!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-forces-numerical-derivative !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Comparison of the analytical forces obtained from the model with forces computed by numerical differentiation using Richardson extrapolation for a randomly distorted non-periodic structure based off the equilibrium face-centered cubic (fcc) structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ----------------------------------------------------------------------------------------------------- Results for KIM Model : MEAM_LAMMPS_OhSeolLee_2020_CoTi__MO_862371677648_002 Supported species : Co Ti random seed = 13 perturbation amplitude = 0.250 number unit cells per side = 2 ----------------------------------------------------------------------------------------------------- Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Co | a0 = 3.5365657806396484 | (Configuration in file "config-Co.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Co 1 4.844058390686214e-01 4.844058390637883e-01 4.83308e-12 5.59233e-11 2 -1.873245057955659e-01 -1.873245058009179e-01 5.35205e-12 9.68947e-12 3 -3.970657339793174e-01 -3.970657339776764e-01 1.64102e-12 7.81718e-10 ----------------------------------------------------------------------------------------------------- 2 Co 1 -1.152455005524658e+00 -1.152455005529554e+00 4.89653e-12 7.44955e-11 2 1.019928950652365e-01 1.019928951153757e-01 5.01392e-11 1.59587e-10 3 1.284631084677859e+00 1.284631084695258e+00 1.73994e-11 1.24431e-10 ----------------------------------------------------------------------------------------------------- 3 Co 1 5.503008864863501e-01 5.503008864945882e-01 8.23808e-12 8.95627e-11 2 9.701145897511383e-01 9.701145897332071e-01 1.79312e-11 6.53193e-11 3 -9.430536420917450e-01 -9.430536421308549e-01 3.91098e-11 1.35599e-09 ----------------------------------------------------------------------------------------------------- 4 Co 1 1.834598281329793e+00 1.834598281266255e+00 6.35378e-11 5.27237e-10 2 3.372187363117622e-01 3.372187363242436e-01 1.24814e-11 1.61584e-10 3 5.131379645887562e-01 5.131379645938936e-01 5.13745e-12 5.80866e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 -1.832254548413368e-01 -1.832254548512709e-01 9.93403e-12 3.25292e-10 2 3.324701399378128e-01 3.324701399537235e-01 1.59108e-11 1.19706e-10 3 9.781914450427963e-01 9.781914450522976e-01 9.50129e-12 1.65207e-10 ----------------------------------------------------------------------------------------------------- 6 Co 1 -3.598660328028200e-01 -3.598660327837192e-01 1.91008e-11 1.87963e-10 2 3.927276298506535e-01 3.927276298393842e-01 1.12693e-11 3.29861e-11 3 2.864370881458561e-01 2.864370881390878e-01 6.76831e-12 2.57173e-09 * ----------------------------------------------------------------------------------------------------- 7 Co 1 1.758394584657615e+00 1.758394584648776e+00 8.83937e-12 5.19154e-11 2 -2.208160193143350e+00 -2.208160193110578e+00 3.27725e-11 4.95075e-11 3 -2.513199143001026e+00 -2.513199143006768e+00 5.74163e-12 1.40200e-10 ----------------------------------------------------------------------------------------------------- 8 Co 1 -1.263278743083922e+00 -1.263278743089895e+00 5.97344e-12 1.75466e-10 2 -1.443018643242862e+00 -1.443018643214871e+00 2.79912e-11 2.04590e-10 3 -1.441599684102383e+00 -1.441599684102817e+00 4.33875e-13 7.12137e-11 ----------------------------------------------------------------------------------------------------- 9 Co 1 3.358340617557479e-01 3.358340617631161e-01 7.36822e-12 8.15202e-10 2 -5.935568799967006e-01 -5.935568800097234e-01 1.30228e-11 5.55503e-11 3 6.227125050849731e-01 6.227125050880400e-01 3.06688e-12 5.09013e-11 ----------------------------------------------------------------------------------------------------- 10 Co 1 -1.928097438657534e+00 -1.928097438645189e+00 1.23455e-11 3.11297e-09 * 2 -1.757324093967954e-01 -1.757324094009798e-01 4.18440e-12 2.06988e-10 3 -1.712138283716773e+00 -1.712138283728045e+00 1.12719e-11 5.36018e-11 ----------------------------------------------------------------------------------------------------- 11 Co 1 -8.232197838509057e-01 -8.232197838160089e-01 3.48968e-11 3.64062e-10 2 4.327613171180937e-01 4.327613171291920e-01 1.10982e-11 3.16586e-10 3 1.784153897331812e-01 1.784153897255142e-01 7.66701e-12 5.24804e-10 ----------------------------------------------------------------------------------------------------- 12 Co 1 7.263567582440373e-01 7.263567582931406e-01 4.91033e-11 6.20260e-09 * 2 3.272027902610394e-02 3.272027902636110e-02 2.57155e-13 1.16677e-09 3 2.196154828511248e-02 2.196154827785815e-02 7.25433e-12 3.38562e-11 ----------------------------------------------------------------------------------------------------- 13 Co 1 -1.445520878776114e+00 -1.445520878772999e+00 3.11506e-12 1.81348e-10 2 -1.580038778336274e+00 -1.580038778358446e+00 2.21716e-11 1.57330e-10 3 -2.319119152355507e+00 -2.319119152342565e+00 1.29421e-11 2.00747e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 2.895378415002587e-01 2.895378415007824e-01 5.23637e-13 2.16957e-11 2 6.937910161883549e-01 6.937910161870052e-01 1.34970e-12 6.20514e-11 3 -1.523195136846668e-01 -1.523195137165357e-01 3.18689e-11 1.06910e-10 ----------------------------------------------------------------------------------------------------- 15 Co 1 2.438926872216976e+00 2.438926872313394e+00 9.64180e-11 7.74596e-10 2 -1.795405448055932e+00 -1.795405448171613e+00 1.15682e-10 4.34770e-10 3 3.203789659187067e-01 3.203789659291080e-01 1.04012e-11 3.33646e-10 ----------------------------------------------------------------------------------------------------- 16 Co 1 1.483410853492960e+00 1.483410853493609e+00 6.48592e-13 3.09297e-10 2 1.556796386519574e+00 1.556796386503342e+00 1.62323e-11 2.10426e-10 3 2.302480735324203e+00 2.302480735309010e+00 1.51932e-11 9.16030e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 1.557184959193729e-02 1.557184960500193e-02 1.30646e-11 4.04084e-11 2 5.823672422230110e-01 5.823672422429365e-01 1.99255e-11 3.97034e-11 3 -5.359083321886661e-01 -5.359083322643644e-01 7.56983e-11 1.48905e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 -3.835184707051285e-01 -3.835184707153534e-01 1.02249e-11 4.22539e-10 2 2.773427162073621e-01 2.773427162635749e-01 5.62128e-11 7.07777e-09 * 3 3.472977211414079e-01 3.472977211233518e-01 1.80562e-11 4.69742e-10 ----------------------------------------------------------------------------------------------------- 19 Co 1 1.608695740460704e+00 1.608695740475991e+00 1.52867e-11 5.90727e-11 2 1.834463938230435e-01 1.834463938298724e-01 6.82895e-12 3.29781e-09 * 3 6.490143840768396e-02 6.490143839972287e-02 7.96109e-12 2.07239e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 1.803277531773012e-01 1.803277531959749e-01 1.86737e-11 2.29133e-10 2 8.736398447938487e-01 8.736398447731367e-01 2.07120e-11 6.94095e-11 3 -4.663883243250440e-01 -4.663883243521050e-01 2.70610e-11 3.57159e-09 * ----------------------------------------------------------------------------------------------------- 21 Co 1 -1.781296378174930e+00 -1.781296378199071e+00 2.41411e-11 2.35535e-10 2 7.919283698900983e-01 7.919283698805314e-01 9.56690e-12 1.99186e-10 3 1.507948897055873e+00 1.507948897089143e+00 3.32705e-11 2.71869e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 -6.872567542368390e-01 -6.872567542075428e-01 2.92961e-11 3.86848e-10 2 1.704518791349711e+00 1.704518791316765e+00 