Hessian Matrix calculation

[ali]

Hi, everyone.
I will appreciate it, if anyone answer my question.

I want to calculate the hessian matrix for a material with cubic symmetry like sc, bcc, fcc materials by vasp.4.6:

one of row of the matrix is as below:

1X 1Y 1Z 2X
1X 0.238518 0.000000 0.000000 2.425284

Some of the parameter that i used in my INCAR file:

IBRION = 5
NFREE = 2
POTIM = 0.015


I used the KPOINTS:

Line-mode
cart
0 0 0 ! gamma
0 0 1 ! X

I have some problems with the result:

1 - The sign of the value of some elements like main diagonal (1X-1X) are sensitive to choose the KPOINTS,how should i select my KPOINTS if i want to obtain all diagonal elemnts positive?

2 - I don't know why elements such as (1X-1Y or 1X-2Z, etc)
are zero?

Thanks in advance.

[panda]

Can't you just calculate it numerically? I am confused as to what you are asking, but here is some information on how to calculate the Hessian

http://www.dreamincode.net/forums/showtopic53310.htm

[physicalattraction]

1) For the calculation of the Hessian matrix, VASP moves the atoms a certain distance (POTIM) out of their equilibrium position, relaxes the electronic system, and calculates the electronic forces on the atoms. During this electronic relaxation, integration over the full k-space is required. That is why I recommend you not to use the line mode in making a k-grid, which is more suited for band structure calculations, but using a Monkhorst-Pack grid. I don't know of which size, but you should be sure that the equilibrium is converged with respect to the number of k-points before calculating the Hessian matrix.
2) The 1X-2Z element is the force on atom 2 in the z-direction if atom 1 is moved in the x-direction. You could imagine that these forces are nearly zero, depending on your system, but the fact that is is exactly zero is worrisome. Maybe it's due to the line mode KPOINTS file.

[panda]

Oh, sorry, for some reason I was thinking they wanted to do it by hand to compare with VASP, I understand the question now, thanks for clarifying.