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 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
In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the ex...In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.展开更多
The Kohn-Sham density functional theory(KS-DFT)has played an important role in materials simulation for a long time.To better serve the industry,it is desirable to have an integrated solution that supports different c...The Kohn-Sham density functional theory(KS-DFT)has played an important role in materials simulation for a long time.To better serve the industry,it is desirable to have an integrated solution that supports different calculation tasks by KSDFT with different corrections and modifications.In this work,we present Hylanemos,a plane wave pseudopotential(PW-PP)KS-DFT package written entirely in the Julia programming language,which could offer such a solution.First,we analyze the code design to get the flexibility needed to implement such a solution.Then,we show that its accuracy and speed are comparable to widely-used packages.Next,we show its ability to perform common tasks such as single point(SP)calculations,geometry optimization,and transition state calculations.Finally,the LDA+Gutzwiller(LDA+G)method is presented,a feature not commonly found in DFT packages.In addition,we have also developed a set of ultrasoft(US)PP through parameter adjustment and optimization.This set of PP,called Eacomp PP,has a low cutoff energy(<18 Ha)and exhibits excellent performance in our benchmarks.Combining a performant package and optimized potentials will facilitate our in-depth efforts in promoting industrialization.展开更多
We show that the eigenfunctions of Kohn-Sham equations can be decomposed as ■ = F ψ, where F depends on the Coulomb potential only and is locally Lipschitz, while ψ has better regularity than ■.
Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysi...Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.展开更多
The self-consistent Kohn-Sham equations for many-electron atoms are solved using the Coulomb wave function Discrete Variable Method (CWDVR). Wigner type functional is used to incorporate correlation functional. The di...The self-consistent Kohn-Sham equations for many-electron atoms are solved using the Coulomb wave function Discrete Variable Method (CWDVR). Wigner type functional is used to incorporate correlation functional. The discrete variable method is used for the uniform and optimal spatial grid discretization and solution of the Kohn-Sham equation. The equation is numerically solved using the CWDVR method. First time we have reported the solution of the Kohn-Sham equation on the ground state problem for the many-electronic atoms by the CWDVR method. Our results suggest CWDVR approach shown to be an efficient and precise solution of ground-state energies of atoms. We illustrate that the calculated electronic energies for He, Li, Be, B, C, N and O atoms are in good agreement with other best available values.展开更多
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 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the Boya postdoctoral fellowship from Peking University and the support fromthe China Postdoctoral Science Foundation(No.2023M740107)the Natural Science Starting Project of SWPU(No.2024QHZ030)+2 种基金the support from The Science and Technology Development Fund,Macao SAR(No.0068/2024/RIA1)National Natural Science Foundation of China(No.11922120)MYRG of University of Macao(No.MYRG-CRG2024-00042-FST).
文摘In this paper,the unconditionally energy-stable and orthonormalitypreserving iterative scheme proposed in[X.Wang et al.(2024),J.Comput.Phys.,498:112670]is extended both theoretically and numerically,including(i)the exchangecorrelation energy is introduced into the model for a more comprehensive description of the quantum system,utilizing the local density approximation used by the National Institution of Science and Technology Standard Reference Database;(ii)both the unconditional energy-stability and orthonormality-preservation are attained in the newly derived scheme;(iii)a C0 tetrahedral spectral element method is adopted for the quality spatial discretization,of which a quality initial condition can be designed using low order one for effectively accelerating the simulation.A series of numerical experiments validate the effectiveness of our method,encompassing various atoms and molecules.All the computations successfully reveal the anticipated spectral accuracy and the exponential error dependence to the cubic root of the degree of freedom number.Moreover,the efficiency of the extended framework is discussed in detail on updating schemes.
基金supported by the National Natural Science Foundation of China(Grant No.12426301)。
文摘The Kohn-Sham density functional theory(KS-DFT)has played an important role in materials simulation for a long time.To better serve the industry,it is desirable to have an integrated solution that supports different calculation tasks by KSDFT with different corrections and modifications.In this work,we present Hylanemos,a plane wave pseudopotential(PW-PP)KS-DFT package written entirely in the Julia programming language,which could offer such a solution.First,we analyze the code design to get the flexibility needed to implement such a solution.Then,we show that its accuracy and speed are comparable to widely-used packages.Next,we show its ability to perform common tasks such as single point(SP)calculations,geometry optimization,and transition state calculations.Finally,the LDA+Gutzwiller(LDA+G)method is presented,a feature not commonly found in DFT packages.In addition,we have also developed a set of ultrasoft(US)PP through parameter adjustment and optimization.This set of PP,called Eacomp PP,has a low cutoff energy(<18 Ha)and exhibits excellent performance in our benchmarks.Combining a performant package and optimized potentials will facilitate our in-depth efforts in promoting industrialization.
基金supported by National Natural Science Foundation of China (Grant No. 91330202)the Funds for Creative Research Groups of China (Grant No. 11321061)+1 种基金National Basic Research Program of China (Grant No. 2011CB309703)the National Center for Mathematics and Interdisciplinary Sciences of the Chinese Academy of Sciences
文摘We show that the eigenfunctions of Kohn-Sham equations can be decomposed as ■ = F ψ, where F depends on the Coulomb potential only and is locally Lipschitz, while ψ has better regularity than ■.
基金Thework ofG.Baowas supported in part by the NSF grantsDMS-0968360,DMS-1211292the ONR grant N00014-12-1-0319+3 种基金a Key Project of the Major Research Plan of NSFC(No.91130004)a special research grant from Zhejiang UniversityThe research of G.H.Hu was supported in part by MYRG2014-00111-FST and MRG/016/HGH/2013/FST from University of Macao,085/2012/A3 from FDCT of Macao S.A.R.,and National Nat-ural Science Foundation of China(Grant No.11401608)The research of D.Liu was supported by NSF grants DMS-0968360 and NSF-DMS 1418959.
文摘Numerical oscillation of the total energy can be observed when the Kohn-Sham equation is solved by real-space methods to simulate the translational move of an electronic system.Effectively remove or reduce the unphysical oscillation is crucial not only for the optimization of the geometry of the electronic structure,but also for the study of molecular dynamics.In this paper,we study such unphysical oscillation based on the numerical framework in[G.Bao,G.H.Hu,and D.Liu,An h-adaptive fi-nite element solver for the calculations of the electronic structures,Journal of Computational Physics,Volume 231,Issue 14,Pages 4967-4979,2012],and deliver some numerical methods to constrain such unphysical effect for both pseudopotential and all-electron calculations,including a stabilized cubature strategy for Hamiltonian operator,and an a posteriori error estimator of the finite element methods for Kohn-Sham equation.The numerical results demonstrate the effectiveness of our method on restraining unphysical oscillation of the total energies.
文摘The self-consistent Kohn-Sham equations for many-electron atoms are solved using the Coulomb wave function Discrete Variable Method (CWDVR). Wigner type functional is used to incorporate correlation functional. The discrete variable method is used for the uniform and optimal spatial grid discretization and solution of the Kohn-Sham equation. The equation is numerically solved using the CWDVR method. First time we have reported the solution of the Kohn-Sham equation on the ground state problem for the many-electronic atoms by the CWDVR method. Our results suggest CWDVR approach shown to be an efficient and precise solution of ground-state energies of atoms. We illustrate that the calculated electronic energies for He, Li, Be, B, C, N and O atoms are in good agreement with other best available values.
