B-spline solver for one-electron Schrödinger equation

Romanowski, Zbigniew

doi:10.1080/00268976.2011.631055

Cited by 6 publications

(2 citation statements)

References 46 publications

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“…The source codes used for the PEA calculations, which include the potential exploration tool and the 1D and 3D Schrödinger equation solvers, , are published on the web…”

Section: Discussion and Conclusionmentioning

confidence: 99%

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Bonfà¹,

Sartori²,

Renzi³

2015

J. Phys. Chem. C

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We revise the simple and yet powerful approach of the Double Adiabatic Approximation (DAA) to study positive muon embedding sites in condensed matter. This method introduces a tractable and reasonably accurate description of the quantum nature of the muon in Density Functional Theory (DFT) simulations aiming at identifying muon sites. Moreover, this approach overcomes the limitations of the harmonic approximation in terms of both computational efforts and accuracy. Notably, it also improves treatment of muon diffusion. We use the DAA and Nudged Elastic Band calculations to determine the muon sites and the activation energies between equivalent sites in MnSi and copper. In metallic Cu, the proposed phonon-assisted mechanism for the low-temperature muon diffusion in the lattice is confirmed. ■ INTRODUCTIONMuon spin rotation and relaxation (μSR) spectroscopy is an experimental technique that provides the time evolution of the muon spin polarization by exploiting the anisotropic emission of the decay positron.The main field of application of μSR is material science, but it is also adopted in chemistry for studying molecular dynamics and radical kinetics. 1−3 Both μ − SR and μ + SR exist, but, since μ − undergoes nuclear capture and the surviving μ − fall into atomic orbitals extremely close to the nuclei, μ + SR is more commonly used to investigate condensed matter.μSR experiments provide a measure of the microscopic field distribution at the interstitial site(s) where the μ + stop inside the sample. A seemingly embarrassing point is that these sites are usually unknown to the experimenter and the additional lack of knowledge on the perturbation generated locally by the positive muon probably represent the most common criticisms of the experimental technique. Even though in a large variety of cases ignoring the muon position does not represent a limitation, having access to information on interstitial sites and on muon-induced perturbations might be crucial to evaluate electronic properties such as long-range magnetic orders or localized magnetic moments.Predicting the position of interstitial muon sites is not a trivial task. During the final stages of thermalization in the sample the scattering between the muon and the atoms of the compound leads to a kinetic energy degradation from hundreds to tenths of electronvolts. Nonetheless, the identification of diamagnetic muon sites with approaches based on the Density Functional Theory (DFT) is emerging as a new and valuable strategy to routinely assist μSR experiments interpretation. After the pioneering work of Van de Walle et al., in recent years, this method, which provides information on the electronic and crystalline perturbations introduced by the muon, has been validated in many experimental cases with great success. 4−13 There are two main difficulties in the DFT approach. One is inherited from the mean-field description which cannot always correctly describe some classes of materials, like strongly correlated electrons systems or even some semiconductors mist...

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“…The source codes used for the PEA calculations, which include the potential exploration tool and the 1D and 3D Schrödinger equation solvers, , are published on the web…”

Section: Discussion and Conclusionmentioning

confidence: 99%

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Bonfà¹,

Sartori²,

Renzi³

2015

J. Phys. Chem. C

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“…( 2), q μ and ρ( → r i ) are the muon charge and electron density at the relaxed ion positions → r i , respectively. The above Schrödinger equation can be solved numerically by finite different method [24]. For that purpose, a cubic space around the muon position is discretized into 20 × 20 × 20 meshes where each corner points is assigned with 3D kinetic energy and the muon potential energy satisfying the following equation:…”

Section: Computational Schemementioning

confidence: 99%

3D long-range magnetic ordering in (C2H5NH3)2CuCl4 compound revealed by internal magnetic field from muon spin rotation and first principal calculation

Suprayoga

Nugroho

Onggo

et al. 2018

Physica B: Condensed Matter

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We report the results of muon spin rotation measurement that reveal a 3D long-range magnetic ordering in the inorganic CuCl 4 layers separated by (C 2 H 5 NH 3 ) organic ligands. The measured temperature dependent internal magnetic field down to 300 mK shows the 3D long-range magnetic ordering with magnetic transition at the Néel temperature of T N = 10.06 K and critical exponent of 0.31. The ground state internal dipole field is calculated by considering muon zero-point motion effect at the muon stop position determined by first principal DFT calculation, in combination with magnetization density calculated on the basis of a specific magnetic structure model. The calculated result is shown in good agreement with the measured value of internal field at the ground state temperature, thereby justifying the magnetic structure model adopted for this system and explaining the 3D nature of magnetic ordering. This model may therefore be applicable to the study of other magnetic materials.

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B-splines and NURBS based finite element methods for Kohn–Sham equations

Masud

Kannan

2012

Computer Methods in Applied Mechanics and Engineering

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B-spline solver for one-electron Schrödinger equation

Cited by 6 publications

References 46 publications

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

Efficient and Reliable Strategy for Identifying Muon Sites Based on the Double Adiabatic Approximation

3D long-range magnetic ordering in (C2H5NH3)2CuCl4 compound revealed by internal magnetic field from muon spin rotation and first principal calculation

B-splines and NURBS based finite element methods for Kohn–Sham equations

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