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add one more tabulation example showing how to smoothly replace part of a function in a different potential

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Axel Kohlmeyer
2022-12-19 12:13:25 -05:00
parent 91325d49c5
commit bc8812c391
2 changed files with 69 additions and 9 deletions
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19
tools/tabulate/README.md
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@ -16,15 +16,16 @@ force will be determined through numerical differentiation.
Please see the individual tabulation scripts in this folder for examples:
| ------------------------------|----------------------------------------------------------------------------|
| File | Description |
| ------------------------------|----------------------------------------------------------------------------|
| pair_lj_tabulate.py | creates two Lennard-Jones pair potential tables with different parameters |
| bond_morse_tabulate.py | creates a table for a Morse bond potential table |
| angle_harmonic_tabulate.py | creates a table for a harmonic angle potential table |
| dihedral_harmonic_tabulate.py | creates a table for a harmonic dihedral potential table |
| pair_hybrid_tabulate.py | creates a Morse/Lennard-Jones hybrid potential table with smooth switching |
| ------------------------------|----------------------------------------------------------------------------|
| ------------------------------|-------------------------------------------------------------------------------|
| File | Description |
| ------------------------------|-------------------------------------------------------------------------------|
| pair_lj_tabulate.py | creates two Lennard-Jones pair potential tables with different parameters |
| bond_morse_tabulate.py | creates a table for a Morse bond potential table |
| angle_harmonic_tabulate.py | creates a table for a harmonic angle potential table |
| dihedral_harmonic_tabulate.py | creates a table for a harmonic dihedral potential table |
| pair_hybrid_tabulate.py | creates a Morse/Lennard-Jones hybrid potential table with smooth switching |
| pair_zbladd_tabulate.py | creates a table for hybrid/overlay to use ZBL repulsion with an EAM potential |
| ------------------------------|-------------------------------------------------------------------------------|
Common command line flags:

59
tools/tabulate/pair_zbladd_tabulate.py Executable file
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@ -0,0 +1,59 @@
#!/usr/bin/env python
from tabulate import PairTabulate
################################################################################
import math
# this table contains a correction to be added to the Al_zhou.eam.alloy potential via hybrid/overlay
# the purpose is to smoothly replace the original pairwise repulsion with the ZBL potential.
# the combined potential switches from ZBL to EAM w/o embedding and then subtracts the full EAM term.
# this way the table can be added to the eam/alloy pair style via hybrid/overlay
# due to using a Fermi-like switching function (tanh()) there are no discontinuities in energy or force
def eam_2body(r):
biga = 0.251519 # metal units
bigb = 0.313394 # metal units
rzero = 2.886166
alpha = 6.942419
beta = 3.702623
lamda = 0.790264
kappa = 0.395132
return (biga * math.exp(-alpha * (r/rzero - 1.0))) / (1.0 + math.pow(r/rzero - kappa, 20)) \
- (bigb * math.exp(-beta * (r/rzero - 1.0))) / (1.0 + math.pow(r/rzero - lamda, 20))
def zbl_energy(r):
qqr2e = 14.399645 # for metal units
pzbl = 0.23
a0 = 0.46850
c1 = 0.02817
c2 = 0.28022
c3 = 0.50986
c4 = 0.18175
d1 = 0.20162
d2 = 0.40290
d3 = 0.94229
d4 = 3.19980
zi = 13.0 # aluminium
zj = 13.0 # aluminium
prefactor = zi * zj * qqr2e / r
rbya = r * (math.pow(zi, pzbl) + math.pow(zj, pzbl)) / a0
f = prefactor * (c4*math.exp(-d4*rbya) + c3*math.exp(-d3*rbya) \
+ c2*math.exp(-d2*rbya) + c1*math.exp(-d1*rbya))
return f
def combined(r):
rmid = 2.886166
switch_on = 0.5*(math.tanh(math.exp(1.0)*(r - rmid))+1.0)
return (1.0-switch_on)*zbl_energy(r) + (switch_on-1.0)*eam_2body(r)
################################################################################
if __name__ == "__main__":
ptable = PairTabulate(combined, units='metal', \
comment='Correct Al_zhou EAM with ZBL using hybrid/overlay')
ptable.run('AL_EAM_ZBL_CORR')
# NOTE use/create table with an outer cutoff of 10.1025 to match the EAM potential cutoff.