# Calculation of x y z coordinates in CFG file

I have a question about calculation of x y z coordinates in CFG files. Below is a part of CFG file I obtained.
As showing, it shows H0 vectors and atom (Ni) data. For each Ni atom, 9 data correspond to xs,ys,zs,x,y,z,xu,yu,zu.

In my understanding, and according to atomeye web page, atom coordinates (x,y,z) can be calculated from H0 vectors and (xs,ys,zs).

=============this is from atom eye webpage (http://li.mit.edu/Archive/Graphics/A/)=================

The atom specifications are the rows above, one row for each atom, with the meaning of each column entry explained in the comments. The reduced coordinates s1,s2,s3 should be between 0 and 1. The Cartesian coordinates of the atoms can be determined from the reduced coordinates as,

`````` x  =  s1 * H(1,1)  +  s2 * H(2,1)  +  s3 * H(3,1)
y  =  s1 * H(1,2)  +  s2 * H(2,2)  +  s3 * H(3,2)
z  =  s1 * H(1,3)  +  s2 * H(2,3)  +  s3 * H(3,3)
``````

The AtomEye formula assumes the origin of the periodic cell is (0,0,0). If you subtract the coordinates of the origin from the exported data, you should recover the values calculated according to the atom formula.

Thank you for your answer. As you said, differences between calculated (x,y,z) and exported (x,y,z) was all the same in a single CFG file.

exported calculated subtraction
x y z x y z x y z
1.48795 0.225426 1.94652 1.403711 0.285961 1.948233 -0.08424 0.060535 0.001713
1.44636 4.53038 2.08057 1.362129 4.590921 2.082278 -0.08423 0.060541 0.001708
1.50273 2.33132 0.055367 1.418497 2.391854 0.057073 -0.08423 0.060534 0.001706
0.072626 2.17524 2.28348 -0.01161 2.235773 2.285189 -0.08424 0.060533 0.001709

From the result, I can conclude that calculated (x,y,z) are only shifted atom locations while maintaining relative distances between atoms unchanged. Am i right?

Also, I found out different CFG files showed different subtraction values between exported (x,y,z) and calculated (x,y,z). Can you tell me how I can find “the origin” (x,y,z) values?

There are multiple ways to set the origin in LAMMPS and multiple ways to get it. A good overview is given here:

http://lammps.sandia.gov/doc/Howto_triclinic.html

Aidan