Basis set expansion of the dirac operator without variational collapse

Kutzelnigg, Werner

doi:10.1002/qua.560250112

Cited by 356 publications

(194 citation statements)

References 31 publications

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“…• relativistic densities using the eXact two-Component (X2C) Hamiltonian [82]; • four-component spin-orbit free [83,84] (scalar-relativistic) densities; • one-component scalar-relativistic densities employing the Douglas-Kroll-Hess (DKH) Hamiltonian [85][86][87][88][89][90][91];…”

Section: Hamiltonian Operatormentioning

confidence: 99%

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Knecht

Fux

Meer³

et al. 2011

Theor Chem Acc

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The electrostatic contribution to the Mössbauer isomer shift of mercury for the series HgF n (n = 1, 2, 4) with respect to the neutral atom has been investigated in the framework of four-and two-component relativistic theory. Replacing the integration of the electron density over the nuclear volume by the contact density (that is, the electron density at the nucleus) leads to a 10% overestimation of the isomer shift. The systematic nature of this error suggests that it can be incorporated into a correction factor, thus justifying the use of the contact density for the calculation of the Mössbauer isomer shift. The performance of a large selection of density functionals for the calculation of contact densities has been assessed by comparing with finite-field four-component relativistic coupled-cluster with single and double and perturbative triple excitations [CCSD(T)] calculations. For the absolute contact density of the mercury atom, the Density Functional Theory (DFT) calculations are in error by about 0.5%, a result that must be judged against the observation that the change in contact density along the series HgF n (n = 1, 2, 4), relevant for the isomer shift, is on the order of 50 ppm with respect to absolute densities. Contrary to previous studies of the 57 Fe isomer shift (F Neese, Inorg Chim Acta 332:181, 2002), for mercury, DFT is not able to reproduce the trends in the isomer shift provided by reference data, in our case CCSD(T) calculations, notably the non-monotonous decrease in the contact density along the series HgF n (n = 1, 2, 4). Projection analysis shows the expected reduction of the 6s 1/2 population at the mercury center with an increasing number of ligands, but also brings into light an opposing effect, namely the increasing polarization of the 6s 1/2 orbital due to increasing effective charge of the mercury atom, which explains the nonmonotonous behavior of the contact density along the series. The same analysis shows increasing covalent contributions to bonding along the series with the effective charge of the mercury atom reaching a maximum of around ?2 for HgF 4 at the DFT level, far from the formal charge ?4 suggested by the oxidation state of this recently observed species. Whereas the geometries for the linear HgF 2 and square-planar HgF 4 molecules were taken from previous computational studies, we optimized the equilibrium distance of HgF at the four-component Fock-space CCSD/aug-cc-pVQZ level, giving spectroscopic constants r e = 2.007 Å and x e = 513.5 cm -1 .Dedicated to Professor Pekka Pyykkö on the occasion of his 70th birthday and published as part of the Pyykkö Festschrift Issue.Electronic supplementary material The online version of this article

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Section: Hamiltonian Operatormentioning

confidence: 99%

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Knecht

Fux

Meer³

et al. 2011

Theor Chem Acc

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“…Unfortunately at present there are no effective algorithms for molecular calculations in a fully relativistic manner. The difficulties are both technical and theoretical (Kutzelnigg 1984). However, assuming that chemical bonds are mainly formed by the non-relativistic valence electrons, we can consider the inner shells of the relativistic electrons as a frozen core.…”

Section: Calculation Of the Low-lying Electronic States Of The Pbf Momentioning

confidence: 99%

Calculation of the P- and T-odd spin-rotational Hamiltonian of the PbF molecule

Kozlov¹,

Fomichev²,

Dmitriev³

et al. 1987

J. Phys. B: At. Mol. Phys.

101

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Abstract. The electron wavefunctions for two states of the PbF molecule are calculated. For the ground state of the molecule, tensor components of the hyperfine interaction of the valence electron with the nuclear spin of Pb, electric and magnetic dipole moments and electron matrix elements of P-odd and P, T-odd interactions are calculated. In accordance with the calculation an effective spin-rotational Hamiltonian for the molecule is given. The Hamiltonian includes the parity-non-conserving terms and the interaction with the external fields. The spin-rotational spectrum of the PbF molecule is found to be rather complicated; this is connected with the large anisotropy of the hyperfine A tensor. The results of the present work can be used in planning future experiments on the search for P-odd and P, T-odd phenomena in molecules.

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“…is equivalent to the four-component DE when an RKB basis set is used [68][69][70][71]. The mDE is the target equation to be exactly decoupled by a matrix transformation.…”

Section: From Four To Two Componentsmentioning

confidence: 99%

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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Basis set expansion of the dirac operator without variational collapse

Cited by 356 publications

References 31 publications

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Mössbauer spectroscopy for heavy elements: a relativistic benchmark study of mercury

Calculation of the P- and T-odd spin-rotational Hamiltonian of the PbF molecule

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

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