I am writing an implementation of REBO from the Brenner 2002 paper, and am comparing against LAMMPS as a test. During the implementation, a number of questions have come up that may be able to be answered by people who better understand the history of REBO and AIREBO.
Fortunately, I’ve managed to find the answers to at least two of my concerns in advance (the factors of 1/2 in piRC: https://lammps.sandia.gov/threads/msg20308.html, and the changes in PCC(1, 1) and PCC(0, 2): https://github.com/lammps/lammps/pull/986). But many questions remain:
(1). REBO and AIREBO define different fitting parameters for the g splines, particularly for hydrogen atoms. AIREBO also adds terms to lambda_ijk (Stuart, A14). In both cases, LAMMPS uses the AIREBO values for both REBO and AIREBO. Is this done on purpose?
(2). In REBO, the coordination numbers used in the g, T, and piRC splines are NiX = sum of all weights from site i to atoms of type X (e.g. NiC = 3 in graphite). AIREBO instead uses NijX, which does not count the bond for the current interaction (e.g. NijC = 2 in graphite). Yet both papers use the same reference values for them just about everywhere (e.g. both define the transition range for the g spline as N = 3.2 to 3.7).
LAMMPS always uses NijX regardless of the potential. Given how the two formulations are irreconcilable, I assume this was simply an error in Brenner (2002)?
(3). There’s a bunch of madness surrounding FCC (a.k.a. piCC) even once the scale factor of 2 in Brenner is taken into account, including one thing that appears to be wrong in both papers as well as LAMMPS.
In Brenner (2002) Table 4, the following values appear for the FCC spline: (comments from the table)
FCC(2, 2, 2) 0.02200000 Benzene
FCC(2, 2, 3) 0.03970587 Average
FCC(2, 2, 4) 0.03308822 from
FCC(2, 2, 5) 0.02647058 difference
FCC(2, 2, 6) 0.01985293 F(2, 2, 2)
FCC(2, 2, 7) 0.01323529 to
FCC(2, 2, 8) 0.00661764 difference
FCC(2, 2, 9) 0.00000000 F(2, 2, 9)
dFCC(2, 2, 4–8)/dk = -0.006618
FCC(1, 2, 3) = -0.0200000000 C6H5
FCC(1, 2, 4) = -0.0233778774 Average from
FCC(1, 2, 5) = -0.0267557548 F(1,2,3) to F(1,2,6)
FCC(1, 2, 6–9) = -0.030133632 Graphite vacancy
dFCC(1, 2, 4–5)/dk = -0.020044
The AIREBO paper and LAMMPS both replicate these identically. (fixing the factor of 2, of course)
(3a): In the first group, the comment contradicts the values. Only elements from F(2,2,3)-F(2,2,9) follow a line equation; F(2,2,2) is not part of that line. Because the range of k used in dFCC/dk is consistent with a line from (2,2,3)-(2,2,9), I assume the the comment is wrong and that F(2,2,3) was obtained from a fitting species?
(3b): In the second group, F(1,2,3)-F(1,2,6) does follow a line equation, but the value written for dFCC/dk is not even close to the actual slope of the line. (-0.0033779 expected versus -0.020044 written). Has anyone brought this up before?
Thank you for your time,