[Pw_forum] My vague understanding of internal degrees of freedom

[Hongsheng Zhao]

On 07/22/2011 03:49 PM, xiaochuan Ge wrote:
> Dear Hongsheng Zhao,
> I am not sure about what you want to ask. But I guess if what you mean
> by "internal degrees" is what you have specified, a system having or
> not having the internal degrees does not depend on the shape of of the
> cell.  You may check the input description of pw.x, I think the "no
> internal degrees of freedom" is mentioned for scf calculation is
> because in "relax" the atomic coordinates are allowed to evolve during
> the calculation, while when scf is specified only electronic
> configurations have the freedom to evolve keeping all the atomic
> coordinates fixed.
> I hope that I have answered your question, excuse me if I have
> misunderstood your real puzzle.

Let me give you more detailed descriptions.  Say, we can use the 
following method to calculate the elastic constant:

Imply a series of deformations on the cell. Then calculate the stress 
tensor for each strain step.  For this purpose, generally, we need to do 
non-variable relaxation calculations ater we manually applied each 
strain/deformation.  In order to  improve the computational efficiency. 
   We may want to keep the lattice vectors perpendicular to the strain's 
direction fixed and then obtain the stress tensor corresponding to the 
stretched/compressed direction.  Finally, we use this to derive the 
elastic constants.

In this case, for each strain step, if there are no  internal degrees of 
freedom for the system, the single-point energy calculations should be OK.

For example, if the unit cell of our system is a simple cubic one, 
there are no atoms in the internal of cell.  So I I think this should be 
the case we noted as: "no
internal degrees of freedom".  Another example is that the body centered 
  cubic unit cell, in this case, we have atom in the internal of cell, 
but the position of internal atom is resides at high-symmetry position 
which should be most stable position for that atom, so the relaxation 
for that atom after each  strain step is also unnecessary.  Of course, 
in all of these calculations,  we should use fractional coordinations 
for all of the atoms in the input file so that the atoms positions can 
be updated to its new deformation positons uniformly with each strain 
step.  In this case, I think  the single-point energy calculations  for 
each strain step should be OK.

But for a Wurtzite ZnO, this is not the case, when we impose a strain, 
say, along the z axis, considering that there are atoms in general 
positions  in the unit cell, so we must relax the atoms positions for 
each strain step, other than a single-point energy calculations  for 
each strain step.

Based on the above description,  let we back to my question again:  I 
want know for a specific system, how we know whether there are "internal 
degrees of freedom" or not.  How to judge it?

I hope I stated my issue clearly this time.

Regards

> Best wishes,
> Ge Xiaochuan
>
> 2011/7/22<pw_forum-request at pwscf.org>:
>> My vague understanding of internal degrees of freedom
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-- 
Hongsheng Zhao <zhaohscas at yahoo.com.cn>
School of Physics and Electrical Information Science,
Ningxia University, Yinchuan 750021, China