In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the （k ＋ 1）-th eigenvalue in terms of the first k eigenvalues independent of the domains.
The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the p...The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.展开更多
KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the...KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF)scheme.To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms,we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox.We compare the performance of KSSOLV-GPU on three types of GPU,including RTX3090,V100,and A100,with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.展开更多
The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of pla...The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.展开更多
文摘In this article, we consider the eigenvalue problem for the bi-Kohn Laplacian and obtain universal bounds on the （k ＋ 1）-th eigenvalue in terms of the first k eigenvalues independent of the domains.
文摘The kernel energy method(KEM) has been shown to provide fast and accurate molecular energy calculations for molecules at their equilibrium geometries.KEM breaks a molecule into smaller subsets,called kernels,for the purposes of calculation.The results from the kernels are summed according to an expression characteristic of KEM to obtain the full molecule energy.A generalization of the kernel expansion to density matrices provides the full molecule density matrix and orbitals.In this study,the kernel expansion for the density matrix is examined in the context of density functional theory(DFT) Kohn-Sham(KS) calculations.A kernel expansion for the one-body density matrix analogous to the kernel expansion for energy is defined,and is then converted into a normalizedprojector by using the Clinton algorithm.Such normalized projectors are factorizable into linear combination of atomic orbitals(LCAO) matrices that deliver full-molecule Kohn-Sham molecular orbitals in the atomic orbital basis.Both straightforward KEM energies and energies from a normalized,idempotent density matrix obtained from a density matrix kernel expansion to which the Clinton algorithm has been applied are compared to reference energies obtained from calculations on the full system without any kernel expansion.Calculations were performed both for a simple proof-of-concept system consisting of three atoms in a linear configuration and for a water cluster consisting of twelve water molecules.In the case of the proof-of-concept system,calculations were performed using the STO-3 G and6-31 G(d,p) bases over a range of atomic separations,some very far from equilibrium.The water cluster was calculated in the 6-31 G(d,p) basis at an equilibrium geometry.The normalized projector density energies are more accurate than the straightforward KEM energy results in nearly all cases.In the case of the water cluster,the energy of the normalized projector is approximately four times more accurate than the straightforward KEM energy result.The KS density matrices of this study are applicable to quantum crystallography.
基金supported by the National Natural Science Foundation of China (No.21688102,No.21803066,and No.22003061)the Chinese Academy of Sciences Pioneer Hundred Talents Program (KJ2340000031,KJ2340007002)+7 种基金the National Key Research and Development Program of China(2016YFA0200604)the Anhui Initiative in Quantum Information Technologies (AHY090400)the Strategic Priority Research of Chinese Academy of Sciences(XDC01040100)CAS Project for Young Scientists in Basic Research (YSBR-005)the Fundamental Research Funds for the Central Universities (WK2340000091,WK2060000018)the Hefei National Laboratory for Physical Sciences at the Microscale (SK2340002001)the Research Start-Up Grants (KY2340000094)the Academic Leading Talents Training Program(KY2340000103) from University of Science and Technology of China
文摘KSSOLV(Kohn-Sham Solver)is a MATLAB(Matrix Laboratory)toolbox for solving the Kohn-Sham density functional theory(KS-DFT)with the plane-wave basis set.In the KS-DFT calculations,the most expensive part is commonly the diagonalization of Kohn-Sham Hamiltonian in the self-consistent field(SCF)scheme.To enable a personal computer to perform medium-sized KS-DFT calculations that contain hundreds of atoms,we present a hybrid CPU-GPU implementation to accelerate the iterative diagonalization algorithms implemented in KSSOLV by using the MATLAB built-in Parallel Computing Toolbox.We compare the performance of KSSOLV-GPU on three types of GPU,including RTX3090,V100,and A100,with conventional CPU implementation of KSSOLV respectively and numerical results demonstrate that hybrid CPU-GPU implementation can achieve a speedup of about 10 times compared with sequential CPU calculations for bulk silicon systems containing up to 128 atoms.
文摘The valence subband energies and wave functions of a tensile strained quantum well are calculated by the plane wave expansion method within the 6×6 Luttinger Kohn model.The effect of the number and period of plane waves used for expansion on the stability of energy eigenvalues is examined.For practical calculation,it should choose the period large sufficiently to ensure the envelope functions vanish at the boundary and the number of plane waves large enough to ensure the energy eigenvalues keep unchanged within a prescribed range.
基金Supported by the Study of Some Problems on Holomorphic Function Space and Operator Theory(11671357)the National Natural Science Foundation of China(11771139)+1 种基金the Natural Science Foundation of Guangxi(2015jjBA10049)partially supported by the Hu Guozan Study-Abroad Grant for graduates(China)for her visit to UC Irvine in 2015–2016 when part of this work was done
文摘We give the sharp lower bound for Ricci curvature on the real ellipsoid in Cn＋l,and prove the Lichnerowicz-Obata theorem for Kohn Laplacian.
