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stress

# Stress

To enable the calculation of the stress tensor you have to add stress to the compilation options of potfit.

The stress tensor has to be given in the configuration file with the prefix #S. If no #S line is found for a configuration, then the calculation of stresses is disabled for this configuration.

#### Stress calculation

potfit and IMD calculate the virial stress, which is based on a generalization of the virial theorem of Clausius1 for gas pressure. It can be written as

$$\boldsymbol\sigma^{\text{virial}} = \frac{1}{2\Omega}\sum_i\sum_{j\neq i}\boldsymbol r_{ij}\otimes\boldsymbol f_{ij}$$

where $\Omega$ is the total volume, $i$ and $j$ the atomic indices, $\boldsymbol r_{ij}=\boldsymbol r_j-\boldsymbol r_i$ and $\boldsymbol f_{ij}$ the interatomic force applied on atom $i$ by atom $j$,

$$\boldsymbol f_{ij}=\frac{\partial\phi(r_{ij})}{\partial r_{ij}}\frac{\boldsymbol r_{ij}}{r_{ij}}.$$

#### Target function

The deviation of the stress tensor components is added to the target function like the forces and energies

$$Z_F(\boldsymbol\xi)= \sum_{k=1}^{3N}u_k(F_k(\boldsymbol\xi)-F_k^0)^2 + \sum_{l=1}^{M}w_E(E_l(\boldsymbol\xi)-E_l^0)^2 + \sum_{l=1}^{6M}w_S(S_l(\boldsymbol\xi)-S_l^0)^2$$

with the stress weight $$w_S.$$

1. Clausius R. J. E.: On a mechanical theorem applicable to heat. Phil. Mag. 40 122–7, 1870 Link 