Questions about ABOP to Tersoff conversion and ZnO ABOP

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1

Dear All,

Erhart and Albe have published some so called analytical bond-order potentials (ABOP) for different materials. ABOP has a form similar to Tersoff potential, thus can be converted. I have two questions about ABOPs:

(1) Following is a SiC Tersoff potential file converted from an ABOP in the LAMMPS package (file name: SiC_Erhart-Albe.tersoff):

2

Aidan might be able to advise.

Steve

3

Dear All,

Erhart and Albe have published some so called analytical bond-order
potentials (ABOP) for different materials. ABOP has a form similar to
Tersoff potential, thus can be converted. I have two questions about ABOPs:

(1) Following is a SiC Tersoff potential file converted from an ABOP in
the LAMMPS package (file name: SiC_Erhart-Albe.tersoff):

# Si and C mixture, parameterized for Tersoff potential
# this file is from ulomek(at)imm.rwth-aachen.de
# values are from Erhart/Albe - Phys Rev B, 71, 035211 (2005)

# m=n=beta=1
# R,D,gamma,c,d ->same
# lambda1=beta*sqrt(2*S)
# lambda2=beta*sqrt(2/S)
# lambda3=2*mu=0
# costheta0=-h
# A=D0/(S-1)*exp(lambda1*r0)
# B=S*D0/(S-1)*exp(lambda2*r0)

# Tersoff parameters for various elements and mixtures
# multiple entries can be added to this file, LAMMPS reads the ones it
needs
# these entries are in LAMMPS "metal" units:
# A,B = eV; lambda1,lambda2,lambda3 = 1/Angstroms; R,D = Angstroms
# other quantities are unitless

# format of a single entry (one or more lines):
# element 1, element 2, element 3,
# m, gamma, lambda3, c, d, costheta0, n,
# beta, lambda2, B, R, D, lambda1, A

C C C 1 0.11233 0 181.91 6.28433 -0.5556 1 1 1.93090093 175.426651
2 0.15 4.18426232 2019.8449

Si Si Si 1 0.114354 0 2.00494 0.81472 -0.259 1 1 1.53810493 219.521624
2.82 0.14 2.83318929 2145.7128

Si C C 1 0.011877 0 273987 180.314 -0.68 1 1.76807421 225.189481 2.4
0.2 3.26563307 1779.36144

C Si Si 1 0.011877 0 273987 180.314 -0.68 1 1 1.76807421 225.189481
2.4 0.2 3.26563307 1779.36144

Si Si C 1 0.011877 0 273987 180.314 -0.68 0 0 0 2.4 0.2 0 0

C C Si 1 0.011877 0 273987 180.314 -0.68 0 0 0 0 2.4 0.2 0 0

C Si C 1 0.11233 0 181.910 6.28433 -0.5556 0 0 0 0 2 0.15 0 0

Si C Si 1 0.114354 0 2.00494 0.81472 -0.259 0 0 0 0 2.82 0.14 0 0

I was wondering if there is an error in this potential file: according to
LAMMPS' manual, the first element should be the atom in the middle, the
second is the one connect to it, and the third one has an influence to the
bond between the first two elements. So I was wondering if the last four
lines should be:

C Si C 1 0.011877 0 273987 180.314 -0.68 0 0 0 2.4 0.2 0 0

Si C Si 1 0.011877 0 273987 180.314 -0.68 0 0 0 0 2.4 0.2 0 0

C C Si 1 0.11233 0 181.910 6.28433 -0.5556 0 0 0 0 2 0.15 0 0

Si Si C 1 0.114354 0 2.00494 0.81472 -0.259 0 0 0 0 2.82 0.14 0 0

However, according to the original paper, only the nearest neighbor is
considered. Therefore, the last four lines actually never count if a
simulation is ran under a mild temperature and pressure condition, and
writing them out is just let LAMMPS to recognize them. I am not sure if I
am correct.

