February 2023
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Classical molecular dynamics simulation is performed mostly using the established velocity Verlet integrator or other symplectic propagation schemes. In this work, an alternative formulation of numerical propagators for classical molecular dynamics is introduced based on an expansion of the time evolution operator in series of Chebyshev and Newton polynomials. The suggested propagators have, in principle, arbitrary order of accuracy which can be controlled by the choice of expansion order after that the series is truncated. However, the expansion converges only after a minimum number of terms is included in the expansion and this number increases linearly with the time step size. Measurements of the energy drift demonstrate the acceptable long-time stability of the polynomial propagators. It is shown that a system of interacting Lennard-Jones particles is tractable by the proposed technique and that the scaling with the expansion order is only polynomial while the scaling with the number of particles is the same as with the conventional velocity Verlet. The proposed method is, in principle, extendable for further interaction force fields and for integration with a thermostat, and can be parallelized to speed up the computation of every time step.
![Screening of the charge carrier mobility of derivatives of the Alq3 material. A) Using a multi‐scale workflow a novel material (green) could be developed exhibiting a two orders of magnitude higher mobility than the original material (red), reproduced with permission.[⁵²] Copyright 2021, John Wiley and Sons. B) The workflow consists of a parametrization stage based on single molecule DFT. A forcefield is generated, which is then used to generate thin‐film morphology using simulated PVD.[⁵⁰] For each pair in this morphology the electronic structure is relaxed in a self‐consistent way.[⁵¹] Finally the mobility is calculated using a generalized effective medium model.[⁵³] C) Implementation of the workflow in the SimStack workflow application. The complexity of the multiscale problem is hidden from the user by automatically interfacing the required applications for each scale. After the initial workflow assembly, the only significant remaining input is the structure of the initial molecule.](https://www.researchgate.net/publication/357105525/figure/fig3/AS:11431281246399553@1716369073531/Screening-of-the-charge-carrier-mobility-of-derivatives-of-the-Alq3-material-A-Using-a_Q320.jpg)
![Workflow execution and reporting using Pipeline Pilot. a) visual form of the executed workflow in ref. [62] describing how to calculate the transport properties of a battery electrolyte. The green numbers denote the number of records passed, either four molecules or five samples b) report summary for a single protocol run describing the calculated properties and their statistical uncertainties for a single Li salt concentration and at a single temperature. c) Data from multiple runs for different temperatures and salt concentrations.](https://www.researchgate.net/publication/357105525/figure/fig5/AS:11431281246436592@1716369073886/Workflow-execution-and-reporting-using-Pipeline-Pilot-a-visual-form-of-the-executed_Q320.jpg)
![Free energy change along the reaction path in presence of water via the S4 scheme in absence (a) and in presence (b) of Fe dopant at position M2. The state (1) = [M-* + 2H2O] has been used as reference, i.e. ΔG0(1)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {G}_{0}^{(1)}=0$$\end{document} eV and ΔG0(5)=4.92\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\Delta {G}_{0}^{(5)}=4.92$$\end{document} eV. The free energy diagram of the OER/ORR processes at the M5 edge site is shown for the ideal catalyst (empty bars), the case with zero bias (green bars) and the cases with OER and ORR biases (red and blue bars, respectively)](https://www.researchgate.net/publication/343317324/figure/fig4/AS:962195798126609@1606416763954/Free-energy-change-along-the-reaction-path-in-presence-of-water-via-the-S4-scheme-in_Q320.jpg)
