Publications

Abstract not provided.

This report summarizes activities undertaken during FY08-FY10 for the LDRD Peridynamics as a Rigorous Coarse-Graining of Atomistics for Multiscale Materials Design. The goal of our project was to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. The goal of our project is to develop a coarse-graining of finite temperature molecular dynamics (MD) that successfully transitions from statistical mechanics to continuum mechanics. Our coarse-graining overcomes the intrinsic limitation of coupling atomistics with classical continuum mechanics via the FEM (finite element method), SPH (smoothed particle hydrodynamics), or MPM (material point method); namely, that classical continuum mechanics assumes a local force interaction that is incompatible with the nonlocal force model of atomistic methods. Therefore FEM, SPH, and MPM inherit this limitation. This seemingly innocuous dichotomy has far reaching consequences; for example, classical continuum mechanics cannot resolve the short wavelength behavior associated with atomistics. Other consequences include spurious forces, invalid phonon dispersion relationships, and irreconcilable descriptions/treatments of temperature. We propose a statistically based coarse-graining of atomistics via peridynamics and so develop a first of a kind mesoscopic capability to enable consistent, thermodynamically sound, atomistic-to-continuum (AtC) multiscale material simulation. Peridynamics (PD) is a microcontinuum theory that assumes nonlocal forces for describing long-range material interaction. The force interactions occurring at finite distances are naturally accounted for in PD. Moreover, PDs nonlocal force model is entirely consistent with those used by atomistics methods, in stark contrast to classical continuum mechanics. Hence, PD can be employed for mesoscopic phenomena that are beyond the realms of classical continuum mechanics and atomistic simulations, e.g., molecular dynamics and density functional theory (DFT). The latter two atomistic techniques are handicapped by the onerous length and time scales associated with simulating mesoscopic materials. Simulating such mesoscopic materials is likely to require, and greatly benefit from multiscale simulations coupling DFT, MD, PD, and explicit transient dynamic finite element methods FEM (e.g., Presto). The proposed work fills the gap needed to enable multiscale materials simulations.

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A finite temperature version of 'exact-exchange' density functional theory (EXX) has been implemented in Sandia's Socorro code. The method uses the optimized effective potential (OEP) formalism and an efficient gradient-based iterative minimization of the energy. The derivation of the gradient is based on the density matrix, simplifying the extension to finite temperatures. A stand-alone all-electron exact-exchange capability has been developed for testing exact exchange and compatible correlation functionals on small systems. Calculations of eigenvalues for the helium atom, beryllium atom, and the hydrogen molecule are reported, showing excellent agreement with highly converged quantumMonte Carlo calculations. Several approaches to the generation of pseudopotentials for use in EXX calculations have been examined and are discussed. The difficult problem of finding a correlation functional compatible with EXX has been studied and some initial findings are reported.

We report the implementation of an iterative scheme for calculating the Optimized Effective Potential (OEP). Given an energy functional that depends explicitly on the Kohn-Sham wave functions, and therefore, implicitly on the local effective potential appearing in the Kohn-Sham equations, a gradient-based minimization is used to find the potential that minimizes the energy. Previous work has shown how to find the gradient of such an energy with respect to the effective potential in the zero-temperature limit. We discuss a density-matrix-based derivation of the gradient that generalizes the previous results to the finite temperature regime, and we describe important optimizations used in our implementation. We have applied our OEP approach to the Hartree-Fock energy expression to perform Exact Exchange (EXX) calculations. We report our EXX results for common semiconductors and ordered phases of hydrogen at zero and finite electronic temperatures. We also discuss issues involved in the implementation of forces within the OEP/EXX approach.

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We present here the details of the implementation of the parallel tempering Monte Carlo technique into a LAMMPS, a heavily used massively parallel molecular dynamics code at Sandia. This technique allows for many replicas of a system to be run at different simulation temperatures. At various points in the simulation, configurations can be swapped between different temperature environments and then continued. This allows for large regions of energy space to be sampled very quickly, and allows for minimum energy configurations to emerge in very complex systems, such as large biomolecular systems. By including this algorithm into an existing code, we immediately gain all of the previous work that had been put into LAMMPS, and allow this technique to quickly be available to the entire Sandia and international LAMMPS community. Finally, we present an example of this code applied to folding a small protein.

This LDRD project has involved the development and application of Sandia's massively parallel materials modeling software to several significant biophysical systems. They have been successful in applying the molecular dynamics code LAMMPS to modeling DNA, unstructured proteins, and lipid membranes. They have developed and applied a coupled transport-molecular theory code (Tramonto) to study ion channel proteins with gramicidin A as a prototype. they have used the Towhee configurational bias Monte-Carlo code to perform rigorous tests of biological force fields. they have also applied the MP-Sala reacting-diffusion code to model cellular systems. Electroporation of cell membranes has also been studied, and detailed quantum mechanical studies of ion solvation have been performed. In addition, new molecular theory algorithms have been developed (in FasTram) that may ultimately make protein solvation calculations feasible on workstations. Finally, they have begun implementation of a combined molecular theory and configurational bias Monte-Carlo code. They note that this LDRD has provided a basis for several new internal (e.g. several new LDRD) and external (e.g. 4 NIH proposals and a DOE/Genomes to Life) proposals.