Yes, you are correct. The converter is not correct in the conversion as
well.

(2) There is also a ABOP developed for ZnO (Paul Erhart *et al* 2006 *J.
Phys.: Condens. Matter* *18* 6585). Similarly, I converted it to a
Tersoff form by my self:

Zn Zn Zn 1.0 0.000043909 0.0 77.916 0.91344 -1.0 1.0 1.0 1.7965
115.16 2.85 0.2 3.2614 2258.7

O O O 1.0 0.82595 0.0 0.035608 0.046496 -0.45056 1.0 1.0
2.7733 527.65 2.45 0.2 3.8449 1388.1

O Zn Zn 1.0 0.019335 0.0 0.014108 0.084028 -0.30545 1.0 1.0
2.5136 6304.3 2.6 0.2 2.6280 7344.2

Zn O O 1.0 0.019335 0.0 0.014108 0.084028 -0.30545 1.0 1.0
2.5136 6304.3 2.6 0.2 2.6280 7344.2

O Zn O 1.0 0.019335 0.0 0.014108 0.084028 -0.30545 0 0 0 0
2.6 0.2 0 0

Zn O Zn 1.0 0.019335 0.0 0.014108 0.084028 -0.30545 0 0 0 0
2.6 0.2 0 0

Zn Zn O 1.0 0.000043909 0.0 77.916 0.91344 -1.0 0 0 0 0 2.85
0.2 0 0

O O Zn 1.0 0.82595 0.0 0.035608 0.046496 -0.45056 0 0 0 0
2.45 0.2 0 0

I hope I haven't made any stupid mistake, because I obtained similar
results of the lattice parameters and cohesive energy of wurtzite-ZnO by a
lattice statics simulation. The problem is, when I preform a MD simulation
at even 300 K, the wurtzite structure of ZnO collapsed. I was wondering if
I did something wrong or the potential itself is not suitable for MD
simulations?

The potential file looks alright to me. But nobody can know if it is a
good potential for finite temperature MD.

Ray

4

Hi Fan,

So I was wondering if the last four lines should be: Si Si C etc?

See below

However, according to the original paper, only the nearest neighbor is considered. Therefore, the last four lines actually never count if a simulation is ran under a mild temperature and pressure condition, and writing them out is just let LAMMPS to recognize them. I am not sure if I am correct.

So in other words, the original authors did not specify parameters for these combinations of atoms. In that case, there is no right answer to the first question above. Nonetheless, LAMMPS requires that these parameters be provided, so anything that does not crash the code is equally good. And if the simulation does generate Si-Si or C-C bonds, e.g by melting, then the potential is no good. Nothing LAMMPS can do about that.

The problem is, when I preform a MD simulation at even 300 K, the wurtzite structure of ZnO collapsed. I was wondering if I did something wrong or the potential itself is not suitable for MD simulations?

At best, you can only expect the potential to work for conditions that are reported in the paper. If those did not include wurtzite at 300 K, then it is possible you are suffering from a feature of the potential.

5

Hi Steve, Ray, and Aidan,

Thank you all for your kind help!!!

So it could be summarized as a somewhat negative result that Erhart’s ZnO ABOP may not suit for MD simulations. I planed to use it to compute thermal conductivity of ZnO by MD simulations. I hope other LAMMPS users who are interested in ZnO material or ABOP can check and test the potential that I posted here and tell us yours results.

Best Wishes,
Fan

6

Fan,

I wouldn’t reach this conclusion without contacting the authors of the potential first. Perhaps you can ask them if they can spot anything wrong with your potential file, too. Sometimes small differences in implementations in different codes can result in huge discrepancies in results. All in all, contact the authors would be the next reasonable step to take.

Ray

7

Hi Ray,

Yes, I agree. Actually I had contacted the author before I posted my questions here. But haven’t got response yet. I will update here if I heard from the authors.

Regards
Fan