Session B24: Focus Session: Multiscale Modeling - Methodology and applications

Recent Advances in Accelerated Molecular Dynamics Methods

Many important materials processes take place on time scales that vastly exceed the nanoseconds accessible to molecular dynamics simulation. Typically, this long-time dynamical evolution is characterized by a succession of thermally activated infrequent events involving defects in the material. Over the last 14 years, we have been developing a new class of methods, accelerated molecular dynamics, in which the known characteristics of infrequent-event systems are exploited to make reactive events take place more frequently, in a dynamically correct way. For certain processes, this approach has been remarkably successful, offering a view of complex dynamical evolution on time scales of microseconds, milliseconds, and sometimes beyond. Examples include metallic surface diffusion and growth, radiation damage annealing, and dynamics of nanotubes and nanoscale clusters. After an introduction to these methods, I will present some recent advances and results, and then describe the major ongoing challenges and our current thinking on how to overcome them.   

Multiscale (atomistic to mesoscopic) modeling of carbon nanotube materials

A principal challenge in the development of computational models for investigation of collective dynamic phenomena in multi- component molecular systems or nanocomposites is presented by the gap between the atomistic description of the elementary structural units and the effective material behavior and properties. We approach this challenge through the development of computational models for dynamic simulations at intermediate (mesoscopic) length and time scales. An example of a mesoscopic model that is being currently designed in our group for carbon nanotube (CNT)-based materials and nanocomposites will be discussed in the presentation. The mesoscopic dynamic model for CNT materials is based on a coarse-grained representation of individual CNTs as chains of stretchable cylindrical segments [1] and a computationally- efficient ``tubular potential'' method describing the van der Waals interactions among the CNT segments [2]. Mesoscopic descriptions of CNT buckling and fracture are developed based on the results of atomistic simulations and incorporated into the model. Mesoscopic simulations performed for a system composed of randomly distributed and oriented CNTs predict a spontaneous self-assembly of CNTs into a continuous network of bundles with partial hexagonal ordering of CNTs within the bundles [2]. The structures produced in the simulations are similar to the structures of CNT films and mats observed in experiments. The first results illustrating the applications of the model for investigation of the response of CNT materials to dynamic mechanical loading, analysis of the structural dependence of the thermal transport properties [3] and gas permeability in CNT films will be briefly discussed in the presentation. Challenges and possible future directions in the development of a realistic mesoscopic description of nanocomposite materials will be outlined.\\[4pt] [1] L.V. Zhigilei, C. Wei, D. Srivastava, Phys. Rev. B 71, 165417, 2005.\newline [2] A.N. Volkov, L.V. Zhigilei, J. Phys. Chem. C 114, 5513, 2010; ACS Nano 4, 6187, 2010.\newline [3] A.N. Volkov, L.V. Zhigilei, Phys. Rev. Lett. 104, 215902, 2010.   

Toward Distinct Element Method Simulations of Carbon Nanotube Systems

We propose distinct element method modeling of carbon nanotube systems. The atomic-level description of an individual nanotube is coarse-grained into a chain of spherical elements that interact by parallel bonds located at their contacts. The spherical elements can lump multiple translational unit cells of the carbon nanotube and have both translational and rotational degrees of freedom. The discrete long ranged interaction between nanotubes is included in a van der Waals contact of nonmechanical nature that acts simultaneously with the parallel bonds. The created mesoscopic model is put into service by simulating a realistic carbon nanotube ring. The ring morphology arises from the energy balance stored in both parallel and van der Waals bonds.   

