!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : Tersoff_LAMMPS_Tersoff_PRB39_1989_GeSi__MO_350526375143_000 Supported species : Ge Si 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 = Ge | a0 = 4.02358818054 | (Configuration in file "config-Ge.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ge 1 2.764587175330084e+00 2.764587175325790e+00 4.29434e-12 1.90052e-11 2 2.187227872947783e+00 2.187227872945934e+00 1.84830e-12 6.70899e-11 3 5.630407128046520e-02 5.630407129444726e-02 1.39821e-11 2.49972e-11 ----------------------------------------------------------------------------------------------------- 2 Ge 1 1.960566177435548e-01 1.960566177471066e-01 3.55188e-12 3.01246e-11 2 7.987443995116763e-01 7.987443995082670e-01 3.40927e-12 1.20333e-11 3 2.689493921572184e+00 2.689493921563856e+00 8.32756e-12 1.27565e-11 ----------------------------------------------------------------------------------------------------- 3 Ge 1 -1.933717173719901e+00 -1.933717173706457e+00 1.34446e-11 8.26630e-11 2 1.004667463321234e+00 1.004667463353638e+00 3.24036e-11 1.49841e-09 * 3 6.821279919085953e-01 6.821279918632560e-01 4.53393e-11 3.06583e-10 ----------------------------------------------------------------------------------------------------- 4 Ge 1 3.226889191909830e+00 3.226889191919138e+00 9.30811e-12 3.96927e-11 2 4.546537272943879e+00 4.546537272958693e+00 1.48139e-11 5.77227e-11 3 2.823795554873053e+00 2.823795554874310e+00 1.25677e-12 3.15259e-11 ----------------------------------------------------------------------------------------------------- 5 Ge 1 -2.960724322603647e-01 -2.960724322604903e-01 1.25677e-13 2.37440e-11 2 -7.615620588815013e-01 -7.615620588850250e-01 3.52374e-12 1.52739e-10 3 -8.888721731200763e-01 -8.888721731183918e-01 1.68443e-12 3.97786e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 1.161369687824278e+00 1.161369687830651e+00 6.37224e-12 2.39655e-11 2 5.094733390900190e-01 5.094733390937972e-01 3.77820e-12 1.99328e-11 3 -2.469085878757569e+00 -2.469085878749575e+00 7.99405e-12 1.11884e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 3.677422550463376e+00 3.677422550463841e+00 4.64961e-13 1.72351e-11 2 -6.097631807485610e+00 -6.097631807480496e+00 5.11413e-12 8.45457e-12 3 -2.837691134549053e-01 -2.837691134554842e-01 5.78926e-13 4.11930e-11 ----------------------------------------------------------------------------------------------------- 8 Ge 1 -5.075492417159726e+00 -5.075492417165605e+00 5.87885e-12 5.90941e-11 2 5.699938797297117e+00 5.699938797296378e+00 7.38964e-13 2.62084e-11 3 7.172307655183001e-01 7.172307654914825e-01 2.68177e-11 1.54349e-10 ----------------------------------------------------------------------------------------------------- 9 Ge 1 -1.653955431018800e-01 -1.653955431070977e-01 5.21774e-12 9.23722e-12 2 -4.645587031489653e+00 -4.645587031479854e+00 9.79838e-12 7.34204e-11 3 4.283644273832073e+00 4.283644273829334e+00 2.73914e-12 4.55715e-11 ----------------------------------------------------------------------------------------------------- 10 Ge 1 -1.601493644507483e+00 -1.601493644508125e+00 6.41931e-13 8.77765e-12 2 2.956068887418153e+00 2.956068887414561e+00 3.59224e-12 5.90772e-12 3 -2.863627608259417e+00 -2.863627608260913e+00 1.49658e-12 5.09144e-11 ----------------------------------------------------------------------------------------------------- 11 Ge 1 -3.962552158289610e+00 -3.962552158289008e+00 6.02185e-13 1.28304e-10 2 -3.951809428949586e+00 -3.951809428979737e+00 3.01510e-11 6.50555e-11 3 2.152816864014312e+00 2.152816864023093e+00 8.78098e-12 9.22284e-11 ----------------------------------------------------------------------------------------------------- 12 Ge 1 -4.214327445764092e-01 -4.214327445829125e-01 6.50330e-12 3.49786e-10 * 2 3.282993476864671e-01 3.282993476839915e-01 2.47558e-12 1.63367e-11 3 4.585084745550397e-02 4.585084745789746e-02 2.39348e-12 5.06421e-11 ----------------------------------------------------------------------------------------------------- 13 Ge 1 6.915299241704035e-01 6.915299241824843e-01 1.20808e-11 5.33870e-11 2 -6.833073160789668e+00 -6.833073160779572e+00 1.00968e-11 4.32108e-11 3 -7.074134321691498e+00 -7.074134321691659e+00 1.60760e-13 9.36140e-12 ----------------------------------------------------------------------------------------------------- 14 Ge 1 -1.113172699865180e+00 -1.113172699872814e+00 7.63478e-12 9.15414e-11 2 -2.191649236369041e-01 -2.191649236229350e-01 1.39691e-11 1.19973e-11 3 -8.675211855877731e-01 -8.675211855900954e-01 2.32225e-12 3.98276e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 2.520399386804717e+00 2.520399386814602e+00 9.88498e-12 8.59419e-11 2 -3.783016120310990e+00 -3.783016120306853e+00 4.13669e-12 8.99503e-12 3 2.445156456497346e-01 2.445156457092449e-01 5.95103e-11 1.01972e-10 ----------------------------------------------------------------------------------------------------- 16 Ge 1 1.185137147102370e+00 1.185137147116645e+00 1.42746e-11 6.48748e-11 2 7.687592387312788e+00 7.687592387317165e+00 4.37694e-12 2.13687e-11 3 1.762146869316225e+00 1.762146869281865e+00 3.43598e-11 1.65317e-11 ----------------------------------------------------------------------------------------------------- 17 Ge 1 9.577950505029311e-01 9.577950505028077e-01 1.23457e-13 7.91709e-11 2 1.899928472074343e+00 1.899928472063451e+00 1.08926e-11 7.04845e-11 3 -4.465862975474850e+00 -4.465862975448703e+00 2.61471e-11 1.07722e-10 ----------------------------------------------------------------------------------------------------- 18 Ge 1 -3.226990725636763e+00 -3.226990725753522e+00 1.16759e-10 2.55879e-10 2 1.723879023576989e+00 1.723879023589051e+00 1.20619e-11 1.07330e-10 3 -1.585329316408950e+00 -1.585329316448190e+00 3.92399e-11 8.96966e-10 * ----------------------------------------------------------------------------------------------------- 19 Ge 1 1.164791891307655e+00 1.164791891316743e+00 9.08806e-12 3.31954e-11 2 4.523435187209267e-01 4.523435187230938e-01 2.16710e-12 4.02122e-11 3 6.378525799598316e-01 6.378525799514853e-01 8.34632e-12 1.74722e-11 ----------------------------------------------------------------------------------------------------- 20 Ge 1 6.833965014986751e-01 6.833965014845462e-01 1.41289e-11 1.13956e-10 2 3.119349162015497e-01 3.119349162063438e-01 4.79411e-12 1.63705e-11 3 -6.467702078246251e-01 -6.467702078202791e-01 4.34608e-12 2.50276e-11 ----------------------------------------------------------------------------------------------------- 21 Ge 1 -1.865145372163692e-01 -1.865145371528477e-01 6.35215e-11 4.05987e-10 * 2 6.142323116764567e-02 6.142323118110612e-02 1.34604e-11 5.41701e-06 * 3 1.349782860926763e+00 1.349782860933836e+00 7.07301e-12 1.57931e-10 ----------------------------------------------------------------------------------------------------- 22 Ge 1 1.098987185297754e+00 1.098987185297881e+00 1.26565e-13 1.73959e-11 2 5.045947595816200e+00 5.045947595826052e+00 9.85256e-12 5.44453e-12 3 5.228292887704646e+00 5.228292887690759e+00 1.38867e-11 1.14135e-10 ----------------------------------------------------------------------------------------------------- 23 Ge 1 -1.930903223638526e+00 -1.930903223633082e+00 5.44387e-12 2.71281e-11 2 1.315630994519239e+00 1.315630994529165e+00 9.92606e-12 2.14873e-11 3 -2.828295168785782e-01 -2.828295168748596e-01 3.71858e-12 1.20059e-11 ----------------------------------------------------------------------------------------------------- 24 Ge 1 -2.620145979100832e+00 -2.620145979116640e+00 1.58078e-11 7.60121e-11 2 6.833625543234282e-01 6.833625543236601e-01 2.31926e-13 2.47613e-11 3 -1.946999543614197e+00 -1.946999543629698e+00 1.55012e-11 9.25733e-11 ----------------------------------------------------------------------------------------------------- 25 Ge 1 -5.060444105629087e-01 -5.060444105521330e-01 1.07757e-11 9.92361e-11 2 -3.778799168996177e+00 -3.778799168998836e+00 2.65832e-12 6.36700e-11 3 6.030562165162269e-01 6.030562165161691e-01 5.77316e-14 2.09145e-11 ----------------------------------------------------------------------------------------------------- 26 Ge 1 -3.316918296559082e+00 -3.316918296570206e+00 1.11235e-11 6.57323e-11 2 3.367886719783874e+00 3.367886719754962e+00 2.89120e-11 1.65502e-10 3 -2.042629632669876e-01 -2.042629632648007e-01 2.18692e-12 5.45460e-11 ----------------------------------------------------------------------------------------------------- 27 Ge 1 8.928889430958344e-01 8.928889430828221e-01 1.30124e-11 9.94341e-11 2 -5.130717276338197e+00 -5.130717276364472e+00 2.62750e-11 6.34017e-11 3 -7.972906437343343e-02 -7.972906437541244e-02 1.97901e-12 4.35088e-11 ----------------------------------------------------------------------------------------------------- 28 Ge 1 2.069667531860664e-03 2.069667520761372e-03 1.10993e-11 1.42822e-11 2 5.162909905822863e-02 5.162909905346182e-02 4.76681e-12 1.40820e-11 3 -1.846280400444299e+00 -1.846280400453638e+00 9.33831e-12 8.98481e-12 ----------------------------------------------------------------------------------------------------- 29 Ge 1 1.784715663712193e+00 1.784715663720827e+00 8.63398e-12 1.24658e-10 2 -5.455639002747747e+00 -5.455639002755124e+00 7.37632e-12 4.80735e-11 3 1.126025765244915e+00 1.126025765264396e+00 1.94817e-11 6.29519e-11 ----------------------------------------------------------------------------------------------------- 30 Ge 1 1.221390225489703e+00 1.221390225470250e+00 1.94529e-11 5.55933e-11 2 1.650285556644544e+00 1.650285556638696e+00 5.84843e-12 1.16024e-09 * 3 2.194138374299501e+00 2.194138374431425e+00 1.31924e-10 1.47670e-10 ----------------------------------------------------------------------------------------------------- 31 Ge 1 -3.597967109110103e-01 -3.597967109005262e-01 1.04841e-11 5.44559e-11 2 -1.822512787000664e+00 -1.822512787004909e+00 4.24460e-12 8.84982e-10 * 3 -3.061102992102928e+00 -3.061102992071937e+00 3.09903e-11 4.04961e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 3.487215887320828e+00 3.487215887321818e+00 9.89431e-13 1.51150e-11 2 1.967113172106179e-01 1.967113172210320e-01 1.04141e-11 2.73481e-12 3 1.969101771187740e+00 1.969101771188574e+00 8.33555e-13 6.67748e-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 dicontinuities. Maximum error obtained for particle = 28, direction = 1: |F_model - F_numer| error = --------------------------------- = 5.36284e-09 max{(|F_model|+|F_numer|)/2, 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 = Si | a0 = 3.89748287201 | (Configuration in file "config-Si.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -1.155171982040118e+00 -1.155171982042148e+00 2.03082e-12 6.87295e-12 2 -3.958592147799034e+00 -3.958592147804062e+00 5.02798e-12 1.60956e-11 3 -3.507286528775827e+00 -3.507286528777411e+00 1.58362e-12 1.95201e-09 * ----------------------------------------------------------------------------------------------------- 2 Si 1 6.186796107912778e+00 6.186796107915462e+00 2.68319e-12 9.08988e-11 2 -3.405122512797456e+00 -3.405122512804825e+00 7.36922e-12 3.05251e-10 3 -2.252203963965121e+00 -2.252203963883881e+00 8.12399e-11 1.02619e-06 * ----------------------------------------------------------------------------------------------------- 3 Si 1 3.291905022422873e+00 3.291905022444468e+00 2.15947e-11 9.97642e-11 2 3.847167530166213e-01 3.847167530071059e-01 9.51539e-12 3.44241e-11 3 1.137936472342591e-01 1.137936472492529e-01 1.49938e-11 8.52970e-11 ----------------------------------------------------------------------------------------------------- 4 Si 1 -2.511373107667317e+00 -2.511373107663375e+00 3.94174e-12 8.62816e-11 2 3.478080774459519e+00 3.478080774457800e+00 1.71818e-12 1.75610e-10 3 3.708816392075962e+00 3.708816392072220e+00 3.74234e-12 1.09162e-11 ----------------------------------------------------------------------------------------------------- 5 Si 1 -4.280079755390489e+00 -4.280079755388170e+00 2.31992e-12 7.90177e-11 2 3.245457925460633e+00 3.245457925454699e+00 5.93392e-12 5.29581e-10 3 3.065307279127572e+00 3.065307279110698e+00 1.68745e-11 2.59747e-10 ----------------------------------------------------------------------------------------------------- 6 Si 1 -2.460482828404989e-01 -2.460482828368322e-01 3.66673e-12 7.59921e-11 2 -4.293657551584095e-01 -4.293657551736893e-01 1.52798e-11 4.17361e-11 3 8.372015158884867e-01 8.372015159164687e-01 2.79821e-11 4.59764e-11 ----------------------------------------------------------------------------------------------------- 7 Si 1 -8.410841032071632e+00 -8.410841032085367e+00 1.37348e-11 1.43581e-10 2 3.739253189745155e+00 3.739253189741123e+00 4.03233e-12 2.76104e-11 3 1.745762952588454e+00 1.745762952600217e+00 1.17630e-11 1.82725e-10 ----------------------------------------------------------------------------------------------------- 8 Si 1 -1.278846708061703e+00 -1.278846708136709e+00 7.50064e-11 1.25890e-10 2 -6.063414112947029e+00 -6.063414112921005e+00 2.60245e-11 7.70504e-11 3 2.110067650663305e+00 2.110067650624019e+00 3.92859e-11 2.58543e-06 * ----------------------------------------------------------------------------------------------------- 9 Si 1 -9.472554451722220e-01 -9.472554451814434e-01 9.22140e-12 1.27178e-11 2 6.757243806640493e-01 6.757243806653566e-01 1.30729e-12 8.42841e-11 3 -7.360601490640165e-01 -7.360601490372509e-01 2.67656e-11 7.40744e-11 ----------------------------------------------------------------------------------------------------- 10 Si 1 6.389125186585354e+00 6.389125186573686e+00 1.16680e-11 4.14548e-11 2 4.874751424481760e-01 4.874751424440418e-01 4.13419e-12 6.34339e-11 3 2.752369326423999e+00 2.752369326439685e+00 1.56857e-11 5.78710e-11 ----------------------------------------------------------------------------------------------------- 11 Si 1 1.404091676376974e-01 1.404091676635266e-01 2.58292e-11 4.77341e-10 2 4.428556789532959e+00 4.428556789550949e+00 1.79892e-11 8.19496e-11 3 3.130029329151167e+00 3.130029329139441e+00 1.17262e-11 5.78737e-12 ----------------------------------------------------------------------------------------------------- 12 Si 1 2.869928114668342e+00 2.869928114668882e+00 5.39568e-13 7.70424e-11 2 -7.406959988842967e-01 -7.406959988825731e-01 1.72362e-12 4.41001e-10 3 4.575441919377560e+00 4.575441919369865e+00 7.69429e-12 1.21283e-10 ----------------------------------------------------------------------------------------------------- 13 Si 1 -2.338140196885508e+00 -2.338140196865279e+00 2.02292e-11 2.74181e-10 2 -4.528018530277437e+00 -4.528018530282857e+00 5.42055e-12 3.26009e-10 3 -7.053062157393386e-01 -7.053062157572050e-01 1.78664e-11 4.45385e-11 ----------------------------------------------------------------------------------------------------- 14 Si 1 5.752357449715626e+00 5.752357449715598e+00 2.75335e-14 6.42162e-11 2 3.465142712625555e+00 3.465142712760650e+00 1.35095e-10 5.32973e-10 3 -3.227753805824212e+00 -3.227753805567405e+00 2.56807e-10 2.58018e-09 * ----------------------------------------------------------------------------------------------------- 15 Si 1 3.113793148671556e+00 3.113793148659151e+00 1.24056e-11 4.57683e-11 2 5.951552253773287e-01 5.951552253258092e-01 5.15195e-11 5.13298e-10 3 -1.883049228275878e+00 -1.883049228262989e+00 1.28895e-11 2.75821e-09 * ----------------------------------------------------------------------------------------------------- 16 Si 1 -1.015345470569752e+01 -1.015345470569333e+01 4.19398e-12 4.07070e-11 2 1.974551918686979e+00 1.974551918612994e+00 7.39857e-11 3.20965e-11 3 4.268364990947064e-01 4.268364990989574e-01 4.25093e-12 1.22643e-09 * ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.050195615943514e-01 -2.050195613694496e-01 2.24902e-10 1.73848e-07 * 2 1.828638231426120e+00 