An Algorithm for Computing Gradients of Functionals in Structural Materials Science

Abstract

When describing and modeling the crystal structure of a material, interatomic interaction potentials are used. To solve the problems of parametric identification of potentials, which consists of the selection of potential parameters, the use of various optimization methods has recently become increasingly important. In this case, it becomes necessary to determine the gradients of some quantities characterizing the substance with respect to parameters of potential. Based on the Fast Automatic Differentiation-technique, an algorithm has been built to determine the exact values of the gradients of bulk modulus and shear modulus of the test substance with respect to potential parameters in the case when the total interatomic energy of the atoms’ system is determined using the Tersoff’s potential.