3.29456e-11 1.12529e-10 3 2.065459881550363e+00 2.065459881485497e+00 6.48663e-11 1.33256e-09 ----------------------------------------------------------------------------------------------------- 23 Co 1 -5.283018796225778e-01 -5.283018796654618e-01 4.28840e-11 3.04461e-10 2 4.352243275442043e-01 4.352243274924975e-01 5.17067e-11 1.17323e-10 3 -3.290485484926066e-01 -3.290485484599363e-01 3.26703e-11 5.47403e-10 ----------------------------------------------------------------------------------------------------- 24 Co 1 4.791290534376360e-01 4.791290534408263e-01 3.19034e-12 3.67025e-10 2 -9.981400484543620e-02 -9.981400468850654e-02 1.56930e-10 4.74970e-09 * 3 -1.482946643358400e+00 -1.482946643367105e+00 8.70481e-12 2.22252e-09 * ----------------------------------------------------------------------------------------------------- 25 Co 1 -1.292576302144441e+00 -1.292576302150058e+00 5.61706e-12 7.43507e-09 * 2 -8.652067828684505e-01 -8.652067828510035e-01 1.74470e-11 6.42156e-11 3 4.971907244293135e-01 4.971907244629118e-01 3.35983e-11 1.22557e-08 * ----------------------------------------------------------------------------------------------------- 26 Co 1 -1.871450202538286e-01 -1.871450203032860e-01 4.94575e-11 2.17346e-09 * 2 2.568661273963114e-01 2.568661273720786e-01 2.42328e-11 6.32215e-11 3 -5.392396478833059e-01 -5.392396477311939e-01 1.52112e-10 3.80378e-10 ----------------------------------------------------------------------------------------------------- 27 Co 1 1.290261294830110e+00 1.290261294823762e+00 6.34759e-12 2.56992e-10 2 -3.142674027308471e+00 -3.142674027327020e+00 1.85483e-11 4.34426e-11 3 -6.757841762571805e-02 -6.757841761227884e-02 1.34392e-11 2.73463e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 -1.124422587498330e+00 -1.124422587506591e+00 8.26028e-12 4.66229e-11 2 1.336356641156548e+00 1.336356641139063e+00 1.74856e-11 1.73299e-09 3 -4.805835505207574e-01 -4.805835505252276e-01 4.47020e-12 3.36282e-09 * ----------------------------------------------------------------------------------------------------- 29 Co 1 -6.689013198848318e-01 -6.689013198800607e-01 4.77107e-12 2.39758e-10 2 4.867466371969610e-01 4.867466371935782e-01 3.38274e-12 3.50075e-10 3 2.018824185133034e+00 2.018824185258544e+00 1.25511e-10 8.84587e-10 ----------------------------------------------------------------------------------------------------- 30 Co 1 -4.239734965087219e-01 -4.239734964583229e-01 5.03990e-11 2.30309e-10 2 1.257423313036651e+00 1.257423312988802e+00 4.78495e-11 2.85660e-10 3 1.175290873043559e+00 1.175290873011758e+00 3.18008e-11 2.84736e-10 ----------------------------------------------------------------------------------------------------- 31 Co 1 -6.931063011468737e-01 -6.931063011076259e-01 3.92477e-11 8.71019e-11 2 -9.306041041108645e-01 -9.306041041382208e-01 2.73563e-11 1.22476e-10 3 -4.433915156838137e-01 -4.433915156840890e-01 2.75224e-13 4.29704e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 1.450410177463741e+00 1.450410177475040e+00 1.12985e-11 8.52822e-10 2 -1.491761728577898e-02 -1.491761726262549e-02 2.31535e-11 3.67079e-10 3 -3.616803145529472e-01 -3.616803145539877e-01 1.04050e-12 2.90424e-10 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 32, direction = 2: |F_model - F_numer| error = ----------------------- = 1.55209e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MONOATOMIC STRUCTURE -- Species = Ti | a0 = 4.133002281188965 | (Configuration in file "config-Ti.