Session V9: Computational Methods: Multiscale Modeling

Step decoration studied with first-principles statistical mechanics

With respect to oxidation catalysis or oxide formation, surface defects like steps, kinks, or vacancies are widely believed to play a decisive role, e.g. in form of active sites or as nucleation centers. Despite this suggested importance, first-principles investigations qualifying this role for gas-phase conditions that are representative of these applications are scarce. This is mostly due to the limitations of electronic-structure calculations in tackling the large system sizes and huge configuration spaces involved. We overcome these limitations with a first-principles statistical mechanics approach coupling density-functional theory (DFT) calculations with grand-canonical Monte Carlo simulations, and apply it to obtain the phase diagram of on-surface O adsorption at a (111) step on a Pd(100) surface. The link between the electronic and mesoscopic techniques is achieved by a lattice-gas Hamiltonian expansion, in which we parameterize the lateral interactions affected by the step from DFT calculations at a Pd(117) vicinal surface, and all remaining lateral interactions from calculations at Pd(100). For a wide range of O gas-phase conditions we find the (111) step to be decorated by a characteristic zig-zag structure. Intriguingly, this structure prevails even up to the elevated temperatures characteristic for catalytic combustion reactions, where only small amounts of disordered oxygen remain at the Pd(100) surface.   

Non-Adiabatic Transition Path Sampling: Application to a Model Proton-Transfer Reaction

A new algorithmic method is discussed, Non-Adiabatic Path Sampling (NAPS), which combines features of transition path sampling (TPS) and molecular dynamics with quantum transitions (MDQT). The goal is to ultimately address problems which involve excited and coupled electronic states, as well as large systems and long timescales ($e.g.$, semiconductor photocatalysis). TPS focuses specifically on trajectories that take a system from reactants to products, which allows the study of chemical processes that are dominated by rare but important events whose timescales are outside the range of direct simulation. In the MDQT algorithm, the nuclear dynamics of the system do not occur on a single Born-Oppenheimer potential energy surface, but rather may involve non-adiabatic transitions between many coupled electronic states. The NAPS algorithm uses the statistical framework of TPS to analyze MDQT trajectories, using the advantages of each method to get results for otherwise inaccessible systems. The algorithm is tested on a simple model of proton transfer: A quantum-mechanical proton in a double-well quartic potential bi-linearly coupled to a thermal bath of classical harmonic oscillators. Results from the model are compared to numerically exact results available in the literature.   

First-passage Monte Carlo for materials under irradiation

The key challenge in simulations of irradiated materials is that of time scale. Typically, atomistic simulations extend to less than one nanosecond whereas kinetic Monte Carlo (kMC) simulations struggle to reach hours of simulated irradiation. Based on a time-dependent Green's function formalism, our new kMC algorithm extends the simulated time horizon from minutes to tens and hundreds of years while retaining uncompromising accuracy. This presents an exciting opportunity to extrapolate, through accurate numerical simulations, the material behavior observed under the short and violent irradiation exposures used in the accelerated material tests, to the much longer reactor material lifetimes.   

OPAL: A New Multiscale Software Architecture Based on MPI-2

Software integration for multi-scale simulations is a time-consuming process. Common practice is to turn the higher level calculation code ( e.g. DFT ) into a subroutine of the lower level calculation code ( e.g. MD ). This method often requires non-trivial effort. To avoid these difficulties, we have developed a software package OPAL, within which a minimal development effort is required to build a working multi-scale environment. We report our effort of integrating DL\_POLY and SIESTA codes for hybrid quantum-classical simulations. This work is supported the NSF through ITR-medium (NSF/DMR/ITR-0218957) program. The authors want to thank NERSC, CNMS/ORNL and the University of Florida High Performance Computing Center for providing computational resources and support that have contributed to the research results reported within this paper.   

MP2 calculations for solid state systems

We present {\it ab initio} total energy calculations at the level of Hartree-Fock + 2nd-order M\o ller-Plesset perturbation theory (HF+MP2) for extended systems using periodic boundary conditions and a plane wave basis set. To characterize the accuracy of this level of theory, HF+MP2 lattice constants, bulk moduli, and atomizations energies for several archetypical semiconducting and insulating solid state systems are compared to those from density functional theory calculations and experiment. The HF+MP2 description of van der Waals interactions is illustrated for several noble gas solids. Important computational aspects of HF+MP2 calculations within the plane wave full potential projector-augmented-wave (PAW) formalism, most notably the basis set extrapolation of the MP2 correlation energy, are addressed as well.   

