The Experts below are selected from a list of 324 Experts worldwide ranked by ideXlab platform
Di Liu - One of the best experts on this subject based on the ideXlab platform.
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towards translational invariance of total energy with finite element methods for kohn sham Equation
Communications in Computational Physics, 2016Co-Authors: Gang Bao, Di LiuAbstract: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 finite 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.
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Real-time adaptive finite element solution of time-dependent Kohn-Sham Equation
Journal of Computational Physics, 2015Co-Authors: Gang Bao, Di LiuAbstract:In our previous paper (Bao et al., 2012 1), a general framework of using adaptive finite element methods to solve the Kohn-Sham Equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham Equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.
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Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique
Journal of Scientific Computing, 2012Co-Authors: Gang Bao, Di LiuAbstract:A mesh redistribution method is introduced to solve the Kohn-Sham Equation. The standard linear finite element space is employed for the spatial discretization, and the self-consistent field iteration scheme is adopted for the derived nonlinear generalized eigenvalue problem. A mesh redistribution technique is used to optimize the distribution of the mesh grids according to wavefunctions obtained from the self-consistent iterations. After the mesh redistribution, important regions in the domain such as the vicinity of the nucleus, as well as the bonding between the atoms, may be resolved more effectively. Consequently, more accurate numerical results are obtained without increasing the number of mesh grids. Numerical experiments confirm the effectiveness and reliability of our method for a wide range of problems. The accuracy and efficiency of the method are also illustrated through examples.
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An h-adaptive finite element solver for the calculations of the electronic structures
Journal of Computational Physics, 2012Co-Authors: Gang Bao, Di LiuAbstract:In this paper, a framework of using h-adaptive finite element method for the Kohn-Sham Equation on the tetrahedron mesh is presented. The Kohn-Sham Equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.
Notker Rosch - One of the best experts on this subject based on the ideXlab platform.
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a two component variant of the douglas kroll relativistic linear combination of gaussian type orbitals density functional method spin orbit effects in atoms and diatomics
Journal of Chemical Physics, 2001Co-Authors: Markus Mayer, Sven Kruger, Notker RoschAbstract:The scalar relativistic variant of the linear combination of Gaussian-type orbitals—fitting functions—density-functional (R-LCGTO-FF-DF) method is extended to a two-component scheme which permits a self-consistent treatment of the spin–orbit interaction. The method is based on the Douglas–Kroll transformation of the four-component Dirac–Kohn–Sham Equation. The present implementation in the program PARAGAUSS neglects spin–orbit effects in the electron–electron interaction. This approximation is shown to be satisfactory as long as bonding is restricted to s, p, and d orbitals. The method is applied to the diatomics Au2, Bi2, Pb2, PbO, and TlH using both a local density (LDA) and a gradient-corrected approximation (GGA) of the exchange-correlation functional. At the LDA level, bond lengths and vibrational frequencies are reproduced with high accuracy. For the determination of binding energies the open-shell reference atoms Au, Tl, Pb, Bi have been treated by a jj coupling approach based on a self-consistent ...
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Density- and density-matrix-based coupled Kohn–Sham methods for dynamic polarizabilities and excitation energies of molecules
The Journal of Chemical Physics, 1999Co-Authors: Andreas Görling, Habbo H Heinze, Sergey Ph Ruzankin, Markus Staufer, Notker RoschAbstract:Basis set methods for calculating dynamic polarizabilities and excitation energies via coupled Kohn–Sham Equations within time-dependent density functional theory are introduced. The methods can be employed after solving the ground state Kohn–Sham Equations with a fitting function approach. Successful applications of the methods to test molecules are presented. Coupled Kohn–Sham methods based on the linear response of the Kohn–Sham density matrix are derived from the standard coupled Kohn–Sham Equation based on the linear response of the electron density and the relations between the two types of coupled Kohn–Sham Equations are investigated. The choice of norm functions associated with basis set representations of the coupled Kohn–Sham Equations is discussed and shown to be a critical point of basis set approaches to time-dependent density functional theory.
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density and density matrix based coupled kohn sham methods for dynamic polarizabilities and excitation energies of molecules
Journal of Chemical Physics, 1999Co-Authors: Andreas Görling, Habbo H Heinze, Sergey Ph Ruzankin, Markus Staufer, Notker RoschAbstract:Basis set methods for calculating dynamic polarizabilities and excitation energies via coupled Kohn–Sham Equations within time-dependent density functional theory are introduced. The methods can be employed after solving the ground state Kohn–Sham Equations with a fitting function approach. Successful applications of the methods to test molecules are presented. Coupled Kohn–Sham methods based on the linear response of the Kohn–Sham density matrix are derived from the standard coupled Kohn–Sham Equation based on the linear response of the electron density and the relations between the two types of coupled Kohn–Sham Equations are investigated. The choice of norm functions associated with basis set representations of the coupled Kohn–Sham Equations is discussed and shown to be a critical point of basis set approaches to time-dependent density functional theory.
