Basis set representation of the electron density at an atomic nucleus

Mastalerz, Remigius; Widmark, Per‐Olof; Roos, Björn O.; Lindh, Roland; Reiher, Markus

doi:10.1063/1.3491239

Cited by 31 publications

(46 citation statements)

References 49 publications

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“…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. This feature thus makes GTOs a natural expansion set for relativistic orbitals for which one may rely on well-established basis sets augmented by steep functions (as e.g., demonstrated recently for contact densities at iron nuclei [18]).…”

Section: Introductionsupporting

confidence: 66%

“…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. This feature thus makes GTOs a natural expansion set for relativistic orbitals for which one may rely on well-established basis sets augmented by steep functions (as e.g., demonstrated recently for contact densities at iron nuclei [18]). By employing an extendednucleus model, one may also go beyond the contact density approximation and explicitly calculate the change in nucleus-electron interaction corresponding to the nuclear transition measured in Mössbauer spectroscopy.…”

Section: Introductionsupporting

confidence: 66%

“…To particularly ensure basis set saturation at the Hg nucleus with respect to an accurate computation of the contact density may nevertheless require an augmentation with tight s and p functions [18]. Our calibration studies at the Hartree-Fock level by means of the numerical atomic GRASP code [107] revealed a sufficient convergence by supplementing the Dyall TZ ðQZÞ basis set in an eventempered fashion with two more tight ff ¼ 864721150:0; 230133640:0g (ff ¼ 864477130:0; 230139440:0g) s functions and one tight ff¼130716620:0g (ff¼194566990:0g) p function (see Table A in the supporting information for more details).…”

Section: Basis Set Considerationsmentioning

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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Section: Introductionsupporting

confidence: 66%

Section: Introductionsupporting

confidence: 66%

Section: Basis Set Considerationsmentioning

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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“…Contact densities are most sensitive to the proper set-up of transformation of operators [93,94,[98][99][100]. Picture change affected results are dramatically wrong.…”

Section: Contact Densitiesmentioning

confidence: 99%

“…If the transformation of the property operator is neglected, a picture change error [89,90] is introduced, whose magnitude depends on the type of property considered [91][92][93][94][95][96][97]. In general, the picture change error is large for core properties.…”

Section: Transformed Expectation Valuesmentioning

confidence: 99%

Exact decoupling of the relativistic Fock operator

Peng¹,

Reiher²

2012

Perspectives on Theoretical Chemistry

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It is generally acknowledged that the inclusion of relativistic effects is crucial for the theoretical description of heavy-element-containing molecules. Four-component Dirac-operator-based methods serve as the relativistic reference for molecules and highly accurate results can be obtained-provided that a suitable approximation for the electronic wave function is employed. However, four-component methods applied in a straightforward manner suffer from high computational cost and the presence of pathologic negative-energy solutions. To remove these drawbacks, a relativistic electron-only theory is desirable for which the relativistic Fock operator needs to be exactly decoupled. Recent developments in the field of relativistic two-component methods demonstrated that exact decoupling can be achieved following different strategies. The theoretical formalism of these exact-decoupling approaches is reviewed in this paper followed by a comparison of efficiency and results.Keywords Relativistic electronic structure theory Á Fock operator Á Douglas-Kroll-Hess method Á X2C method Á Picture change error 1 Introduction

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Basis Sets

2016

Multiconfigurational Quantum Chemistry

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Basis set representation of the electron density at an atomic nucleus

Cited by 31 publications

References 49 publications

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

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

Exact decoupling of the relativistic Fock operator

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