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First Principles Computation of Materials Properties

Purpose

The Materials Properties part of the Caltech ASCI/ASAP center, uses a hierarchical approach to materials modeling in which parameters are derived from quantum mechanics (QM), through averaging over successively larger scales of time and length. This approach leads to a rigorous description of continuum parameters required in describing crack initiation, spallation, chemical decomposition, etc. These computational techniques are directed toward calculating phase behavior of metals, reaction kinetics relevant for HE, and structural information for metallic alloys at high temperatures and pressures. In addition, our approach obtains basic data for describing mechanical properties of materials, which leads to improved continuum mechanical parameters, constitutive relations, and transport properties from the atomistic simulations.

Results

Presentations from May 17, 1999 Research Review:

Movies of Dimethyl Nitramine Reacting

Also from the May 17 Research Review. Movies are in Quicktime format:

Presentations from Year One Annual Review:

Presentations from MSC99:

Tools

Density functional theory: It is now established that QM at the level of density functional theory (DFT), using the Generalized Gradient Approximation (GGA) provides excellent accuracy for ground state properties of materials involving main group compounds (C, Si, Ge) and ordinary transition metals (Fe, Cu). However, for descriptions of excited states and their reactions, phase transitions in transition elements, or heavy metals (e.g., Ce) problems with the current methods remain. DFT is the only practical approach for accurate first principles descriptions of the materials properties of interest here. Most quantum mechanical methods applied to crystals use DFT with plane wave basis functions to describe the electronic wave function. These basis functions are useful in describing static, bulk properties of materials and we will make heavy use of these methods for various applications. The Linearized Augmented Plane Wave (LAPW) method is suitable for periodic crystalline systems with 30 atoms per periodic cell. It leads to acceptable accuracy and we have used it for a number of applications. We have also developed a projector mixed basis code similar to LAPW in accuracy, but scaling as O(N) rather than O(N3). We have already used this code to study systems with up to 300 atoms per periodic cell. For many applications QM at the highest level may be accurate but too slow to investigate dynamics. It is useful to have a hierarchy of QM methodologies extending from very accurate but slow to very fast but more approximate. For example, we have developed a new tight-binding total-energy method (TB-QM) that shows great promise in use for thermal equations of state and molecular dynamics simulations. In TB-QM, the tight-binding parameters are fit to the total energies and band structures of accurate LAPW computations. This is a first-principles method that is parametrized from computationally intensive methods and then used for fast and accurate computations to obtain thermal properties. Applying this procedure to Fe at high pressures, we obtained excellent agreement with the measured Hugoniot. Plane waves however are insufficient for describing reactive processes such as fracture, and dislocation migration. Consequently, we have developed the Gaussian Dual Space (GDS-DFT) method that uses Gaussian basis functions localized on the individual atoms instead of plane waves. This requires combining calculations from real space and from reciprocal space, but leads to a number of advantages in calculating forces, force constants, and reactive surfaces. Force fields: Despite enormous progress in theory and computation, QM is impractical by many orders of magnitude for most problems of interest to dynamic response of solids. Thus our general approach is to apply QM to predict the structural, mechanical, and phase properties of prototype systems, some of which can be validated by comparison to experiment. We then average over the electrons to obtain force fields (FF), charges, polarizabilities, and other parameters that describe the forces and properties in terms of atomic positions (Newton's equation) rather than electrons (Schrödinger equation). To describe the reactive processes required in this proposal (detonation, energy propagation, spallation, crack initiation, and strain gradient effects in plastic deformation) places enormous demands on the form of the FF. We will employ realistic, multibody interactions developed from fits to accurate results on smaller systems. Molecular dynamics: Given the FF the dynamics can be described via Newtonian dynamics (including various refinements to obtain a Gibbs ensemble). Our recent advances (the CMM/RCMM, fast multipole algorithm and the NEIMO internal coordinate dynamics algorithm) have demonstrated accurate MD simulations (including Coulomb interactions without cutoffs) with a million particles (distances ~ 25nm) for times scales of 10 ns using up to 500 processors. This has been incorporated into the MPSim general MD software written and optimized for simulations using massively parallel computers.

