Spin-dependent unitary group approach to the Pauli–Breit Hamiltonian. II. First order energy level shifts due to spin–spin interaction

Gould, M. D.; Battle, J. S.

doi:10.1063/1.465897

Cited by 13 publications

(2 citation statements)

References 20 publications

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“…4,5 However, this method employs two-component complex orbitals and cannot be easily interfaced with conventional quantum chemistry programs, which mostly employ one-component real-valued orbitals. In the first category, the SOC operator is included in the Fock operator to optimize orbitals and the spin-orbit effect is rigorously accounted for.…”

Section: Introductionmentioning

confidence: 99%

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

Zeng

Fedorov

Kłobukowski

2011

The Journal of Chemical Physics

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The efficacy of several multiconfiguration self-consistent field (MCSCF) methods in the subsequent spin-orbit coupling calculations was studied. Three MCSCF schemes to generate molecular orbitals were analyzed: state-specific, state-averaged, and dynamically weighted MCSCF. With Sn(2)(+) as the representative case, we show that the state-specific MCSCF orbitals lead to discontinuities in potential energy curves when avoided crossings of electronic states occur; this problem can be solved using the state-averaged or dynamically weighted MCSCF orbitals. The latter two schemes are found to give similar results when dynamic electron correlation is considered, which we calculated at the level of multiconfigurational quasidegenerate perturbation theory (MCQDPT). We employed the recently developed Douglas-Kroll spin-orbit adapted model core potential, ZFK3-DK3, and the dynamically weighted MCSCF scheme to calculate the spectroscopic constants of the mono-hydrides and compared them to the results obtained using the older set of potentials, MCP-TZP. We also showed that the MCQDPT tends to underestimate the dissociation energies of the hydrides and discussed to what extent coupled-cluster theory can be used to improve results.

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Section: Introductionmentioning

confidence: 99%

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

Zeng

Fedorov

Kłobukowski

2011

The Journal of Chemical Physics

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“…Finally, as already pointed out above, UGA also provides a good starting point for the handling of spin-effects in which case we require matrix elements of U(2n) generators. Much work has been done in this direction and is still going on [28,40,41,[103][104][105][106][107][108][109][110][111][112][113].…”

Section: With X †mentioning

confidence: 99%

Valence bond approach and Verma bases

Paldus

Planelles

2018

J Math Chem

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The unitary group approach (UGA) to the many-fermion problem is based on the Gel'fand-Tsetlin (G-T) representation theory of the unitary or general linear groups. It exploits the group chain U(n) ⊃ U(n − 1) ⊃ • • • ⊃ U(2) ⊃ U(1) and the associated G-T triangular tableau labeling basis vectors of the relevant irreducible representations (irreps). The general G-T formalism can be drastically simplified in the many-electron case enabling an efficient exploitation in either configuration interaction (CI) or coupled cluster (CC) approaches to the molecular electronic structure. However, while the reliance on the G-T chain provides an excellent general formalism from the mathematical point of view, it has no specific physical significance and dictates a fixed Yamanouchi-Kotani coupling scheme, which in turn leads to a rather arbitrary linear combination of distinct components of the same multiplet with a given orbital occupancy. While this is of a minor importance in molecular orbital (MO) based CI approaches, it is very inconvenient when relying on the valence bond (VB) scheme, since the G-T states do not correspond to canonical Rumer structures. While this shortcoming can be avoided by relying on the Clifford algebra UGA (CAUGA) formalism, which enables an exploitation of a more or less arbitrary coupling scheme, it is worthwhile to point out the suitability of the so-called Verma basis sets for the VB-type approaches. Keywords Valence bond (VB) method • unitary group approach (UGA) • Verma bases • covalent and ionic VB structures • π-electron model • canonical vs non-canonical VB structures

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Symmetric group approach to relativistic CI. II. Reduction of matrices in the spin space

Flocke

Barysz

Karwowski³

et al. 1997

Int. J. Quant. Chem.

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An algorithm for the evaluation of matrix representations of products of permutation operators and of one-and two-electron spin-dependent operators in a spin-adapted basis of the N-electron spin space is presented. In particular, the case of the basis functions in which pЈ electrons are described by products of singlet-coupled pairs is considered in Ž . detail. The N-electron spin integrals are, in this case, reduced explicitly to the N y pЈ electron ones.

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Spin-dependent unitary group approach to the Pauli–Breit Hamiltonian. II. First order energy level shifts due to spin–spin interaction

Cited by 13 publications

References 20 publications

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

Performance of dynamically weighted multiconfiguration self-consistent field and spin-orbit coupling calculations of diatomic molecules of Group 14 elements

Valence bond approach and Verma bases

Symmetric group approach to relativistic CI. II. Reduction of matrices in the spin space

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