Gauge-invariant Ritz's method for electrodynamics

Sato

2013

J. Comput. Chem. Jpn.

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An anion (negative ion) such as O 2− , which is stable in a molecule/solid, sometimes cannot bind an attached electron in a vacuum and emits an electron. To describe an anion, the author previously developed the SIWB (surrounding or solid Coulomb-potential-induced well for basis set) method for a linear combination of atomic orbitals (LCAO) calculated numerically in a discrete variational (DV) density functional theory (DFT). For the generation of basis atomic orbitals, the DV method usually adds a well potential to the potential for electrons to stabilize the electrons. There was no reasonable method for determining the depth and radius of the well and the usual well depth has a relatively deep value of about −1 Eh independent of electron attachment tendency. In contrast, the SIWB method adds a well potential solely for generating and improving anion basis atomic orbital functions and uniquely determines the depth and radius of the well, which is relatively shallow, considering the Coulomb potential arising from the surrounding nuclei and electron cloud in a molecule/solid. This article aims to attempt calculations for the one-electron wave function of a molecule including an anion using the finite element method, which adopts a basis set localized in a small region on a space lattice that is suitable for the wave function behavior of an anion. The finite element results were compared not only to results from the usual LCAO method with a relatively deep well (denoted as LCAO−N), but also to those from the improved LCAO method with the SIWB scheme (denoted as LCAO−SIWB). It emerged from the present study that the finite element results for the anion are consistent with the LCAO−SIWB results.

Section: Introductionmentioning

confidence: 99%

Comparison of Finite Element Approach and LCAO Analysis with SIWB Method for a Molecule Including an Anion in a Discrete Variational Density Functional Theory

Sato

2013

J. Comput. Chem. Jpn.

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“…For a more sophisticated description of antiferromagnetism, it may be useful to examine the electronic state using advanced theories such as GGA that considers the derivatives of the charge density as well as other terms such as the exact fractional exchange interaction. We intend to adopt other approaches in the future64, 65. We add that calculated result by using numerical atomic orbitals is independent of basis size66.…”

Section: Introductionmentioning

confidence: 99%

CaCuO₂ antiferromagnetism using shallow well added solely to atomic potential for generating O²⁻ basis set of periodic molecular orbitals with consideration of coulomb potential in solid in an LDA

Int J of Quantum Chemistry

2011

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ABSTRACT:The antiferromagnetism in an infinite-layer copper oxide CaCuO 2 was analyzed by adding a well potential solely to the atomic potential of an O 2À ion in constructing a basis set for a Bloch-type periodic linear combination of numerically calculated atomic orbitals. (The well is not added to the solid Hamiltonian.) In this method that solves a secular equation to find all electron states, the original KohnÀSham local density approximation (LDA) was employed. (Magnetic properties calculated with generalized gradient approximation are more similar to those with the original KohnÀSham LDA than VoskoÀWilkÀNusair results.) The Cu oxides contain the O 2À ion, which is stable in a solid but emits an electron in a vacuum. This implies that the atomic wave equation of electrons for an isolated O 2À in a vacuum lacks real solutions unless a well potential is added to the atomic potential. The well potential for the O 2À basis set was calculated using the Coulomb potential generated by nuclei and electron clouds surrounding O 2À in a solid. A relatively shallow well potential within an ion radius compared to the well depth usually used results in significant delocalization of electrons at the O 2À site. This periodic molecular orbital method predicts insulating antiferromagnetic ordering in CaCuO 2 .

“…We formulated the field theory [9][10][11][12], which is expressed in terms of the step-function-type basis functions to realize the removal of the ultraviolet divergences. In this subsection, the formalism is described so as to express the fields in terms of the step-function-type basis functions in the form used by this paper.…”

Section: Field Theory In Terms Of the Step-function-type Basis Functionsmentioning

confidence: 99%

“…In our previous paper [9][10][11][12], we formulated a field theory in terms of the stepa e-mail: km.fukushima@mx2.ttcn.ne.jp b e-mail: hikaru_sato@gaia.eonet.ne.jp function-type basis functions (SFT field theory), which is based on the finite element theory [9,[12][13][14] (the formulation is rather different from that by Bender et al), and cuts off high-frequency oscillations of wave functions at short distances. Owing to the space-time continuum and differentiable step-function-type basis functions, this formalism is Poincaré covariant and removes ultraviolet divergences at short distances.…”

Section: Introductionmentioning

confidence: 99%

Derivation of the cut-off length from the quantum quadratic enhancement of a mass in vacuum energy constant Lambda

Sato

2018

Eur. Phys. J. C

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Ultraviolet self-interaction energies in field theory sometimes contain meaningful physical quantities. The self-energies in such as classical electrodynamics are usually subtracted from the rest mass. For the consistent treatment of energies as sources of curvature in the Einstein field equations, this study includes these subtracted selfenergies into vacuum energy expressed by the constant Lambda (used in such as Lambda-CDM). In this study, the self-energies in electrodynamics and macroscopic classical Einstein field equations are examined, using the formalisms with the ultraviolet cut-off scheme. One of the cut-off formalisms is the field theory in terms of the step-functiontype basis functions, developed by the present authors. The other is a continuum theory of a fundamental particle with the same cut-off length. Based on the effectiveness of the continuum theory with the cut-off length shown in the examination, the dominant self-energy is the quadratic term of the Higgs field at a quantum level (classical selfenergies are reduced to logarithmic forms by quantum corrections). The cut-off length is then determined to reproduce today's tiny value of Lambda for vacuum energy. Additionally, a field with nonperiodic vanishing boundary conditions is treated, showing that the field has no zero-point energy.