1.828638231614097e+00 1.87977e-10 1.48668e-09 * 3 1.492187182982383e+00 1.492187183016681e+00 3.42986e-11 4.16636e-10 ----------------------------------------------------------------------------------------------------- 18 Si 1 3.377205240703766e+00 3.377205239975189e+00 7.28577e-10 3.18731e-09 * 2 -3.448532369363785e+00 -3.448532368941619e+00 4.22167e-10 2.82662e-08 * 3 -1.304137652634735e+00 -1.304137652633654e+00 1.08114e-12 3.37695e-10 ----------------------------------------------------------------------------------------------------- 19 Si 1 1.723878540046847e+00 1.723878540061949e+00 1.51017e-11 2.08547e-10 2 8.842157315020315e-01 8.842157315031677e-01 1.13620e-12 1.02947e-10 3 -3.711412876086881e-01 -3.711412876085362e-01 1.51990e-13 3.11325e-11 ----------------------------------------------------------------------------------------------------- 20 Si 1 -1.326547427350669e+00 -1.326547427373234e+00 2.25644e-11 4.01881e-11 2 -4.757184503720155e+00 -4.757184503717559e+00 2.59615e-12 1.63933e-10 3 1.572044424523277e+00 1.572044424494186e+00 2.90916e-11 7.06062e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 4.322136427673961e+00 4.322136427694018e+00 2.00568e-11 4.37606e-11 2 1.840906746069300e+00 1.840906746099818e+00 3.05183e-11 1.06311e-10 3 -5.106087255744098e+00 -5.106087255743978e+00 1.19904e-13 1.59180e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 1.001381008745101e+00 1.001381008740756e+00 4.34475e-12 5.88884e-12 2 -2.255689303128721e+00 -2.255689303133712e+00 4.99067e-12 2.98122e-11 3 2.281423767241097e+00 2.281423767252093e+00 1.09961e-11 4.40257e-11 ----------------------------------------------------------------------------------------------------- 23 Si 1 -1.095110231035734e+00 -1.095110231034012e+00 1.72262e-12 6.37534e-12 2 7.837892459387513e-01 7.837892459307160e-01 8.03535e-12 8.15070e-12 3 6.359515857616758e-02 6.359515857909423e-02 2.92665e-12 9.62345e-12 ----------------------------------------------------------------------------------------------------- 24 Si 1 -2.383139941375547e+00 -2.383139941390627e+00 1.50795e-11 6.99081e-11 2 -8.791454865122096e-02 -8.791454868535860e-02 3.41376e-11 8.98156e-11 3 1.054322843046705e-01 1.054322843202181e-01 1.55476e-11 4.74174e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 -5.122602056718285e-01 -5.122602056700906e-01 1.73794e-12 6.93505e-11 2 1.139543802190531e+00 1.139543802203124e+00 1.25935e-11 4.17446e-11 3 -3.396657684904239e+00 -3.396657684891035e+00 1.32041e-11 6.66658e-11 ----------------------------------------------------------------------------------------------------- 26 Si 1 -1.807075226377306e+00 -1.807075226339461e+00 3.78451e-11 1.27029e-10 2 -5.393493303416962e-01 -5.393493303539940e-01 1.22978e-11 3.83017e-11 3 -3.004081835062311e-01 -3.004081834930638e-01 1.31673e-11 1.47985e-10 ----------------------------------------------------------------------------------------------------- 27 Si 1 5.139403591035342e+00 5.139403591026022e+00 9.32054e-12 1.11678e-10 2 1.064831380745116e+00 1.064831380768365e+00 2.32492e-11 4.69282e-11 3 1.224134814151626e+00 1.224134814156171e+00 4.54548e-12 4.63178e-11 ----------------------------------------------------------------------------------------------------- 28 Si 1 2.121381269153459e+00 2.121381269133364e+00 2.00946e-11 1.59202e-11 2 6.361865469224345e-01 6.361865469215520e-01 8.82516e-13 5.12195e-11 3 -1.715874314496279e+00 -1.715874314494687e+00 1.59206e-12 1.93121e-10 ----------------------------------------------------------------------------------------------------- 29 Si 1 -1.324155475116861e+00 -1.324155475108187e+00 8.67417e-12 1.58858e-10 2 4.059967744446501e+00 4.059967744437146e+00 9.35518e-12 2.44107e-11 3 1.928719627055644e+00 1.928719627068422e+00 1.27782e-11 4.41998e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -5.924309903597152e+00 -5.924309903567737e+00 2.94147e-11 9.02238e-11 2 -4.686566263662793e-01 -4.686566263690140e-01 