very strongly by relativistic effects. This article discusses representative examples, provides a rationale why relativistic effects are large for atoms with high nuclear charges, and lists a selection of quantum chemistry program packages that are capable of relativistic NMR calculations.

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