Graph-based linear scaling electronic structure theory

Abstract

We show how graph theory can be combined with quantum theory to calculate the electronic structure of large complex systems. The graph formalism is general and applicable to a broad range of electronic structure methods and materials, including challenging systems such as biomolecules. The methodology combines well-controlled accuracy, low computational cost, and natural low-communication parallelism. This combination addresses substantial shortcomings of linear scaling electronic structure theory, in particular with respect to quantum-based molecular dynamics simulations.

17 pages, 5 figures

References in corpus (15)

• O(N) methods in electronic structure calculations
• An Efficient and Accurate Car-Parrinello-like Approach to Born-Oppenheimer Molecular Dynamics
• Parallel Sparse Matrix-Matrix Multiplication and Indexing: Implementation and Experiments
• Time-reversible Born-Oppenheimer molecular dynamics
• Calculations on millions of atoms with DFT: Linear scaling shows its potential
• Expansion algorithm for the density matrix
• Linear scaling Krylov subspace method for large scale {\it ab initio} electronic structure calculations of metals
• Wavefunction extended Lagrangian Born-Oppenheimer molecular dynamics
• Density Matrix Perturbation Theory
• Ab initio linear scaling response theory: Electric polarizability by perturbed projection
• Generalized Extended Lagrangian Born-Oppenheimer Molecular Dynamics
• Implicit Purification for Temperature-Dependent Density Matrices
• First principles molecular dynamics without self-consistent field optimization
• Analysis of the Time Reversible Born-Oppenheimer Molecular Dynamics
• Non-monotonic recursive polynomial expansions for linear scaling calculation of the density matrix

Cited by in corpus (10)

• Layer VQE: A Variational Approach for Combinatorial Optimization on Noisy Quantum Computers
• Detecting Multiple Communities Using Quantum Annealing on the D-Wave System
• Next generation extended Lagrangian first principles molecular dynamics
• Enabling particle applications for exascale computing platforms
• Functional Tensor-Train Chebyshev Method for Multidimensional Quantum Dynamics Simulations
• Canonical-ensemble extended Lagrangian Born-Oppenheimer molecular dynamics for the linear scaling density functional theory
• Using Graph Partitioning for Scalable Distributed Quantum Molecular Dynamics
• Graph-based Quantum Response Theory and Shadow Born-Oppenheimer Molecular Dynamics
• A Submatrix-Based Method for Approximate Matrix Function Evaluation in the Quantum Chemistry Code CP2K
• Task-based Parallel Computation of the Density Matrix in Quantum-based Molecular Dynamics using Graph Partitioning