Linear Scaling Electronic Structure Calculations Research Articles

Preconditioned conjugate gradient method for the sparse generalized eigenvalue problem in electronic structure calculations

The use of localized basis sets is essential in linear-scaling electronic structure calculations, and since such basis sets are mostly non-orthogonal, it is necessary to solve the generalized eigenvalue problem Hx=εSx. In this work, an iterative method for finding the lowest few eigenvalues and corresponding eigenvectors for the generalized eigenvalue problem based on the conjugate gradient method is presented. The method is applied to first-principles electronic structure calculations within density-functional theory using a localized spherical-wave basis set, first introduced in the context of linear-scaling methods [Comput. Phys. Commun. 102 (1997) 17]. The method exhibits linear convergence of the solution, the rate of which is improved by a preconditioning scheme using the kinetic energy matrix.

Electronic structure properties of solvated biomolecules: A quantum approach for macromolecular characterization

Linear-scaling electronic structure calculations of solvated biomolecules have been carried out using a semiempirical Hamiltonian and a new smooth solvation potential. These methods afford a new way of generating macromolecular properties that include quantum electronic structure. In addition to the widely used classical electrostatic potential maps based on empirically derived static point charges, now fully quantum mechanical electrostatic potentials that include electronic polarization are possible. Linear-scaling electronic structure methods provide a host of response properties of the electron density such as linear response functions, local hardness functions, and Fukui functions. It is the hope that these indices will extend insight into problems of biological macromolecular characterization. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 1562–1571, 2000

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 orbitals. The number of localized orbitals is allowed to exceed the number of occupied orbitals. Comparison with other variational principles is made and numerical tests presented. @S0163-1829~97!01939-5# Most electronic structure calculations are based on a oneelectron Hamiltonian, either within semiempirical approaches such as tight-binding and semiempirical quantum chemical models, or within first-principle approaches such as the density functional and Hartree-Fock-based method. The one-electron Hamiltonian provides building blocks for the construction of the electronic wave function or the electron density. Conventional direct and iterative diagonalization algorithms for obtaining eigenvalues require an overall computational effort which grows as the cubic of the number of atoms. This has been a major limiting factor for the application of the electronic structure methods to large systems. The possibility of obtaining the sum of eigenvalues in electronic structure calculations with effort scaling linearly with the size of the system was first demonstrated in the