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!!!!! VERIFICATION CHECK: vc-dimer-continuity-c1 !!!!!
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Description: Determines whether a model has a continuous energy and first
derivative, i.e. belongs to the C^1 continuity class, for all
possible dimers. For a model supporting N species, there are N +
N!/(2(N-2)! distinct dimers for all possible species combinations.
(For example if N=3, there are 3+3!/2=6 dimers. If the species are
A,B,C, the 6 dimers are AA, BB, CC, AB, AC, BC.) For each dimer,
the equilibrium separation and cutoff are determined. The
continuity across the cutoff is assessed. Then an analysis is
performed to detect any discontinuities from half the equilibrium
distance to the cutoff. Although the verification check only
requires C^1 continuity to pass, continuity up to 3rd order is
checked and reported.
Author: Ellad Tadmor
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Results for KIM Model : MEAM_LAMMPS_KimKoLee_2020_NaSn__MO_329881861557_000
Supported species : Na Sn
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DIMER Na--Na
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 3.15913098e+00 -7.68351733e-01 33 67 none
Cutoff separation: 4.80000000e+00 0.00000000e+00 28 30 none
C u t o f f S m o o t h n e s s
value continuous
Energy 0.00000000e+00 yes
1st-Deriv 1.53399729e-01 ** NO **
2nd-Deriv -3.35733847e-01 ** NO **
3rd-Deriv -2.00959664e+03 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.57957,4.80000] at 323 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-NaNa.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-NaNa.dat")
==> Suspected discontinuity encountered at r=4.76956549e+00 (|T^5| = 1.19044480e+00)
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-NaNa.dat")
==> Suspected discontinuity encountered at r=4.67956549e+00 (|T^5| = 1.16936345e+00)
==> Suspected discontinuity encountered at r=4.69956549e+00 (|T^5| = 1.56945781e+00)
==> Suspected discontinuity encountered at r=4.70956549e+00 (|T^5| = 1.37273101e+00)
==> Suspected discontinuity encountered at r=4.73956549e+00 (|T^5| = 1.90633658e+00)
==> Suspected discontinuity encountered at r=4.74956549e+00 (|T^5| = 6.49936136e+00)
==> Suspected discontinuity encountered at r=4.75956549e+00 (|T^5| = 2.65064557e+01)
==> Suspected discontinuity encountered at r=4.76956549e+00 (|T^5| = 3.13931475e+02)
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-NaNa.dat")
==> Suspected discontinuity encountered at r=4.66956549e+00 (|T^5| = 2.16093127e+00)
==> Suspected discontinuity encountered at r=4.67956549e+00 (|T^5| = 2.32663749e+02)
==> Suspected discontinuity encountered at r=4.68956549e+00 (|T^5| = 7.02106532e+02)
==> Suspected discontinuity encountered at r=4.69956549e+00 (|T^5| = 6.84259219e+02)
==> Suspected discontinuity encountered at r=4.70956549e+00 (|T^5| = 2.07473774e+02)
==> Suspected discontinuity encountered at r=4.71956549e+00 (|T^5| = 3.31800099e+01)
==> Suspected discontinuity encountered at r=4.72956549e+00 (|T^5| = 7.25014732e+01)
==> Suspected discontinuity encountered at r=4.73956549e+00 (|T^5| = 2.34032015e+02)
==> Suspected discontinuity encountered at r=4.74956549e+00 (|T^5| = 8.22240784e+02)
==> Suspected discontinuity encountered at r=4.75956549e+00 (|T^5| = 4.37711798e+03)
==> Suspected discontinuity encountered at r=4.76956549e+00 (|T^5| = 2.39868321e+05)
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DIMER Sn--Sn
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 2.67587379e+00 -3.79788233e+00 32 64 none
Cutoff separation: 4.80000001e+00 0.00000000e+00 26 28 none
C u t o f f S m o o t h n e s s
value continuous
Energy 0.00000000e+00 yes
1st-Deriv 2.06476007e-01 ** NO **
2nd-Deriv -9.76672938e-01 ** NO **
3rd-Deriv 7.04959978e+03 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.33794,4.80000] at 347 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-SnSn.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-SnSn.dat")
... No discontinuities found.
