Interior Eigenvalues from Density Matrix Expansions in Quantum Mechanical Molecular Dynamics
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Summary
This work identifies two different phases of the recursive polynomial expansion, the conditioning and purification phases, and shows how such eigenvalue estimates can be extracted from the recursive expansion by a simple and robust procedure at a negligible computational cost.
- Type
- article
- Published
- 2014-03-11
- Cited by
- 27
- References
- 71
- Access
- Open access
- OpenAlex
- https://openalex.org/W2027400570
- Semantic Scholar
- https://api.semanticscholar.org/CorpusID:36373126
Keywords
Eigenvalues and eigenvectors, Mathematics, Density matrix, Acceleration, Quantum
References
- Simulating Hamiltonian dynamics
- Real-world predictions from ab initio molecular dynamics simulations.
- Inhomogeneous Electron Gas
- Interatomic Forces in Condensed Matter
- Templates for the Solution of Algebraic Eigenvalue Problems
- Density-Functional Theory
- Transforms for idempotency purification of density matrices in linear-scaling electronic-structure calculations
- Multilevel domain decomposition for electronic structure calculations
- Nonmonotonic Recursive Polynomial Expansions for Linear Scaling Calculation of the Density Matrix.
- A simplified density matrix minimization for linear scaling self-consistent field theory
- Density-matrix electronic-structure method with linear system-size scaling.
- Crystal structures of zirconia from first principles and self-consistent tight binding
- Lagrangian formulation with dissipation of Born-Oppenheimer molecular dynamics using the density-functional tight-binding method.
- Computation of interior eigenvalues in electronic structure calculations facilitated by density matrix purification.
- Fock matrix dynamics
- Ab initio molecular dynamics: basic concepts, current trends and novel applications
- A Class of Methods for Solving Nonlinear Simultaneous Equations
- Fast method for quantum mechanical molecular dynamics
- Density functional theory
- Controlling Errors in Recursive Fermi-Dirac Operator Expansions with Applications in Electronic Structure Theory
Cited by
- Parameterless stopping criteria for density matrix expansions in electronic structure calculations
- Comparison of accelerated recursive polynomial expansions for electronic structure calculations
- Graph-based linear scaling electronic structure theory.
- Efficient parallel linear scaling construction of the density matrix for Born-Oppenheimer molecular dynamics.
- Recursive Factorization of the Inverse Overlap Matrix in Linear-Scaling Quantum Molecular Dynamics Simulations.
- Parameterless Stopping Criteria for Recursive Density Matrix Expansions.
- Numerical Methods for Molecular Dynamics with Nearly Crossing Potential Surfaces
- Efficient Computation of Sparse Matrix Functions for Large-Scale Electronic Structure Calculations: The CheSS Library.
- Linear Scaling Pseudo Fermi-Operator Expansion for Fractional Occupation.
- Efficient computation of the density matrix with error control on distributed computer systems
- Multiple eigenvectors around the homo-lumo gap as a cheap by-product in linear scaling electronic structure calculations
- CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations.
- GPU-Accelerated Semi-Empirical Born Oppenheimer Molecular Dynamics using PyTorch.
- Sparse approximate matrix-matrix multiplication for density matrix purification with error control
- Mixed Precision Fermi-Operator Expansion on Tensor Cores from a Machine Learning Perspective.
- Quantum-Based Molecular Dynamics Simulations Using Tensor Cores.
- The Middle Science: Traversing Scale In Complex Many-Body Systems
- Quantum Perturbation Theory Using Tensor Cores and a Deep Neural Network.
- A variational formulation of the Harris functional as a correction to approximate Kohn-Sham density functional theory.
- Susceptibility formulation of density matrix perturbation theory.
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