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 4.124626996176164e-01 4.124626996085513e-01 9.06514e-12 3.59449e-11 2 -2.065383690971361e-01 -2.065383691003665e-01 3.23042e-12 1.96289e-10 3 2.821056026706005e-01 2.821056026896480e-01 1.90475e-11 1.77611e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.964885858563943e-01 -9.964885858521370e-01 4.25737e-12 1.32021e-10 2 -3.193928173175093e-01 -3.193928173420244e-01 2.45151e-11 5.17619e-11 3 8.241208739728962e-01 8.241208739660639e-01 6.83231e-12 1.27698e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -3.489588645853905e-01 -3.489588645767596e-01 8.63087e-12 3.76179e-11 2 1.111388905545804e+00 1.111388905554568e+00 8.76388e-12 7.15139e-11 3 -7.279716099966461e-01 -7.279716099940478e-01 2.59837e-12 7.46969e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.136102715022786e-01 7.136102715035522e-01 1.27354e-12 9.14996e-11 2 -9.805613977743068e-01 -9.805613977650324e-01 9.27447e-12 1.46121e-10 3 -8.997347606838652e-03 -8.997347561589679e-03 4.52490e-11 7.62490e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -9.567274438360384e-01 -9.567274438445227e-01 8.48432e-12 2.69286e-11 2 -1.030113350155971e-01 -1.030113350076960e-01 7.90114e-12 3.10811e-11 3 -6.800365129424554e-02 -6.800365130373555e-02 9.49001e-12 8.98780e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -1.377242739110670e-01 -1.377242739039435e-01 7.12344e-12 6.70440e-11 2 3.171120446076195e-01 3.171120446281013e-01 2.04818e-11 1.87000e-10 3 2.008054435242614e-01 2.008054435385949e-01 1.43335e-11 9.68675e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.088263633705479e-01 2.088263633688652e-01 1.68268e-12 3.67181e-10 2 7.117526109339389e-02 7.117526105967054e-02 3.37234e-11 1.34499e-10 3 5.673077932147456e-01 5.673077932010854e-01 1.36602e-11 1.15462e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -4.260557521607466e-02 -4.260557520535146e-02 1.07232e-11 2.41518e-10 2 5.280624304288153e-01 5.280624304338676e-01 5.05229e-12 6.09206e-10 3 -2.341060467195727e+00 -2.341060467186757e+00 8.96971e-12 2.35620e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.891272094828655e-01 -1.891272094854941e-01 2.62865e-12 1.64950e-10 2 -3.315714494895720e-01 -3.315714494908310e-01 1.25905e-12 6.83846e-10 3 -2.376322612048486e-01 -2.376322612048278e-01 2.07612e-14 5.36175e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.166055449248622e+00 1.166055449265897e+00 1.72746e-11 7.57949e-11 2 3.229374025268053e-02 3.229374023961930e-02 1.30612e-11 1.69138e-10 3 2.229090397467477e-01 2.229090397439181e-01 2.82963e-12 5.48463e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.229639105512995e+00 1.229639105540338e+00 2.73428e-11 2.27980e-10 2 7.895906608170469e-01 7.895906608130927e-01 3.95417e-12 7.98133e-11 3 -4.387785565900694e-01 -4.387785565957166e-01 5.64715e-12 2.33585e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -2.650487665657221e-01 -2.650487665662200e-01 4.97880e-13 9.17497e-11 2 1.511652599862608e-01 1.511652599950435e-01 8.78278e-12 2.35935e-09 * 3 5.794640233506589e-01 5.794640233508336e-01 1.74638e-13 2.01881e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.905351901568619e-01 1.905351901359850e-01 2.08769e-11 9.13361e-11 2 6.618413703060451e-01 6.618413702370093e-01 6.90358e-11 1.48246e-10 3 -7.564860416328198e-02 -7.564860416299654e-02 2.85438e-13 1.37133e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -4.683842776943140e-01 -4.683842776791573e-01 1.51567e-11 1.56132e-11 2 -4.156790577093556e-01 -4.156790577097589e-01 4.03233e-13 9.08782e-11 3 3.949879170301536e-01 3.949879170332882e-01 3.13460e-12 1.24990e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.335196690651017e-01 8.335196690708225e-01 5.72087e-12 2.36752e-10 2 2.196634035172840e-03 2.196634041114694e-03 5.94185e-12 1.83888e-09 * 3 -9.600254741317690e-01 -9.600254741412617e-01 9.49274e-12 1.43773e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.009621165836492e+00 -1.009621165833203e+00 