Quantum electrodynamical density‐matrix functional theory and group theoretical consideration of its solution

Ohsaku, Tadafumi; Yamanaka, Shusuke; Yamaki, Daisuke; Yamaguchi, Kizashi

doi:10.1002/qua.940

Cited by 7 publications

(7 citation statements)

References 46 publications

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“…The computational scheme is illustrated in Figure 6. We already discussed similar strategies in the case of spin‐free Hamiltonian 21 and QED Hamiltonian 22.…”

Section: Resultsmentioning

confidence: 99%

Spin correlation functions by generalized spin orbital density functional and multireference approaches

Yamanaka¹,

Takeda²,

Kawakami³

et al. 2003

Int J of Quantum Chemistry

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ABSTRACT:We presented the comparative study of spin correlation functions of generalized spin orbital density functional theory (GSO-DFT) and configuration interaction (CI) wave function (WF) approaches, in particular for simple models. The differences between them are ascribed to that of their symmetry frameworks, which is similar to that between the Heisenberg (HB) model and its mean-field approximation. Therefore, the prescriptions to spin-frustrated and -degenerated systems are examined from the viewpoint of the HB model and its solutions. Both nondynamic electron correlation and spin-dependent interactions are found to be important in the surface crossing regions. The GSO complete-active-space (CAS) CI and CAS self-consistent field (SCF) are also discussed as the multireference approaches for the systems.

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“…The computational scheme is illustrated in Figure 6. We already discussed similar strategies in the case of spin‐free Hamiltonian 21 and QED Hamiltonian 22.…”

Section: Resultsmentioning

confidence: 99%

Spin correlation functions by generalized spin orbital density functional and multireference approaches

Yamanaka¹,

Takeda²,

Kawakami³

et al. 2003

Int J of Quantum Chemistry

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“…Even more generally, one could consider functionals of the local density matrix n( r) = 〈Ψ|n( r)|Ψ〉, as proposed in Ref. [13]. For simplicity, in the following, the opposite charge density and opposite charge current will be referred to as charge density and charge current.…”

Section: Density-functional Theory Based On Effective Quantum Electrodynamicsmentioning

confidence: 99%

“…Eschrig et al [11,12] took another approach to RDFT based on Lieb's Legendre transformation using a normalordered QED Hamiltonian. Ohsaku et al [13] proposed a local-density-matrix functional theory based on a QED Hamiltonian with an one-photon-propagator fermion-fermion interaction. Despite these formal foundations of RDFT based on QED, in practice four-component RDFT is invariably applied in the Kohn-Sham (KS) scheme with a non-quantized electromagnetic field and in the no-pair approximation (i.e., neglecting contributions from electron-positron pairs) [14][15][16][17][18][19][20][21], most of the time using non-relativistic exchange-correlation density functionals.…”

Section: Introductionmentioning

confidence: 99%

Relativistic density-functional theory based on effective quantum electrodynamics

Toulouse

2021

SciPost Chem.

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A relativistic density-functional theory based on a Fock-space effective quantum-electrodynamics (QED) Hamiltonian using the Coulomb or Coulomb-Breit two-particle interaction is developed. This effective QED theory properly includes the effects of vacuum polarization through the creation of electron-positron pairs but does not include explicitly the photon degrees of freedom. It is thus a more tractable alternative to full QED for atomic and molecular calculations. Using the constrained-search formalism, a Kohn-Sham scheme is formulated in a quite similar way to non-relativistic density-functional theory, and some exact properties of the involved density functionals are studied, namely charge-conjugation symmetry and uniform coordinate scaling. The usual no-pair Kohn-Sham scheme is obtained as a well-defined approximation to this relativistic density-functional theory.

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“…* marm3. 14@gmail.com Already in 2002 Ohsaku et al introduced a local (relativistic) quantum electro-dynamical (QED) RDMFT [40] theory in which the nonlocality properties of the firstorder reduced density matrix (1-RDM) were not exploited and the so-called noninteracting kinetic energy needed to be evaluated with an auxiliary noninteracting system. This complication may be avoided by using the full 1-RDM as all one-body interactions can then be evaluated as explicitly known functionals of the 1-RDM.…”

Section: Introductionmentioning

confidence: 99%

Relativistic reduced density matrix functional theory

Rodríguez-Mayorga¹,

Giesbertz²,

Visscher³

2022

Preprint

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As a new approach to efficiently describe correlation effects in the relativistic quantum world we propose to consider reduced density matrix functional theory, where the key quantity is the firstorder reduced density matrix (1-RDM). In this work, we first introduce the theoretical foundations to extend the applicability of this theory to the relativistic domain. Then, using the so-called no-pair (np) approximation, we arrive at an approximate treatment of the relativistic effects by focusing on electronic wavefunctions and neglecting explicit contributions from positrons. Within the np approximation the theory becomes similar to the nonrelativistic case, with as unknown only the functional that describes the electron-electron interactions in terms of the 1-RDM. This requires the construction of functional approximations, and we therefore also present the relativistic versions of some common RDMFT approximations that are used in the nonrelativistic context and discuss their properties.

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Quantum electrodynamical density‐matrix functional theory and group theoretical consideration of its solution

Cited by 7 publications

References 46 publications

Spin correlation functions by generalized spin orbital density functional and multireference approaches

Spin correlation functions by generalized spin orbital density functional and multireference approaches

Relativistic density-functional theory based on effective quantum electrodynamics

Relativistic reduced density matrix functional theory

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