New approaches to the prediction of thermodynamic stability of crystal structures

We present new methods for numerical crystal structure optimization and prediction of structural stability on the basis of density functional theory calculations.[1] Comparison to established approaches to the calculation of lattice free energies differing in numerical complexity and accuracy of the results is provided. We show applications of these methods to complex insulators, semiconductors, and metals, and point out variations of our approaches making them suitable for these different classes of materials. We furthermore briefly outline alternative approaches to the prediction of compound stability avoiding the calculation of free energies. [1] J. Voss and T. Vegge, {\it to be published} (2007)   

Solidifying semiconductor nanocrystals from melts: Molecular dynamics simulations

Understanding the nucleation of semiconductor nanocrystals is of fundamental importance in the field of nanoscience. In this study we employ classical molecular dynamics simulations to explore the crystallization of Si nanocrystals from the melt. We focus on the differences between homogeneous and heterogeneous nucleations, where the heterogeneous case is investigated by simulating a liquid slab. In particular, we use the recently developed forward fluxing method [R.J. Allen, D. Frenkel, and P.R. ten Wolde, JCP 124 024102(2006)] to model the evolution of nucleation processes from melts and to compute nucleation rates. We demonstrate that free surfaces act as catalytic nucleation sites by significantly promoting the formation of solid-like small clusters. The presence of solid-like clusters in proximity of the surfaces is found to occur at temperature higher than those at which solid seed nucleation occurs in bulk liquids, highlighting the important role of heterogeneous nucleation under low under-cooling conditions.   

Ab-Initio Density Functional Calculation of Interatomic Potentials for Large-scale Atomistic Material Simulations.

We propose a new method to calculate interatomic potentials, utilizing an ab-initio density functional formalism. The calculated interatomic potentials can be used for large scale atomistic material simulations and predictions. We benchmark the method for the case of copper. We utilized the ab-initio interatomic potential to calculate various properties of transition metal copper, including the lattice constant, the bulk modulus, thermal expansion coefficient, monovacancy formation energy, and phonon frequencies. The calculated results agree very well with experimental values. We further calculated the properties of BCC Cu, utilizing the interatomic potential derived from the electronic structure calculations of FCC Cu, to demonstrate the predictive capabilities of the interatomic potential. The predicted properties of BCC Cu agree very well with experimental and ab-initio density functional results. Part of the work was performed during the stay of G. L. Zhao at Princeton University. The authors gratefully acknowledge the financial support of the National Science Foundation (Award No. 0508245).   

A New Look at the Evaluation of Embedded Atom Potential Models.

The embedded atom method (EAM) potentials have been used extensively since introduced by Daw and Baskes in the mid 1980's due to their simple incorporation of many-body effects that are missed by simple pair potentials. The computational cost of the inclusion of this additional physics has traditionally been a second pass over the pair data. We will report on an implementation of the EAM model within a molecular dynamics algorithm (MD) that does not require this second pass, substantially reducing the computer time and memory required for evaluation of the potential. The second pass is avoided by using a forward extrapolation in time of the density derivative of the embedding function $dF(\rho(t))/d\rho$. The error in this approximation is controllable and consistent with the error introduced by the finite time step numerical integrators used in the MD.   

Electronic structure from Maximum Entropy optimization: Applications to band energy and electronic force computation

We apply a new entropy optimization scheme to study the electronic density of states for complex disordered materials from a knowledge of spectral moments. We employ the Shannon entropy functional in our work and maximize it subject to the moment constraints to construct the spectral distribution of large Hamiltonian matrix[1]. We illustrate the efficiency and the usefulness of the method by reconstructing a number of exact functions, which are difficult to reproduce by other function reconstruction techniques. The local and global convergence properties of the resulting distribution is studied and the band energy and Fermi level are computed with a high degree of precision. An extension of this method to calculate electronic forces is presented for the purpose of using in large-scale molecular dynamics simulation of materials.   

