!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! VERIFICATION CHECK: vc-periodicity-support !!!!! !!!!! !!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! Description: Check that the model supports periodic boundary conditions correctly. If the simulation box is increased by an integer factor along a periodic direction, the total energy must multiply by that factor and the forces on atoms that are periodic copies of each other must be the same. The check is performed for a randomly distorted non-periodic face-centered cubic (FCC) cube base structure. Separate configurations are tested for each species supported by the model, as well as one containing a random distribution of all species. For each configuration, all possible combinations of periodic boundary conditions are tested: TFF, FTF, FFT, TTF, TFT, TTF, TTT (where 'T' indicates periodicity along a direction, and 'F' indicates no periodicity). The verification check passes if the energy of all configurations that the model is able to compute support all periodic boundary conditions correctly. Configurations used for testing are provided as auxiliary files. Author: Ellad Tadmor ------------------------------------------------------------------------------------------------------------------------ Results for KIM Model : EAM_Dynamo_LandaWynblattSiegel_2000_AlPb__MO_699137396381_005 Supported species : Al Pb random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTT (Configuration in file "config-Al-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.0631524821784 2^p V(r_1,...,r_N) = -0.0631524821784 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.84735328e+00 -6.47156522e+00 -8.02047449e+00 | -6.84735328e+00 -6.47156522e+00 -8.02047449e+00 1 4.82740472e+00 3.37310135e+00 -3.04358160e+00 | 4.82740472e+00 3.37310135e+00 -3.04358160e+00 2 5.54746679e+00 -4.44823866e+00 6.20863084e+00 | 5.54746679e+00 -4.44823866e+00 6.20863084e+00 3 -3.52751824e+00 7.54670253e+00 4.85542526e+00 | -3.52751824e+00 7.54670253e+00 4.85542526e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TTF (Configuration in file "config-Al-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 2.26997929741 2^p V(r_1,...,r_N) = 2.26997929741 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.23723477e+00 -6.48839246e+00 -5.88014380e+00 | -9.23723477e+00 -6.48839246e+00 -5.88014380e+00 1 6.86346286e+00 5.47730087e+00 -8.41675100e+00 | 6.86346286e+00 5.47730087e+00 -8.41675100e+00 2 7.70438236e+00 -7.43022016e+00 1.01756083e+01 | 7.70438236e+00 -7.43022016e+00 1.01756083e+01 3 -5.33061045e+00 8.44131175e+00 4.12128647e+00 | -5.33061045e+00 8.44131175e+00 4.12128647e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFT (Configuration in file "config-Al-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.40313897104 2^p V(r_1,...,r_N) = 5.40313897104 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.01302746e+00 -8.07297972e+00 -1.12552986e+01 | -8.01302746e+00 -8.07297972e+00 -1.12552986e+01 1 1.07508505e+01 9.96975279e+00 -6.60481077e+00 | 1.07508505e+01 9.96975279e+00 -6.60481077e+00 2 7.54857905e+00 -9.44067363e+00 9.82848043e+00 | 7.54857905e+00 -9.44067363e+00 9.82848043e+00 3 -1.02864021e+01 7.54390057e+00 8.03162897e+00 | -1.02864021e+01 7.54390057e+00 8.03162897e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = TFF (Configuration in file "config-Al-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.1524629615 2^p V(r_1,...,r_N) = 10.1524629615 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.88423780e+00 -8.76438441e+00 -9.18465544e+00 | -7.88423780e+00 -8.76438441e+00 -9.18465544e+00 1 8.58174271e+00 9.77537798e+00 -6.93478707e+00 | 8.58174271e+00 9.77537798e+00 -6.93478707e+00 2 8.58207019e+00 -9.43121449e+00 9.22283662e+00 | 8.58207019e+00 -9.43121449e+00 9.22283662e+00 3 -9.27957510e+00 8.42022092e+00 6.89660589e+00 | -9.27957510e+00 8.42022092e+00 6.89660589e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTT (Configuration in file "config-Al-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.11803274563 