[CPMD-list] origin and error bar of PIMD energies

[Lan-Feng Yuan (lyuan@Princeton.EDU)]

  Dear Axel and CPMD users,

  Thank you very much. So there is no choice at all ... Anyway, if I do simulations of 1-2 ps for isolated molecules, how much would these translational and rotational degrees of freedom do? Will each of them obtain 1/2kT and therefore 3kT altogether? Or we can just ignore them?

  In a recent test of mine, the nuclear masses of H2O are changed to 30, 30, 1, and the frequencies become 885, 1063, 3533 cm-1, whose ZPEs add up to 0.340 eV. With 8 beads, 300 K, 4 a.u. timestep, after 10000 steps of PIMD, the average quantum energy is higher than the ground state energy by 0.351 or 0.358 eV (virial or primitive estimator). 3kT here is 0.078 eV. So it seems that PIMD agrees with the harmonic vibrational energy to 0.01 or 0.02 eV, which looks good enough. From this I guess that that translation and rotation are absent in energies.

  But if so, it leads to another question: what is the internal error bar of PIMD? All the energy terms are vibrating depening on timestep, so there is an intrinsic spread for them. For example, in that test the quantum kinetic energy (virial) is 0.007838 +- 0.00165284 Ha, and I don't think more steps of simulation can reduce this fluctuation by much. Do we just accept it as part of error bar, or try to subtract its effect in error analysis?

  Thanks a lot! Regards,

  Lan-Feng

> On Thu, 14 Jul 2005, Lan-Feng Yuan (lyuan at Princeton.EDU) wrote:
> 
> LY>   Hi, dear CPMD users,
> LY> 
> 
> dear lan-feng,
> 
> LY>   I want to make sure that the energies from CP and path 
> integral MD
> LY> only include vibrational contributions, not translational and
> LY> rotational. It seems that the keyword SUBTRACT COMVEL ROLVEL would
> LY> subtract global momentuam and angular momentum every given 
> steps. The
> LY> manual says that the use of these keywords is strongly 
> recommended for
> LY> long runs (e.g. >10 ps) and/or low density systems (e.g. isolated
> LY> molecules, gas phase). Since I want to model water monomer and 
> dimer,LY> its use is "stronly recommended". However, the manual 
> also says that
> LY> since the subtracted kinetic energy is put back into the 
> system by
> LY> simple rescaling of the ionic velocities, these options is not 
> fullyLY> compatible with NOSE thermostats ... But I surely need 
> Nose chains in
> LY> PIMD. So what to do?
> 
> actually, SUBTRACT COMVEL/ROTVEL is not supported 
> by the PI-MD drivers at all. so there is not much
> of a choice. in general, you should be aware of the
> fact, that the path-integral code has not been 
> significantly updated for years and is somewhat 
> 'lagging behind' in terms of features compared to
> the other MD drivers.
> 
> as for using SUBTRACT COMVEL/ROTVEL in combination
> with nose-hoover chains. you _can_ use it, but
> due to the rescaling, the ensemble is not exactly
> preserved anymore. there may be a smarter way of
> doing it, but so far nobody has come up with it.
> on the other hand, if you use a fequency between 
> 20 and 100 the rescaling should be rather small. 
> in the end it, is a trade-off between keeping the 
> correct ensemble and losing kinetic energy into  
> rotation and translation.
> 
> best regards,
> 	axel.
> 
> LY> 
> LY>   Thank you very much! Regards,
> LY> 
> LY>   Lan-Feng
> LY> 
> LY> ----------------------------
> LY> Dr. Lan-Feng Yuan,
> LY> Postdoctoral Associate,
> LY> Department of Chemistry,
> LY> Princeton University,
> LY> Princeton, NJ 08544, USA
> LY> Office Phone: 1-609-258-1834
> LY> Fax: 1-609-258-6746
> LY> ----------------------------
> LY> 
> LY> 
> LY> _______________________________________________
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> LY> http://cpmd.org/mailman/listinfo/cpmd-list
> LY> 
> LY> 
> 
> -- 
> 
> =======================================================================
> Dr. Axel Kohlmeyer   e-mail: axel.kohlmeyer at theochem.ruhr-uni-
> bochum.deLehrstuhl fuer Theoretische Chemie          Phone: ++49 
> (0)234/32-26673
> Ruhr-Universitaet Bochum - NC 03/53         Fax:   ++49 (0)234/32-
> 14045D-44780 Bochum  http://www.theochem.ruhr-uni-
> bochum.de/~axel.kohlmeyer/=======================================================================
> If you make something idiot-proof, the universe creates a better 
> idiot.
>