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Search results for: ORTHOGONAL FUNCTIONS
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Linear-scaling calculation of Hartree-Fock exchange energy with Non-orthogonal Generalised Wannier Functions
PublicationWe present a method for the calculation of four-centre two-electron repulsion integrals in terms of localised non-orthogonal generalised Wannier functions (NGWFs). Our method has been imple- mented in the ONETEP program and is used to compute the Hartree-Fock exchange energy component of Hartree-Fock and Density Functional Theory (DFT) calculations with hybrid exchange-correlation functionals. As the NGWFs are optimised in situ...
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Scattering From a Cylindrical Object of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple and intuitive solution to scattering problems in shielded and open structures is presented. The main idea of the analysis is based on the direct field matching technique involving the usage of projection of the fields at the boundary on a fixed set of orthogonal basis functions. Different convex shapes and various obstacle materials are considered to verify the validity of the method in open and closed structures. The...
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Propagation in the Open Cylindrical Guide of Arbitrary Cross Section With the Use of Field Matching Method
PublicationA simple solution to propagation problem in open waveguides and dielectric fibers of arbitrary convex cross section is presented. The idea of the analysis is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. A complex root tracing algorithm is utilized to find the propagation coefficients of the investigated guides. Different convex...
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Scattering and Propagation Analysis for the Multilayered Structures Based on Field Matching Technique
PublicationA semi-analytical method is employed to the analysis of scattering and guiding problems in multilayer dielectric structures. The approach allows to investigate objects with arbitrary convex cross section and is based on the direct field matching technique involving the usage of the field projection at the boundary on a fixed set of orthogonal basis functions. For the scattering problems the scattered field in the far zone is calculated...
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Approximate solution for Euler equations of stratified water via numerical solution of coupled KdV system
PublicationWe consider Euler equations with stratified background state that is valid for internal water waves. The solution of the initial-boundary problem for Boussinesq approximation in the waveguide mode is presented in terms of the stream function. The orthogonal eigenfunctions describe a vertical shape of the internal wave modes and satisfy a Sturm-Liouville problem. The horizontal profile is defined by a coupled KdV system which is...
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Zero-range potentials for Dirac particles: Bound-state problems
PublicationA model in which a massive Dirac particle in $\mathbb{R}^{3}$ is bound by $N\geqslant1$ spatially distributed zero-range potentials is presented. Interactions between the particle and the potentials are modeled by subjecting a particle's bispinor wave function to certain limiting conditions at the potential centers. Each of these conditions is parametrized by a $2\times2$ Hermitian matrix (or, equivalently, a real scalar and a...
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The ONETEP linear-scaling density functional theory program
PublicationWe present an overview of the ONETEP program for linear-scaling density functional theory (DFT) calculations with large basis set (planewave) accuracy on parallel computers. The DFT energy is computed from the density matrix, which is constructed from spatially localized orbitals we call Non-orthogonal Generalized Wannier Functions (NGWFs), expressed in terms of periodic sinc (psinc) functions. During the calculation, both the...
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Distinguishing of cocrystals from simple eutectic mixtures: phenolic acids as potential pharmaceutical coformers
PublicationThe multiparameter model comprising 1D and 2D QSPR/QSAR descriptors was proposed and validated for phenolic acid binary systems. This approach is based on the optimization of regression coefficients for maximization of the percentage of true positives in the pool of systems comprising either simple binary eutectics or cocrystals. The training set consisted of 58 eutectics and 168 cocrystals. The solid dispersions collection used...
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Massively parallel linear-scaling Hartree–Fock exchange and hybrid exchange–correlation functionals with plane wave basis set accuracy
PublicationWe extend our linear-scaling approach for the calculation of Hartree–Fock exchange energy using localized in situ optimized orbitals [Dziedzic et al., J. Chem. Phys. 139, 214103 (2013)] to leverage massive parallelism. Our approach has been implemented in the ONETEP (Order-N Electronic Total Energy Package) density functional theory framework, which employs a basis of non-orthogonal generalized Wannier functions (NGWFs) to achieve...
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Orthogonality relations for the associated Legendre functions of imaginary order
PublicationOrthogonality relations for the associated Legendre functions of imaginary order are derived. They are expressed in terms of the Dirac delta function. The method is based on some known properties of the associated Legendre functions and the Dirac delta distribution. A special case of one of the relations has appeared in some recent applications.
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A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices
PublicationThe orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices is evaluated in a closed form. It is found to be proportional to a sum of two terms, both depending on the second upper indices and containing the Dirac delta distribution.