2^p V(r_1,...,r_N) = 5.11803274563 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.05467779e+01 -8.09231139e+00 -9.27087163e+00 | -1.05467779e+01 -8.09231139e+00 -9.27087163e+00 1 8.45483678e+00 9.27110121e+00 -7.86887006e+00 | 8.45483678e+00 9.27110121e+00 -7.86887006e+00 2 9.54831984e+00 -1.00907261e+01 7.95649945e+00 | 9.54831984e+00 -1.00907261e+01 7.95649945e+00 3 -7.45637869e+00 8.91193630e+00 9.18324224e+00 | -7.45637869e+00 8.91193630e+00 9.18324224e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FTF (Configuration in file "config-Al-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 0.469931084739 2^p V(r_1,...,r_N) = 0.469931084739 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.88504472e+00 -7.69415321e+00 -6.20842895e+00 | -8.88504472e+00 -7.69415321e+00 -6.20842895e+00 1 5.25643687e+00 7.52122038e+00 -6.76645790e+00 | 5.25643687e+00 7.52122038e+00 -6.76645790e+00 2 7.24816657e+00 -4.15558530e+00 1.01691757e+01 | 7.24816657e+00 -4.15558530e+00 1.01691757e+01 3 -3.61955872e+00 4.32851813e+00 2.80571114e+00 | -3.61955872e+00 4.32851813e+00 2.80571114e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Al, PBC = FFT (Configuration in file "config-Al-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.40699844089 2^p V(r_1,...,r_N) = 8.40699844089 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.27093228e+00 -7.91014501e+00 -1.18453989e+01 | -8.27093228e+00 -7.91014501e+00 -1.18453989e+01 1 1.04963218e+01 8.58661564e+00 -7.58450033e+00 | 1.04963218e+01 8.58661564e+00 -7.58450033e+00 2 6.89399903e+00 -8.25337254e+00 1.08135349e+01 | 6.89399903e+00 -8.25337254e+00 1.08135349e+01 3 -9.11938858e+00 7.57690191e+00 8.61636435e+00 | -9.11938858e+00 7.57690191e+00 8.61636435e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TTT (Configuration in file "config-Pb-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.3005631687 2^p V(r_1,...,r_N) = 10.3005631687 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.57451703e+00 -5.57291602e+00 -7.59789366e+00 | -6.57451703e+00 -5.57291602e+00 -7.59789366e+00 1 5.55107682e+00 6.35039711e+00 -5.02392237e+00 | 5.55107682e+00 6.35039711e+00 -5.02392237e+00 2 6.79173472e+00 -6.30317605e+00 6.83414030e+00 | 6.79173472e+00 -6.30317605e+00 6.83414030e+00 3 -5.76829452e+00 5.52569497e+00 5.78767574e+00 | -5.76829452e+00 5.52569497e+00 5.78767574e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TTF (Configuration in file "config-Pb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 10.4725470015 2^p V(r_1,...,r_N) = 10.4725470015 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -6.12038080e+00 -5.50311785e+00 -6.63760114e+00 | -6.12038080e+00 -5.50311785e+00 -6.63760114e+00 1 5.39524053e+00 6.16900032e+00 -5.88041305e+00 | 5.39524053e+00 6.16900032e+00 -5.88041305e+00 2 6.44921395e+00 -5.57499267e+00 7.56011782e+00 | 6.44921395e+00 -5.57499267e+00 7.56011782e+00 3 -5.72407368e+00 4.90911020e+00 4.95789637e+00 | -5.72407368e+00 4.90911020e+00 4.95789637e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TFT (Configuration in file "config-Pb-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.90208346615 2^p V(r_1,...,r_N) = 6.90208346615 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.60217126e+00 -4.38599353e+00 -3.94461125e+00 | -4.60217126e+00 -4.38599353e+00 -3.94461125e+00 1 4.94232272e+00 3.15402075e+00 -5.52857892e+00 | 4.94232272e+00 3.15402075e+00 -5.52857892e+00 2 4.62149355e+00 -4.67196289e+00 5.66181988e+00 | 4.62149355e+00 -4.67196289e+00 5.66181988e+00 3 -4.96164501e+00 5.90393567e+00 3.81137029e+00 | -4.96164501e+00 5.90393567e+00 3.81137029e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = TFF (Configuration in file "config-Pb-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.97235468229 2^p V(r_1,...,r_N) = 6.97235468229 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.53154576e+00 -4.58451405e+00 -3.93200339e+00 | -4.53154576e+00 -4.58451405e+00 -3.93200339e+00 1 4.93758101e+00 4.45406083e+00 -5.23772194e+00 | 