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-SnSn.dat")
==> Suspected discontinuity encountered at r=4.67793689e+00 (|T^5| = 1.20935715e+00)
==> Suspected discontinuity encountered at r=4.69793689e+00 (|T^5| = 3.80866238e+00)
==> Suspected discontinuity encountered at r=4.70793689e+00 (|T^5| = 2.29919699e+00)
==> Suspected discontinuity encountered at r=4.73793689e+00 (|T^5| = 1.79282762e+00)
==> Suspected discontinuity encountered at r=4.74793689e+00 (|T^5| = 4.99624174e+00)
==> Suspected discontinuity encountered at r=4.75793689e+00 (|T^5| = 1.76490506e+01)
==> Suspected discontinuity encountered at r=4.76793689e+00 (|T^5| = 1.50602632e+02)
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-SnSn.dat")
==> Suspected discontinuity encountered at r=4.67793689e+00 (|T^5| = 3.01734833e+02)
==> Suspected discontinuity encountered at r=4.68793689e+00 (|T^5| = 8.46792919e+02)
==> Suspected discontinuity encountered at r=4.69793689e+00 (|T^5| = 6.96809513e+02)
==> Suspected discontinuity encountered at r=4.70793689e+00 (|T^5| = 9.44855169e+01)
==> Suspected discontinuity encountered at r=4.71793689e+00 (|T^5| = 1.05128667e+02)
==> Suspected discontinuity encountered at r=4.72793689e+00 (|T^5| = 6.09386731e+01)
==> Suspected discontinuity encountered at r=4.73793689e+00 (|T^5| = 1.71488223e+02)
==> Suspected discontinuity encountered at r=4.74793689e+00 (|T^5| = 5.55246787e+02)
==> Suspected discontinuity encountered at r=4.75793689e+00 (|T^5| = 2.62734969e+03)
==> Suspected discontinuity encountered at r=4.76793689e+00 (|T^5| = 6.24460669e+04)
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DIMER Na--Sn
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E n e r g y E x t r e m a
distance energy #iter #fn-calls warnings
Equilibrium separation: 2.70249250e+00 -2.02073039e+00 32 65 none
Cutoff separation: 4.80000000e+00 -3.15120811e-16 26 28 none
C u t o f f S m o o t h n e s s
value continuous
Energy -3.15120811e-16 yes
1st-Deriv 2.33285591e-01 ** NO **
2nd-Deriv 6.04516168e+02 ** NO **
3rd-Deriv 1.12978586e+04 ** NO **
C o n t i n u i t y
Checking continuity for r = [1.35125,4.80000] at 345 points (Delta r = 0.01000)
Local edge detection based on a normalized 5th-order local difference formula T^5 is used to determine the presence of discontinuities. The tolerance is |T^5|>1.00000.
(For details see Anne Gelb and Eitan Tadmor, J. Sci. Comp., 28:279-306, 2006.)
Checking Energy (energy vs. distance in file "dimer-energy-NaSn.dat")
... No discontinuities found.
Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-NaSn.dat")
... No discontinuities found.
Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-NaSn.dat")
==> Suspected discontinuity encountered at r=4.68124625e+00 (|T^5| = 2.21668108e+00)
==> Suspected discontinuity encountered at r=4.69124625e+00 (|T^5| = 3.17829736e+00)
==> Suspected discontinuity encountered at r=4.71124625e+00 (|T^5| = 1.42727962e+00)
==> Suspected discontinuity encountered at r=4.74124625e+00 (|T^5| = 3.27642259e+00)
==> Suspected discontinuity encountered at r=4.75124625e+00 (|T^5| = 1.11999319e+01)
==> Suspected discontinuity encountered at r=4.76124625e+00 (|T^5| = 4.90641039e+01)
Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-NaSn.dat")
==> Suspected discontinuity encountered at r=4.67124625e+00 (|T^5| = 4.73218330e+01)
==> Suspected discontinuity encountered at r=4.68124625e+00 (|T^5| = 1.83526274e+02)
==> Suspected discontinuity encountered at r=4.69124625e+00 (|T^5| = 8.46703636e+02)
==> Suspected discontinuity encountered at r=4.70124625e+00 (|T^5| = 9.51668447e+02)
==> Suspected discontinuity encountered at r=4.71124625e+00 (|T^5| = 3.45566476e+02)
==> Suspected discontinuity encountered at r=4.72124625e+00 (|T^5| = 3.53734783e+01)
==> Suspected discontinuity encountered at r=4.73124625e+00 (|T^5| = 1.23095800e+02)
==> Suspected discontinuity encountered at r=4.74124625e+00 (|T^5| = 3.96003465e+02)
==> Suspected discontinuity encountered at r=4.75124625e+00 (|T^5| = 1.44741877e+03)
==> Suspected discontinuity encountered at r=4.76124625e+00 (|T^5| = 8.83322547e+03)
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SUMMARY of Model Continuity Results Across All Dimers:
continuous
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Energy yes
1st-Deriv ** NO **
2nd-Deriv ** NO **
3rd-Deriv ** NO **
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Continuity must be C^1 or higher to pass this verification check.
Grade: F
Comment: The model is C^0 continuous. This means that the model has continuous energy, but a discontinuous first derivative.