!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_000 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 4.844058390637879e-01 4.83347e-12 5.59235e-11 2 -1.873245057955659e-01 -1.873245058009178e-01 5.35191e-12 9.68939e-12 3 -3.970657339793174e-01 -3.970657339776760e-01 1.64141e-12 7.81719e-10 ----------------------------------------------------------------------------------------------------- 2 Co 1 -1.152455005524658e+00 -1.152455005529553e+00 4.89497e-12 7.44953e-11 2 1.019928950652365e-01 1.019928951153756e-01 5.01391e-11 1.59587e-10 3 1.284631084677859e+00 1.284631084695258e+00 1.73994e-11 1.24432e-10 ----------------------------------------------------------------------------------------------------- 3 Co 1 5.503008864863501e-01 5.503008864945877e-01 8.23763e-12 8.95632e-11 2 9.701145897511383e-01 9.701145897332062e-01 1.79321e-11 6.53191e-11 3 -9.430536420917450e-01 -9.430536421308551e-01 3.91100e-11 1.35599e-09 ----------------------------------------------------------------------------------------------------- 4 Co 1 1.834598281329793e+00 1.834598281266254e+00 6.35392e-11 5.27235e-10 2 3.372187363117622e-01 3.372187363242433e-01 1.24811e-11 1.61584e-10 3 5.131379645887562e-01 5.131379645938933e-01 5.13711e-12 5.80865e-10 ----------------------------------------------------------------------------------------------------- 5 Co 1 -1.832254548413368e-01 -1.832254548512707e-01 9.93386e-12 3.25292e-10 2 3.324701399378128e-01 3.324701399537233e-01 1.59106e-11 1.19706e-10 3 9.781914450427963e-01 9.781914450522966e-01 9.50029e-12 1.65207e-10 ----------------------------------------------------------------------------------------------------- 6 Co 1 -3.598660328028200e-01 -3.598660327837189e-01 1.91011e-11 1.87963e-10 2 3.927276298506535e-01 3.927276298393839e-01 1.12696e-11 3.29860e-11 3 2.864370881458561e-01 2.864370881390880e-01 6.76809e-12 2.57173e-09 * ----------------------------------------------------------------------------------------------------- 7 Co 1 1.758394584657615e+00 1.758394584648775e+00 8.84026e-12 5.19143e-11 2 -2.208160193143350e+00 -2.208160193110576e+00 3.27742e-11 4.95106e-11 3 -2.513199143001026e+00 -2.513199143006766e+00 5.73985e-12 1.40197e-10 ----------------------------------------------------------------------------------------------------- 8 Co 1 -1.263278743083922e+00 -1.263278743089894e+00 5.97256e-12 1.75465e-10 2 -1.443018643242862e+00 -1.443018643214870e+00 2.79921e-11 2.04590e-10 3 -1.441599684102383e+00 -1.441599684102816e+00 4.32987e-13 7.12137e-11 ----------------------------------------------------------------------------------------------------- 9 Co 1 3.358340617557479e-01 3.358340617631163e-01 7.36838e-12 8.15202e-10 2 -5.935568799967006e-01 -5.935568800097231e-01 1.30225e-11 5.55507e-11 3 6.227125050849731e-01 6.227125050880395e-01 3.06644e-12 5.09008e-11 ----------------------------------------------------------------------------------------------------- 10 Co 1 -1.928097438657534e+00 -1.928097438645189e+00 1.23448e-11 3.11297e-09 * 2 -1.757324093967954e-01 -1.757324094009796e-01 4.18424e-12 2.06989e-10 3 -1.712138283716773e+00 -1.712138283728043e+00 1.12703e-11 5.36018e-11 ----------------------------------------------------------------------------------------------------- 11 Co 1 -8.232197838509057e-01 -8.232197838160082e-01 3.48974e-11 3.64062e-10 2 4.327613171180937e-01 4.327613171291916e-01 1.10978e-11 3.16586e-10 3 1.784153897331812e-01 1.784153897255140e-01 7.66717e-12 5.24804e-10 ----------------------------------------------------------------------------------------------------- 12 Co 1 7.263567582440373e-01 7.263567582931411e-01 4.91037e-11 6.20260e-09 * 2 3.272027902610394e-02 