A comparative study of two molecular mechanics models based on harmonic potentials

We show that the two molecular mechanics models, the stick-spiral and the beam models, predict considerably different mechanical properties of materials based on energy equivalence. The difference between the two models is independent of the materials since all parameters of the beam model are obtained from the harmonic potentials. We demonstrate this difference for finite width graphene nanoribbons and a single polyethylene chain comparing results of the molecular dynamics (MD) simulations with harmonic potentials and the finite element method with the beam model. We also find that the difference strongly depends on the loading modes, chirality and width of the graphene nanoribbons, and it increases with decreasing width of the nanoribbons under pure bending condition. The maximum difference of the predicted mechanical properties using the two models can exceed 300% in different loading modes. Comparing the two models with the MD results of AIREBO potential, we find that the stick-spiral model overestimates and the beam model underestimates the mechanical properties in narrow armchair graphene nanoribbons under pure bending condition.Comment: 40 pages, 21 figure

Ab initio RNA folding

RNA molecules are essential cellular machines performing a wide variety of functions for which a specific three-dimensional structure is required. Over the last several years, experimental determination of RNA structures through X-ray crystallography and NMR seems to have reached a plateau in the number of structures resolved each year, but as more and more RNA sequences are being discovered, need for structure prediction tools to complement experimental data is strong. Theoretical approaches to RNA folding have been developed since the late nineties when the first algorithms for secondary structure prediction appeared. Over the last 10 years a number of prediction methods for 3D structures have been developed, first based on bioinformatics and data-mining, and more recently based on a coarse-grained physical representation of the systems. In this review we are going to present the challenges of RNA structure prediction and the main ideas behind bioinformatic approaches and physics-based approaches. We will focus on the description of the more recent physics-based phenomenological models and on how they are built to include the specificity of the interactions of RNA bases, whose role is critical in folding. Through examples from different models, we will point out the strengths of physics-based approaches, which are able not only to predict equilibrium structures, but also to investigate dynamical and thermodynamical behavior, and the open challenges to include more key interactions ruling RNA folding.Comment: 28 pages, 18 figure

Efficient construction of free energy profiles of breathing metal–organic frameworks using advanced molecular dynamics simulations

In order to reliably predict and understand the breathing behavior of highly flexible metal–organic frameworks from thermodynamic considerations, an accurate estimation of the free energy difference between their different metastable states is a prerequisite. Herein, a variety of free energy estimation methods are thoroughly tested for their ability to construct the free energy profile as a function of the unit cell volume of MIL-53(Al). The methods comprise free energy perturbation, thermodynamic integration, umbrella sampling, metadynamics, and variationally enhanced sampling. A series of molecular dynamics simulations have been performed in the frame of each of the five methods to describe structural transformations in flexible materials with the volume as the collective variable, which offers a unique opportunity to assess their computational efficiency. Subsequently, the most efficient method, umbrella sampling, is used to construct an accurate free energy profile at different temperatures for MIL-53(Al) from first principles at the PBE+D3(BJ) level of theory. This study yields insight into the importance of the different aspects such as entropy contributions and anharmonic contributions on the resulting free energy profile. As such, this thorough study provides unparalleled insight in the thermodynamics of the large structural deformations of flexible materials

Coupling of Length Scales and Atomistic Simulation of MEMS Resonators

We present simulations of the dynamic and temperature dependent behavior of Micro-Electro-Mechanical Systems (MEMS) by utilizing recently developed parallel codes which enable a coupling of length scales. The novel techniques used in this simulation accurately model the behavior of the mechanical components of MEMS down to the atomic scale. We study the vibrational behavior of one class of MEMS devices: micron-scale resonators made of silicon and quartz. The algorithmic and computational avenue applied here represents a significant departure from the usual finite element approach based on continuum elastic theory. The approach is to use an atomistic simulation in regions of significantly anharmonic forces and large surface area to volume ratios or where internal friction due to defects is anticipated. Peripheral regions of MEMS which are well-described by continuum elastic theory are simulated using finite elements for efficiency. Thus, in central regions of the device, the motion of millions of individual atoms is simulated, while the relatively large peripheral regions are modeled with finite elements. The two techniques run concurrently and mesh seamlessly, passing information back and forth. This coupling of length scales gives a natural domain decomposition, so that the code runs on multiprocessor workstations and supercomputers. We present novel simulations of the vibrational behavior of micron-scale silicon and quartz oscillators. Our results are contrasted with the predictions of continuum elastic theory as a function of size, and the failure of the continuum techniques is clear in the limit of small sizes. We also extract the Q value for the resonators and study the corresponding dissipative processes.Comment: 10 pages, 10 figures, to be published in the proceedings of DTM '99; LaTeX with spie.sty, bibtex with spiebib.bst and psfi

Comparative study of semiclassical approaches to quantum dynamics

Quantum states can be described equivalently by density matrices, Wigner functions or quantum tomograms. We analyze the accuracy and performance of three related semiclassical approaches to quantum dynamics, in particular with respect to their numerical implementation. As test cases, we consider the time evolution of Gaussian wave packets in different one-dimensional geometries, whereby tunneling, resonance and anharmonicity effects are taken into account. The results and methods are benchmarked against an exact quantum mechanical treatment of the system, which is based on a highly efficient Chebyshev expansion technique of the time evolution operator.Comment: 32 pages, 8 figures, corrected typos and added references; version as publishe

Molecular dynamics study of solvation effects on acid dissociation in aprotic media

Acid ionization in aprotic media is studied using Molecular Dynamics techniques. In particular, models for HCl ionization in acetonitrile and dimethylsulfoxide are investigated. The proton is treated quantum mechanically using Feynman path integral methods and the remaining molecules are treated classically. Quantum effects are shown to be essential for the proper treatment of the ionization. The potential of mean force is computed as a function of the ion pair separation and the local solvent structure is examined. The computed dissociation constants in both solvents differ by several orders of magnitude which are in reasonable agreement with experimental results. Solvent separated ion pairs are found to exist in dimethylsulfoxide but not in acetonitrile. Dissociation mechanisms in small clusters are also investigated. Solvent separated ion pairs persist even in aggregates composed of rather few molecules, for instance, as few as thirty molecules. For smaller clusters or for large ion pair separations cluster finite-size effects come into play in a significant fashion.Comment: Plain LaTeX. To appear in JCP(March 15). Mpeg simulations available at http://www.chem.utoronto.ca/staff/REK/Videos/clusters/clusters.htm