Application of the fast automatic differentiation for calculation of gradients of material's Bulk modulus and Shear modulus

Alla Albu^a, Vladimir Zubov<sup>ab

a</sup> Dorodnicyn Computing Centre, Federal Research Center "Computer Science and Control" of Russian Academy of Sciences, 40, Vavilova Str., 119333, Moscow, Russia
^b Moscow Institute of Physics and Technology (State University), 9 Institutskiy per., Dolgoprudny, Moscow Region 141701, Russia

Abstract: In computer modeling of crystal structures the gradient optimization methods are often used. This raises the need to calculate the exact gradients of the Bulk modulus and the Shear modulus of materials. With help of the Fast Automatic Differentiation the formulas that allow the calculation of the exact above-mentioned gradients were derived in the case where the total interatomic energy of the system is determined by Tersoff's Potential.

Keywords and phrases: Tersoff potential, gradient, fast automatic differentiation.

MSC: 49J20, 93C20

Received: 27.01.2017

Language: English

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