# berry phase

marc marcvanh... at gmail.com
Tue Dec 11 11:24:34 CET 2007

OK, thank you very much for the information.  I'm going into it a
little bit more and let you know how it evolves.

until then,

take care!

marc

On Dec 11, 12:22 am, Teodoro Laino <teodor... at gmail.com> wrote:
> 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