3.272027902636112e-02 2.57176e-13 1.16677e-09 3 2.196154828511248e-02 2.196154827785813e-02 7.25435e-12 3.38562e-11 ----------------------------------------------------------------------------------------------------- 13 Co 1 -1.445520878776114e+00 -1.445520878772998e+00 3.11595e-12 1.81348e-10 2 -1.580038778336274e+00 -1.580038778358444e+00 2.21703e-11 1.57331e-10 3 -2.319119152355507e+00 -2.319119152342563e+00 1.29443e-11 2.00749e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 2.895378415002587e-01 2.895378415007822e-01 5.23415e-13 2.16955e-11 2 6.937910161883549e-01 6.937910161870046e-01 1.35036e-12 6.20508e-11 3 -1.523195136846668e-01 -1.523195137165357e-01 3.18688e-11 1.06911e-10 ----------------------------------------------------------------------------------------------------- 15 Co 1 2.438926872216976e+00 2.438926872313392e+00 9.64158e-11 7.74596e-10 2 -1.795405448055932e+00 -1.795405448171612e+00 1.15680e-10 4.34770e-10 3 3.203789659187067e-01 3.203789659291076e-01 1.04009e-11 3.33646e-10 ----------------------------------------------------------------------------------------------------- 16 Co 1 1.483410853492960e+00 1.483410853493608e+00 6.47482e-13 3.09297e-10 2 1.556796386519574e+00 1.556796386503341e+00 1.62332e-11 2.10425e-10 3 2.302480735324203e+00 2.302480735309008e+00 1.51954e-11 9.16034e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 1.557184959193729e-02 1.557184960500192e-02 1.30646e-11 4.04084e-11 2 5.823672422230110e-01 5.823672422429355e-01 1.99245e-11 3.97027e-11 3 -5.359083321886661e-01 -5.359083322643642e-01 7.56981e-11 1.48906e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 -3.835184707051285e-01 -3.835184707153532e-01 1.02247e-11 4.22539e-10 2 2.773427162073621e-01 2.773427162635750e-01 5.62129e-11 7.07777e-09 * 3 3.472977211414079e-01 3.472977211233516e-01 1.80564e-11 4.69742e-10 ----------------------------------------------------------------------------------------------------- 19 Co 1 1.608695740460704e+00 1.608695740475989e+00 1.52853e-11 5.90734e-11 2 1.834463938230435e-01 1.834463938298725e-01 6.82904e-12 3.29781e-09 * 3 6.490143840768396e-02 6.490143839972283e-02 7.96113e-12 2.07239e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 1.803277531773012e-01 1.803277531959747e-01 1.86735e-11 2.29133e-10 2 8.736398447938487e-01 8.736398447731359e-01 2.07128e-11 6.94095e-11 3 -4.663883243250440e-01 -4.663883243521053e-01 2.70612e-11 3.57159e-09 * ----------------------------------------------------------------------------------------------------- 21 Co 1 -1.781296378174930e+00 -1.781296378199069e+00 2.41394e-11 2.35536e-10 2 7.919283698900983e-01 7.919283698805308e-01 9.56746e-12 1.99186e-10 3 1.507948897055873e+00 1.507948897089142e+00 3.32692e-11 2.71869e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 -6.872567542368390e-01 -6.872567542075423e-01 2.92967e-11 3.86848e-10 2 1.704518791349711e+00 1.704518791316764e+00 3.29472e-11 1.12529e-10 3 2.065459881550363e+00 2.065459881485495e+00 6.48686e-11 1.33256e-09 ----------------------------------------------------------------------------------------------------- 23 Co 1 -5.283018796225778e-01 -5.283018796654614e-01 4.28836e-11 3.04461e-10 2 4.352243275442043e-01 4.352243274924971e-01 5.17071e-11 1.17323e-10 3 -3.290485484926066e-01 -3.290485484599360e-01 3.26705e-11 5.47403e-10 ----------------------------------------------------------------------------------------------------- 24 Co 1 4.791290534376360e-01 4.791290534408260e-01 3.19000e-12 3.67025e-10 2 -9.981400484543620e-02 -9.981400468850656e-02 1.56930e-10 4.74970e-09 * 3 -1.482946643358400e+00 -1.482946643367105e+00 8.70526e-12 2.22252e-09 * ----------------------------------------------------------------------------------------------------- 