4.93758101e+00 4.45406083e+00 -5.23772194e+00 2 4.20280080e+00 -4.85663715e+00 4.41278992e+00 | 4.20280080e+00 -4.85663715e+00 4.41278992e+00 3 -4.60883604e+00 4.98709038e+00 4.75693540e+00 | -4.60883604e+00 4.98709038e+00 4.75693540e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FTT (Configuration in file "config-Pb-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.05136707385 2^p V(r_1,...,r_N) = 4.05136707385 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -3.88349324e+00 -3.88057429e+00 -3.79667979e+00 | -3.88349324e+00 -3.88057429e+00 -3.79667979e+00 1 5.51938505e+00 4.57341406e+00 -4.22413853e+00 | 5.51938505e+00 4.57341406e+00 -4.22413853e+00 2 2.65621606e+00 -4.19228536e+00 3.81810976e+00 | 2.65621606e+00 -4.19228536e+00 3.81810976e+00 3 -4.29210786e+00 3.49944559e+00 4.20270856e+00 | -4.29210786e+00 3.49944559e+00 4.20270856e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FTF (Configuration in file "config-Pb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 6.04201632268 2^p V(r_1,...,r_N) = 6.04201632268 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.05213461e+00 -5.27308468e+00 -4.62273494e+00 | -4.05213461e+00 -5.27308468e+00 -4.62273494e+00 1 4.06112102e+00 4.67053487e+00 -4.49850977e+00 | 4.06112102e+00 4.67053487e+00 -4.49850977e+00 2 5.16277216e+00 -3.50338473e+00 3.21325919e+00 | 5.16277216e+00 -3.50338473e+00 3.21325919e+00 3 -5.17175857e+00 4.10593454e+00 5.90798552e+00 | -5.17175857e+00 4.10593454e+00 5.90798552e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pb, PBC = FFT (Configuration in file "config-Pb-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 13.9153528628 2^p V(r_1,...,r_N) = 13.9153528628 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -8.95196064e+00 -7.28885487e+00 -7.18622636e+00 | -8.95196064e+00 -7.28885487e+00 -7.18622636e+00 1 8.90085724e+00 4.98716940e+00 -8.73424492e+00 | 8.90085724e+00 4.98716940e+00 -8.73424492e+00 2 7.69889385e+00 -8.78053015e+00 1.00366958e+01 | 7.69889385e+00 -8.78053015e+00 1.00366958e+01 3 -7.64779046e+00 1.10822156e+01 5.88377543e+00 | -7.64779046e+00 1.10822156e+01 5.88377543e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = TTT (Configuration in file "config-AlPb-TTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.96413420212 2^p V(r_1,...,r_N) = 8.96413420212 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.02635227e+00 -6.13725751e+00 -5.71590446e+00 | -7.02635227e+00 -6.13725751e+00 -5.71590446e+00 1 1.01062946e+01 5.45077742e+00 -9.03715990e+00 | 1.01062946e+01 5.45077742e+00 -9.03715990e+00 2 8.83351778e+00 -7.85558914e+00 6.18661652e+00 | 8.83351778e+00 -7.85558914e+00 6.18661652e+00 3 -1.19134601e+01 8.54206924e+00 8.56644784e+00 | -1.19134601e+01 8.54206924e+00 8.56644784e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = TTF (Configuration in file "config-AlPb-TTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 8.11841550805 2^p V(r_1,...,r_N) = 8.11841550805 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -1.07734433e+01 -5.91135955e+00 -7.26508926e+00 | -1.07734433e+01 -5.91135955e+00 -7.26508926e+00 1 1.09961654e+01 7.97309414e+00 -6.64513570e+00 | 1.09961654e+01 7.97309414e+00 -6.64513570e+00 2 7.55408828e+00 -8.20976133e+00 7.79046745e+00 | 7.55408828e+00 -8.20976133e+00 7.79046745e+00 3 -7.77681042e+00 6.14802673e+00 6.11975750e+00 | -7.77681042e+00 6.14802673e+00 6.11975750e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = TFT (Configuration in file "config-AlPb-TFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 7.09683271183 2^p V(r_1,...,r_N) = 7.09683271183 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -9.88020911e+00 -6.38984970e+00 -9.05756062e+00 | -9.88020911e+00 -6.38984970e+00 -9.05756062e+00 1 9.25507721e+00 6.45930468e+00 -6.04245324e+00 | 9.25507721e+00 6.45930468e+00 -6.04245324e+00 2 9.56052472e+00 -9.41552044e+00 8.91176246e+00 | 9.56052472e+00 -9.41552044e+00 8.91176246e+00 3 -8.93539282e+00 9.34606547e+00 6.18825141e+00 | -8.93539282e+00 9.34606547e+00 