Electronic structure calculations and molecular dynamics simulations with linear system-size scaling

Within the framework of linear-scaling Kohn-Sham density functional theory, a robust method for maintaining compact localized orbitals close to the ground state is coupled with nuclear dynamics. This allows to obviate the commonly employed optimization of the one-electron density matrix and thus create an efficient orbital-only molecular dynamics method for weakly-interacting systems. An application to liquid water demonstrates that the low computational overhead of the metho...

We present an algorithm and its parallel implementation for solving a self consistent problem as encountered in Hartree Fock or Density Functional Theory. The algorithm takes advantage of the sparsity of matrices through the use of local molecular orbitals. The implementation allows to exploit efficiently modern symmetric multiprocessing (SMP) computer architectures. As a first application, the algorithm is used within the density functional based tight binding method, for wh...

Linear scaling methods, or O(N) methods, have computational and memory requirements which scale linearly with the number of atoms in the system, N, in contrast to standard approaches which scale with the cube of the number of atoms. These methods, which rely on the short-ranged nature of electronic structure, will allow accurate, ab initio simulations of systems of unprecedented size. The theory behind the locality of electronic structure is described and related to physical ...

A novel low complexity method to perform self-consistent electronic-structure calculations using the Kohn-Sham formalism of density functional theory is presented. Localization constraints are neither imposed nor required thereby allowing direct comparison with conventional cubically scaling algorithms. The method has, to date, the lowest complexity of any algorithm for an exact calculation. A simple one-dimensional model system is used to thoroughly test the numerical stabil...

The past years have witnessed impressive advances in electronic structure calculation, especially in the complexity and size of the systems studied, as well as in computation time. Linear scaling methods based on empirical tight-binding Hamiltonians which can describe chemical bonding, and have a computational time proportional to the number of atoms N in the system, are of particular interest for simulations in material science. By contrast conventional diagonalization schem...

We describe a set of techniques for performing large scale ab initio calculations using multigrid accelerations and a real-space grid as a basis. The multigrid methods provide effective convergence acceleration and preconditioning on all length scales, thereby permitting efficient calculations for ill-conditioned systems with long length scales or high energy cut-offs. We discuss specific implementations of multigrid and real-space algorithms for electronic structure calculat...

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 elect...

We present a novel algorithm which can overcome the drawbacks of the conventional linear scaling method with minimal computational overhead. This is achieved by introducing additional constraints, thus eliminating the redundancy of the orbitals. The performance of our algorithm is evaluated in ab initio molecular-dynamics simulations as well as in a model system.

We survey the underlying theory behind the large-scale and linear scaling DFT code, Conquest, which shows excellent parallel scaling and can be applied to thousands of atoms with exact solutions, and millions of atoms with linear scaling. We give details of the representation of the density matrix and the approach to finding the electronic ground state, and discuss the implementation of molecular dynamics with linear scaling. We give an overview of the performance of the code...

We describe recent progress in developing practical ab initio methods for which the computer effort is proportional to the number of atoms: linear scaling or O(N) methods. It is shown that the locality property of the density matrix gives a general framework for constructing such methods. We then describe our scheme, which operates within density functional theory. Efficient methods for reaching the electronic ground state are summarised, both for finding the density matrix, ...