[Pw_forum] Lattice constant for copper

[Nicola Marzari]

On 3/4/11 12:12 PM, Eric Germaneau wrote:
> Dear Professor Marzari,
>
> Thank you for your comment, but I'm getting very much confused now.
> Well, I thought the Bose-Einstein statistics apply to bosons.
> Are you talking about Fermi-Dirac  statistics?
> Actually, I imaged that Car-Parrinello molecular dynamics approach
> considered the quantum statistic of electrons.
> I'm going to look for some paper on this topic.
> I thank you again,
>
>                                  Eric.


Hi Eric,

vibrations (i.e. ionic motions) are actually bosons - so
in car-parrinello or born-oppenheimer md we treat the electrons
properly (with fermi-dirac statistics) but not the vibrations -
our algorithms assume distinguishable particles, hence maxwell boltzmann.

at room temperature the difference is significant - you can take into
account bose einstein statistics in general terms using a path-integral
formulation (that gives you statistical bose-einstein averages,
and not real dynamics), or around equilibrium by calculating
phonons (sinze you can write out analytically the partition
function of a system of independent harmonic oscillators - look
out for papers on the quasiharmonic approximations).

you could also look at the recent work of ceriotti, bussi and parrinello 
- in particolar the second paper below.

Best,

			nicola


Colored Langevin equation for molecular dynamics simulations

M. Ceriotti, G. Bussi and M. Parrinello,
Langevin equation with colored noise for constant-temperature molecular 
dynamics simulations,
Phys. Rev. Lett. 102, 020601 (2009)
Preprint: arXiv:0812.1168

M. Ceriotti, G. Bussi and M. Parrinello,
Nuclear quantum effects in solids using a colored-noise thermostat,
Phys. Rev. Lett. 103, 030603 (2009)
Preprint: arXiv:0903.4551

M. Ceriotti, G. Bussi and M. Parrinello,
Colored-Noise Thermostats à la Carte,
J. Chem. Theory Comput. 6, 1170 (2010)

-- 
----------------------------------------------------------------------
Prof Nicola Marzari    Department of Materials    University of Oxford
Chair of Materials Modelling  Director, Materials Modelling Laboratory
nicola.marzari at materials.ox.ac.uk     http://mml.materials.ox.ac.uk/NM