Ab initio calculations of the ${} ^2{\bi P}_{{\b 1}\over {\b 2}} \hbox{-}{} ^2{\bi P}_{{\b 3} \over {\b 2}} $ splitting in the thallium atom

Wahlgren, Ulf; Sjøvoll, Merethe; Fagerli, Hilde; Gropen, Odd; Schimmelpfennig, Bernd

doi:10.1007/s002140050268

Cited by 30 publications

(19 citation statements)

References 2 publications

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“…To attain an accuracy level of 400 cm −1 for the \documentclass{article}\pagestyle{empty}\begin{document}${^{2}}P^{o}_{1/2}-{^{2}}P^{o}_{3/2}$\end{document} splitting in the ground state and for excitation energies to low‐lying states of Tl and to take account of the core polarization, one should correlate at least 13 electrons, i.e., include the 5 d shell. This is achieved in the present MRD‐CI calculations with f and g basis functions describing mainly polarization of the 5 d shell (for other recent results see, e.g., 1, 3, 4). Some data from our 13e‐CI calculations of the spin‐orbit (SO) splitting in the ground state of Tl are collected in Table I in comparison with the 3e‐CI results, which in our DF/CI (Dirac–Fock calculations followed by CI) and the GRECP/CI calculations have errors of about 600 cm −1 .…”

Section: Frozen‐core Approximation For Outer‐core Shellssupporting

confidence: 64%

GRECP/MRD-CI calculations of spin-orbit splitting in ground state of Tl and of spectroscopic properties of TlH

Титов

Mosyagin

Alekseyev

et al. 2001

Int. J. Quantum Chem.

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The generalized relativistic effective core potential (GRECP) approach is employed in the framework of multireference single-and double-excitation configuration interaction (MRD-CI) method to calculate the spin-orbit (SO) splitting in the 2 P o ground state of the Tl atom and spectroscopic constants for the 0 + ground state of TlH. The 21-electron GRECP for Tl is used and the outer core 5s and 5p pseudospinors are frozen with the help of the level shift technique. The spin-orbit selection scheme with respect to relativistic multireference states and the corresponding code are developed and applied in the calculations. In this procedure both correlation and spin-orbit interactions are taken into account. A [4,4,4,3,2] basis set is optimized for the Tl atom and employed in the TlH calculations. Very good agreement is found for the equilibrium distance, vibrational frequency, and dissociation energy of the TlH ground state (R e = 1.870 Å, ω e = 1420 cm −1 , D e = 2.049 eV) as compared with the experimental data (R e = 1.868 Å, ω e = 1391 cm −1 , D e = 2.06 eV).SHORT NAME: GRECP/MRD-CI calculations on Tl and TlH

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Section: Frozen‐core Approximation For Outer‐core Shellssupporting

confidence: 64%

GRECP/MRD-CI calculations of spin-orbit splitting in ground state of Tl and of spectroscopic properties of TlH

Титов

Mosyagin

Alekseyev

et al. 2001

Int. J. Quantum Chem.

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“…This is not always the case as can be read from Table VIII. As expected, the scalar contracted basis set 26 gives poor results differing significantly from those in decontracted and recontracted basis sets. The same holds for the ionization energy ͑Table X͒.…”

Section: B Tlsupporting

confidence: 76%

“…Restriction to this part of the DK Hamiltonian is common and has made the DK approach the most widely relativistic approach in quantum chemical calculations. 18,19 When spin-orbit effects are to be included the spinorbit operator is applied usually at the post-one-component HF step 5,[20][21][22][23][24][25][26] to couple multiplets with different spin and space symmetries. This is done either by a quasidegenerate perturbation theory ͑QDPT͒ where configuration interaction ͑CI͒ or MCSCF states are taken as zero-order wave functions ͑so-called LS coupling͒ or by an intermediate coupling scheme in spin-orbit CI ͑SO-CI͒ or by fully variational treatment of spin-orbit coupling in configuration space.…”

Section: Introductionmentioning

confidence: 99%

Inclusion of mean-field spin–orbit effects based on all-electron two-component spinors: Pilot calculations on atomic and molecular properties

Iliaš

Kellö

Visscher

et al. 2001

The Journal of Chemical Physics

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An implementation of a two-component all-electron ( j j/ ) treatment of both scalar and spinorbit relativistic effects in the MOLFDIR program suite is presented. Relativity is accounted for by Douglas-Kroll transformed one-electron operators: scalar ͑spin-free͒ and so called mean-field spinorbit terms. The interelectronic interaction is represented by the nonrelativistic Coulomb operator. High-level correlated calculations of properties of several systems ͑FO, ClO, Cl, O 2 ϩ , O 2 Ϫ , Tl, and TlH͒ where spin-orbit effects play a dominant role are presented and compared with other data. Agreement with Dirac-Coulomb͑-Gaunt͒ reference values is in general very good.

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“…33 The merit of the former is to use ͑four-component͒ atomic information ͑e.g., A 4c and X A ͒ to synthesize the whole molecular four-or two-component Hamiltonian whereas the latter aimed to approximate the spin-orbit part of a chosen two-component Hamiltonian which may include the ones proposed here. ͑35͒ is the same as Eq.…”

Section: B Xqr-ks: Exact Decoupling Of the Matrix Dks Equationmentioning

confidence: 99%

Making four- and two-component relativistic density functional methods fully equivalent based on the idea of “from atoms to molecule”

Peng

Liu

Xiao

et al. 2007

The Journal of Chemical Physics

237

213

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It is shown that four- and two-component relativistic Kohn-Sham methods of density functional theory can be made fully equivalent in all the aspects of simplicity, accuracy, and efficiency. In particular, this has been achieved based solely on physical arguments rather than on mathematical tricks. The central idea can be visualized as "from atoms to molecule," reflecting that the atomic information is employed to "synthesize" the molecular no-pair relativistic Hamiltonian. That is, the molecular relativistic Hamiltonian can, without loss of accuracy, be projected onto the positive energy states of the isolated Dirac atoms with the projector approximated simply by the superposition of the atomic ones. The dimension of the four-component Hamiltonian matrix then becomes the same as that of a two-component one. Another essential ingredient is to formulate quasirelativistic theory on matrix form rather than on operator form. The resultant quasi-four-component, normalized elimination of the small component, and symmetrized elimination of the small component approaches are critically examined by taking the molecules of MH and M(2) (M=At, E117) as examples.

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Ab initio calculations of the ${} ^2{\bi P}_{{\b 1}\over {\b 2}} \hbox{-}{} ^2{\bi P}_{{\b 3} \over {\b 2}} $ splitting in the thallium atom

Cited by 30 publications

References 2 publications

GRECP/MRD-CI calculations of spin-orbit splitting in ground state of Tl and of spectroscopic properties of TlH

GRECP/MRD-CI calculations of spin-orbit splitting in ground state of Tl and of spectroscopic properties of TlH

Inclusion of mean-field spin–orbit effects based on all-electron two-component spinors: Pilot calculations on atomic and molecular properties

Making four- and two-component relativistic density functional methods fully equivalent based on the idea of “from atoms to molecule”

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