6.18825141e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = TFF (Configuration in file "config-AlPb-TFF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.0790150468173 2^p V(r_1,...,r_N) = -0.0790150468173 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.02687216e+00 -3.95179914e+00 -4.11391817e+00 | -4.02687216e+00 -3.95179914e+00 -4.11391817e+00 1 3.49206402e+00 5.48173191e+00 -3.83182028e+00 | 3.49206402e+00 5.48173191e+00 -3.83182028e+00 2 4.07100704e+00 -4.97724966e+00 3.92978263e+00 | 4.07100704e+00 -4.97724966e+00 3.92978263e+00 3 -3.53619890e+00 3.44731690e+00 4.01595582e+00 | -3.53619890e+00 3.44731690e+00 4.01595582e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = FTT (Configuration in file "config-AlPb-FTT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = -0.951135982459 2^p V(r_1,...,r_N) = -0.951135982459 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.30097975e+00 -3.62428343e+00 -2.48776496e+00 | -4.30097975e+00 -3.62428343e+00 -2.48776496e+00 1 4.48925167e+00 3.22918020e+00 -2.18569342e+00 | 4.48925167e+00 3.22918020e+00 -2.18569342e+00 2 3.55693294e+00 -4.20207201e+00 2.03648057e+00 | 3.55693294e+00 -4.20207201e+00 2.03648057e+00 3 -3.74520486e+00 4.59717524e+00 2.63697781e+00 | -3.74520486e+00 4.59717524e+00 2.63697781e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = FTF (Configuration in file "config-AlPb-FTF.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 4.57697350031 2^p V(r_1,...,r_N) = 4.57697350031 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -4.56245234e+00 -8.06714818e+00 -7.31185101e+00 | -4.56245234e+00 -8.06714818e+00 -7.31185101e+00 1 3.85685795e+00 4.79203047e+00 -4.13469498e+00 | 3.85685795e+00 4.79203047e+00 -4.13469498e+00 2 8.72817687e+00 -5.47874322e+00 7.23967591e+00 | 8.72817687e+00 -5.47874322e+00 7.23967591e+00 3 -8.02258249e+00 8.75386092e+00 4.20687008e+00 | -8.02258249e+00 8.75386092e+00 4.20687008e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Al Pb, PBC = FFT (Configuration in file "config-AlPb-FFT.xyz") ------------------------------------------------------------------------------------------------------------------------ The system is doubled in p=0 periodic directions, which means an increase by a factor n=2^0=1 in the number of atoms and in the energy. Energy requirement: V(DBL_p(r_1,...,r_N)) = (2^p) V(r_1,...,r_N), where r_i is the position of atom i, V is the potential energy, and DBL_p is an operator that doubles the configuration in p periodic directions. V(DBL_p(r_1,...,r_N)) = 5.78151911934 2^p V(r_1,...,r_N) = 5.78151911934 Forces requirement: f_k(DBL_p(r_1,...,r_N)) = f_(k % N)(r_1,...,r_N), where r_i is the position of atom i, f_k is the force on atom k (where k runs from 1 to the number of atoms in the doubled configuration), DBL_p doubles the configuration in p periodic directions, N is the number of atoms in the original configuration, and % is the modulo operator. k f_k(DBL_p(r_1,...,r_N)) f_(k % N)(r_1,...,r_N) ------------------------------------------------------------------------------------------------------------------------ 0 -7.91589355e+00 -7.02009072e+00 -5.08089803e+00 | -7.91589355e+00 -7.02009072e+00 -5.08089803e+00 1 5.57451426e+00 1.08600271e+01 -1.20167267e+01 | 5.57451426e+00 1.08600271e+01 -1.20167267e+01 2 8.66766305e+00 -7.59999530e+00 8.43007083e+00 | 8.66766305e+00 -7.59999530e+00 8.43007083e+00 3 -6.32628376e+00 3.76005891e+00 8.66755388e+00 | -6.32628376e+00 3.76005891e+00 8.66755388e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ ======================================================================================================================== ======================================================================================================================== To pass this verification check the model must correctly support periodic boundary conditions for all configurations it was able to compute. Grade: P Comment: Periodic boundary conditions were correctly supported for all configurations that the model was able to compute.