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Is energy conservation satisfied in the current deformation application schemes in molecular dynamic simulations?

Fan Yang's picture

In our recent 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. This paper can be found at:


mohammedlamine's picture

Hello Yang,

There are several kinds of energy (strain energy, sound energy, kinetic energy, heat energy, electrical energy; ..). The disappearance of an energy can produce another form of energy like a stopped (barrier) moving object with a kinetic energy will generate a calorific energy due to strains from internal forces where the object is found hot with a zero velocity. This means that the mechanical energy is conserved and the initial energy is transformed. But it is important to include in the energy conservation principle all the intervening forms of energy.


Fan Yang's picture

Thanks for comment. There are different kinds of energy such as strain energy, sound energy, heat energy. But they are defined in macro scale of continuum mechanics. In the scale of molecular dynamics, the internal energy of the system can be classified into potential energy and kinetic energy. The point is that the change of internal energy should equal the external work during any process, otherwise energy conservation will not be violated. The deformation application in MD is an actually an artificial implementation of the configuration and/or DOFs. It is therefore necessary to check the energy conservation in the deformation process.

Pu Zhang's picture

Thanks for elucidating this fundamental problem. This reminds me that other conservation laws should also be evaluated during the deformation process, e.g. total momentum and angular momentum. However, this may slow down the MD simulation.   

Fan Yang's picture

Thanks for comment. I agree with you on the examination of other conservation laws. Actually the conservation of translational momentum was also investigated in the discussion section of our paper. It may slow down the MD simulation.

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