Ergo: An open-source program for linear-scaling electronic structure calculations

Preconditioned iterative minimization for linear-scaling electronic structure calculations

Linear-scaling electronic structure methods are essential for calculations on large systems. Some of these approaches use a systematic basis set, the completeness of which may be tuned with an adjustable parameter similar to the energy cut-off of plane-wave techniques. The search for the electronic ground state in such methods suffers from an ill-conditioning which is related to the kinetic con...

Absolute-energy-minimum principles for linear-scaling electronic-structure calculations

Two absolute energy minimum principles are developed for first-principle linear-scaling electronic structure calculations. One is with a normalization constraint and the other without any constraint. The density matrix is represented by a set of nonorthogonal localized orbitals and an auxiliary matrix which at the minimum becomes a generalized inverse of the overlap matrix of the localized orbi...

Parallel Sparse Matrix Multiplication for Linear Scaling Electronic Structure Calculations

Linear-scaling electronic-structure techniques, also called O(N) techniques, rely heavily on the multiplication of sparse matrices, where the sparsity arises from spatial cut-offs. In order to treat very large systems, the calculations must be run on parallel computers. We analyse the problem of parallelising the multiplication of sparse matrices with the sparsity pattern required by linear-sca...

Linear Scaling Electronic Structure Methods

Methods exhibiting linear scaling with respect to the size of the system, so called O(N) methods, are an essential tool for the calculation of the electronic structure of large systems containing many atoms. They are based on algorithms which take advantage of the decay properties of the density matrix. In this article the physical decay properties of the density matrix will first be studied fo...

Linear Scaling Electronic Structure Methods