!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-dimer-continuity-c1 !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! 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 ----------------------------------------------------------------------------------------------------- Results for KIM Model : Tersoff_LAMMPS_ZhangNguyen_2021_MoSe__MO_152208847456_001 Supported species : Mo Se ----------------------------------------------------------------------------------------------------- DIMER Mo--Mo ----------------------------------------------------------------------------------------------------- E n e r g y E x t r e m a distance energy #iter #fn-calls warnings Equilibrium separation: 2.53050748e+00 -3.30964407e+00 32 64 none Cutoff separation: 4.67999999e+00 -1.49921170e-16 26 28 none C u t o f f S m o o t h n e s s value continuous Energy -1.49921170e-16 yes 1st-Deriv 1.85291403e-08 yes 2nd-Deriv -1.28189600e+00 ** NO ** 3rd-Deriv 1.89096855e+00 ** NO ** C o n t i n u i t y Checking continuity for r = [1.26525,4.68000] at 342 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-MoMo.dat") ... No discontinuities found. Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-MoMo.dat") ... No discontinuities found. Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-MoMo.dat") ==> Suspected discontinuity encountered at r=2.38525374e+00 (|T^5| = 2.02947595e+00) ==> Suspected discontinuity encountered at r=2.39525374e+00 (|T^5| = 3.03092201e+00) ==> Suspected discontinuity encountered at r=2.40525374e+00 (|T^5| = 2.01068393e+00) Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-MoMo.dat") ==> Suspected discontinuity encountered at r=2.38525374e+00 (|T^5| = 3.61161405e+00) ==> Suspected discontinuity encountered at r=2.39525374e+00 (|T^5| = 5.65409728e+00) ==> Suspected discontinuity encountered at r=2.40525374e+00 (|T^5| = 3.93445422e+00) ==> Suspected discontinuity encountered at r=2.41525374e+00 (|T^5| = 1.02687171e+00) ----------------------------------------------------------------------------------------------------- DIMER Se--Se ----------------------------------------------------------------------------------------------------- E n e r g y E x t r e m a distance energy #iter #fn-calls warnings Equilibrium separation: 2.13919439e+00 -4.27879834e+00 31 63 none Cutoff separation: 4.07535742e+00 -2.32626380e-16 25 27 none C u t o f f S m o o t h n e s s value continuous Energy -2.32626380e-16 yes 1st-Deriv 8.81050102e-08 yes 2nd-Deriv -2.03014750e+01 ** NO ** 3rd-Deriv 8.10672106e+01 ** NO ** C o n t i n u i t y Checking continuity for r = [1.06960,4.07536] at 301 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-SeSe.dat") ... No discontinuities found. Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-SeSe.dat") ... No discontinuities found. Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-SeSe.dat") ==> Suspected discontinuity encountered at r=3.68959720e+00 (|T^5| = 5.40185164e+00) ==> Suspected discontinuity encountered at r=3.69959720e+00 (|T^5| = 2.18427112e+01) ==> Suspected discontinuity encountered at r=3.70959720e+00 (|T^5| = 3.30834403e+01) ==> Suspected discontinuity encountered at r=3.71959720e+00 (|T^5| = 2.22431742e+01) ==> Suspected discontinuity encountered at r=3.72959720e+00 (|T^5| = 5.60075672e+00) Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-SeSe.dat") ==> Suspected discontinuity encountered at r=3.68959720e+00 (|T^5| = 8.83872479e+02) ==> Suspected discontinuity encountered at r=3.69959720e+00 (|T^5| = 4.44461996e+03) ==> Suspected discontinuity encountered at r=3.70959720e+00 (|T^5| = 8.93654265e+03) ==> Suspected discontinuity encountered at r=3.71959720e+00 (|T^5| = 8.98032646e+03) ==> Suspected discontinuity encountered at r=3.72959720e+00 (|T^5| = 4.51015726e+03) ==> Suspected discontinuity encountered at r=3.73959720e+00 (|T^5| = 9.05628897e+02) ----------------------------------------------------------------------------------------------------- DIMER Mo--Se ----------------------------------------------------------------------------------------------------- E n e r g y E x t r e m a distance energy #iter #fn-calls warnings Equilibrium separation: 1.20442222e+00 -2.49656052e+02 27 54 none Cutoff separation: 4.10224410e+00 -8.01459727e-15 27 29 none C u t o f f S m o o t h n e s s value continuous Energy -8.01459727e-15 yes 1st-Deriv 2.09328941e-06 ** NO ** 2nd-Deriv -8.17934671e+02 ** NO ** 3rd-Deriv 2.06646841e+03 ** NO ** C o n t i n u i t y Checking continuity for r = [0.60221,4.10224] at 351 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-MoSe.dat") ... No discontinuities found. Checking 1st-Deriv (1st-deriv vs. distance in file "dimer-energy-deriv-1-MoSe.dat") ==> Suspected discontinuity encountered at r=3.66221111e+00 (|T^5| = 1.41104786e+00) ==> Suspected discontinuity encountered at r=3.67221111e+00 (|T^5| = 3.77545808e+00) ==> Suspected discontinuity encountered at r=3.68221111e+00 (|T^5| = 2.79432924e+00) Checking 2nd-Deriv (2nd-deriv vs. distance in file "dimer-energy-deriv-2-MoSe.dat") ==> Suspected discontinuity encountered at r=3.66221111e+00 (|T^5| = 1.89847761e+02) ==> Suspected discontinuity encountered at r=3.67221111e+00 (|T^5| = 7.65497628e+02) ==> Suspected discontinuity encountered at r=3.68221111e+00 (|T^5| = 1.15647670e+03) ==> Suspected discontinuity encountered at r=3.69221111e+00 (|T^5| = 7.75796141e+02) ==> Suspected discontinuity encountered at r=3.70221111e+00 (|T^5| = 1.94973351e+02) ==> Suspected discontinuity encountered at r=4.07221111e+00 (|T^5| = 6.36849520e+01) Checking 3rd-Deriv (3rd-deriv vs. distance in file "dimer-energy-deriv-3-MoSe.dat") ==> Suspected discontinuity encountered at r=3.66221111e+00 (|T^5| = 5.62434130e+02) ==> Suspected discontinuity encountered at r=3.67221111e+00 (|T^5| = 2.15415040e+03) ==> Suspected discontinuity encountered at r=3.68221111e+00 (|T^5| = 3.08251728e+03) ==> Suspected discontinuity encountered at r=3.69221111e+00 (|T^5| = 1.95274478e+03) ==> Suspected discontinuity encountered at r=3.70221111e+00 (|T^5| = 4.61982520e+02) ==> Suspected discontinuity encountered at r=4.07221111e+00 (|T^5| = 7.84267365e+04) ===================================================================================================== SUMMARY of Model Continuity Results Across All Dimers: continuous ----------------------------- Energy yes 1st-Deriv ** NO ** 2nd-Deriv ** NO ** 3rd-Deriv ** NO ** ===================================================================================================== 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.