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Hello! In this paper https://pdfs.semanticscholar.org/e8a2/02f25555cd8c4f947bbbdff5a61a0ea0efd2.pdf the authors use VASP to determine MgSiO3 viscosity using the Green-Kubo relation

## \eta = \frac{V}{3k_{\rm{B}}T}\int_{0} \left<\sum_\limits{i<j}\sigma_{ij}(t+t_{0}).\sigma_{ij}(t_{0})\right>dt## where ##\sigma_{ij}## (

## \eta = \frac{V}{3k_{\rm{B}}T}\int_{0}^{\infty} dt \left< P_{xy}(t)P_{xy}(0)\right>##, where ##P_{xy}## is the off-diagonal component of the stress tensor ##P_{αβ}## ( α and β are Cartesian components).

OK, so clearly these are essentially exactly the same equation but the second uses only the xy component whereas the first seems to suggest a summation? So which is correct.

Also, VASP outputs the stress tensor components as XX YY ZZ XY YZ ZX. So which of these should I use to input into the Green-Kubo equation? And are there missing components? what about yx, zx, yx?

Thanks in advance.

## \eta = \frac{V}{3k_{\rm{B}}T}\int_{0} \left<\sum_\limits{i<j}\sigma_{ij}(t+t_{0}).\sigma_{ij}(t_{0})\right>dt## where ##\sigma_{ij}## (

*i*and*j*=*x, y, z*) is the stress tensor,*t*is time and*t*0 is the time origin. But I've seen other papers use:## \eta = \frac{V}{3k_{\rm{B}}T}\int_{0}^{\infty} dt \left< P_{xy}(t)P_{xy}(0)\right>##, where ##P_{xy}## is the off-diagonal component of the stress tensor ##P_{αβ}## ( α and β are Cartesian components).

OK, so clearly these are essentially exactly the same equation but the second uses only the xy component whereas the first seems to suggest a summation? So which is correct.

Also, VASP outputs the stress tensor components as XX YY ZZ XY YZ ZX. So which of these should I use to input into the Green-Kubo equation? And are there missing components? what about yx, zx, yx?

Thanks in advance.

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