The molecular mean-field approach for correlated relativistic calculations

Sikkema, Jetze; Visscher, Lucas; Saue, Trond; Iliaš, Miroslav

doi:10.1063/1.3239505

Cited by 221 publications

(234 citation statements)

References 74 publications

(72 reference statements)

Supporting

Mentioning

225

Contrasting

Unclassified

Order By: Relevance

“…For reasons of computational efficiency, the molecular mean-field approximation [98] to the four-component DC Hamiltonian was applied in all molecular wave-functionbased calculations. In this scheme, the required set of two-electron integrals for the post-HF correlation step are computed in molecular orbital basis by neglecting all integrals of the AO basis that involve the small component.…”

Section: Hamiltonian Operatormentioning

confidence: 99%

See 1 more Smart Citation

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

Knecht

Fux

Meer³

et al. 2011

Theor Chem Acc

Self Cite

View full text Add to dashboard Cite

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

show abstract

Section: Hamiltonian Operatormentioning

confidence: 99%

“…The resulting Hamiltonian is denoted 4 DC ÃÃ in Ref. [98]. The relative deviation in the total contact density from the exact 4 DC-CCSD(T), with the full set of two-electron integrals, was in all cases tested less than 0.1 ppm, and we therefore consider this as a reliable approach.…”

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

Self Cite

View full text Add to dashboard Cite

show abstract

“…These issues have been discussed in detail in Ref. [54]. Second, as relativistic many-electron calculations require an external-field no-pair projection one may view this projection to be accomplished by the exactdecoupling approach.…”

Section: The One-step Solutionmentioning

confidence: 99%

“…2) Therefore, the exact-decoupling transformations must be updated if the spinors have changed, e.g., upon their optimization in a self-consistent field procedure (or when the positions of the nuclei, i.e., the molecular structure is changed). In general, this change of the exact-decoupling transformation has been shown to be small [54,79]. An exact-decoupling transformation constructed only for the external electrostatic potential, V eff !…”

Section: The Cumbersome Two-electron Termsmentioning

confidence: 99%

Exact decoupling of the relativistic Fock operator

Peng¹,

Reiher²

2012

Perspectives on Theoretical Chemistry

View full text Add to dashboard Cite

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

show abstract

“…In the correlation treatment, we included 50 electrons and virtual orbitals up to 25 a.u. Here we used the molecular meanfield X2C Hamiltonian [56] with the Gaunt term included. Fock-space coupled-cluster calculations [16] were carried out to obtain the ionization potentials from the filled 7p 3=2 and 7p 1=2 shells of Og.…”

mentioning

confidence: 99%

Heaviest Element Has Unusual Shell Structure

Wilson

2018

Physics

View full text Add to dashboard Cite

Fermion localization functions are used to discuss electronic and nucleonic shell structure effects in the superheavy element oganesson, the heaviest element discovered to date. Spin-orbit splitting in the 7p electronic shell becomes so large (∼10 eV) that Og is expected to show uniform-gas-like behavior in the valence region with a rather large dipole polarizability compared to the lighter rare gas elements. The nucleon localization in Og is also predicted to undergo a transition to the Thomas-Fermi gas behavior in the valence region. This effect, particularly strong for neutrons, is due to the high density of single-particle orbitals. 118 Og, 0.89 þ1.07 −0.31 ms, is too short for chemical "oneatom-at-a-time" studies; hence, its chemical properties must be inferred from advanced atomic calculations based on relativistic quantum theory [6][7][8][9][10][11][12][13][14][15][16][17][18][19]. According to these, Og has a closed-shell ½Rn 5f 14 6d 10 7s 2 7p 6 configuration [13,20,21], with a very large spin-orbit splitting of the 7p shell (9.920 eV at the Dirac-Breit-Hartree-Fock and 10.125 eV at the Fock-space coupled-cluster level; see below). In contrast to its electronic configuration (Og completes the seventh period of the periodic table), it is not expected to behave like a typical rare gas of group 18. For example, the relativistic 7p 3=2 expansion and the relativistic 8s contraction make Og the first rare gas element with a positive electron affinity of 0.064 eV [10,16,22]. This result includes a substantial quantum electrodynamic correction of 0.006 eV [16].Nuclear structure calculations predict 294 Og to be a deformed nucleus [23][24][25][26], eight neutrons away from the next neutron shell closure at 302 Og (N ¼ 184) [27][28][29][30][31][32]. A new factor impacting properties of superheavy nuclei is the strong electrostatic repulsion: The Coulomb force in superheavy nuclei cannot be treated as a small perturbation atop the dominating nuclear interaction; the resulting polarization effects due to Coulomb frustration are expected to influence significantly the proton and neutron

show abstract

The molecular mean-field approach for correlated relativistic calculations

Cited by 221 publications

References 74 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

Heaviest Element Has Unusual Shell Structure

Contact Info

Product

Resources

About