3.28848e-12 1.73018e-10 2 -1.708549041253059e-01 -1.708549041409790e-01 1.56732e-11 2.22869e-10 3 -4.204160439158940e-01 -4.204160439229067e-01 7.01261e-12 1.80224e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 8.322370469052105e-01 8.322370469084277e-01 3.21720e-12 3.62333e-11 2 2.580957739368012e-01 2.580957739171345e-01 1.96667e-11 1.71429e-11 3 -2.455637141933784e-01 -2.455637141977034e-01 4.32507e-12 3.32834e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 -4.396336196740736e-01 -4.396336197205048e-01 4.64312e-11 8.54093e-11 2 -1.150051020696231e+00 -1.150051020681620e+00 1.46108e-11 2.00774e-10 3 -2.198489383863581e-01 -2.198489384101888e-01 2.38308e-11 1.85829e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -4.540492583235693e-01 -4.540492583202246e-01 3.34471e-12 1.58520e-09 * 2 -8.789591565798696e-02 -8.789591565775268e-02 2.34285e-13 1.31252e-10 3 -1.740985093534181e-02 -1.740985086966400e-02 6.56778e-11 2.04577e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 1.120130478432331e-02 1.120130477331817e-02 1.10051e-11 1.17371e-09 2 2.352419070151045e-01 2.352419070061245e-01 8.97996e-12 2.14437e-10 3 1.464854280101517e-01 1.464854280166535e-01 6.50180e-12 2.28115e-06 * ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.948225150931951e-01 -4.948225151102037e-01 1.70086e-11 7.30375e-11 2 -2.079678523765445e+00 -2.079678523731653e+00 3.37925e-11 2.84143e-10 3 1.258864122333259e+00 1.258864122310829e+00 2.24301e-11 1.13841e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.662436739204145e+00 1.662436739231495e+00 2.73495e-11 4.49435e-10 2 -1.281282198707549e+00 -1.281282198711378e+00 3.82983e-12 4.27517e-10 3 -1.132309001548183e+00 -1.132309001550904e+00 2.72160e-12 6.31911e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -6.368228241130318e-01 -6.368228241071219e-01 5.90994e-12 6.66154e-11 2 1.496167989867601e-01 1.496167989955660e-01 8.80587e-12 1.45635e-10 3 -3.697320547058296e-01 -3.697320547105330e-01 4.70335e-12 3.44668e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -3.111385449965559e-01 -3.111385450001483e-01 3.59240e-12 1.25219e-09 2 9.120957521131058e-01 9.120957521179383e-01 4.83247e-12 4.85584e-09 * 3 1.275882968219053e+00 1.275882968159803e+00 5.92497e-11 1.18561e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 5.520435817313596e-01 5.520435817404424e-01 9.08285e-12 2.21935e-09 * 2 7.386353002427279e-01 7.386353002730534e-01 3.03254e-11 2.42281e-09 * 3 9.160457716477322e-01 9.160457716499149e-01 2.18270e-12 5.44105e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 -1.191114861491098e+00 -1.191114861499381e+00 8.28226e-12 1.83922e-11 2 -6.621442400003753e-01 -6.621442400031371e-01 2.76179e-12 1.71619e-10 3 -1.768503147070472e+00 -1.768503147174963e+00 1.04491e-10 6.44267e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.591754086416634e-01 -4.591754086469964e-01 5.33301e-12 1.24480e-09 2 -8.522702704818874e-01 -8.522702704613654e-01 2.05220e-11 5.71149e-11 3 -6.445298623738362e-01 -6.445298623280460e-01 4.57903e-11 5.20878e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -4.663068398764928e-01 -4.663068398738373e-01 2.65549e-12 2.35583e-09 * 2 -3.148662671721846e-01 -3.148662672179112e-01 4.57265e-11 1.86303e-09 * 3 -6.595297587397439e-02 -6.595297587759098e-02 3.61659e-12 8.40746e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.046756253981574e+00 -1.046756253956992e+00 2.45821e-11 7.78435e-11 2 1.749886011342734e+00 1.749886011364999e+00 2.22651e-11 2.17223e-10 3 1.491475922367095e+00 1.491475922350512e+00 1.65825e-11 1.68030e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.765716327399533e-01 1.765716327258492e-01 1.41041e-11 1.00996e-10 2 2.910132031520580e-01 2.910132031516081e-01 