Journal ArticleDOI
Evaluation of the rotation matrices in the basis of real spherical harmonics
TLDR
In this paper, a general algorithm to compute the representation matrix of any point-group symmetry operation in the basis of the real spherical harmonics, paying attention to the use of recurrence relationships that allow the treatment of functions with high angular momenta is presented.Abstract:
Rotation matrices (or Wigner D functions) are the matrix representations of the rotation operators in the basis of spherical harmonics. They are the key entities in the generation of symmetry-adapted functions by means of projection operators. Although their expression in terms of ordinary (complex) spherical harmonics and Euler rotation angles is well known, an alternative representation using real spherical harmonics is desirable. The aim of this contribution is to obtain a general algorithm to compute the representation matrix of any point-group symmetry operation in the basis of the real spherical harmonics, paying attention to the use of recurrence relationships that allow the treatment of functions with high angular momenta.read more
Citations
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Journal ArticleDOI
Implementation of the projector augmented-wave method in the ABINIT code: Application to the study of iron under pressure
TL;DR: The projector augmented wave method (PAW) was implemented in the ABINIT code as discussed by the authors, which allows self-consistent calculations of the electronic structure of a periodic solid within the density functional theory (DFT), including the analytic calculation of forces and stresses.
Journal ArticleDOI
Spatiospectral Concentration on a Sphere
TL;DR: In the asymptotic limit of a small spatial region and a large spherical harmonic bandwidth, the spherical concentration problem reduces to its planar equivalent, which exhibits self-similarity when the Shannon number is kept invariant.
Journal ArticleDOI
Localized spectral analysis on the sphere
TL;DR: In this paper, the authors propose a method analogous to Cartesian multitaper spectral analysis that uses optimally concentrated data tapers to estimate the admittance and coherence spectra between two geophysical data sets on the sphere.
Journal ArticleDOI
Symmetry-Adapted Machine Learning for Tensorial Properties of Atomistic Systems
TL;DR: This work introduces a formalism that extends existing schemes and makes it possible to perform machine learning of tensorial properties of arbitrary rank, and for general molecular geometries, and derives a tensor kernel adapted to rotational symmetry.
Journal ArticleDOI
Structural, thermodynamic, and electronic properties of plutonium oxides from first principles
TL;DR: In this article, the structural, electronic, optical, and thermodynamic properties of plutonium oxides were investigated using the local density approximation/generalized gradient approximation (LDA+U$) method.
References
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Book
Mathematical Methods for Physicists
TL;DR: In this article, the authors present a model for vector analysis based on the Calculus of Variations and the Sturm-Liouville theory, which includes the following: Curved Coordinates, Tensors.
Book
Quantum Theory Of Angular Momemtum
TL;DR: In this article, the authors present a collection of useful formulas besides those related to angular momentum, and compare different notations used by previous authors, and present results relating to different aspects of the angular momentum theory.
Book ChapterDOI
Quantum Theory of Angular Momentum
TL;DR: In this article, a brief summary of the quantum theory of angular momentum is given, which is at the core of the theory of magnetism, as the angular momentum of a charged particle is proportional to its magnetization.