# [lammps-users] The tricubic spline used in AIREBO potential

Dear lammps authors and users

I am learning the airebo potential from the codes and the reference.
I found that the tricubic spline for conjugate term are inconsistent
in the two reference of the potential. Stuart et al. 2000, and
Brenner et al. 2002.

I realized that lammps follows Stuart's paper. And I have another
piece of code that follows Brenner's paper. I print out both splines
and summarize some of the discrepancies below
The discrepancy can also be easily observed in TABLE IX of Stuart and
Table 4 in Brenner

a) Most of the data are different by a factor of 2 in the two papers.
eg. i=1, j=2, k=4 Stuart: F=-0.0011689 Fx=0 Fy=0 Fz=-0.010022
Brenner: F=-0.0233778774 Fx=0 Fy=0 Fz=-0.020044

b) Some of the data F are different by a factor of 2, Fx, Fy, or Fz are
same.
eg. i=2, j=3, k=8 Staurt: F=-0.022355 Fx=0.062418 Fy=0 Fz=0
Brenner: F=-0.044709383 Fx=0.062418 Fy=0 Fz=0

c) if i or j > 3
eg. Brenner F(4 2 4)= F(3 2 4) = -0.04771
Staurt F(4 2 4)=0 F(3 2 4) = -0.022355

d) there are some wired values when i & j >3 in Starurt spline
eg. F(4.5 3.5 5)=4.09563 Fx(4.5 3.5 5)=3.18356 Fy=-12.2869 Fz=0

The discrepancy in spline introduce difference when simulate over
coordinated carbon structures. Can someone tell me if these
discrepancies has already been take cared in lammps or not? Can anyone
comments on the two reference works? I think Staurt is one of the
co-author in Brenner's paper, so they should use the same data set.

Thanks
Haibin

Haibin Chen Ph.D.
Mechanical Engineering Dept
Carnegie Mellon University
Pittsburgh, Pa, 15213