Showing papers by "Francesco Mauri published in 1994"
TL;DR: The method leads to an algorithm whose computational cost scales linearly with the system size and establishes the accuracy and reliability of the method for a wide class of systems and shows that tight-binding molecular-dynamics simulations with a few thousand atoms are feasible on small workstations.
Abstract: We present a method for total-energy minimizations and molecular-dynamics simulations based either on tight-binding or on Kohn-Sham Hamiltonians. The method leads to an algorithm whose computational cost scales linearly with the system size. The key features of our approach are (i) an orbital formulation with single-particle wave functions constrained to be localized in given regions of space, and (ii) an energy functional that does not require either explicit orthogonalization of the electronic orbitals, or inversion of an overlap matrix. The foundations and accuracy of the approach and the performances of the algorithm are discussed, and illustrated with several numerical examples including Kohn-Sham Hamiltonians. In particular, we present calculations with tight-binding Hamiltonians for diamond, graphite, a carbon linear chain, and liquid carbon at low pressure. Even for a complex case such as liquid carbon---a disordered metallic system with differently coordinated atoms---the agreement between standard diagonalization schemes and our approach is very good. Our results establish the accuracy and reliability of the method for a wide class of systems and show that tight-binding molecular-dynamics simulations with a few thousand atoms are feasible on small workstations.
152 citations
TL;DR: Theoretical analysis of the convergence and the stability of fictitious dynamical methods for electrons shows that a particular damped second-order dynamics has a much faster rate of convergence to the ground state than first-order steepest-descent algorithms while retaining their numerical cost per time step.
Abstract: We study the convergence and the stability of fictitious dynamical methods for electrons. first, we show that a particular damped second-order dynamics has a much faster rate of convergence to the ground state than first-order steepest-descent algorithms while retaining their numerical cost per time step. Our damped dynamics has efficiency comparable to that of conjugate gradient methods in typical electronic minimization problems. Then, we analyze the factors that limit the size of the integration time step in approaches based on plane-wave expansions. The maximum allowed time step is dictated by the highest frequency components of the fictitious electronic dynamics. These can result either from the larger wave vector components of the kinetic energy or from the small wave vector components of the Coulomb potential giving rise to the so called charge sloshing problem. We show how to eliminate large wave vector instabilities by adopting a preconditioning scheme in the context of Car-Parrinello ab initio molecular-dynamics simulations of the ionic motion. We also show how to solve the charge sloshing problem when this is present. We substantiate our theoretical analysis with numerical tests on a number of different silicon and carbon systems having both insulating and metallic character.
139 citations
TL;DR: In this paper, the authors present a method to compute high-order derivatives of the total energy of a periodic solid with respect to a uniform electric field using a Wannier representation for the electronic orbitals.
Abstract: We present a method to compute high-order derivatives of the total energy of a periodic solid with respect to a uniform electric field. We apply the 2n+1 theorem to a recently introduced total energy functional which uses a Wannier representation for the electronic orbitals and we find an expression for the static nonlinear susceptibility which is much simpler than the one obtained by standard perturbative expansions. We show that the zero-field expression of the nonlinear susceptibility can be rewritten in a Bloch representation. We test numerically the validity of our approach with a 1D model Hamiltonian.
79 citations
TL;DR: Tight binding molecular dynamics simulations of impacts on the reconstructed diamond(111) surface are presented, carried out with an O(N) method and with cells containing 1140 atoms to provide detailed characterization of the microscopic processes occurring during the collision and allow the identification of three impact regimes.
Abstract: We present tight binding molecular dynamics simulations of ${\mathrm{C}}_{60}$ impacts on the reconstructed diamond(111) surface, carried out with an $O(N)$ method and with cells containing 1140 atoms. The results of our simulations are in very good agreement with experiments. Furthermore they provide a detailed characterization of the microscopic processes occurring during the collision and allow the identification of three impact regimes. Finally, the study of the reactivity between the cluster and the surface gives insight into the deposition mechanisms of ${\mathrm{C}}_{60}$ on semiconducting substrates.
62 citations
Dissertation•
27 Oct 1994
1 citations
Posted Content•
TL;DR: In this article, the authors presented a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory, and provided a proof of the $2n+1$ theorem for a general class of energy functionals in which the orbitals are not constrained to be orthonormal.
Abstract: We present a method to compute high-order derivatives of the total energy which can be used in the framework of density functional theory. We provide a proof of the $2n+1$ theorem for a general class of energy functionals in which the orbitals are not constrained to be orthonormal. Furthermore, by combining this result with a recently introduced Wannier-like representation of the electronic orbitals, we find expressions for the static linear and nonlinear susceptibilities which are much simpler than those obtained by standard perturbative expansions. We test numerically the validity of our approach with a 1D model Hamiltonian.