Analyticity of the density of electronic wavefunctions

Fournais, Søren; Hoffmann‐Ostenhof, M.; Hoffmann‐Ostenhof, Thomas; Sørensen, Thomas Østergaard

doi:10.1007/bf02385580

Cited by 23 publications

(79 citation statements)

References 12 publications

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“…and its total current by j t := j + ρA + curl m, where the magnetization of a state is defined in (15). The Hamiltonian that we consider is the many-body Pauli operator…”

Section: 2mentioning

confidence: 99%

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Garrigue

2019

J Stat Phys

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We prove Hohenberg-Kohn theorems for several models of quantum mechanics. First, we show that for possibly degenerate systems of several types of particles, the pair correlation functions of any ground state contain the information of the interactions and of the external potentials. Then, in the presence of the Zeeman interaction, a strong constraint on external fields is derived for systems having the same ground state densities and magnetizations. Next, we prove that the density and the entropy of a ground state contain the information of both the imposed external potential and temperature. Eventually, we conclude that at positive temperature, Hohenberg-Kohn theorems generically hold.

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“…and its total current by j t := j + ρA + curl m, where the magnetization of a state is defined in (15). The Hamiltonian that we consider is the many-body Pauli operator…”

Section: 2mentioning

confidence: 99%

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Garrigue

2019

J Stat Phys

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“…We also assume throughout this paper that the potential V equals to −Z/|r| in the neighborhood of 0, and belongs to C ∞ loc (R 3 \ R) ∩ L 2 # (Ω). It was shown in [23,24,25] that the exact electron densities are analytic away from the nuclei and satisfy certain cusp conditions at the nuclei. The plane wave approximations can not have as good convergence rate as (2.1) due to the cusps at the nuclear positions.…”

Section: Preliminarymentioning

confidence: 99%

“…For eigenvalue problems with singular potentials in full-potential calculations, plane waves are inefficient bases for describing the cusps at the nuclei positions [23,24,25,28]. In contrast, it is observed that a significant part of the rapid oscillations can be captured by atomic orbitals such as Gaussians and Slater-type orbitals [27,34], which have been widely used in quantum chemistry (we refer to [7,18] for their numerical analysis).…”

Section: Introductionmentioning

confidence: 99%

A discontinuous Galerkin scheme for full-potential electronic structure calculations

Chen

2019

Journal of Computational Physics

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In this paper, we construct an efficient numerical scheme for full-potential electronic structure calculations of periodic systems. In this scheme, the computational domain is decomposed into a set of atomic spheres and an interstitial region, and different basis functions are used in different regions: radial basis functions times spherical harmonics in the atomic spheres and plane waves in the interstitial region. These parts are then patched together by discontinuous Galerkin (DG) method. Our scheme has the same philosophy as the widely used (L)APW methods in materials science, but possesses systematically spectral convergence rate. We provide a rigorous a priori error analysis of the DG approximations for the linear eigenvalue problems, and present some numerical simulations in electronic structure calculations.

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“…For N = 1, we take ρ = |ψ| 2 . The regularity result is the following FHHS2]. The density ρ is real analytic on R 3 \ {R 1 , · · · , R L }.…”

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confidence: 98%

“…In [FHHS1], it is proved that ρ is smooth on R 3 \{R 1 , · · · , R L }. This result is then used in [FHHS2] to derive the analyticity.…”

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confidence: 99%

A New Proof of the Analyticity of the Electronic Density of Molecules

Jecko

2010

Lett Math Phys

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We give a new, short proof of the regularity away from the nuclei of the electronic density of a molecule obtained in [FHHS1, FHHS2]. The new argument is based on the regularity properties of the Coulomb interactions underlined in [Hu, KMSW]. Well-known pseudodifferential techniques for elliptic operators are also used. The paper is published in Letters in Mathematical Physics 93, number 1, pp. 73-83, 2010. The original publication is available at " www.springerlink.com ".

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Analyticity of the density of electronic wavefunctions

Abstract: We prove that the electronic densities of atomic and molecular eigenfunctions are real analytic in R 3 away from the nuclei.Date: November 22, 2002.

Cited by 23 publications

References 12 publications

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

Hohenberg–Kohn Theorems for Interactions, Spin and Temperature

A discontinuous Galerkin scheme for full-potential electronic structure calculations

A New Proof of the Analyticity of the Electronic Density of Molecules

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