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density functional based structure optimization for molecules containing heavy elements analytical energy gradients for the douglas kroll hess scalar relativistic approach to the lcgto df method
Chemical Physics, 1996Co-Authors: Vladimir A Nasluzov, Notker RoschAbstract:The self-consistent scalar-relativistic linear combination of Gaussian-type orbitals density functional (LCGTO-DF) method has been extended to calculate analytical energy gradients. The method is based on the use of a unitary second order Douglas-Kroll-Hess (DKH) transformation for decoupling large and small components of the full four-component Dirac-Kohn-Sham Equation. The approximate DKH transformation most common in molecular calculations has been implemented; this variant employs nuclear potential based projectors and it leaves the electron-electron interaction untransformed. Examples are provided for the geometry optimization of a series of heavy metal systems which feature a variety of metal-ligand bonds, like Au2, AuCl, AuH, Mo(CO)6 and W(CO)6 as well as the d10 complexes [Pd(PH3)2O2] and [Pt(PH3)2O2]. The calculated results, obtained with several gradient-corrected exchange-correlation potentials, compare very well with experimental data and they are of similar or even better accuracy than those of other high quality relativistic calculations reported so far.
Gang Bao - One of the best experts on this subject based on the ideXlab platform.
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towards translational invariance of total energy with finite element methods for kohn sham Equation
Communications in Computational Physics, 2016Co-Authors: Gang Bao, Di LiuAbstract: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 finite 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.
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Real-time adaptive finite element solution of time-dependent Kohn-Sham Equation
Journal of Computational Physics, 2015Co-Authors: Gang Bao, Di LiuAbstract:In our previous paper (Bao et al., 2012 1), a general framework of using adaptive finite element methods to solve the Kohn-Sham Equation has been presented. This work is concerned with solving the time-dependent Kohn-Sham Equations. The numerical methods are studied in the time domain, which can be employed to explain both the linear and the nonlinear effects. A Crank-Nicolson scheme and linear finite element space are employed for the temporal and spatial discretizations, respectively. To resolve the trouble regions in the time-dependent simulations, a heuristic error indicator is introduced for the mesh adaptive methods. An algebraic multigrid solver is developed to efficiently solve the complex-valued system derived from the semi-implicit scheme. A mask function is employed to remove or reduce the boundary reflection of the wavefunction. The effectiveness of our method is verified by numerical simulations for both linear and nonlinear phenomena, in which the effectiveness of the mesh adaptive methods is clearly demonstrated.
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Numerical Solution of the Kohn-Sham Equation by Finite Element Methods with an Adaptive Mesh Redistribution Technique
Journal of Scientific Computing, 2012Co-Authors: Gang Bao, Di LiuAbstract:A mesh redistribution method is introduced to solve the Kohn-Sham Equation. The standard linear finite element space is employed for the spatial discretization, and the self-consistent field iteration scheme is adopted for the derived nonlinear generalized eigenvalue problem. A mesh redistribution technique is used to optimize the distribution of the mesh grids according to wavefunctions obtained from the self-consistent iterations. After the mesh redistribution, important regions in the domain such as the vicinity of the nucleus, as well as the bonding between the atoms, may be resolved more effectively. Consequently, more accurate numerical results are obtained without increasing the number of mesh grids. Numerical experiments confirm the effectiveness and reliability of our method for a wide range of problems. The accuracy and efficiency of the method are also illustrated through examples.
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An h-adaptive finite element solver for the calculations of the electronic structures
Journal of Computational Physics, 2012Co-Authors: Gang Bao, Di LiuAbstract:In this paper, a framework of using h-adaptive finite element method for the Kohn-Sham Equation on the tetrahedron mesh is presented. The Kohn-Sham Equation is discretized by the finite element method, and the h-adaptive technique is adopted to optimize the accuracy and the efficiency of the algorithm. The locally optimal block preconditioned conjugate gradient method is employed for solving the generalized eigenvalue problem, and an algebraic multigrid preconditioner is used to accelerate the solver. A variety of numerical experiments demonstrate the effectiveness of our algorithm for both the all-electron and the pseudo-potential calculations.
Yousef Saad - One of the best experts on this subject based on the ideXlab platform.
