| Gradient enhancing classical quantum mechanical and empirical interatomic potentials Konstantinos Parisis1; Elias Aifantis1; 1ARISTOTLE UNIVERSITY OF THESSALONIKI, Thessaloniki, Greece; PAPER: 300/Multiscale/Keynote (Oral) SCHEDULED: 16:45/Tue. 29 Nov. 2022/Similan 1 ABSTRACT: A proposal is advanced for enhancing classical quantum mechanical and empirical potentials with a Laplacian term incorporating nonlocal effects. It is shown that this results in a “repulsive” branch, in addition to its classical “attractive” branch derived by rigorous quantum mechanical considerations. By properly choosing the gradient coefficient (or internal length) multiplying the Laplacian term, it is shown that the gradient-enhanced London potential recovers the structure of the empirical Lennard-Jones potential, and the same holds for the Stillinger-Weber potential. In the sequel, an attempt is made to address the role of such gradient enhancement for the case of Baskes embedded atom method (EAM) to determine whether or not the Laplacian term can account for non pairwise interactions and angular/orientation effects. Finally, the role of bi-Laplacian and fractional/fractal effects is briefly discussed. References: K. Parisis, F. Shuang, P. Hu, A. Konstantinidis, A. Giannakoudakis and E.C. Aifantis, From gradient elasticity to gradient interatomic potentials: The case-study of gradient London potential, J. Appl. Math. Phys. 8, 1826-1837, 2020. K. Parisis and E.C. Aifantis, Gradients, singularities and interatomic potentials, in: TMS 2021 150th Annual Meeting & Exhibition Supplementary Proceedings, pp. 793-800, 2021. E.C. Aifantis, Gradient Extension of Classical Material Models: From Nuclear & Condensed Matter Scales to Earth & Cosmological Scales, Springer Tracts in Mechanical Engineering, , pp. 417–452, 2021. |
