Atomic scale computational methods application

The application of atomic scale computational methods in the analysis of electrochemical reactions has now reached a level, where accurate prediction of electrocatalysts for the efficient conversion of excess sustainable electricity into synthetic fuels like hydrogen, ammonia, methane, and methanol, or in the design of new materials for the next generation in battery technologies. 

Atomic-Scale Finite Element Method in Multiscale Computation with Applications to Carbon Nanotubes. 

Computational methods used to extend the time scale of atomically detailed simulations have improved in the last 15 years. Accurate MTS simulations, with computational gains up to a factor of 10, have extended the applicability of molecular dynamics simulations and refinements in the computation of medivun-range forces could provide stable results with increasing speedups. It is apparent that stability limitations will prevent the extension of these algorithms to the range of time scales that are needed to study many processes of interest, however. On the other hand, reaction path approaches can be used... 

For the calculation of properties at the atomic scale, ab initio or first-principles approaches, based on a quantum mechanical description of the interactions between electrons and atomic nuclei with the atomic numbers and masses as only input, have the advantage of a wider range of applicability with respect to e.g., different chemical environments of the atomic nuclei compared to empirical methods, at the price of higher computational complexity. The ab initio calculation of the electronic ground state structure within density functional theory [3] in the Kohn-Sham scheme [4] has become a standard approach to study bulk crystal structures, surfaces, and molecular reactions. 

Unfortunately, the determination of exact solutions of the SchrOdinger equation is intractable for almost all systems of practical interest. On the other hand, independent particle models are not sufficiently accurate for most studies of molecular structure. In particular, the Hartree-Fock model, which is the best independent particle model in the variational sense, does not support sufficient accuracy for many applications. Some account of electron correlation effects has to be included in the theoretical apparatus which underpins practical computational methods. Although the energy associated with electron correlation is a small fraction of the total energy of an atom or molecule, it is of the same order as most energies of chemical interest. However, such theories may not be true many-body theories. They may contain terms which scale non-linearly with electron number and are therefore unphysical and should be discarded. Any theory which contains such unphysical terms is not acceptable as a true many-body method. Either the theory is abandoned or corrections, such as that of Davidson [7] which is used in limited configuration interaction studies, are made in an attempt to restore linear scaling. 

The last two decades have witnessed a dramatic rise in computational resources that has facilitated tremendous progress in computational science. In particular, this progress has enabled the application of quantum-based methods such as Flartree-Fock (FIF) theory and density functional theory (DFT) to compute the potential energy surfaces of numerous complex reactions that are critical to understanding catalytic reactions. These approaches provide high fidelity because of their explicit treatment of electronic structure however, their computational cost increases rapidly with system size. Therefore, they are limited to a relatively small number of atoms (<500). To overcome this limitation, classical empirical methods (also known as interatomic potentials) that model molecules and materials at the atomic scale without explicitly treating electrons have been developed and have been employed in molecular dynamics (MD) and Monte Carlo (MC) simulations. Such simulations have been employed to examine catalysis at length and time scales beyond the reach of quantum-based approaches. 

Abstract. Molecular dynamics (MD) simulations of proteins provide descriptions of atomic motions, which allow to relate observable properties of proteins to microscopic processes. Unfortunately, such MD simulations require an enormous amount of computer time and, therefore, are limited to time scales of nanoseconds. We describe first a fast multiple time step structure adapted multipole method (FA-MUSAMM) to speed up the evaluation of the computationally most demanding Coulomb interactions in solvated protein models, secondly an application of this method aiming at a microscopic understanding of single molecule atomic force microscopy experiments, and, thirdly, a new method to predict slow conformational motions at microsecond time scales. 

As an example for an efficient yet quite accurate approximation, in the first part of our contribution we describe a combination of a structure adapted multipole method with a multiple time step scheme (FAMUSAMM — fast multistep structure adapted multipole method) and evaluate its performance. In the second part we present, as a recent application of this method, an MD study of a ligand-receptor unbinding process enforced by single molecule atomic force microscopy. Through comparison of computed unbinding forces with experimental data we evaluate the quality of the simulations. The third part sketches, as a perspective, one way to drastically extend accessible time scales if one restricts oneself to the study of conformational transitions, which arc ubiquitous in proteins and are the elementary steps of many functional conformational motions. 

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