!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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 : SW_BereSerra_2006_GaN__MO_861114678890_000 Supported species : Ga N 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 = Ga | a0 = 3.7290544509887695 | (Configuration in file "config-Ga.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 Ga 1 1.040551232381963e+00 1.040551232381741e+00 2.22267e-13 7.41229e-12 2 -6.050285721321731e-02 -6.050285721313614e-02 8.11642e-14 2.29873e-12 3 -2.398917817705519e-01 -2.398917817702348e-01 3.17107e-13 3.07221e-12 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -5.492510146108338e-01 -5.492510146118588e-01 1.02496e-12 2.71805e-12 2 3.715494449360682e-01 3.715494449356153e-01 4.52915e-13 1.44851e-11 3 1.522924546461125e+00 1.522924546460648e+00 4.76286e-13 3.00782e-12 ----------------------------------------------------------------------------------------------------- 3 Ga 1 6.268931265138995e-02 6.268931265007216e-02 1.31779e-12 2.17910e-11 2 1.162768076519461e+00 1.162768076520412e+00 9.51239e-13 5.81890e-12 3 -1.284081348321333e-01 -1.284081348322604e-01 1.27148e-13 4.34036e-12 ----------------------------------------------------------------------------------------------------- 4 Ga 1 1.134612692320748e+00 1.134612692320046e+00 7.02105e-13 7.40208e-12 2 9.538908174020545e-01 9.538908174015712e-01 4.83280e-13 1.49294e-11 3 8.397312321714343e-01 8.397312321689760e-01 2.45826e-12 9.19265e-13 ----------------------------------------------------------------------------------------------------- 5 Ga 1 2.697926264526144e-01 2.697926264527868e-01 1.72418e-13 4.54276e-12 2 6.687743710584946e-01 6.687743710581174e-01 3.77143e-13 3.70048e-12 3 8.468297068491945e-01 8.468297068492434e-01 4.89608e-14 4.07951e-12 ----------------------------------------------------------------------------------------------------- 6 Ga 1 -7.405161514789104e-01 -7.405161514810931e-01 2.18270e-12 7.96374e-12 2 -4.074896155145064e-01 -4.074896155159457e-01 1.43929e-12 3.68117e-12 3 5.181866317085390e-01 5.181866317090598e-01 5.20806e-13 1.22200e-11 ----------------------------------------------------------------------------------------------------- 7 Ga 1 8.058712173110880e-01 8.058712173103620e-01 7.25975e-13 2.29416e-12 2 -2.401414753230806e+00 -2.401414753232692e+00 1.88649e-12 2.03348e-12 3 -3.113225634238868e+00 -3.113225634238563e+00 3.04645e-13 7.08544e-12 ----------------------------------------------------------------------------------------------------- 8 Ga 1 -2.473821478798132e+00 -2.473821478795357e+00 2.77556e-12 1.02940e-11 2 -1.591088081880338e+00 -1.591088081880759e+00 4.21441e-13 4.21982e-11 3 -1.381452318136278e+00 -1.381452318135181e+00 1.09690e-12 1.27165e-11 ----------------------------------------------------------------------------------------------------- 9 Ga 1 1.087256395708565e+00 1.087256395709986e+00 1.42109e-12 5.39346e-12 2 -1.950514086145777e-01 -1.950514086139401e-01 6.37546e-13 5.21777e-12 3 1.063623498540292e+00 1.063623498540960e+00 6.67910e-13 6.37312e-12 ----------------------------------------------------------------------------------------------------- 10 Ga 1 -3.296872102654941e+00 -3.296872102657555e+00 2.61346e-12 6.27232e-12 2 9.137161391312895e-01 9.137161391309647e-01 3.24740e-13 1.14094e-11 3 -2.033955531901356e+00 -2.033955531900943e+00 4.13003e-13 1.64100e-11 ----------------------------------------------------------------------------------------------------- 11 Ga 1 -3.424202656249559e+00 -3.424202656247943e+00 1.61560e-12 2.39941e-12 2 -4.178270523253600e+00 -4.178270523254828e+00 1.22835e-12 2.95142e-11 3 -1.330835489611831e+00 -1.330835489609745e+00 2.08566e-12 1.07323e-11 ----------------------------------------------------------------------------------------------------- 12 Ga 1 4.485047616240919e-01 4.485047616243575e-01 2.65621e-13 1.25912e-11 2 -1.160598173004786e-01 -1.160598173001614e-01 3.17205e-13 2.18246e-12 3 -5.499490090400834e-01 -5.499490090412467e-01 1.16329e-12 3.38618e-12 ----------------------------------------------------------------------------------------------------- 13 Ga 1 5.962797253632494e-01 5.962797253651807e-01 1.93134e-12 7.61136e-12 2 -2.684919810800308e+00 -2.684919810799411e+00 8.97060e-13 1.95648e-11 3 -4.034377735145076e+00 -4.034377735143202e+00 1.87406e-12 7.71916e-12 ----------------------------------------------------------------------------------------------------- 14 Ga 1 -1.401613373566956e-01 -1.401613373567026e-01 7.02216e-15 5.52536e-12 2 3.077248192430134e-01 3.077248192421324e-01 8.81017e-13 1.15385e-12 3 -2.106192855507743e-01 -2.106192855499383e-01 8.35998e-13 4.75103e-12 ----------------------------------------------------------------------------------------------------- 15 Ga 1 2.933836949028171e+00 2.933836949031105e+00 2.93410e-12 5.31797e-12 2 3.805088330595927e-01 3.805088330628399e-01 3.24718e-12 2.39769e-11 3 1.116361104105353e+00 1.116361104103318e+00 2.03459e-12 1.27720e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 2.731717870972287e+00 2.731717870973667e+00 1.38023e-12 7.47846e-12 2 4.882913906880418e+00 4.882913906881753e+00 1.33493e-12 5.35660e-12 3 1.501842180528236e+00 1.501842180525715e+00 2.52154e-12 3.64337e-11 ----------------------------------------------------------------------------------------------------- 17 Ga 1 6.944873378763268e-02 6.944873378776999e-02 1.37307e-13 2.99206e-12 2 4.337636140659991e-01 4.337636140650639e-01 9.35196e-13 3.26422e-12 3 -9.257257907006892e-01 -9.257257907006039e-01 8.52651e-14 6.59073e-12 ----------------------------------------------------------------------------------------------------- 18 Ga 1 4.678419451756577e-01 4.678419451763519e-01 6.94222e-13 2.85516e-12 2 2.051483556569942e+00 2.051483556571677e+00 1.73506e-12 1.04055e-11 3 -2.070996596302983e+00 -2.070996596304779e+00 1.79501e-12 1.09965e-11 ----------------------------------------------------------------------------------------------------- 19 Ga 1 1.295236266015367e-01 1.295236266016470e-01 1.10217e-13 1.21804e-11 2 -1.166429169799831e+00 -1.166429169800468e+00 6.36380e-13 6.71574e-12 3 7.846477344819693e-01 7.846477344813418e-01 6.27498e-13 1.45347e-11 ----------------------------------------------------------------------------------------------------- 20 Ga 1 1.834754693440001e-01 1.834754693450217e-01 1.02163e-12 8.99181e-12 2 4.016900517277999e-01 4.016900517304874e-01 2.68757e-12 4.09593e-11 3 -1.593465461646325e-01 -1.593465461659947e-01 1.36224e-12 9.94915e-12 ----------------------------------------------------------------------------------------------------- 21 Ga 1 -2.075521977465244e+00 -2.075521977452673e+00 1.25708e-11 1.73452e-11 2 -7.231871686234351e-01 -7.231871686217690e-01 1.66611e-12 3.20144e-11 3 1.323686310803552e+00 1.323686310800220e+00 3.33222e-12 8.25184e-12 ----------------------------------------------------------------------------------------------------- 22 Ga 1 1.753780531536044e+00 1.753780531533986e+00 2.05747e-12 1.82561e-11 2 2.538162414565411e+00 2.538162414575599e+00 1.01883e-11 3.82059e-11 3 2.754069913112798e+00 2.754069913110353e+00 2.44427e-12 3.12417e-11 ----------------------------------------------------------------------------------------------------- 23 Ga 1 -9.628458917600582e-01 -9.628458917608462e-01 7.88036e-13 7.39253e-12 2 7.767962711590769e-01 7.767962711583993e-01 6.77569e-13 2.39675e-12 3 -7.240695828841547e-01 -7.240695828851978e-01 1.04317e-12 1.52889e-12 ----------------------------------------------------------------------------------------------------- 24 Ga 1 1.191263218772760e+00 1.191263218773458e+00 6.98108e-13 1.43685e-12 2 4.136015965139971e-01 4.136015965118207e-01 2.17637e-12 1.81040e-11 3 -1.270257825528798e-03 -1.270257824624756e-03 9.04042e-13 2.56867e-11 ----------------------------------------------------------------------------------------------------- 25 Ga 1 -1.089060088601505e+00 -1.089060088600204e+00 1.30118e-12 8.79585e-12 2 -8.182588468541923e-01 -8.182588468528211e-01 1.37113e-12 2.78757e-11 3 6.013534891850230e-01 6.013534891839326e-01 1.09035e-12 3.35310e-12 ----------------------------------------------------------------------------------------------------- 26 Ga 1 -1.172554628035748e+00 -1.172554628034558e+00 1.18927e-12 9.46931e-12 2 2.936099677163793e+00 2.936099677164304e+00 5.11591e-13 5.20517e-12 3 4.023633745890728e-01 4.023633745890309e-01 4.19664e-14 1.60026e-11 ----------------------------------------------------------------------------------------------------- 27 Ga 1 6.724737064583489e-01 6.724737064592647e-01 9.15823e-13 2.15008e-11 2 -3.149517511413606e+00 -3.149517511412889e+00 7.16760e-13 3.19802e-11 3 6.718547265179955e-01 6.718547265152210e-01 2.77445e-12 3.39273e-12 ----------------------------------------------------------------------------------------------------- 28 Ga 1 -1.246097643977940e+00 -1.246097643977395e+00 5.44897e-13 4.35851e-12 2 8.596710446134841e-01 8.596710446135329e-01 4.88498e-14 7.19458e-12 3 -5.613184734920268e-02 -5.613184734846966e-02 7.33018e-13 4.19622e-12 ----------------------------------------------------------------------------------------------------- 29 Ga 1 4.718883987585286e-01 4.718883987589891e-01 4.60576e-13 3.48904e-12 2 -2.416099361065237e+00 -2.416099361064161e+00 1.07647e-12 5.34564e-11 * 3 1.756117450186026e+00 1.756117450185359e+00 6.67466e-13 1.10130e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 -6.788415920095997e-02 -6.788415920197481e-02 1.01484e-12 1.17945e-11 2 -1.747520468672372e-01 -1.747520468673275e-01 9.02889e-14 6.89102e-12 3 -5.180321537439631e-01 -5.180321537441824e-01 2.19380e-13 8.51241e-12 ----------------------------------------------------------------------------------------------------- 31 Ga 1 7.663227898789473e-01 7.663227898807661e-01 1.81877e-12 2.35951e-11 2 -1.168492133409149e+00 -1.168492133408272e+00 8.76632e-13 4.66382e-12 3 5.059090225358628e-01 5.059090225339784e-01 1.88438e-12 1.84047e-11 ----------------------------------------------------------------------------------------------------- 32 Ga 1 4.216579260629016e-01 4.216579260654139e-01 2.51221e-12 1.03623e-12 2 1.198418471230623e+00 1.198418471230395e+00 2.27596e-13 4.42424e-12 3 1.268786773421631e+00 1.268786773420599e+00 1.03184e-12 7.62945e-13 ----------------------------------------------------------------------------------------------------- * 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 = 24, direction = 3: |F_model - F_numer| error = ----------------------- = 7.11700e-10 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 = N | a0 = 2.635988235473633 | (Configuration in file "config-N.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.784689677067877e+00 1.784689677068272e+00 3.95683e-13 1.35234e-11 2 2.915347364092292e+00 2.915347364088120e+00 4.17222e-12 3.04454e-11 3 1.213323542396565e+00 1.213323542395815e+00 7.49845e-13 3.61133e-12 ----------------------------------------------------------------------------------------------------- 2 N 1 -2.134662094187855e+00 -2.134662094186440e+00 1.41442e-12 5.97433e-12 2 -6.922313926574719e-01 -6.922313926565202e-01 9.51683e-13 1.82749e-11 3 2.781717637190597e+00 2.781717637190539e+00 5.77316e-14 5.13714e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 1.520168094160571e+00 1.520168094159086e+00 1.48503e-12 7.72737e-12 2 -5.588869691980106e-01 -5.588869691949019e-01 3.10874e-12 7.89779e-12 3 -4.574412933450078e-01 -4.574412933499479e-01 4.94005e-12 2.58097e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 -2.892459941083196e-01 -2.892459941095630e-01 1.24345e-12 6.67144e-12 2 -9.116465913868365e-01 -9.116465913871319e-01 2.95430e-13 6.26661e-11 3 -3.951119374345114e+00 -3.951119374342828e+00 2.28573e-12 3.59028e-11 ----------------------------------------------------------------------------------------------------- 5 N 1 -4.102646368764260e+00 -4.102646368768156e+00 3.89644e-12 2.50058e-11 2 -8.023718120875861e-01 -8.023718120874364e-01 1.49769e-13 3.14104e-12 3 -2.009224068451129e+00 -2.009224068450595e+00 5.33795e-13 5.60796e-12 ----------------------------------------------------------------------------------------------------- 6 N 1 2.014007930054656e+00 2.014007930053587e+00 1.06937e-12 2.37352e-11 2 4.066066756703349e+00 4.066066756702451e+00 8.97948e-13 9.49374e-12 3 -4.552328991857775e+00 -4.552328991854401e+00 3.37419e-12 4.60849e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 3.905827720124341e+00 3.905827720127585e+00 3.24363e-12 3.33422e-11 2 -5.277409493009786e+00 -5.277409493013013e+00 3.22675e-12 9.73532e-12 3 3.441928649228275e+00 3.441928649230517e+00 2.24265e-12 7.56994e-12 ----------------------------------------------------------------------------------------------------- 8 N 1 -5.736044413373991e+00 -5.736044413367999e+00 5.99165e-12 2.16174e-11 2 5.421606984481508e+00 5.421606984484985e+00 3.47722e-12 3.43743e-11 3 4.935685368096553e+00 4.935685368093338e+00 3.21432e-12 1.30900e-11 ----------------------------------------------------------------------------------------------------- 9 N 1 3.058678193128528e+00 3.058678193127253e+00 1.27498e-12 5.96323e-12 2 1.702069450518300e-01 1.702069450509572e-01 8.72802e-13 2.89927e-11 3 9.505207908132024e-01 9.505207908074373e-01 5.76506e-12 1.01670e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 -1.494997197908024e+00 -1.494997197904167e+00 3.85780e-12 1.73770e-11 2 -2.650081000013049e+00 -2.650081000012416e+00 6.33271e-13 2.62483e-11 3 2.640607156973332e+00 2.640607156969176e+00 4.15579e-12 4.62386e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 2.244591371140920e+00 2.244591371144832e+00 3.91287e-12 2.11058e-11 2 1.190455299405862e+00 1.190455299401131e+00 4.73066e-12 1.62008e-11 3 -5.060671336060984e+00 -5.060671336061021e+00 3.73035e-14 2.07390e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 2.322288359592358e+00 2.322288359592036e+00 3.21521e-13 6.27787e-11 2 -1.177814723033577e+00 -1.177814723034997e+00 1.42020e-12 2.69915e-11 3 -1.026447727592281e+00 -1.026447727591409e+00 8.71303e-13 2.24003e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 -2.522231007996381e+00 -2.522231007990972e+00 5.40989e-12 1.22586e-11 2 -3.520493352025396e+00 -3.520493352025615e+00 2.18492e-13 1.11759e-11 3 -2.095075110307705e+00 -2.095075110304339e+00 3.36620e-12 3.36531e-11 ----------------------------------------------------------------------------------------------------- 14 N 1 1.364667207920270e+00 1.364667207918887e+00 1.38245e-12 3.64579e-11 2 3.494158186878437e+00 3.494158186882295e+00 3.85780e-12 1.26685e-11 3 -3.227028145349903e+00 -3.227028145347454e+00 2.44826e-12 1.94231e-11 ----------------------------------------------------------------------------------------------------- 15 N 1 5.337703508450821e+00 5.337703508447667e+00 3.15481e-12 6.06359e-12 2 -4.719967760170232e+00 -4.719967760172268e+00 2.03570e-12 1.44322e-10 * 3 5.909856110775714e-01 5.909856110760534e-01 1.51801e-12 3.13476e-11 ----------------------------------------------------------------------------------------------------- 16 N 1 -5.005628222417161e+00 -5.005628222413055e+00 4.10605e-12 2.92157e-11 2 2.411817696058929e+00 2.411817696057761e+00 1.16795e-12 8.86975e-11 3 1.063005442626286e+00 1.063005442625542e+00 7.43849e-13 1.85598e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 -4.680699740269025e+00 -4.680699740272312e+00 3.28626e-12 3.25606e-11 2 -6.818394331815036e+00 -6.818394331817530e+00 2.49401e-12 4.38742e-11 3 -3.066340511588375e+00 -3.066340511585920e+00 2.45448e-12 8.28599e-11 ----------------------------------------------------------------------------------------------------- 