2.73470e-12 5.44525e-11 3 4.811006923664428e+00 4.811006923648256e+00 1.61711e-11 7.92850e-11 ----------------------------------------------------------------------------------------------------- 31 Si 1 -3.036148381120339e+00 -3.036148381120172e+00 1.66978e-13 2.45090e-10 2 3.638867170433395e+00 3.638867170426304e+00 7.09077e-12 7.51639e-11 3 -1.203147895498947e-01 -1.203147895161555e-01 3.37392e-11 4.30973e-11 ----------------------------------------------------------------------------------------------------- 32 Si 1 3.505277294094097e+00 3.505277294101259e+00 7.16183e-12 1.66104e-10 2 -7.668525672255624e+00 -7.668525672283693e+00 2.80682e-11 1.52374e-10 3 -1.131788963403621e+01 -1.131788963404112e+01 4.90630e-12 1.04160e-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 dicontinuities. Maximum error obtained for particle = 24, direction = 2: |F_model - F_numer| error = --------------------------------- = 3.88305e-10 max{(|F_model|+|F_numer|)/2, 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 = Ge Si | a0 = 3.88222043246 | (Configuration in file "config-GeSi.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Si 1 -4.772523951939153e+00 -4.772523951928970e+00 1.01830e-11 6.60688e-10 * 2 -4.427321151393936e+00 -4.427321151391964e+00 1.97176e-12 3.85718e-11 3 -3.781464293352843e+00 -3.781464293353404e+00 5.60885e-13 1.09086e-11 ----------------------------------------------------------------------------------------------------- 2 Si 1 2.873011852557183e+00 2.873011852557766e+00 5.83089e-13 9.34373e-11 2 6.895996553097850e+00 6.895996553082629e+00 1.52207e-11 2.85843e-10 3 -7.798564054930624e+00 -7.798564054968762e+00 3.81375e-11 2.50425e-10 ----------------------------------------------------------------------------------------------------- 3 Si 1 1.948887239172091e+00 1.948887239128089e+00 4.40019e-11 4.40757e-10 2 -6.458238971385073e+00 -6.458238971337214e+00 4.78595e-11 2.11689e-10 3 5.314153744110243e+00 5.314153744137383e+00 2.71401e-11 2.01871e-10 ----------------------------------------------------------------------------------------------------- 4 Ge 1 -3.105244208822366e+00 -3.105244208829601e+00 7.23466e-12 3.35416e-11 2 7.584452718751897e+00 7.584452718762715e+00 1.08180e-11 3.07123e-11 3 5.523985915875808e+00 5.523985915864198e+00 1.16103e-11 2.02531e-10 ----------------------------------------------------------------------------------------------------- 5 Si 1 6.081151461998401e-01 6.081151461926426e-01 7.19746e-12 2.56807e-10 2 -1.539365429863026e+00 -1.539365429869019e+00 5.99321e-12 3.62755e-10 3 -1.842893728804645e+00 -1.842893728799944e+00 4.70091e-12 1.94147e-11 ----------------------------------------------------------------------------------------------------- 6 Ge 1 1.667445038198325e+00 1.667445038209101e+00 1.07760e-11 5.39725e-10 * 2 -3.129538348671848e+00 -3.129538348667102e+00 4.74598e-12 1.47350e-10 3 -3.252756800052260e+00 -3.252756800057085e+00 4.82503e-12 2.16733e-11 ----------------------------------------------------------------------------------------------------- 7 Ge 1 4.234428779009790e+00 4.234428779004595e+00 5.19496e-12 5.04784e-10 * 2 -2.484767307610726e+00 -2.484767307611954e+00 1.22835e-12 6.43290e-11 3 -4.586246699987964e+00 -4.586246699984613e+00 3.35021e-12 4.06146e-11 ----------------------------------------------------------------------------------------------------- 8 Ge 1 -5.891133400670390e-01 -5.891133400641644e-01 2.87459e-12 4.81299e-10 2 -3.258285166953537e-01 -3.258285166653371e-01 3.00166e-11 1.97760e-10 3 2.620887094111517e+00 2.620887094093181e+00 1.83360e-11 1.22225e-10 ----------------------------------------------------------------------------------------------------- 9 Ge 1 4.211341671661114e-01 4.211341671788041e-01 1.26927e-11 6.17356e-12 2 5.514872422833251e-01 5.514872422870791e-01 3.75400e-12 1.55558e-11 3 5.689617048983100e-01 5.689617048829511e-01 1.53589e-11 1.08266e-10 ----------------------------------------------------------------------------------------------------- 10 Si 1 -2.659874257241933e-01 -2.659874257292577e-01 5.06439e-12 1.21272e-10 2 1.122686123466847e+00 1.122686123485700e+00 1.88527e-11 1.74813e-11 3 2.497935434901809e+00 2.497935434905883e+00 4.07452e-12 8.13754e-11 ----------------------------------------------------------------------------------------------------- 11 Ge 1 -4.062310993203633e+00 -4.062310993173745e+00 2.98881e-11 2.89413e-11 2 -1.151896740809463e+00 -1.151896740836238e+00 2.67755e-11 7.46132e-11 3 1.842806088262712e+00 1.842806088194546e+00 6.81664e-11 6.10507e-11 ----------------------------------------------------------------------------------------------------- 12 Si 1 1.477019678781900e+00 1.477019678771867e+00 1.00324e-11 1.65645e-10 2 -1.469709719552080e+00 -1.469709719547575e+00 4.50529e-12 1.43046e-10 3 -1.483084195693891e+00 -1.483084195702193e+00 8.30180e-12 2.15454e-11 ----------------------------------------------------------------------------------------------------- 13 Si 1 5.159138387037161e-01 5.159138386994949e-01 4.22118e-12 1.31806e-10 2 4.068536816839272e+00 4.068536816811336e+00 2.79359e-11 4.97984e-11 3 -2.415819260811875e+00 -2.415819260812798e+00 9.23261e-13 7.76654e-11 ----------------------------------------------------------------------------------------------------- 14 Ge 1 -4.628970867168177e+00 -4.628970867168626e+00 4.49418e-13 4.75406e-11 2 -2.937806724848671e+00 -2.937806724852611e+00 3.94040e-12 1.94236e-11 3 4.425236583061534e+00 4.425236583051714e+00 9.82059e-12 8.34666e-11 ----------------------------------------------------------------------------------------------------- 15 Ge 1 3.119359548748508e+00 3.119359548762360e+00 1.38525e-11 8.59854e-11 2 5.143990437568481e+00 5.143990437603159e+00 3.46780e-11 1.42834e-10 3 1.265319678772150e+00 1.265319678752596e+00 1.95544e-11 7.51172e-10 * ----------------------------------------------------------------------------------------------------- 16 Si 1 4.117142948168180e+00 4.117142948171620e+00 3.43992e-12 9.35447e-11 2 1.585844590380692e+00 1.585844590383177e+00 2.48512e-12 1.06839e-11 3 -8.228341991194871e+00 -8.228341991211245e+00 1.63745e-11 5.39160e-11 ----------------------------------------------------------------------------------------------------- 17 Si 1 -2.766566350360950e-02 -2.766566351737223e-02 1.37627e-11 6.95292e-11 2 -2.400625607332644e+00 -2.400625607334913e+00 2.26974e-12 1.38320e-11 3 1.720895802132596e+00 1.720895802130785e+00 1.81166e-12 9.31359e-11 ----------------------------------------------------------------------------------------------------- 18 Si 1 4.641996218471266e+00 4.641996218456200e+00 1.50662e-11 6.86668e-11 2 -1.265990423412881e+00 -1.265990423430835e+00 1.79541e-11 2.64311e-11 3 -2.451471856329618e+00 -2.451471856306479e+00 2.31393e-11 3.32481e-11 ----------------------------------------------------------------------------------------------------- 19 Si 1 -4.275858147684720e-01 -4.275858147646885e-01 3.78347e-12 3.36144e-11 2 2.265953625358891e+00 2.265953625362650e+00 3.75922e-12 3.84586e-11 3 -7.585456542822184e-01 -7.585456542865907e-01 4.37228e-12 1.35843e-10 ----------------------------------------------------------------------------------------------------- 20 Ge 1 -1.433503494642566e+00 -1.433503494646971e+00 4.40492e-12 1.57054e-10 2 3.078752781415686e+00 3.078752781423575e+00 7.88969e-12 5.35794e-11 3 -4.947698010466409e-01 -4.947698010573854e-01 1.07445e-11 4.83041e-11 ----------------------------------------------------------------------------------------------------- 21 Si 1 -1.008874511834032e+01 -1.008874511832295e+01 1.73745e-11 1.43551e-10 2 -3.211487104800408e+00 -3.211487104790289e+00 1.01190e-11 1.00053e-10 3 2.361303831855641e+00 2.361303831834384e+00 2.12568e-11 1.87147e-10 ----------------------------------------------------------------------------------------------------- 22 Si 1 7.141244465047321e+00 