[Pw_forum] calculating the stress tensor

[Scandolo Sandro]

A number of useful formulae can be found in Paolo Focher's thesis (1994)
(dowloadable from http://www.sissa.it/cm/phd.php ), as well as in a
subsequent publication:

Paolo Focher and Guido L. Chiarotti
Ab-initio Molecular Dynamics simulations of structural phase transitions
in ``Progress in Computational Physics of Matter'', eds. L. Reatto and F.
Manghi, p. 1-42, World Scientific, Singapore, (1995).

(I can fax you the relevant pages of the latter when I'm back to Trieste,
late August).

Best regards,
Sandro


> Hi,
>
> I and another post-doc are working on implementing a non-local
> functional into PWSCF. It is of the general form:
> E_xc[n(r)] = \int dr dr' n(r) phi(r,r') n(r')
>
> where n(r) and phi(r,r') are the charge density and a kernel,
> respectively.
>
> Forces require calculating V_xc which is analytically complicated, but
> has already been done. The next quantity that we want to compute is
> the stress tensor.
>
> Does any happen to have any notes on calculating the stress tensor in
> a PW basis set?
>
> I looked at the original paper on calculating the stress:
>
> O. H. Nielsen and R. M. Martin, Phys. Rev. Lett. 50, 697 (1983).
>
> Eqn. 3 contains the V_xc (mu_xc in their notation) and it also
> contains epsilon_xc which is the exchange-correlation energy per
> particle which cannot be easily written down in a closed analytic form
> for a non-local functional (I think). Otherwise, I don't see any
> higher derivatives of E_xc in the the expression for the stress.
>
> Does anyone have any useful references?
>
> Thanks,
> --
> Nichols A. Romero, Ph.D.
> 1613 Denise Dr. Apt. D
> Forest Hill, MD 21050
> 443-567-8328 (C)
> 410-306-0709 (O)
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