Motivated by the special theory of gradient elasticity (GradEla), a proposal is\nadvanced for extending it to construct gradient models for interatomic potentials,\ncommonly used in atomistic simulations. Our focus is on Londonâ??s\nquantum mechanical potential which is an analytical expression valid until a\ncertain characteristic distance where â??attractiveâ? molecular interactions change\ncharacter and become â??repulsiveâ? and cannot be described by the classical\nform of Londonâ??s potential. It turns out that the suggested internal length\ngradient (ILG) generalization of Londonâ??s potential generates both an â??attractiveâ?\nand a â??repulsiveâ? branch, and by adjusting the corresponding gradient\nparameters, the behavior of the empirical Lennard-Jones potentials is\ntheoretically captured.
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