25 Co 1 -1.292576302144441e+00 -1.292576302150059e+00 5.61751e-12 7.43507e-09 * 2 -8.652067828684505e-01 -8.652067828510028e-01 1.74477e-11 6.42156e-11 3 4.971907244293135e-01 4.971907244629121e-01 3.35986e-11 1.22557e-08 * ----------------------------------------------------------------------------------------------------- 26 Co 1 -1.871450202538286e-01 -1.871450203032861e-01 4.94575e-11 2.17346e-09 * 2 2.568661273963114e-01 2.568661273720783e-01 2.42331e-11 6.32217e-11 3 -5.392396478833059e-01 -5.392396477311935e-01 1.52112e-10 3.80378e-10 ----------------------------------------------------------------------------------------------------- 27 Co 1 1.290261294830110e+00 1.290261294823761e+00 6.34870e-12 2.56992e-10 2 -3.142674027308471e+00 -3.142674027327017e+00 1.85452e-11 4.34435e-11 3 -6.757841762571805e-02 -6.757841761227880e-02 1.34392e-11 2.73463e-10 ----------------------------------------------------------------------------------------------------- 28 Co 1 -1.124422587498330e+00 -1.124422587506589e+00 8.25917e-12 4.66234e-11 2 1.336356641156548e+00 1.336356641139063e+00 1.74849e-11 1.73299e-09 3 -4.805835505207574e-01 -4.805835505252278e-01 4.47042e-12 3.36282e-09 * ----------------------------------------------------------------------------------------------------- 29 Co 1 -6.689013198848318e-01 -6.689013198800601e-01 4.77174e-12 2.39758e-10 2 4.867466371969610e-01 4.867466371935778e-01 3.38318e-12 3.50075e-10 3 2.018824185133034e+00 2.018824185258543e+00 1.25509e-10 8.84586e-10 ----------------------------------------------------------------------------------------------------- 30 Co 1 -4.239734965087219e-01 -4.239734964583226e-01 5.03994e-11 2.30309e-10 2 1.257423313036651e+00 1.257423312988801e+00 4.78502e-11 2.85661e-10 3 1.175290873043559e+00 1.175290873011757e+00 3.18017e-11 2.84736e-10 ----------------------------------------------------------------------------------------------------- 31 Co 1 -6.931063011468737e-01 -6.931063011076255e-01 3.92482e-11 8.71017e-11 2 -9.306041041108645e-01 -9.306041041382200e-01 2.73556e-11 1.22475e-10 3 -4.433915156838137e-01 -4.433915156840886e-01 2.74891e-13 4.29704e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 1.450410177463741e+00 1.450410177475039e+00 1.12972e-11 8.52822e-10 2 -1.491761728577898e-02 -1.491761726262547e-02 2.31535e-11 3.67079e-10 3 -3.616803145529472e-01 -3.616803145539876e-01 1.04039e-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 4.124626996085510e-01 9.06547e-12 3.59451e-11 2 -2.065383690971361e-01 -2.065383691003664e-01 3.23028e-12 1.96289e-10 3 2.821056026706005e-01 2.821056026896477e-01 1.90472e-11 1.77611e-10 ----------------------------------------------------------------------------------------------------- 2 Ti 1 -9.964885858563943e-01 -9.964885858521363e-01 4.25804e-12 1.32021e-10 2 -3.193928173175093e-01 -3.193928173420241e-01 2.45148e-11 5.17615e-11 3 8.241208739728962e-01 8.241208739660633e-01 6.83298e-12 1.27698e-10 ----------------------------------------------------------------------------------------------------- 3 Ti 1 -3.489588645853905e-01 -3.489588645767592e-01 8.63126e-12 3.76179e-11 2 1.111388905545804e+00 1.111388905554567e+00 8.76299e-12 7.15137e-11 3 -7.279716099966461e-01 -7.279716099940471e-01 2.59903e-12 7.46971e-11 ----------------------------------------------------------------------------------------------------- 4 Ti 1 7.136102715022786e-01 7.136102715035515e-01 1.27287e-12 9.15005e-11 2 -9.805613977743068e-01 -9.805613977650315e-01 9.27536e-12 1.46119e-10 3 -8.997347606838652e-03 -8.997347561589670e-03 4.52490e-11 7.62490e-11 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -9.567274438360384e-01 -9.567274438445218e-01 8.48344e-12 2.69283e-11 2 -1.030113350155971e-01 -1.030113350076959e-01 7.90117e-12 3.10811e-11 3 -6.800365129424554e-02 -6.800365130373542e-02 9.48988e-12 8.98781e-11 ----------------------------------------------------------------------------------------------------- 6 Ti 1 -1.377242739110670e-01 -1.377242739039433e-01 7.12361e-12 6.70436e-11 2 3.171120446076195e-01 3.171120446281011e-01 2.04816e-11 1.87000e-10 3 2.008054435242614e-01 2.008054435385948e-01 1.43333e-11 9.68675e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 2.088263633705479e-01 2.088263633688653e-01 1.68263e-12 3.67181e-10 2 7.117526109339389e-02 7.117526105967047e-02 3.37234e-11 1.34499e-10 3 5.673077932147456e-01 5.673077932010850e-01 1.36605e-11 1.15461e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -4.260557521607466e-02 -4.260557520535142e-02 1.07232e-11 2.41518e-10 2 5.280624304288153e-01 5.280624304338666e-01 5.05129e-12 6.09206e-10 3 -2.341060467195727e+00 -2.341060467186755e+00 8.97193e-12 2.35621e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 -1.891272094828655e-01 -1.891272094854940e-01 2.62851e-12 1.64950e-10 2 -3.315714494895720e-01 -3.315714494908306e-01 1.25860e-12 6.83845e-10 3 -2.376322612048486e-01 -2.376322612048279e-01 2.06501e-14 5.36175e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 1.166055449248622e+00 1.166055449265895e+00 1.72733e-11 7.57947e-11 2 3.229374025268053e-02 3.229374023961928e-02 1.30613e-11 1.69138e-10 3 2.229090397467477e-01 2.229090397439178e-01 2.82985e-12 5.48464e-11 ----------------------------------------------------------------------------------------------------- 11 Ti 1 1.229639105512995e+00 1.229639105540337e+00 2.73421e-11 2.27980e-10 2 7.895906608170469e-01 7.895906608130920e-01 3.95484e-12 7.98130e-11 3 -4.387785565900694e-01 -4.387785565957162e-01 5.64676e-12 2.33585e-10 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -2.650487665657221e-01 -2.650487665662197e-01 4.97657e-13 9.17496e-11 2 1.511652599862608e-01 1.511652599950436e-01 8.78286e-12 2.35935e-09 * 3 5.794640233506589e-01 5.794640233508331e-01 1.74194e-13 2.01881e-10 ----------------------------------------------------------------------------------------------------- 13 Ti 1 1.905351901568619e-01 1.905351901359849e-01 2.08770e-11 9.13360e-11 2 6.618413703060451e-01 6.618413702370088e-01 6.90362e-11 1.48246e-10 3 -7.564860416328198e-02 -7.564860416299650e-02 2.85480e-13 1.37133e-10 ----------------------------------------------------------------------------------------------------- 14 Ti 1 -4.683842776943140e-01 -4.683842776791566e-01 1.51574e-11 1.56136e-11 2 -4.156790577093556e-01 -4.156790577097591e-01 4.03455e-13 9.08781e-11 3 3.949879170301536e-01 3.949879170332879e-01 3.13433e-12 1.24989e-11 ----------------------------------------------------------------------------------------------------- 15 Ti 1 8.335196690651017e-01 8.335196690708219e-01 5.72020e-12 2.36751e-10 2 2.196634035172840e-03 2.196634041114695e-03 5.94186e-12 1.83888e-09 * 3 -9.600254741317690e-01 -9.600254741412609e-01 9.49196e-12 1.43774e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 -1.009621165836492e+00 -1.009621165833203e+00 3.28915e-12 1.73017e-10 2 -1.708549041253059e-01 -1.708549041409789e-01 1.56730e-11 2.22869e-10 3 -4.204160439158940e-01 -4.204160439229064e-01 7.01234e-12 1.80224e-10 ----------------------------------------------------------------------------------------------------- 17 Ti 1 8.322370469052105e-01 8.322370469084269e-01 3.21643e-12 3.62333e-11 2 2.580957739368012e-01 2.580957739171346e-01 1.96665e-11 1.71432e-11 3 -2.455637141933784e-01 -2.455637141977036e-01 4.32521e-12 3.32834e-09 * ----------------------------------------------------------------------------------------------------- 18 Ti 1 -4.396336196740736e-01 -4.396336197205042e-01 4.64307e-11 8.54092e-11 2 -1.150051020696231e+00 -1.150051020681619e+00 1.46116e-11 2.00773e-10 3 -2.198489383863581e-01 -2.198489384101887e-01 2.38306e-11 1.85829e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 -4.540492583235693e-01 -4.540492583202249e-01 3.34449e-12 1.58520e-09 * 2 -8.789591565798696e-02 -8.789591565775264e-02 2.34326e-13 1.31252e-10 3 -1.740985093534181e-02 -1.740985086966399e-02 6.56778e-11 2.04577e-10 ----------------------------------------------------------------------------------------------------- 20 Ti 1 1.120130478432331e-02 1.120130477331816e-02 1.10051e-11 1.17371e-09 2 2.352419070151045e-01 2.352419070061243e-01 8.98018e-12 2.14437e-10 3 1.464854280101517e-01 1.464854280166536e-01 6.50191e-12 2.28115e-06 * ----------------------------------------------------------------------------------------------------- 21 Ti 1 -4.948225150931951e-01 -4.948225151102034e-01 1.70083e-11 7.30372e-11 2 -2.079678523765445e+00 -2.079678523731651e+00 3.37943e-11 2.84146e-10 3 1.258864122333259e+00 1.258864122310827e+00 2.24321e-11 1.13841e-10 ----------------------------------------------------------------------------------------------------- 22 Ti 1 1.662436739204145e+00 1.662436739231493e+00 2.73481e-11 4.49434e-10 2 -1.281282198707549e+00 -1.281282198711377e+00 3.82849e-12 4.27517e-10 3 -1.132309001548183e+00 -1.132309001550903e+00 2.72049e-12 6.31911e-10 ----------------------------------------------------------------------------------------------------- 23 Ti 1 -6.368228241130318e-01 -6.368228241071214e-01 5.91038e-12 6.66154e-11 2 1.496167989867601e-01 1.496167989955658e-01 8.80571e-12 1.45635e-10 3 -3.697320547058296e-01 -3.697320547105327e-01 4.70307e-12 3.44668e-10 ----------------------------------------------------------------------------------------------------- 24 Ti 1 -3.111385449965559e-01 -3.111385450001484e-01 3.59252e-12 1.25219e-09 2 9.120957521131058e-01 9.120957521179387e-01 4.83291e-12 4.85584e-09 * 3 1.275882968219053e+00 1.275882968159802e+00 5.92510e-11 1.18561e-10 ----------------------------------------------------------------------------------------------------- 25 Ti 1 5.520435817313596e-01 5.520435817404427e-01 9.08307e-12 2.21935e-09 * 2 7.386353002427279e-01 7.386353002730536e-01 3.03256e-11 2.42281e-09 * 3 9.160457716477322e-01 9.160457716499153e-01 2.18314e-12 5.44105e-09 * ----------------------------------------------------------------------------------------------------- 26 Ti 1 -1.191114861491098e+00 -1.191114861499380e+00 8.28138e-12 1.83924e-11 2 -6.621442400003753e-01 -6.621442400031367e-01 2.76135e-12 1.71618e-10 3 -1.768503147070472e+00 -1.768503147174964e+00 1.04492e-10 6.44267e-09 * ----------------------------------------------------------------------------------------------------- 27 Ti 1 -4.591754086416634e-01 -4.591754086469960e-01 5.33262e-12 1.24480e-09 2 -8.522702704818874e-01 -8.522702704613648e-01 2.05226e-11 5.71153e-11 3 -6.445298623738362e-01 -6.445298623280462e-01 4.57900e-11 5.20877e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -4.663068398764928e-01 -4.663068398738375e-01 2.65526e-12 2.35583e-09 * 2 -3.148662671721846e-01 -3.148662672179113e-01 4.57266e-11 1.86303e-09 * 3 -6.595297587397439e-02 -6.595297587759090e-02 3.61651e-12 8.40746e-11 ----------------------------------------------------------------------------------------------------- 29 Ti 1 -1.046756253981574e+00 -1.046756253956991e+00 2.45834e-11 7.78437e-11 2 1.749886011342734e+00 1.749886011364998e+00 2.22635e-11 2.17223e-10 3 1.491475922367095e+00 1.491475922350511e+00 1.65834e-11 