Lagrangian Time-Reversible Born-Oppenheimer Molecular Dynamics

A Lagrangian generalization of time-reversible Born-Oppenheimer molecular dynamics [Niklasson et al., Phys. Rev. Lett., vol.97, 123001 (2006)] is proposed. The new formulation enables highly efficient symplectic or geometric integrations of both the nuclear and the electronic degrees of freedom that are stable and energy conserving even under incomplete self-consistency convergence. It is demonstrated how the accuracy is improved by over an order of magnitude compared to previous formulations at the same level of computational cost. The proposed Lagrangian includes extended electronic degrees of freedom as auxiliary dynamical variables in addition to the nuclear coordinates and momenta. While the nuclear degrees of freedom propagate on the Born-Oppenheimer potential energy surface, the extended auxiliary electronic degrees of freedom evolve as a harmonic oscillator centered around the adiabatic propagation of the self-consistent ground state (http://arxiv.org/abs/0711.3466).   

First-principles calculation combined with multicanonical simulation

To tackle statistical complexities in condensed matters such as phase transitions of atomic structures with first-principles calculations, Yoshimoto have studied the combination of first-principles calculations and multicanonical methods. By the multicanonical methods, phase space of atomic coordinates can be explored efficiently. Among phase transitions, Yoshimoto focused crystal$\leftrightarrow$liquid transition because it is a basic procedure for material synthesis and formation of objects (casting). The talk will present his recent results : a direct (not a coexisting) simulation of the crystal$\leftrightarrow$liquid transition by a kind of two-component multicanonical ensemble, a {\em multi-order multi-thermal ensemble}, with an order parameter defined with structure factors that characterize the transition, and optimization of a model interatomic potential in terms of the ensemble from an accurate one called {\em thermodynamic downfolding} of a potential. These provide a principle to project a first-principles approach on a model-based approach conserving thermodynamic properties of multiple phases to a maximum extent. The talk will cover the successful applications of the method to the transition of Si and MgO. Ref: Y. Yoshimoto, J. Chem. Phys. 125, 184103 (2006)   

Topological Properties of Microstructures in Nanocrystalline Materials.

Recent experiments show that the topological properties of microstructures in nanocrystalline materials play an important role in the mechanical properties of nanocrystalline materials. However, the fundamental structure-property relationship has not been fully understood due to the difficulties in determining and controlling the microscopic properties of nanocrystalline materials experimentally. In this study, we investigate how different topological properties affect the thermal and mechanical responses of nanocrystalline materials, including grain size distribution, surface area distribution, triple junction length distribution, grain boundary misorientation, etc. Digital microstructures with desired topological properties are generated using Inverse Monte Carlo method and are then relaxed and deformed by large-scale molecular dynamic simulation. In order to characterize the relaxed and deformed digital samples, we use a new grain boundary characterization method to accurately determine the position and thickness of each grain boundary during both relaxation and deformation. Finally, this newly developed algorithm enables us to study the correlation between topological and mechanical properties of nanocrystalline materials.   

XML Tools for First-Principles Molecular Dynamics Simulations

We present a set of XML Schema specifications for the representation of electronic structure data and first-principles molecular dynamics (FPMD) simulation data. The schemas (available at http://www.quantum-simulation.org) include the description of FPMD simulation samples and pseudopotentials in an extensible and code-neutral way. Automatic validation of simulation samples can be achieved using publicly available XML parsers such as Apache Xerces-C. We present examples of web-based remote collaboration in which simulation samples and pseudopotentials are accessed using the http protocol. Data analysis using XSLT scripts and a visualization program for remote inspection of simulation samples will also be demonstrated.   

Approximating Densities of States with Gaps using Maximally Broken Time-Reversal Symmetry

When a finite cluster of atoms is used to approximate the electronic structure of a macroscopic system, the appropriate boundary condition for electronic states on the surface of the cluster is maximal flow of probability current through the boundary, or maximal breaking of time-reversal symmetry for the states. For continued fraction representations of electronic Greenians, this boundary condition gives excellent results for both the first and second sheets when there is a single band of states. In this work, the approximation is extended to Greenians for multiple bands separated by gaps, such as arise in semiconductors.