Coarse-Grained Monte Carlo Simulations of Continuous Systems

Various types of Monte Carlo simulations are used extensively to simulate an enormous range of material properties. Restricting particle positions to fixed lattice sites can substantially increase the computational efficiency of a simulation, and this benefit increases as the lattice becomes coarser. However, the confinement of particle positions to a rigid lattice necessarily reduces the available configurational degrees of freedom in a system and this constraint can become very important at elevated temperatures. In this presentation, we discuss a new framework for performing Metropolis Monte Carlo and kinetic Monte Carlo (KMC) simulations of continuous systems on coarse, rigid lattices, while preserving the phase-space contributions of the missing degrees-of-freedom. The approach relies on the pre-computation of coarse-grained interaction potentials using equilibrium sampling of small systems. The coarse-grained simulation methodologies are shown to reproduce both equilibrium (e.g. phase diagram), and non-equilibrium (e.g. aggregation dynamics) features in the corresponding fully resolved systems. In the latter case, the coarse potential is used to compute rates for moves in a coarse-grained KMC system.   

Quantum-mechanical and QM/MM simulations of proton dissociation free energies in solution

Chemical reactions often occur in the presence of a solvent, in particular water for biological systems. To describe such processes a quantum mechanical (QM) description of the reaction site is needed, combined with a large number of solvent molecules that affect the reaction via their electrostatic fields and free energy effects of their long-range structure. We have simulated the dissociation of a proton from the side chain of a tyrosine molecule, as a realistic model system. We compute a free energy difference, using umbrella integration, from the average restraint force as a function of O$^-$-H$^+$ distance as the proton is transferred from the side-chain to nearby water molecules to form H$_3$O$^+$. We use a combination of periodic QM calculations using DFT and force-mixing QM/MM simulations implemented in QUIP and CP2K. The pure QM calculations are used for reference values and for determining appropriate restraint conditions for the free energy calculations. The force-mixing QM/MM method, which gives accurate forces throughout the system, is used to evaluate free energies for comparison with experiment. We extrapolate the free energy for the initial transfer of the proton to the bulk solvated proton regime by analytically computing electrostatic and entropy contributions.   

Understanding Vibrational Spectra of Silicon Nanocrystals

After the discovery of light emission from porous Si, nanostructured Si became a promising material for opto-electronic applications. For two decades lots of both experimental and theoretical works done in order to understand mechanisms behind the interaction of light with low dimensional forms of Si. In this work we employed MD simulation technique. The simulation details are similar to our earlier work except we used Large Scale Atomistic Molecular Modeling Package Software (LAMMPS) with ReaxFF package as an integrator. We used constant pressure constant temperature (NPT) ensemble with a simulation box size around 4.2 nm. We inserted silicon nanocrystals into amorphous silicon dioxide matrix with diameter ranging from 2 nm to 3.2 nm using a scheme defined in our previous work7. We also simulated free standing hydrogen passivated nanocrystals with same diameters to compare effects of oxide matrix on the nanocrystals. The effect of strain on vibrational spectra of Silicon Nanocrystals is studied as a function of nanocrystal diameter using reactive molecular dynamics simulations technique for both embedded and hydrogen passivated nanocrystals. With use of refined parameters our calculations reproduce the redshift of the Raman active transverse optical peak of Si-Si vibrations with decreasing the nanocrystal size.   

\textit{Ab initio} study of the \textit{thermodynamic properties and the} phonon calculations of Zircon and Reidite

Zircon and Reidite are the polymorphs of Zirconium Silicate which find its importance geologically, because of its natural hosting to various radioactive elements in the crust of the earth. High permittivity also makes it a promising material for the gate dielectric material in metal-oxide semiconductors. Knowledge of the thermodynamic properties and the phonon based calculations is very critical to understand the high temperature and high pressure properties in order to consider its application as an effective natural storage for the radioactive wastes. These properties are thoroughly studied both computationally and experimentally for zircon, while significantly less attention was paid to reidite in the literature. The thermodynamic properties and phonon calculations of Zircon and Reidite were studied using ab initio based periodic density-functional theory (DFT) based calculations using the generalized gradient approximation (GGA). Various properties such as free energy, internal energy, entropy, heat capacity and thermal displacement as a function of temperature is calculated using the PHONON software. Various phonon based density of states and dispersion curves are calculated and compared with the experimental data. No first principles based computational results were reported up to now. Calculated bulk properties agree very well with the experimental data in the literature.   

