# [gmx-developers] The development of a new implementation of RahmanParrinello

ramon at juguete.quim.ucm.es ramon at juguete.quim.ucm.es
Wed Oct 12 22:20:57 CEST 2005

```With regard to anisotropic pressure, I would recommend to be
careful and support only isotropic pressure (though compresibility
and cell may be anisotropic). Thus ref_p should have only one
component.

Parrinello and Rahman provide equations for general stress tensor,
but they are somewhat complicated and arbitrary. One has to define
a reference state, that should match the average cell box.

Note that using the standard definition of pressure, an anisotropic
pressure is necessary non-conservative. Let us have a orthorrombic cell
with edges of lengths a, b, c. Let us have anisotropic pressure with
diagonal components px, py, pz (for simplifying, non diagonal components
are zero in this example). The work for increasing a in da is b*c*px*da
(work = force*dx = pressure*surface*da). Now one can enlarge a and b in
two ways: first a and then b, or first b and then a. The work performed
is different using these two paths:

W_1 = da*b*c*px + (a + da)*c*db*py
W_2 = db*a*c*py + (b + db)*a*da*px

so one could have a loop where the system enthalpy is not conserved.

So anisotropic pressure is rather non obvious.

Gromacs implements anisotropic external pressure, but it is wrong. Gromacs does
the obvious extension of (P - Pext) to the anisotropic case, but that leads to
a non conservative equations of motion that derive from no hamiltonian. I filled
bug #14.

With regards to the issues of the original Rahman Parrinello mentioned in the link
that you gave, I think it is quite about making philosophy. After reading the paper
of Renata M. Wentzcovitch Phys. Rev. B 44 (1991), no. 5, 2358-2361, it seems that
the problem with the dynamics denpending of the choice of cell is "corrected"
by replacing trace(boxv*transpose(boxv)) by trace(boxv*f*transpose(boxv)) in the
hamiltonian. But when one introduces a compresibility, it is inserted exactly
in the same place as f. Thus the arbitrary choice of cell is related to the arbitrary
choice of compresibility: that is, with a different cell, a different compresibility
would lead to the same dynamics.

Hope this helps,

Ramon

```