Proposed work

Ab initio quantum mechanics: Using pseudo-spectral techniques, (involving multigrid and de-aliasing strategies), we recently made significant progress in extending the capabilities for accurate ab initio QM calculations to large finite systems. These methods with explicit exchange can, in principle, perform computations with scaling for all levels of electron correlations. We propose to continue optimizing the current methods for massively parallel computers and to develop improved methods suitable for accurate calculations on molecules with thousands of atoms. These ab initio methods allow reactive processes and excited states to be considered at high accuracy (for small systems). Such accuracy is required to describe the reactions in HE. Density functional theory: We propose to apply the method we used for Fe to study a range of 3d, 4d, and 5d transition metal equations of state to ultra high pressures (1 TPa). Results of LAPW computations give the static equation of state. The thermal electronic contribution to the high temperature equation of state is also extracted accurately from these self-consistent calculations. A tight-binding parametrization will be developed, and the phonon contribution to the thermal equation of state will be obtained from the particle-in-cell model, which is very accurate at high temperatures. With an MD code based on this method, we have been studying the viscosity of Fe liquid at MBar pressures with promising results. We propose here to study shock-induced melting using the MD code, starting with shock melting of iron. A particular goal is to understand superheating in shock melting. There is considerable opportunity to further improve the density functional approach, even given the successes of DFT using the generalized gradient approximation. Recently, we improved the GGA to increase the accuracy for excitation energies, and we propose to continue research to develop new functionals and effective core potentials accurate for such systems. An accurate ab initio description of electron correlation is computationally feasible only for molecules with a few atoms. DFT calculations include electron correlation to obtain accurate geometries and energies for the ground states of many systems; however, some systems lead to enormous errors and problems are encountered with excited states. We propose two approaches to solving this problem by using fixed-node diffusion quantum Monte Carlo (QMC) calculations of the electronic energy (which produce the exact energy of the electronic wave function given a set of nodal patterns). One approach will use accurate generalized valence bond (GVB) wavefunctions to simulate the static part of the electron correlation while providing the nodes. The other will use DFT wavefunctions but with corrections in the functionals to exclude correlation effects contained in QMC.

Force fields and molecular dynamics: Most QM studies simulate static properties of systems. For dynamic properties, usually an FF derived from the QM is used for the MD. For high-temperature, high-pressure systems in which bonds are in a constant state of flux, it may not be possible to obtain a sufficiently accurate FF, particularly for metallic systems. The alternative is to carry out Car-Parinello-type ab initio molecular dynamics in which the forces are obtained from QM rather than an FF. Previously, such QM-MD calculations typically were performed with a crude LDA approximation to the wavefunction. We propose to extend the more rigorous QM methods (which already calculate analytic forces) to be useful for QM-MD. We are developing new many-body potentials capable of describing defect properties and equations of state for alloys. The parameters can be fitted to the TB-QM results discussed above or directly to QM. We expect these calculations will allow us to apply MD to assemblies with up to atoms. This approach will be used to consider crack propagation, strain gradient effects in plastic deformation, as well as cohesive models for use in our work on fracture described in section 2.2.3. A few large simulations of crack initiation have been done, but they involved simplified pair potentials or 2D lattices. For strain gradient effects in plastic deformation, our intent is to determine how well our simulations mimic the macroscopic world for experiment, and continuum theory.

Meso-dynamics: Using a synthetic nonequilibrium MD formalism for studying complex materials, we are developing MPSim/NE, a new general-purpose molecular dynamics program for studying transport properties of materials under various flow conditions. This allows us to extract viscosities as a function of flow rate and diffusion parameters in polymers and metals. This allows the atoms to be collected into a coarse grain, mesoscale description suitable for describing the phenomena on the range of microns and microseconds. It is at this mesoscale that we make contact between the predictions of atomistic theory and experimental observations in extreme shock conditions. At the mesoscale, we carry out nonequilibrium MD studies at an atomistic level but describe the results in terms of constitutive equations whose parameters can be used in continuum modeling. This leads to a rigorous description of parameters describing crack initiation, spallation, non-Newtonian flow, chemical decomposition, etc.

Computational science requirements: The introduction of pseudo-spectral techniques into QM calculations is a major advance in terms of operation count but further research in scalable matrix computations is required in order to achieve optimal performance on the ASCI platforms. Research is also required to insure scalable performance of fast multipole algorithms on the ASCI platforms. These issues are addressed in section 2.2.


Last modified: Fri Jul 30 12:41:13 1999

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