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chebyshev filtered subspace iteration method free of sparse diagonalization for solving the kohn sham Equation
Journal of Computational Physics, 2014Co-Authors: Yunkai Zhou, James R Chelikowsky, Yousef SaadAbstract:First-principles density functional theory (DFT) calculations for the electronic structure problem require a solution of the Kohn-Sham Equation, which requires one to solve a nonlinear eigenvalue problem. Solving the eigenvalue problem is usually the most expensive part in DFT calculations. Sparse iterative diagonalization methods that compute explicit eigenvectors can quickly become prohibitive for large scale problems. The Chebyshev-filtered subspace iteration (CheFSI) method avoids most of the explicit computation of eigenvectors and results in a significant speedup over iterative diagonalization methods for the DFT self-consistent field (SCF) calculations. However, the original formulation of the CheFSI method utilizes a sparse iterative diagonalization at the first SCF step to provide initial vectors for subspace filtering at latter SCF steps. This diagonalization is expensive for large scale problems. We develop a new initial filtering step to avoid completely this diagonalization, thus making the CheFSI method free of sparse iterative diagonalizations at all SCF steps. Our new approach saves memory usage and can be two to three times faster than the original CheFSI method.
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Using Chebyshev-Filtered Subspace Iteration and Windowing Methods to Solve the Kohn-Sham Problem
Practical Aspects of Computational Chemistry I, 2011Co-Authors: Grady Schofield, James R Chelikowsky, Yousef SaadAbstract:Ground state electronic properties of a material can be obtained using density functional theory and obtaining a solution of the Kohn-Sham Equation. The traditional method of solving the Equation is to use eigensolver-based approaches. In general, eigensolvers constitute a bottleneck when handling systems with a large number of atoms. Here we discuss variations on an approach based on a nonlinear Chebyshev-filtered subspace iteration. This approach avoids computing explicit eigenvectors except to initiate the process. Our method centers on solving the original nonlinear Kohn-Sham Equation by a nonlinear form of the subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. The method achieves self-consistency within a similar number of self-consistent field iterations as eigensolver-based approaches. However, the replacement of the standard diagonalization at each self-consistent iteration by a polynomial filtering step results in a significant speedup over methods based on standard diagonalization, often by more than an order of magnitude. Algorithmic details of a parallel implementation of this method are proposed in which only the eigenvalues within a specified energy window are extracted. Numerical results are presented to show that the method enables one to perform a class of challenging applications.
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Parallel self-consistent-field calculations via Chebyshev-filtered subspace acceleration.
Physical review. E Statistical nonlinear and soft matter physics, 2006Co-Authors: Yunkai Zhou, Yousef Saad, Murilo L Tiago, James R ChelikowskyAbstract:Solving the Kohn-Sham eigenvalue problem constitutes the most computationally expensive part in self-consistent density functional theory (DFT) calculations. In a previous paper, we have proposed a nonlinear Chebyshev-filtered subspace iteration method, which avoids computing explicit eigenvectors except at the first self-consistent-field (SCF) iteration. The method may be viewed as an approach to solve the original nonlinear Kohn-Sham Equation by a nonlinear subspace iteration technique, without emphasizing the intermediate linearized Kohn-Sham eigenvalue problems. It reaches self-consistency within a similar number of SCF iterations as eigensolver-based approaches. However, replacing the standard diagonalization at each SCF iteration by a Chebyshev subspace filtering step results in a significant speedup over methods based on standard diagonalization. Here, we discuss an approach for implementing this method in multi-processor, parallel environment. Numerical results are presented to show that the method enables to perform a class of highly challenging DFT calculations that were not feasible before.
G F Bertsch - One of the best experts on this subject based on the ideXlab platform.
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real time and real space density functional calculation for electron dynamics in crystalline solids
International Conference on Conceptual Structures, 2011Co-Authors: Kazuhiro Yabana, Tomohito Otobe, Yasushi Shinohara, Junichi Iwata, G F BertschAbstract:Abstract We report a first-principles computational method to describe many-electron dynamics in crystalline solids. The method is based on the time-dependent density functional theory, solving the time-dependent Kohn-Sham Equation in real time and real space. The calculation is effciently parallelized by distributing computations of different k-points among processors. To illustrate the usefulness of the method and effciency of the parallel computation, we show calculations of electron dynamics in bulk crystalline Si induced by intense, ultrashort laser pulses.
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real time real space implementation of the linear response time dependent density functional theory
Physica Status Solidi B-basic Solid State Physics, 2006Co-Authors: Kazuhiro Yabana, Junichi Iwata, Takashi Nakatsukasa, G F BertschAbstract:We review our methods to calculate optical response of molecules in the linear response time-dependent density-functional theory. Three distinct formalisms which are implemented in the three-dimensional grid representation are explained in detail. They are the real-time method solving the time-dependent Kohn–Sham Equation in the time domain, the modified Sternheimer method which calculates the response to an external field of fixed frequency, and the matrix eigenvalue approach. We also illustrate treatments of the scattering boundary condition, needed to accurately describe photoionization processes. Finally, we show how the real-time formalism for molecules can be used to determine the response of infinite periodic systems. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
