# [lammps-users] build a triclinic box

Dear all,

1. I want to build a triclinic box. In PDB format, it is described as
CRYST1 13.264 29.721 23.568 91.71 88.11 123.45
It denotes LA LB LC a b r accordingly.

The vectors for xyz are

### z 0.77779 -0.329605 23.568

1. In the command of read data, it uses the following to describe a box:
· xlo xhi = simulation box boundaries in x dimension
· ylo yhi = simulation box boundaries in y dimension
· zlo zhi = simulation box boundaries in z dimension
· xy xz yz = simulation box tilt factors for triclinic domain

So I set as follow:

0 13.264 xlo xhi
0 29.721 ylo yhi
0 23.568 zlo zhi
-16.3825 0.7729 -0.329395 xy xz yz #no npt for triclinic in Lammps

The tilt factors are set like these because the manual (page 543) say 3 edge vectors starting from the origin given by a =(xhi−xlo,0,0); b = (xy,yhi−ylo,0); c = (xz,yz,zhi−zlo). Please point out the errors if there is any. Thanks

1. Two questions.
3.1 volume. Since the volume is independent to the tilt factors ( manual page 225 ) and equal to xyz, then the final volume 9290.96 is quite bigger than that in PDB format 7747.48. I can not understand why the tilt factor do not change the volume.
3.2 skew the box less than half box. Just as showd in my case, the big tilt angle 123.45 make the xy as -16.3825. If I treat it with -16.3825+ 13.264 (LA) = -6.37. It induces a totally different box then. It is diffult to learn from the example of the manual as bellow:
For example, if xlo = 2 and xhi = 12, then the x box length is 10 and the xy tilt factor must be between −5 and 5.
Similarly, both xz and yz must be between −(xhi−xlo)/2 and +(yhi−ylo)/2. Note that this is not a limitation, since
if the maximum tilt factor is 5 (as in this example), then configurations with tilt = …, −15, −5, 5, 15, 25, … are all equivalent. How are they equivalent?

Any comments will be highlly appreciated. Thanks a lot.

Best wishes,
Yours Kitty.

I can not understand why the tilt factor do not change the volume.

Think of a 2d example. Start with an orthogonal rectangle. It's area
is the sum of 2 triangles. For a triangle the area is base times height.
If you tilt the rectanangle (parallelogram), the way the tilt
factors are defined in LAMMPS, then neither the base or height
changes for either triangle. So the area is preserved. Same for volume
in 3d.

Steve