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The influence of periodic edge conditions for the simulation of some quantities of interest for separative chemistry

Abstract : The objective of this thesis is to study the influence of periodic conditions and in particular the corrections to be made, depending on the period considered, in the calculation of certain quantities of interest from molecular dynamics simulations. The latter are particularly useful for the understanding of solvation phenomena of molecules in solution and are naturally useful for the study of radioactive waste management. We are particularly interested in the study of the potential of Mean Force, described in the McMillan and Mayer formalism between two charged solutes in solution. We start by calculating analytically the potential of such a system by considering periodic edge conditions of period L. The calculation is based on the forces acting on one of the particles and on the clever joining of the terms of the obtained sum. We can finally verify that, at large distances, the potential converges to a coulombic potential, and we obtain a corrective term in L-5. From simulations using the Umbrella Sampling method combined with the WHAM method, we correct the McMillan and Mayer potential of sodium chloride, and lanthanides, from the term obtained in order to observe the resulting association constant. Moreover, we study the diffusion coefficient of a particle in a confined medium. Our calculation is based on the passage of the Stokes equation in Fourier, which gives us ODEs with distributions that we solve to obtain the velocity of the particle. Then, limited developments lead to the diffusion coefficient including a corrective term in L-1.
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Submitted on : Tuesday, December 7, 2021 - 4:50:25 PM
Last modification on : Friday, August 5, 2022 - 12:01:59 PM

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  • HAL Id : tel-03469446, version 1

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Anne-Françoise De Guerny. The influence of periodic edge conditions for the simulation of some quantities of interest for separative chemistry. Analysis of PDEs [math.AP]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS086⟩. ⟨tel-03469446⟩

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