[Pw_forum] calculating the stress tensor

[Nichols A. Romero]

Sandro,

I am replying to this old e-mail now because the funds have become available
to do some work in this area.

I looked in Paolo Focher's thesis and there are some very helpful equations,
so thank you. However, the eqn.'s are limited to LDA.

Does anyone know where I could find the relevant equation(s) for the GGA
functional contribution to the stress tensor? I imagine it should not be
that different from LDA, but I want to be sure.


On 7/13/06, Scandolo Sandro <scandolo at ictp.it> wrote:
>
> 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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> > Pw_forum at pwscf.org
> > http://www.democritos.it/mailman/listinfo/pw_forum
> >
>
>
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-- 
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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