[Pw_forum] Re: CP for metals

[Paul Tangney]

Hi all,

I agree with most of what Kostya says,  but I have some comments.

 >Hi all,
 >
 > I'd like to point out that electronic thermostats is a pretty
 >dangeorous thing to use for any production calculations unless one
 >really knows what is going on there.

And nobody ever does, I think.

 >
 > The main issue is that there is usually some "natural" fictitious
 >kinetic energy that electrons gain from the ionic motion ("drag"). One
 >could easily quantify how much of the fictitious energy comes from this
 >drag by doing a CP run, then a couple of CG (same as BO) steps, and
 >then going back to CP. The fictitious electronic energy at the last CP
 >restart will be purely due to the drag effect.

I'm not sure I understand precisely what you are proposing here, but
if you are proposing to restart CP with finite ionic velocities
and stationary orbitals, you will give the orbitals a "kick" that 
substantially increases their fictitious kinetic energy (FKE) above the 
amount that is purely due to drag. (See the review by Remler and Madden
or Tangney,Scandolo JCP  116, 14 2002)

 >
 > The thermostat on electrons will either try to overexcite the
 >otherwise "cold" electrons, or, will try to take them down to an
 >unnaturally cold state where their fictitious kinetic energy is even
 >below what would be just due pure drag. Neither of this is good.

Yes, I totally agree.

 >
 > I think the only workable regime with an electronic thermostat is a
 >mild overexcitation of the electrons, however, to do this one will need
 >to know rather precisely what is the fictititious kinetic energy due to
 >the drag.
 >

This is certainly the *best* way to use a thermostat, but I wouldn't
call it *workable* because you can never know the FKE precisely enough:
The problem is that the fluctuations in the FKE due
to ionic vibrations (i.e. the drag part) are absolutely enormous
compared to the mild over-excitation that would be tolerable.

A tolerable over-excitation is one that doesn't lead to large errors in 
the forces.
Lets say the orbitals have precisely the right amount of FKE, i.e. the
drag part and no more. Then lets say we excited them a little more, by
giving them an extra 0.0001 hartree per atom of FKE. Since this part of
the FKE has a completely unknown effect (the drag part often does too,
but that's a different story), you can, roughly speaking, think of this
a little bit like exciting the electrons further away from the ground
state by 0.0001 a.u./atom.  Now if you look at how well the forces are
converged in a s.c.f calculation when the energy is converged to
0.0001 a.u./atom you will see that this can have a dramatic effect
on the forces. In ice at 250K, for example,if the orbitals are far
enough away from the ground state  that the energy is 0.0001
a.u/atom away from the ground state energy, the magnitude of
the difference between the forces and the converged
forces are of about the same magnitude as the forces themselves!!
The picture of Car-Parrinello forces performing small oscillations
around the ground state forces (which is a fallacy anyway)
breaks down.

I've put a plot to illustrate this here:

http://civet.berkeley.edu/tangney/CP_FKE/

I've plotted the predicted drag FKE and the FKE that actually
came out of the simulation on the same plot. The prediction is very 
good, and the very tiny difference between them (also plotted)
corresponds to r.m.s. errors in the forces on the water molecules
of about 13% of the r.m.s forces.
Now, using a thermostat, depending on the strength of the coupling,
you would be fixing the FKE to a particular value and so the difference
between the drag part and the total FKE would be larger
(probably, by much more than an order of magnitude) than the difference
shown here. The effect on the forces could be huge.


Paul




-- 
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Dr. Paul Tangney
Theory of Nanostructured Materials Facility
The Molecular Foundry
Lawrence Berkeley National Lab.         E-mail: PTTangney at lbl.gov
1 Cyclotron Road, Bldg 66                  Phone: (510) 642-2635
Berkeley, CA 94720                         Fax :  (510) 643-9345
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