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[Xavier Gonze <gonze@pcpm.ucl.ac.be>]

Dear Yaroslav, 

Thanks for the very detailed description of your problem.

Actually, the _expression_ for the total energy is not variational with respect to the number

of k points, unlike with respect to the basis set. Indeed, the k points

are used to replace an integral by a finite sum, while the planewaves form

a basis set, whose size increase should decrease the total energy.

So, there is no wrong behaviour of the data that you show.

Of course, it might happen that for some specific set of sets of k points,

an increase of the number of k points leads to a systematic decrease

of the total energy, but is not a guaranteed behaviour ...

Concerning the ngkpt for a 1D crystal, you can use 1x1xN, but there is nothing

wrong using MxMxN, as both should tend to the same value when the lateral cell size 

increases, and you make a convergence study with respect to that (lateral cell size) parameter.

Of course, the real issue here is the CPU time : it might be that the lateral size to be used

is a bit larger with 1x1xN than with 2x2xN (let's say). Working only with 1x1xN is however likely more

economical. It is more simple in any case. But never forget to make a convergence study with

respect to the lateral size of your system. And never forget to test the convergence of the

property you are interested in. (Do not restrict convergence studies to absolute total energy if you are

interested in something else !).

Xavier

On 11 Apr 2006, at 06:00, Shtogun, Yaroslav wrote:

Dear Abinits users,

 

            I try to study the convergence with respect to number of k points, like in lesson 3.

 My crystal is 1D – crystal - (7,0)  carbon nanotubes (please, see my input and output in attachment).

 General if we specify many k points the GS energy will be less (from lesson 3).

So, in my calculation I specified different ngkpt:

 

ngkpt1 1 1 4      # This is a 1x1x4 grid based on the primitive vectors

ngkpt2 1 1 8

ngkpt3 1 1 12

ngkpt4 1 1 16

ngkpt5 1 1 20

ngkpt6 1 1 24

ngkpt7 1 1 32

ngkpt8 1 1 36

 

    these grids correspond  to next value of k points:

 

     ngfft       250     250      36

      nkpt1        2

      nkpt2        4

      nkpt3        6

      nkpt4        8

      nkpt5       10

      nkpt6       12

      nkpt7       16

      nkpt8       18

 

  in my out file (see attachment) the energy increase when number of k points increase - what is wrong, but I don’t understand why.

 

    etotal1  -1.5974610701E+02

    etotal2  -1.5974100236E+02

    etotal3  -1.5974076391E+02

    etotal4  -1.5974091974E+02

    etotal5  -1.5974082211E+02

    etotal6  -1.5974086755E+02

    etotal7  -1.5974084928E+02

    etotal8  -1.5974079487E+02

 

  I did one more calculation with next three ngkpt’s:  

 

ngkpt1 1 1 4      # This is a 1x1x4 grid based on the primitive vectors

ngkpt2 2 2 4

ngkpt3 4 4 4

 

      nkpt1        2

      nkpt2        2

      nkpt3        8

 

    etotal1  -1.5974610701E+02

    etotal2  -1.5974591557E+02                                                   

    etotal3  -1.5974599029E+02

 

  in this calculation I got the same dependents, the energy increase with number of k points.

   I really confuse with this results. It seems like 1x1x4 is the lowest grid but why the energy increase.

 

   Can somebody explain this strange behavior or some ideas?

 One more question – how to specify right the ngkpt for 1D crystal, is it 1x1xN or MxMxN?

 

      Thank you in advance  

<7_0_1_418.in>

<7_0_1_418.out>