# [CP2K:474] berry phase

Teodoro Laino teodor... at gmail.com
Tue Dec 11 00:22:23 CET 2007

Ciao Marc,

On 10 Dec 2007, at 17:41, marc wrote:

>
> Hey all,
>
> I have a problem concerning the calculation of dipole moments in
> cp2k.  I'm doing classical  molecular mechanics using force fields, so
> can I use cp2k for this?  What we want to do is calulate an IR-
Yes you can.

> spectrum using M.D..  I already ran a calculation, and cp2k gives
> three dipole moments for each simulation step:
>
> 1. MM DIPOLE BERRY PHASE ( A.U.)|
> 2. MM DIPOLE BERRY PHASE (Debye)|

These are the dipoles.. while this one is the derivative of just one
of the two:

> 3. MM DIPOLE (NON BERRY PHASE) DERIVATIVE (A.U.)|
>
> Has the berry phase output any revelance when doing classical M.D.
> using force fields?
Yes sure! Unless you work in free boundary conditions (i.e. isolated
systems), you can't
define the dipole moment as you would normally do i.e. (in latex
notation)

d = - \int \rho(r) * r   (in au units)

This equation looks very trivial, but it exploits an essential fact:
the density of any finite N charge system vanishes exponentially at
infinity.
Moreover, the problem with the expression above is that the integral
is ill-defined due to the unbounded nature of the position operator.
Pioneering work (only in the early 1990s!!) can be considered:

(1) M. Posternak, A. Baldereschi, A. Catellani, R. Resta, Phys. Rev.
Lett.  64 (1990) 1777

followed by real breakthrough in 1992, with the modern theory of
polarization:

(2) R. Rest a, Ferroelectrics 136 (1992) 51;
(3) R. D. King-Smith, D. Vanderbilt, Phys. Rev. B 47 (1993) 1651;
(4) D. Vanderbilt, D. King-Smith, Phys. Rev. B 48 (1993) 4442;

For more details based on the Berry-phase in the polarization field
you may have a look at:

(5) R. Resta, J. Phys. Condens 12 (2000) R107.

AN IMPORTANT WARNING: the version implemented in FIST gives the right
number only for orthorhombic cells.
obviously it can be expanded also to non-orthorhombic cells.

Let me know if you need I extend it to non-orthorhombic cells.

Have Fun! ;-)
Teo

> I also was wondering what the berry phase
> actually has to do with dipole moments?  Can someone give a reference
> which explains this berry phase related to classical M.D.?

> regards,
>
> marc
>
>
> >