7.141244465055248e+00 7.92699e-12 1.53054e-10 2 4.855570773429103e+00 4.855570773424547e+00 4.55636e-12 1.08444e-10 3 1.565695876481028e+00 1.565695876464320e+00 1.67082e-11 2.37806e-10 ----------------------------------------------------------------------------------------------------- 23 Ge 1 9.573002615120816e-01 9.573002615310136e-01 1.89320e-11 2.22062e-11 2 -1.461875329014568e+00 -1.461875328974677e+00 3.98908e-11 3.66831e-11 3 1.445793157438198e+00 1.445793157439358e+00 1.15974e-12 1.50366e-10 ----------------------------------------------------------------------------------------------------- 24 Ge 1 -6.448482063752907e+00 -6.448482063771459e+00 1.85514e-11 1.20813e-10 2 -3.465472434015591e+00 -3.465472434010873e+00 4.71800e-12 1.87294e-10 3 2.429558292900793e+00 2.429558292899681e+00 1.11200e-12 3.75859e-11 ----------------------------------------------------------------------------------------------------- 25 Si 1 3.647263262423363e+00 3.647263262428315e+00 4.95248e-12 1.12035e-10 2 -1.166258845814515e+00 -1.166258845800440e+00 1.40750e-11 5.85754e-12 3 4.067059327840667e+00 4.067059327850005e+00 9.33831e-12 1.25068e-10 ----------------------------------------------------------------------------------------------------- 26 Ge 1 -2.843615521931794e+00 -2.843615521946358e+00 1.45639e-11 1.02156e-08 * 2 1.209476474989621e+00 1.209476474990204e+00 5.83089e-13 1.43569e-10 3 3.323977271769182e+00 3.323977271755290e+00 1.38920e-11 3.28564e-11 ----------------------------------------------------------------------------------------------------- 27 Ge 1 -1.297934620888625e+00 -1.297934620880014e+00 8.61089e-12 1.93605e-10 2 -1.668248231781684e+00 -1.668248231794582e+00 1.28986e-11 1.89278e-10 3 1.133869468929503e+00 1.133869468928620e+00 8.83738e-13 1.73347e-10 ----------------------------------------------------------------------------------------------------- 28 Si 1 -6.335567305484182e-01 -6.335567305449615e-01 3.45668e-12 3.77312e-11 2 -4.738502337448945e+00 -4.738502337440543e+00 8.40217e-12 6.84794e-11 3 -5.578273952307395e+00 -5.578273952304706e+00 2.68940e-12 2.47515e-10 ----------------------------------------------------------------------------------------------------- 29 Ge 1 -2.307014691847223e-01 -2.307014691524809e-01 3.22414e-11 4.66415e-11 2 1.257048352031148e+00 1.257048352063756e+00 3.26081e-11 4.96228e-11 3 6.993157035232804e-01 6.993157034931770e-01 3.01035e-11 5.25160e-11 ----------------------------------------------------------------------------------------------------- 30 Si 1 -1.011682254217644e+00 -1.011682254242293e+00 2.46483e-11 9.13825e-11 2 -2.753947652339947e+00 -2.753947652352653e+00 1.27058e-11 7.80260e-11 3 7.627000680445883e-01 7.627000680383478e-01 6.24056e-12 3.80945e-11 ----------------------------------------------------------------------------------------------------- 31 Ge 1 3.174459125328863e+00 3.174459125324681e+00 4.18154e-12 4.40119e-11 2 5.255731700544382e+00 5.255731700538849e+00 5.53335e-12 7.59623e-11 3 -8.640358919288773e-01 -8.640358919544999e-01 2.56226e-11 9.42753e-11 ----------------------------------------------------------------------------------------------------- 32 Ge 1 1.322901969215111e+00 1.322901969213567e+00 1.54432e-12 1.50857e-11 2 1.181352686634142e+00 1.181352686621856e+00 1.22853e-11 5.18778e-11 3 -3.318686418583486e-02 -3.318686418742281e-02 1.58795e-12 6.22030e-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 dicontinuities. Maximum error obtained for particle = 17, direction = 1: |F_model - F_numer| error = --------------------------------- = 4.97466e-10 max{(|F_model|+|F_numer|)/2, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 5.36284e-09 Machine precision = 2.22045e-16 Grade: A Comment: The letter grade A was assigned because the normalized error in the computation was 5.36284e-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. 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.