[CPMD-list] CPMD tests

[Juerg Hutter]

Hi

> Dear Prof. Hutter,
>
> Thank you for your help. I have been reading
> the following article : Tangney,Scandolo J. Chem.
> Phys. 116, 14 (2002). According to this article
> the premise on which CPMD is justified in your article
> and in the mathematical "proofs" that you refer to is
> not strictly correct.

This is not correct. The reference 86 and 87 are actual
proofs.

>
> These arguments all seem to rely on the premise that
> electronic motion consists of high-frequency
> oscillations about the ground state. However, this
> ignores the slow motion of the orbitals due
> to the ionic-timescale evolution of the ground state.
> When account is taken of this motion, it is shown
> that the electrons don't oscillate about the
> ground state at all and large errors in the forces
> result.

The mathematical result is that there is always a
electron mass mu small enough such that errors
in the calculation are smaller than a given value.

>
> For ionic systems these errors appear very large but
> they are negligible for silicon. If it is right I
> guess this paper answers my question and CPMD doesn't
> describe the ground state very well. But then, why is
> it still being used ?
>
> Am I missing something ?
>

Let me summarize

1) Theory: There is always a mu small enough to make
   CP dynamics as accurate as requested. CP dynamics
   is stable. Remember: this is for statistical averages,
   not for one single configuration.
2) Practical issues: For many systems the mass mu
   can be chosen such that accuracy and efficiency
   are satisfactory.
   However, there are systems (especially metals but
   also other systems) where there are problems due
   to drag forces for large mu. This is even worse
   if you use g-vector scaled masses. For many of
   these systems you can use the rigid-ion correction.
   As far as I know this was already pointed out by
   Bloechl and Parrinello in the early 90's.
   For some systems, not even this correction works
   and you can't use CP or you have to use a very
   small mu and computational costs are very high.

BO dynamics

1) Theory: if you don't use exact forces (and nobody
   uses exact forces) BO dynamics is not stable,
   meaning that the total energy in the system is not
   conserved.

2) Practice: you can always converge the wavefunctions
   good enough in order to get forces that allow
   for accurate dynamics over the time frame required
   for your problem. However, this makes the calculation
   more expensive.

For some systems you get best efficency and accuracy with
CP, for other systems BO dynamics gives better performance.
It's important in both cases (CP and BO) to know what are the
parameters to control and the quantities to observe.

Juerg Hutter