Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules

Andrae, Dirk

doi:10.1016/s0370-1573(00)00007-7

Cited by 119 publications

(124 citation statements)

References 202 publications

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“…In what follows we specialize for simplicity to parity-preserving interactions and spinless compact central objects, and so strictly speaking the interactions we find suffice in themselves to describe finite-size effects in the He + ion or muonic states in even-even nuclei [24,[26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44][45]. The effects we find also apply to nuclei with spin (such as hydrogen) once the effective theory of the first-quantized source is supplemented by the extra interactions that a nuclear spin allows.…”

Section: Jhep09(2017)007mentioning

confidence: 99%

Point-particle effective field theory III: relativistic fermions and the Dirac equation

Burgess¹,

Hayman²,

Rummel³

et al. 2017

J. High Energ. Phys.

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We formulate point-particle effective field theory (PPEFT) for relativistic spinhalf fermions interacting with a massive, charged finite-sized source using a first-quantized effective field theory for the heavy compact object and a second-quantized language for the lighter fermion with which it interacts. This description shows how to determine the near-source boundary condition for the Dirac field in terms of the relevant physical properties of the source, and reduces to the standard choices in the limit of a point source. Using a first-quantized effective description is appropriate when the compact object is sufficiently heavy, and is simpler than (though equivalent to) the effective theory that treats the compact source in a second-quantized way. As an application we use the PPEFT to parameterize the leading energy shift for the bound energy levels due to finite-sized source effects in a model-independent way, allowing these effects to be fit in precision measurements. Besides capturing finite-source-size effects, the PPEFT treatment also efficiently captures how other short-distance source interactions can shift bound-state energy levels, such as due to vacuum polarization (through the Uehling potential) or strong interactions for Coulomb bound states of hadrons, or any hypothetical new short-range forces sourced by nuclei.

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Section: Jhep09(2017)007mentioning

confidence: 99%

Point-particle effective field theory III: relativistic fermions and the Dirac equation

Burgess¹,

Hayman²,

Rummel³

et al. 2017

J. High Energ. Phys.

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“…where R is some model-specific radial size parameter that characterizes the extension of q n [11,13,48]. The electrostatic electron-nucleus interaction is given by…”

Section: Validity Of the Contact Density Approximationmentioning

confidence: 99%

“…The next step is to take a specific model for the charge density of the nucleus and establish an explicit expression for DE c . A detailed comparison of various models is given by Andrae [11,13], and we refer to this work for illustrative plots of the various nuclear potentials. Relevant for the present discussion are the Gaussian model that is used to obtain relativistic electron densities, and the homogeneously charged sphere model.…”

Section: Validity Of the Contact Density Approximationmentioning

confidence: 99%

“…The nuclear radius parameter R G can be related to the radius parameter R of the homogeneous sphere model by comparing radial second momenta [11,13] …”

Section: Validity Of the Contact Density Approximationmentioning

confidence: 99%

“…This limiting short-range behavior is, however, an artifact of the simple point charge model and is radically different for the more physical model of an extended nucleus. In the relativistic case, it is already common to introduce an extended-nucleus model [11][12][13][14] because this facilitates the use of Gaussian type orbitals (GTOs). GTOs have zero slope at the nucleus, which is consistent with the exact solutions for extended-nuclear models [15][16][17][18] in both non-relativistic and relativistic theory.…”

Section: Introductionmentioning

confidence: 99%

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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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Relativistic Electronic Structure Theory for Molecular Spectroscopy

Mastalerz

Reiher

2011

Handbook of High‐resolution Spectroscopy

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This review provides a concise introduction to relativistic electronic structure theory with a focus on the prediction of parameters relevant for molecular spectroscopy. For this purpose, a brief overview of wave‐function‐based electronic structure methods with a special focus on the calculation of electron correlation effects is given. These are essential for an accurate prediction of spectroscopic parameters from first‐principles calculations. Then approximate relativistic Hamiltonians are discussed in detail regarding their accuracy and range of application. The a posteriori calculation of spin–orbit effects from correlated wave functions is briefly described and reviewed. The presentation concludes with an extensive discussion of calculated results for prototypical molecules. The focus is mainly on small molecules to which highly accurate relativistic methods can be applied and close agreement with experimental data can be achieved.

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Finite nuclear charge density distributions in electronic structure calculations for atoms and molecules

Cited by 119 publications

References 202 publications

Point-particle effective field theory III: relativistic fermions and the Dirac equation

Point-particle effective field theory III: relativistic fermions and the Dirac equation

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

Relativistic Electronic Structure Theory for Molecular Spectroscopy

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