18 N 1 4.247645087807259e+00 4.247645087801266e+00 5.99254e-12 6.62874e-11 2 5.415044285903773e-01 5.415044285917584e-01 1.38112e-12 1.01317e-11 3 -2.408267064996933e+00 -2.408267064994649e+00 2.28351e-12 5.40945e-12 ----------------------------------------------------------------------------------------------------- 19 N 1 4.605684952768171e+00 4.605684952765641e+00 2.53042e-12 1.50990e-11 2 -8.029164001962538e-01 -8.029164001939095e-01 2.34424e-12 1.65872e-11 3 1.545849375393056e+00 1.545849375395171e+00 2.11431e-12 2.09039e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 -1.860071944458817e+00 -1.860071944457530e+00 1.28675e-12 1.83069e-11 2 3.578784553058592e+00 3.578784553060254e+00 1.66223e-12 1.15485e-11 3 4.696510745822551e+00 4.696510745825994e+00 3.44258e-12 1.73053e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 -3.877775559628373e+00 -3.877775559626472e+00 1.90070e-12 1.36855e-11 2 1.120478918829210e-01 1.120478918833600e-01 4.39065e-13 2.83601e-11 3 -5.430506534663208e+00 -5.430506534663573e+00 3.65041e-13 2.79474e-11 ----------------------------------------------------------------------------------------------------- 22 N 1 1.636255340190598e+00 1.636255340189675e+00 9.23039e-13 1.45016e-10 * 2 -3.753514054205309e+00 -3.753514054204847e+00 4.61409e-13 3.48339e-11 3 5.891485692880000e-01 5.891485692843520e-01 3.64797e-12 1.65186e-10 * ----------------------------------------------------------------------------------------------------- 23 N 1 3.158428496559839e+00 3.158428496552663e+00 7.17559e-12 1.20769e-10 * 2 -2.969639045770565e-01 -2.969639045774610e-01 4.04454e-13 2.44751e-11 3 3.075519681403736e+00 3.075519681400114e+00 3.62155e-12 3.67146e-11 ----------------------------------------------------------------------------------------------------- 24 N 1 -6.635872443736819e-01 -6.635872443811658e-01 7.48390e-12 6.82010e-11 2 2.531875612609560e+00 2.531875612611232e+00 1.67200e-12 2.43001e-11 3 4.236934022532622e-01 4.236934022524821e-01 7.80098e-13 2.57830e-11 ----------------------------------------------------------------------------------------------------- 25 N 1 -4.292813461724538e+00 -4.292813461722553e+00 1.98508e-12 4.09983e-12 2 2.663411078026032e+00 2.663411078027694e+00 1.66178e-12 1.07545e-10 * 3 1.007663793795680e-01 1.007663793804354e-01 8.67417e-13 4.40531e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 2.907228902404482e+00 2.907228902405800e+00 1.31806e-12 1.80993e-11 2 2.327783174351742e+00 2.327783174352310e+00 5.68434e-13 3.30282e-11 3 4.234990919780716e-01 4.234990919790878e-01 1.01624e-12 2.24333e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 2.956409047488481e+00 2.956409047489966e+00 1.48503e-12 1.28093e-11 2 7.462460621954312e-01 7.462460621914353e-01 3.99591e-12 1.09572e-11 3 3.926979823064988e+00 3.926979823063659e+00 1.32960e-12 3.50346e-11 ----------------------------------------------------------------------------------------------------- 28 N 1 1.029616561948282e+00 1.029616561947189e+00 1.09290e-12 1.07931e-11 2 -9.302823124501813e-01 -9.302823124498053e-01 3.76033e-13 8.59735e-11 3 -1.494302649592743e+00 -1.494302649592522e+00 2.20712e-13 2.89746e-12 ----------------------------------------------------------------------------------------------------- 29 N 1 -3.744963109780508e+00 -3.744963109778864e+00 1.64357e-12 4.99445e-11 2 2.264188843933221e+00 2.264188843929018e+00 4.20286e-12 3.21765e-11 3 3.709466195028607e+00 3.709466195018286e+00 1.03211e-11 1.25076e-10 * ----------------------------------------------------------------------------------------------------- 30 N 1 -2.175060852006412e-01 -2.175060851992604e-01 1.38078e-12 7.79032e-12 2 1.220843130779554e+00 1.220843130783472e+00 3.91820e-12 3.34472e-11 3 2.428911308815113e+00 2.428911308816082e+00 9.69447e-13 1.01852e-10 ----------------------------------------------------------------------------------------------------- 