4.49973e-13 1.21750e-10 3 4.516599882408419e-01 4.516599882511269e-01 1.02850e-11 4.47931e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -3.487555154096780e-02 -3.487555156857142e-02 2.76036e-11 2.35871e-10 2 1.025102624247542e+00 1.025102624235062e+00 1.24800e-11 2.60276e-10 3 5.979694204669702e-01 5.979694204723064e-01 5.33618e-12 2.04610e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.960242786877566e+00 1.960242786917170e+00 3.96039e-11 8.03172e-10 2 -6.871591109923175e-02 -6.871591107843811e-02 2.07936e-11 5.31217e-10 3 5.322992463915274e-01 5.322992463825883e-01 8.93907e-12 9.75368e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 4, direction = 3: |F_model - F_numer| error = ----------------------- = 5.02915e-09 max{|F_numer|, eps} Comparison of analytical forces obtained from the model, the force computed as a numerical derivative of the energy, the difference between them, and the uncertainty in the numerical estimate of the force. The computed equilibrium lattice constant for the crystal (a0) is given in the heading. MIXED STRUCTURE -- Species = Co Ti | a0 = 3.760482749748917 | (Configuration in file "config-CoTi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ti 1 9.167912351634403e-01 9.167912351649355e-01 1.49525e-12 4.55462e-10 2 7.659407281707619e-01 7.659407281672094e-01 3.55249e-12 2.36175e-10 3 8.394323712949371e-01 8.394323713026764e-01 7.73936e-12 1.77648e-09 * ----------------------------------------------------------------------------------------------------- 2 Co 1 -2.132160397129743e+00 -2.132160397154860e+00 2.51172e-11 2.09277e-10 2 -1.759270033317583e+00 -1.759270033320388e+00 2.80509e-12 8.41951e-11 3 1.426146551827371e+00 1.426146551810227e+00 1.71436e-11 3.32599e-09 * ----------------------------------------------------------------------------------------------------- 3 Co 1 -6.674362121370837e-01 -6.674362121887539e-01 5.16702e-11 2.59837e-10 2 1.146682250667666e+00 1.146682250669248e+00 1.58229e-12 4.36602e-11 3 -6.986518406612046e-01 -6.986518406628492e-01 1.64468e-12 2.29864e-09 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 1.098643972794551e+00 1.098643972804598e+00 1.00469e-11 3.63874e-10 2 -2.619529352106432e+00 -2.619529352092676e+00 1.37561e-11 4.01677e-10 3 -4.243096191745493e-01 -4.243096190289257e-01 1.45624e-10 1.05568e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -9.722484270931613e-01 -9.722484270865568e-01 6.60449e-12 2.95348e-11 2 -1.145818231023972e-01 -1.145818230827862e-01 1.96110e-11 7.80861e-11 3 -1.114578280685337e+00 -1.114578280649959e+00 3.53779e-11 6.29676e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -1.155143024313789e-01 -1.155143024116694e-01 1.97095e-11 1.16590e-10 2 1.396242657323419e-01 1.396242656856696e-01 4.66723e-11 4.99759e-10 3 2.826777771513025e-01 2.826777771123941e-01 3.89085e-11 3.79337e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.076464856643498e+00 1.076464856641471e+00 2.02682e-12 4.08087e-11 2 9.488289929724315e-02 9.488289925317951e-02 4.40636e-11 1.72738e-10 3 9.164411026816589e-01 9.164411027820594e-01 1.00400e-10 1.33645e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -3.811236297851614e+00 -3.811236297813773e+00 3.78413e-11 2.23459e-10 2 -1.381040783770736e+00 -1.381040783774775e+00 4.03899e-12 4.95022e-10 3 1.983665835478152e+00 1.983665835446022e+00 3.21301e-11 4.24502e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 1.300938384581534e-02 1.300938383645273e-02 9.36261e-12 4.08377e-11 2 -1.349812030882309e+00 -1.349812030874128e+00 8.18101e-12 9.42459e-11 3 -2.360375217884426e+00 -2.360375217930829e+00 4.64033e-11 3.04633e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.811832742566718e+00 -1.811832742587780e+00 2.10618e-11 