Can lattice vectors have negative components for DFT calculations?

Question

I am using VASP for DFT calculation where the lattice vectors of POSCAR file for the hexagonal system are as follows. This I generated using VESTA

    ABC (1/1/1)
     1.0
    6.7220001221         0.0000000000         0.0000000000
   -3.3610000610         5.8214228700         0.0000000000
    0.0000000000         0.0000000000         3.4809999466
    Aa   Bb   Cc
    3    3    3
   Direct
   0.254999995         0.000000000         0.000000000
   0.000000000         0.254999995         0.000000000
   0.745000005         0.745000005         0.000000000
   0.595000029         0.000000000         0.500000000
   0.000000000         0.595000029         0.500000000
   0.404999971         0.404999971         0.500000000
   0.333333343         0.666666687         0.000000000
   0.666666687         0.333333343         0.000000000
   0.000000000         0.000000000         0.500000000

In the second line of the lattice vectors there is a negative component. My question is should i have to omit the negative sign before starting calculation? I calculated with and with out negative sign, I found the E0 value is different. Why this is so? Please help.

Answer 1

One should not change lattice vectors based on their signs if they originate from standard programs (here VESTA).

We tend to prefer simple and positive lattice vectors, but a simple cubic system with lattice vectors rotated 180 around the z axis is an equally good lattice vector (this would have negative x and y components).

From the looks of it, you might be able to only get positive lattice vectors by rotating around z axis with some angle, but again, it is only a semantical difference, not a computational one.

You should look at the geometry in a vizualizer to check that the coordinates are as expected, I would guess you would see a big difference if you remove the negative sign.

If you remove the sign, you are simulating a different geometry. I would encourage you to draw the xy plane, with and without the negative sign, then it should be pretty clear.

From a DFT developers point of view, these rotation of systems provides a handy integrity check that ensures that one have not hard-coded some limitations on the signs and orientations of lattice vectors; rigorous programs should be able to handle any lattice vectors so long as they are not parallel.