31 N 1 -2.813750350417477e+00 -2.813750350415495e+00 1.98286e-12 1.15712e-11 2 5.683609001186648e-01 5.683609001141054e-01 4.55935e-12 3.38087e-11 3 -1.841611219554878e+00 -1.841611219558253e+00 3.37530e-12 4.13247e-12 ----------------------------------------------------------------------------------------------------- 32 N 1 -6.572676561984014e-01 -6.572676562015183e-01 3.11684e-12 6.15896e-11 2 -3.311730811392524e+00 -3.311730811392315e+00 2.08722e-13 3.32374e-11 3 -1.917754743123311e+00 -1.917754743121909e+00 1.40221e-12 3.23586e-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 = 24, direction = 1: |F_model - F_numer| error = ----------------------- = 1.12779e-11 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 = Ga N | a0 = 3.4580722052744024 | (Configuration in file "config-GaN.xyz") ----------------------------------------------------------------------------------------------------- Part Spec Dir Force_model Force_numer |Force diff| uncertainty ----------------------------------------------------------------------------------------------------- 1 N 1 1.041713794644368e+00 1.041713794643454e+00 9.14158e-13 6.33138e-12 2 1.057766340867894e+00 1.057766340871624e+00 3.73035e-12 2.70806e-11 3 1.757884557539342e-02 1.757884557496956e-02 4.23859e-13 1.03131e-12 ----------------------------------------------------------------------------------------------------- 2 Ga 1 -6.175205447488947e+00 -6.175205447493906e+00 4.95870e-12 4.35492e-11 2 8.138370627609037e-01 8.138370627625042e-01 1.60050e-12 2.11273e-11 3 -2.788451837649111e+00 -2.788451837650860e+00 1.74838e-12 8.97695e-11 ----------------------------------------------------------------------------------------------------- 3 N 1 -1.588358374722141e-01 -1.588358374727200e-01 5.05929e-13 8.22667e-12 2 -2.072323114304904e+00 -2.072323114306529e+00 1.62492e-12 4.03455e-12 3 -1.336282416032508e+00 -1.336282416030815e+00 1.69353e-12 3.07132e-11 ----------------------------------------------------------------------------------------------------- 4 N 1 9.490479753012772e-01 9.490479753016552e-01 3.78031e-13 2.25908e-11 2 1.898208435750744e+00 1.898208435747319e+00 3.42437e-12 4.05120e-11 3 1.570976217571908e+00 1.570976217578237e+00 6.32872e-12 8.66907e-12 ----------------------------------------------------------------------------------------------------- 5 Ga 1 1.164134217782591e+00 1.164134217781645e+00 9.45910e-13 1.08518e-11 2 -4.597833504514241e+00 -4.597833504513168e+00 1.07292e-12 2.72342e-11 3 -2.201818802404108e-01 -2.201818802421949e-01 1.78407e-12 5.68112e-12 ----------------------------------------------------------------------------------------------------- 6 Ga 1 2.166145858860804e+00 2.166145858865379e+00 4.57590e-12 3.95413e-11 2 -1.163728594798342e+00 -1.163728594798503e+00 1.60982e-13 8.20344e-12 3 -4.516420598938272e-01 -4.516420598928414e-01 9.85823e-13 2.30232e-11 ----------------------------------------------------------------------------------------------------- 7 N 1 -1.202222672222939e+00 -1.202222672210391e+00 1.25475e-11 4.25742e-11 2 1.471201348591249e+00 1.471201348591163e+00 8.63754e-14 2.85154e-11 3 -3.084105666280990e+00 -3.084105666280385e+00 6.04405e-13 3.36633e-11 ----------------------------------------------------------------------------------------------------- 8 Ga 1 4.540207109417990e+00 4.540207109408705e+00 9.28502e-12 2.81375e-11 2 -1.565077400202380e+00 -1.565077400204790e+00 2.41029e-12 1.23549e-10 3 2.926339867366723e+00 2.926339867374207e+00 7.48424e-12 8.77654e-12 ----------------------------------------------------------------------------------------------------- 9 Ga 1 2.862722837184934e-01 2.862722837189462e-01 4.52749e-13 6.54277e-12 2 2.617539543698910e+00 2.617539543694377e+00 4.53326e-12 2.26152e-11 3 2.851162007735522e+00 2.851162007738639e+00 3.11617e-12 2.11662e-11 ----------------------------------------------------------------------------------------------------- 10 N 1 7.863780437807000e-01 7.863780437804642e-01 2.35811e-13 1.46742e-11 2 -2.718930271945987e-02 -2.718930271901623e-02 4.43638e-13 8.26900e-12 3 1.054486389008058e+00 1.054486389008546e+00 4.88498e-13 9.13536e-12 ----------------------------------------------------------------------------------------------------- 11 N 1 -5.745524057275745e+00 -5.745524057272535e+00 3.20988e-12 2.37028e-11 2 -1.274112945140011e+00 -1.274112945142689e+00 2.67786e-12 9.63576e-11 3 -1.946032847695095e+00 -1.946032847693858e+00 1.23679e-12 6.80558e-11 ----------------------------------------------------------------------------------------------------- 12 N 1 -3.568279079740090e-01 -3.568279079697243e-01 4.28474e-12 1.46264e-11 2 -3.098816606172046e+00 -3.098816606171354e+00 6.91447e-13 1.30354e-11 3 -1.130784961157737e+00 -1.130784961156991e+00 7.46514e-13 1.47378e-11 ----------------------------------------------------------------------------------------------------- 13 N 1 7.234458134362757e-01 7.234458134352026e-01 1.07303e-12 2.92621e-11 2 4.925907804230111e-02 4.925907804118685e-02 1.11426e-12 7.26003e-12 3 -3.910120618511387e+00 -3.910120618506657e+00 4.72999e-12 8.72963e-10 * ----------------------------------------------------------------------------------------------------- 14 Ga 1 9.721180156160165e-01 9.721180156155788e-01 4.37761e-13 1.43289e-11 2 2.641457693906835e+00 2.641457693913878e+00 7.04281e-12 1.54317e-11 3 -4.787150570320439e+00 -4.787150570320934e+00 4.94715e-13 2.52429e-11 ----------------------------------------------------------------------------------------------------- 15 Ga 1 3.827903187580763e+00 3.827903187578718e+00 2.04503e-12 1.90732e-11 2 -2.586879297697823e+00 -2.586879297699930e+00 2.10720e-12 1.56741e-11 3 5.278547366096528e+00 5.278547366094065e+00 2.46292e-12 2.51745e-11 ----------------------------------------------------------------------------------------------------- 16 Ga 1 -2.780842401169902e+00 -2.780842401172367e+00 2.46514e-12 2.69340e-12 2 6.159454035413392e+00 6.159454035417891e+00 4.49862e-12 5.49862e-11 3 -1.391635382171966e+00 -1.391635382171818e+00 1.47882e-13 6.88365e-11 ----------------------------------------------------------------------------------------------------- 17 N 1 1.385439456748936e+00 1.385439456754548e+00 5.61240e-12 2.34059e-11 2 1.082937560892207e+00 1.082937560891197e+00 1.00964e-12 3.26761e-12 3 2.065047906688383e-01 2.065047906669334e-01 1.90489e-12 3.63795e-11 ----------------------------------------------------------------------------------------------------- 18 Ga 1 -7.474136904589280e+00 -7.474136904598754e+00 9.47420e-12 2.39798e-10 * 2 -6.567415850491888e+00 -6.567415850486670e+00 5.21805e-12 3.84466e-11 3 4.202645999687324e+00 4.202645999676938e+00 1.03855e-11 2.60219e-10 * ----------------------------------------------------------------------------------------------------- 19 N 1 1.650496200017663e+00 1.650496200015077e+00 2.58638e-12 4.38294e-12 2 3.030287744619394e+00 3.030287744620968e+00 1.57474e-12 1.76015e-11 3 -1.349054485758904e+00 -1.349054485763483e+00 4.57923e-12 2.40696e-11 ----------------------------------------------------------------------------------------------------- 20 N 1 9.214693751356211e-01 9.214693751368264e-01 1.20526e-12 1.09429e-11 2 1.633839885981370e+00 1.633839885981243e+00 1.27454e-13 2.12421e-11 3 -2.502052391860807e+00 -2.502052391859305e+00 1.50280e-12 4.60765e-11 ----------------------------------------------------------------------------------------------------- 21 N 1 5.167151867218256e-01 5.167151867229093e-01 1.08369e-12 3.25060e-11 2 2.031098084735736e+00 2.031098084735036e+00 6.99441e-13 2.92810e-11 3 5.920613628640002e-01 5.920613628707077e-01 6.70741e-12 7.99008e-11 ----------------------------------------------------------------------------------------------------- 22 Ga 1 -2.096487200474693e-01 -2.096487200393893e-01 8.07993e-12 1.14186e-11 2 -1.549814289622329e+00 -1.549814289620837e+00 1.49147e-12 5.62035e-11 3 3.767443485299987e+00 3.767443485299860e+00 1.27010e-13 5.62403e-11 ----------------------------------------------------------------------------------------------------- 23 N 1 -1.594862993179528e+00 -1.594862993182678e+00 3.14970e-12 7.03346e-11 2 3.177190589364126e+00 3.177190589366124e+00 1.99796e-12 4.85167e-12 3 -2.302329418989351e+00 -2.302329418986614e+00 2.73737e-12 1.28049e-11 ----------------------------------------------------------------------------------------------------- 24 Ga 1 1.334685252268861e+00 1.334685252274602e+00 5.74096e-12 2.15641e-11 2 -5.255554892495232e+00 -5.255554892503928e+00 8.69527e-12 3.01776e-11 3 3.286262465621623e+00 3.286262465625223e+00 3.60023e-12 2.19131e-11 ----------------------------------------------------------------------------------------------------- 25 Ga 1 1.607156121233806e+00 1.607156121231156e+00 2.65055e-12 2.72371e-11 2 -2.216871370106347e-01 -2.216871370072179e-01 3.41679e-12 2.06867e-11 3 -1.058339249563259e+00 -1.058339249561512e+00 1.74705e-12 2.96487e-11 ----------------------------------------------------------------------------------------------------- 26 N 1 -3.802241685713290e-01 -3.802241685750876e-01 3.75866e-12 4.49857e-12 2 -1.443501019829678e+00 -1.443501019829998e+00 3.19744e-13 6.34210e-11 3 2.243304520921261e+00 2.243304520920434e+00 8.26894e-13 6.32454e-11 ----------------------------------------------------------------------------------------------------- 27 N 1 -1.155200330173880e+00 -1.155200330179288e+00 5.40856e-12 3.51543e-11 2 1.949131744023450e-01 1.949131744049998e-01 2.65482e-12 2.08550e-11 3 -2.931331292088624e-01 -2.931331292034882e-01 5.37415e-12 4.83027e-11 ----------------------------------------------------------------------------------------------------- 28 Ga 1 2.319001872307231e+00 2.319001872308520e+00 1.28875e-12 9.08500e-11 2 -6.250332184000672e-01 -6.250332184042078e-01 4.14058e-12 2.61071e-11 3 -1.871630975815725e+00 -1.871630975817778e+00 2.05280e-12 2.00528e-12 ----------------------------------------------------------------------------------------------------- 29 Ga 1 1.281078605982798e-01 1.281078606086788e-01 1.03990e-11 6.81570e-11 2 4.238468966013596e+00 4.238468966013296e+00 3.00204e-13 1.34449e-10 * 3 2.636561230343449e+00 2.636561230340960e+00 2.48868e-12 2.61657e-11 ----------------------------------------------------------------------------------------------------- 30 Ga 1 4.298369643531931e-01 4.298369643522639e-01 9.29201e-13 2.33474e-11 2 -9.069143108986419e-01 -9.069143109004197e-01 1.77780e-12 6.85833e-11 3 -5.618897609678283e-01 -5.618897609622354e-01 5.59286e-12 1.68222e-11 ----------------------------------------------------------------------------------------------------- 31 N 1 1.314491795894425e+00 1.314491795895165e+00 7.40741e-13 1.49123e-10 * 2 4.626109932179833e-01 4.626109932102441e-01 7.73920e-12 2.06600e-11 3 -3.735075820675158e-01 -3.735075820701294e-01 2.61358e-12 4.12474e-11 ----------------------------------------------------------------------------------------------------- 32 Ga 1 -8.312349452538859e-01 -8.312349452526151e-01 1.27076e-12 3.43372e-11 2 3.958109460386936e-01 3.958109460279127e-01 1.07809e-11 6.21120e-12 3 7.244506854251040e-01 7.244506854274091e-01 2.30505e-12 4.31635e-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 = 29, direction = 1: |F_model - F_numer| error = ----------------------- = 8.11737e-11 max{|F_numer|, eps} ===================================================================================================== Grade is based on maximum error across all systems (for a model supporting multiple species): Maximum error = 7.11700e-10 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 7.11700e-10 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.