On the energy conservation during the active deformation in molecular dynamics simulations

In this paper, we examined the energy conservation for the current schemes of applying active deformation in molecular dynamics (MD) simulations. Specifically, two methods are examined. One is scaling the dimension of the simulation box and the atom positions via an affine transformation, suitable for the periodic system. The other is moving the rigid walls that interact with the atoms in the system, suitable for the non-periodic system. Based on the calculation of the external work and the internal energy change, we present that the atom velocities also need to be updated in the first deformation method; otherwise the energy conservation cannot be satisfied. The classic updating scheme is examined, in which any atom crossing the periodic boundary experiences a velocity delta that is equal to the velocity difference between the opposite boundaries. In addition, a new scheme which scales the velocities of all the atoms according to the strain increment is proposed, which is more efficient and realistic than the classic scheme. It is also demonstrated that the Virial stress instead of its interaction part is the correct stress definition that corresponds to Cauchy stress in the continuum mechanics.