1.68030e-11 ----------------------------------------------------------------------------------------------------- 30 Ti 1 1.765716327399533e-01 1.765716327258491e-01 1.41043e-11 1.00996e-10 2 2.910132031520580e-01 2.910132031516078e-01 4.50251e-13 1.21750e-10 3 4.516599882408419e-01 4.516599882511271e-01 1.02853e-11 4.47931e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -3.487555154096780e-02 -3.487555156857139e-02 2.76036e-11 2.35871e-10 2 1.025102624247542e+00 1.025102624235061e+00 1.24807e-11 2.60275e-10 3 5.979694204669702e-01 5.979694204723059e-01 5.33573e-12 2.04610e-10 ----------------------------------------------------------------------------------------------------- 32 Ti 1 1.960242786877566e+00 1.960242786917167e+00 3.96008e-11 8.03169e-10 2 -6.871591109923175e-02 -6.871591107843814e-02 2.07936e-11 5.31217e-10 3 5.322992463915274e-01 5.322992463825879e-01 8.93952e-12 9.75374e-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 9.167912351649348e-01 1.49447e-12 4.55463e-10 2 7.659407281707619e-01 7.659407281672097e-01 3.55216e-12 2.36175e-10 3 8.394323712949371e-01 8.394323713026768e-01 7.73970e-12 1.77648e-09 * ----------------------------------------------------------------------------------------------------- 2 Co 1 -2.132160397129743e+00 -2.132160397154857e+00 2.51141e-11 2.09276e-10 2 -1.759270033317583e+00 -1.759270033320387e+00 2.80376e-12 8.41942e-11 3 1.426146551827371e+00 1.426146551810228e+00 1.71432e-11 3.32599e-09 * ----------------------------------------------------------------------------------------------------- 3 Co 1 -6.674362121370837e-01 -6.674362121887535e-01 5.16698e-11 2.59837e-10 2 1.146682250667666e+00 1.146682250669248e+00 1.58162e-12 4.36609e-11 3 -6.986518406612046e-01 -6.986518406628497e-01 1.64513e-12 2.29864e-09 * ----------------------------------------------------------------------------------------------------- 4 Ti 1 1.098643972794551e+00 1.098643972804597e+00 1.00457e-11 3.63875e-10 2 -2.619529352106432e+00 -2.619529352092672e+00 1.37601e-11 4.01673e-10 3 -4.243096191745493e-01 -4.243096190289251e-01 1.45624e-10 1.05568e-10 ----------------------------------------------------------------------------------------------------- 5 Ti 1 -9.722484270931613e-01 -9.722484270865563e-01 6.60494e-12 2.95353e-11 2 -1.145818231023972e-01 -1.145818230827861e-01 1.96111e-11 7.80861e-11 3 -1.114578280685337e+00 -1.114578280649959e+00 3.53786e-11 6.29672e-11 ----------------------------------------------------------------------------------------------------- 6 Co 1 -1.155143024313789e-01 -1.155143024116693e-01 1.97096e-11 1.16590e-10 2 1.396242657323419e-01 1.396242656856695e-01 4.66724e-11 4.99759e-10 3 2.826777771513025e-01 2.826777771123938e-01 3.89088e-11 3.79337e-10 ----------------------------------------------------------------------------------------------------- 7 Ti 1 1.076464856643498e+00 1.076464856641470e+00 2.02793e-12 4.08105e-11 2 9.488289929724315e-02 9.488289925317944e-02 4.40637e-11 1.72738e-10 3 9.164411026816589e-01 9.164411027820583e-01 1.00399e-10 1.33645e-10 ----------------------------------------------------------------------------------------------------- 8 Ti 1 -3.811236297851614e+00 -3.811236297813769e+00 3.78448e-11 2.23459e-10 2 -1.381040783770736e+00 -1.381040783774774e+00 4.03810e-12 4.95023e-10 3 1.983665835478152e+00 1.983665835446020e+00 3.21319e-11 4.24505e-10 ----------------------------------------------------------------------------------------------------- 9 Ti 1 1.300938384581534e-02 1.300938383645271e-02 9.36262e-12 4.08377e-11 2 -1.349812030882309e+00 -1.349812030874127e+00 8.18190e-12 9.42459e-11 3 -2.360375217884426e+00 -2.360375217930827e+00 4.64011e-11 3.04631e-10 ----------------------------------------------------------------------------------------------------- 10 Ti 1 -1.811832742566718e+00 -1.811832742587779e+00 2.10605e-11 3.08302e-10 2 4.183439424694121e-01 4.183439424828502e-01 1.34381e-11 4.49581e-09 * 3 -3.955316933297813e+00 -3.955316933300411e+00 2.59748e-12 7.02749e-11 ----------------------------------------------------------------------------------------------------- 11 Co 1 2.845492970840234e-01 2.845492970613284e-01 2.26950e-11 1.60496e-10 2 9.485746783887640e-01 9.485746784477995e-01 5.90356e-11 3.04067e-09 * 3 -2.380376925248193e-01 -2.380376925646190e-01 3.97998e-11 7.76181e-11 ----------------------------------------------------------------------------------------------------- 12 Ti 1 -1.059126179198277e+00 -1.059126179197835e+00 4.42313e-13 2.00028e-10 2 1.206476726848581e+00 1.206476726856581e+00 8.00005e-12 5.16025e-11 3 2.991200728530207e+00 2.991200728504518e+00 2.56888e-11 3.13404e-10 ----------------------------------------------------------------------------------------------------- 13 Co 1 1.321657178114848e+00 1.321657178098575e+00 1.62730e-11 8.78719e-12 2 2.289682383501490e+00 2.289682383452771e+00 4.87184e-11 1.49341e-10 3 1.405101974716196e-01 1.405101974532268e-01 1.83929e-11 3.05388e-10 ----------------------------------------------------------------------------------------------------- 14 Co 1 -4.738803573674299e-01 -4.738803574029098e-01 3.54799e-11 1.26473e-10 2 -4.945964072458787e-01 -4.945964072370955e-01 8.78325e-12 4.52826e-11 3 8.761819595328428e-01 8.761819595024631e-01 3.03797e-11 1.36843e-10 ----------------------------------------------------------------------------------------------------- 15 Ti 1 2.137068539609734e+00 2.137068539627735e+00 1.80012e-11 1.04725e-10 2 -1.224425186634701e-02 -1.224425187723767e-02 1.08907e-11 7.10304e-10 3 -1.754076587827525e+00 -1.754076587807123e+00 2.04023e-11 1.65762e-10 ----------------------------------------------------------------------------------------------------- 16 Ti 1 3.682141698595087e+00 3.682141698561205e+00 3.38827e-11 2.00452e-09 * 2 -1.437397945202072e+00 -1.437397945210609e+00 8.53717e-12 5.08402e-11 3 2.555067559803528e+00 2.555067559784987e+00 1.85407e-11 3.75334e-10 ----------------------------------------------------------------------------------------------------- 17 Co 1 1.034757193819518e+00 1.034757193776023e+00 4.34945e-11 5.87945e-11 2 7.383887479851022e-01 7.383887479589722e-01 2.61300e-11 3.77299e-09 * 3 3.548931027638357e-02 3.548931025744455e-02 1.89390e-11 2.08171e-10 ----------------------------------------------------------------------------------------------------- 18 Co 1 9.853182686269621e-01 9.853182685986133e-01 2.83489e-11 1.20896e-09 2 3.209342809974314e-01 3.209342809936159e-01 3.81545e-12 4.16312e-10 3 1.009961090917681e+00 1.009961090711942e+00 2.05739e-10 2.08601e-10 ----------------------------------------------------------------------------------------------------- 19 Ti 1 2.508132831320828e-01 2.508132831400536e-01 7.97085e-12 3.07255e-10 2 3.050203487799280e-02 3.050203486558955e-02 1.24033e-11 2.22483e-10 3 -3.851630285884623e-01 -3.851630285766823e-01 1.17800e-11 2.14134e-10 ----------------------------------------------------------------------------------------------------- 20 Co 1 -3.280739281990049e-01 -3.280739281960314e-01 2.97351e-12 1.63197e-10 2 6.181205233648797e-01 6.181205233193250e-01 4.55547e-11 4.10771e-12 3 -9.770723459295628e-01 -9.770723459283587e-01 1.20415e-12 1.19379e-09 ----------------------------------------------------------------------------------------------------- 21 Co 1 -4.214046036088543e-01 -4.214046036156788e-01 6.82449e-12 2.41559e-10 2 