3.08302e-10 2 4.183439424694121e-01 4.183439424828501e-01 1.34380e-11 4.49581e-09 * 3 -3.955316933297813e+00 -3.955316933300415e+00 2.60192e-12 7.02749e-11 ----------------------------------------------------------------------------------------------------- 11 Co 1 2.845492970840234e-01 2.845492970613283e-01 2.26951e-11 1.60496e-10 2 9.485746783887640e-01 9.485746784477991e-01 5.90351e-11 3.04067e-09 * 3 -2.380376925248193e-01 -2.380376925646193e-01 3.98000e-11 7.76180e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.059126179198277e+00 -1.059126179197834e+00 4.42757e-13 2.00028e-10 2 1.206476726848581e+00 1.206476726856581e+00 8.00027e-12 5.16032e-11 3 2.991200728530207e+00 2.991200728504521e+00 2.56861e-11 3.13407e-10 ----------------------------------------------------------------------------------------------------- 13 Co 1 1.321657178114848e+00 1.321657178098576e+00 1.62717e-11 8.78586e-12 2 2.289682383501490e+00 2.289682383452774e+00 4.87157e-11 1.49340e-10 3 1.405101974716196e-01 1.405101974532269e-01 1.83928e-11 3.05388e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 -4.738803573674299e-01 -4.738803574029101e-01 3.54802e-11 1.26473e-10 2 -4.945964072458787e-01 -4.945964072370958e-01 8.78292e-12 4.52826e-11 3 8.761819595328428e-01 8.761819595024622e-01 3.03806e-11 1.36845e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.137068539609734e+00 2.137068539627737e+00 1.80034e-11 1.04726e-10 2 -1.224425186634701e-02 -1.224425187723768e-02 1.08907e-11 7.10304e-10 3 -1.754076587827525e+00 -1.754076587807125e+00 2.04006e-11 1.65761e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.682141698595087e+00 3.682141698561208e+00 3.38791e-11 2.00452e-09 * 2 -1.437397945202072e+00 -1.437397945210611e+00 8.53850e-12 5.08400e-11 3 2.555067559803528e+00 2.555067559784989e+00 1.85389e-11 3.75332e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 1.034757193819518e+00 1.034757193776024e+00 4.34934e-11 5.87950e-11 2 7.383887479851022e-01 7.383887479589719e-01 2.61303e-11 3.77299e-09 * 3 3.548931027638357e-02 3.548931025744458e-02 1.89390e-11 2.08171e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 9.853182686269621e-01 9.853182685986142e-01 2.83480e-11 1.20896e-09 2 3.209342809974314e-01 3.209342809936162e-01 3.81517e-12 4.16312e-10 3 1.009961090917681e+00 1.009961090711943e+00 2.05738e-10 2.08602e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 2.508132831320828e-01 2.508132831400539e-01 7.97107e-12 3.07255e-10 2 3.050203487799280e-02 3.050203486558957e-02 1.24032e-11 2.22483e-10 3 -3.851630285884623e-01 -3.851630285766825e-01 1.17798e-11 2.14134e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 -3.280739281990049e-01 -3.280739281960316e-01 2.97329e-12 1.63197e-10 2 6.181205233648797e-01 6.181205233193259e-01 4.55538e-11 4.10716e-12 3 -9.770723459295628e-01 -9.770723459283582e-01 1.20459e-12 1.19379e-09 ----------------------------------------------------------------------------------------------------- 21 Co 1 -4.214046036088543e-01 -4.214046036156792e-01 6.82482e-12 2.41559e-10 2 6.824844732326752e-01 6.824844731423509e-01 9.03243e-11 1.86944e-10 3 -6.881438386887602e-01 -6.881438386857007e-01 3.05944e-12 1.88429e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 -7.932965982870016e-01 -7.932965982369137e-01 5.00879e-11 3.06813e-09 * 2 6.700913850214277e-01 6.700913849728261e-01 4.86017e-11 4.61129e-10 3 1.656724970861309e-01 1.656724971418436e-01 5.57127e-11 1.30477e-10 ----------------------------------------------------------------------------------------------------- 23 Co 1 -5.013438207120334e-01 -5.013438207300518e-01 1.80184e-11 5.36856e-11 2 8.138848028686582e-01 8.138848028974962e-01 2.88380e-11 7.28266e-11 3 -3.725357656898577e-01 -3.725357656602539e-01 2.96038e-11 1.54349e-10 ----------------------------------------------------------------------------------------------------- 24 Co 1 3.621253703126966e-01 3.621253703300379e-01 1.73413e-11 2.45306e-10 2 -7.920557503835793e-01 -7.920557502406222e-01 1.42957e-10 3.64514e-10 3 -7.532114041702276e-01 -7.532114041687723e-01 1.45528e-12 3.55999e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 1.065068568099867e+00 1.065068568106037e+00 6.16929e-12 9.99001e-12 2 1.227152179120120e+00 1.227152179143427e+00 2.33074e-11 6.99778e-09 * 3 1.231863311072055e+00 1.231863311032110e+00 3.99449e-11 2.71582e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 4.950041636806589e-01 4.950041636884932e-01 7.83434e-12 8.56143e-11 2 -1.333062051604046e+00 -1.333062051726576e+00 1.22530e-10 3.16382e-10 3 -1.444793898038533e+00 -1.444793897997697e+00 4.08362e-11 1.97490e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.961397662941451e+00 1.961397662891560e+00 4.98916e-11 4.64474e-10 2 -3.007238693055774e+00 -3.007238692962622e+00 9.31517e-11 8.99898e-10 3 -8.191426481810982e-01 -8.191426482021962e-01 2.10980e-11 3.74422e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.134565076973384e+00 -2.134565076931919e+00 4.14646e-11 2.82614e-09 * 2 1.363524369390693e+00 1.363524369378444e+00 1.22493e-11 2.70939e-11 3 4.502600574207860e-01 4.502600574182776e-01 2.50838e-12 5.21692e-09 * ----------------------------------------------------------------------------------------------------- 29 Co 1 -1.422697209818548e+00 -1.422697209796909e+00 2.16398e-11 1.04740e-10 2 -2.341868562022717e-01 -2.341868561846289e-01 1.76428e-11 1.08183e-10 3 8.932979776408201e-01 8.932979776510175e-01 1.01974e-11 4.19891e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 8.457148096338396e-02 8.457148094541181e-02 1.79722e-11 8.81070e-11 2 1.629503603502925e+00 1.629503603525368e+00 2.24434e-11 2.64330e-10 3 1.741265478752744e+00 1.741265478760794e+00 8.05001e-12 1.06368e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.942636124164732e-01 -4.942636124195177e-01 3.04451e-12 6.82353e-11 2 1.568974967961321e-01 1.568974968003422e-01 4.21010e-12 1.67346e-10 3 -2.866152181709151e-01 -2.866152181906488e-01 1.97338e-11 1.72518e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 3.696976123630906e-01 3.696976123960065e-01 3.29159e-11 2.81602e-10 2 -7.266757934948709e-01 -7.266757934954617e-01 5.90861e-13 1.19058e-11 3 -1.267109487425129e+00 -1.267109487459050e+00 3.39211e-11 7.55642e-11 ----------------------------------------------------------------------------------------------------- * Starred lines are suspected outliers and are not included when determining the error. A calculation is considered an outlier if it has an uncertainty that lies at an abnormal distance from the other uncertainties in this set of calculations. Outliers are determined using the box plot construction with fences. An outlier could indicate a problem with the the numerical differentiation or problems with the potential energy, such as discontinuities. Maximum error obtained for particle = 15, direction = 2: |F_model - F_numer| error = ----------------------- = 8.89451e-10 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.02915e-09 Machine precision = 2.22045e-16 Note: Lower grades can reflect errors in the analytical forces, a lack of smoothness in the potential, or loss of precision in the numerical derivative computation. Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 5.02915e-09 compared with a machine precision of 2.22045e-16. The letter grade was based on 'score=log10(error/eps)', with ranges A=[0, 7.5], B=(7.5, 10.0], C=(10.0, 12.5], D=(12.5, 15.0), F>15.0. 'A' is the best grade, and 'F' indicates failure.