One-dimensional model of interacting-step fluctuations on vicinal surfaces: Analytical formulas and kinetic Monte-Carlo simulations

We study a 1+1D, stochastic, Burton-Cabrera-Frank (BCF) model of interacting steps fluctuating on a vicinal crystal. The step energy accounts for entropic and nearest-neighbor elastic-dipole interactions. Our goal is to formulate and validate a self-consistent mean-field (MF) formalism to approximately solve the system of coupled, nonlinear stochastic differential equations (SDEs) governing fluctuations in surface motion. We derive formulas for the time-dependent terrace width distribution (TWD) and its steady-state limit. By comparison with kinetic Monte-Carlo simulations, we show that our MF formalism improves upon models in which step interactions are linearized. We also indicate how fitting parameters of our steady state MF TWD may be used to determine the mass transport regime and step interaction energy of certain experimental systems.\footnote{P. Patrone, T. L. Einstein, D. Margetis, Phys. Rev. E, in press.}   

Real-time visualization of excited-state dynamics in molecular chains

Time-dependent density-functional theory allows one to calculate excitation energies and the associated transition densities in principle exactly. The transition density matrix (TDM) provides additional information on electron-hole localization and coherence of a specific excitation. We have extended the TDM concept into the real-time domain in order to visualize the excited-state dynamics in conjugated molecules. Our computational scheme is based on solving the time-dependent Kohn-Sham equations with the OCTOPUS code and then calculating the time-dependent Kohn-Sham TDM using a spatial partitioning scheme. The method is applied to show in real time how locally created electron-hole pairs spread out over neighboring conjugated molecular chains. The coupling mechanism, electron-hole coherence, and the possibility of charge separation are discussed.   

Thermal conductivity of bulk crystals from first-principles lattice dynamics

Based on first-principles density-functional calculations, we have developed and tested a force field for Silicon, which can be used for Molecular dynamics simulations and the calculation of its thermal properties. This force field uses the exact Taylor expansion of the total energy about the equilibrium positions up to 4th order. In this sense, it becomes systematically exact for small enough displacements, and can reproduce the thermodynamic properties of Si with high fidelity. Having the harmonic force constants, one can easily calculate the phonon spectrum of this system. The cubic force constants, on the other hand, will allow us to compute phonon lifetimes and scattering rates. Results on equilibrium Green-Kubo molecular dynamics simulations of thermal conductivity as well as an alternative calculation of the latter based on the relaxation-time approximation will be reported. The accuracy and ease of computation of the lattice thermal conductivity using these methods will be compared. Results on other non-trivial materials such as Heuslers will also be presented. This approach paves the way for the construction of accurate bulk interatomic potentials and force constants database, from which lattice dynamics and thermal properties can be calculated and used in larger scale simulation methods such as Monte Carlo.   

Optimizing laser pulses for controlled excitation of materials and molecules

This talk extends the ideas of recent papers, including [1] Zhou et al., Phys. Rev. B 82, 075433 (2010); [2] Lin et al., J. Phys. Cond. Mat. 21, 485503 (2009); and [3] Allen, Phys. Rev. B 78, 064305 (2008). There are three basic points: (1) A combination of analytical models and density-functional-based simulations provides guidance for tailoring laser pulses to achieve optimum vibrational and electronic excitation. In [1] it was found that the maximum relative response of a specific vibrational mode with period T is achieved when the FWHM duration of a pulse is equal to 0.42 T, and later work by Jiang et al. provided a similar criterion for the duration and delay times in a series of pulses. (2) It is possible for microscopic (density-functional-based) simulations to provide input for larger-scale simulations, in the form of stresses etc. (as demonstrated in [2]) and excitation-dependent interatomic potentials. (3) It is possible to extend current techniques for simulations of the coupled dynamics of electrons, nuclei, and the radiation field in highly-excited materials, using for example nonequilbrium Green's functions.