6.824844732326752e-01 6.824844731423503e-01 9.03250e-11 1.86944e-10 3 -6.881438386887602e-01 -6.881438386857003e-01 3.05989e-12 1.88429e-10 ----------------------------------------------------------------------------------------------------- 22 Co 1 -7.932965982870016e-01 -7.932965982369141e-01 5.00875e-11 3.06813e-09 * 2 6.700913850214277e-01 6.700913849728241e-01 4.86037e-11 4.61131e-10 3 1.656724970861309e-01 1.656724971418435e-01 5.57126e-11 1.30477e-10 ----------------------------------------------------------------------------------------------------- 23 Co 1 -5.013438207120334e-01 -5.013438207300513e-01 1.80179e-11 5.36853e-11 2 8.138848028686582e-01 8.138848028974955e-01 2.88374e-11 7.28261e-11 3 -3.725357656898577e-01 -3.725357656602536e-01 2.96040e-11 1.54349e-10 ----------------------------------------------------------------------------------------------------- 24 Co 1 3.621253703126966e-01 3.621253703300377e-01 1.73410e-11 2.45306e-10 2 -7.920557503835793e-01 -7.920557502406215e-01 1.42958e-10 3.64514e-10 3 -7.532114041702276e-01 -7.532114041687719e-01 1.45572e-12 3.55999e-10 ----------------------------------------------------------------------------------------------------- 25 Co 1 1.065068568099867e+00 1.065068568106036e+00 6.16862e-12 9.99001e-12 2 1.227152179120120e+00 1.227152179143428e+00 2.33078e-11 6.99778e-09 * 3 1.231863311072055e+00 1.231863311032109e+00 3.99456e-11 2.71582e-10 ----------------------------------------------------------------------------------------------------- 26 Ti 1 4.950041636806589e-01 4.950041636884929e-01 7.83401e-12 8.56143e-11 2 -1.333062051604046e+00 -1.333062051726575e+00 1.22529e-10 3.16381e-10 3 -1.444793898038533e+00 -1.444793897997696e+00 4.08371e-11 1.97490e-10 ----------------------------------------------------------------------------------------------------- 27 Ti 1 1.961397662941451e+00 1.961397662891558e+00 4.98934e-11 4.64472e-10 2 -3.007238693055774e+00 -3.007238692962619e+00 9.31544e-11 8.99900e-10 3 -8.191426481810982e-01 -8.191426482021955e-01 2.10973e-11 3.74421e-10 ----------------------------------------------------------------------------------------------------- 28 Ti 1 -2.134565076973384e+00 -2.134565076931921e+00 4.14633e-11 2.82614e-09 * 2 1.363524369390693e+00 1.363524369378443e+00 1.22506e-11 2.70939e-11 3 4.502600574207860e-01 4.502600574182778e-01 2.50816e-12 5.21692e-09 * ----------------------------------------------------------------------------------------------------- 29 Co 1 -1.422697209818548e+00 -1.422697209796908e+00 2.16409e-11 1.04741e-10 2 -2.341868562022717e-01 -2.341868561846287e-01 1.76430e-11 1.08183e-10 3 8.932979776408201e-01 8.932979776510166e-01 1.01965e-11 4.19892e-10 ----------------------------------------------------------------------------------------------------- 30 Ti 1 8.457148096338396e-02 8.457148094541175e-02 1.79722e-11 8.81070e-11 2 1.629503603502925e+00 1.629503603525367e+00 2.24420e-11 2.64329e-10 3 1.741265478752744e+00 1.741265478760792e+00 8.04845e-12 1.06368e-10 ----------------------------------------------------------------------------------------------------- 31 Ti 1 -4.942636124164732e-01 -4.942636124195174e-01 3.04429e-12 6.82359e-11 2 1.568974967961321e-01 1.568974968003422e-01 4.21002e-12 1.67346e-10 3 -2.866152181709151e-01 -2.866152181906486e-01 1.97335e-11 1.72519e-10 ----------------------------------------------------------------------------------------------------- 32 Co 1 3.696976123630906e-01 3.696976123960066e-01 3.29159e-11 2.81601e-10 2 -7.266757934948709e-01 -7.266757934954612e-01 5.90306e-13 1.19058e-11 3 -1.267109487425129e+00 -1.267109487459048e+00 3.39198e-11 7.55620e-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.