!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_HaleWongZimmerman_2008PairHybrid_PdAgH__MO_104806802344_005 Supported species : Ag H Pd random seed = 13 lattice constant (orig) = 3.000 perturbation amplitude = 0.300 number unit cells per side = 1 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTT (Configuration in file "config-Ag-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)) = 2.21984804453 2^p V(r_1,...,r_N) = 2.21984804453 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 -8.08720194e+00 -1.13150604e+01 -1.26083026e+01 | -8.08720194e+00 -1.13150604e+01 -1.26083026e+01 1 6.19160324e+00 4.22633048e+00 -4.06045467e+00 | 6.19160324e+00 4.22633048e+00 -4.06045467e+00 2 6.71145558e+00 -5.62103158e+00 7.63839324e+00 | 6.71145558e+00 -5.62103158e+00 7.63839324e+00 3 -4.81585689e+00 1.27097615e+01 9.03036406e+00 | -4.81585689e+00 1.27097615e+01 9.03036406e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TTF (Configuration in file "config-Ag-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)) = 5.20904987837 2^p V(r_1,...,r_N) = 5.20904987837 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 -1.10645586e+01 -7.96341684e+00 -7.16115992e+00 | -1.10645586e+01 -7.96341684e+00 -7.16115992e+00 1 8.39954218e+00 6.49293206e+00 -1.02889923e+01 | 8.39954218e+00 6.49293206e+00 -1.02889923e+01 2 1.23568449e+01 -1.31196420e+01 1.22378430e+01 | 1.23568449e+01 -1.31196420e+01 1.22378430e+01 3 -9.69182848e+00 1.45901268e+01 5.21230927e+00 | -9.69182848e+00 1.45901268e+01 5.21230927e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFT (Configuration in file "config-Ag-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)) = 8.89890174811 2^p V(r_1,...,r_N) = 8.89890174811 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 -1.05850061e+01 -1.32868868e+01 -1.71022763e+01 | -1.05850061e+01 -1.32868868e+01 -1.71022763e+01 1 1.42564339e+01 1.40497913e+01 -8.41051721e+00 | 1.42564339e+01 1.40497913e+01 -8.41051721e+00 2 9.33819690e+00 -1.23524015e+01 1.29773205e+01 | 9.33819690e+00 -1.23524015e+01 1.29773205e+01 3 -1.30096247e+01 1.15894970e+01 1.25354730e+01 | -1.30096247e+01 1.15894970e+01 1.25354730e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = TFF (Configuration in file "config-Ag-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)) = 18.7121974331 2^p V(r_1,...,r_N) = 18.7121974331 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 -1.81422901e+01 -1.74449844e+01 -2.77610590e+01 | -1.81422901e+01 -1.74449844e+01 -2.77610590e+01 1 1.22132815e+01 1.43914302e+01 -9.87489532e+00 | 1.22132815e+01 1.43914302e+01 -9.87489532e+00 2 2.19881415e+01 -1.54024196e+01 2.23952820e+01 | 2.19881415e+01 -1.54024196e+01 2.23952820e+01 3 -1.60591330e+01 1.84559738e+01 1.52406723e+01 | -1.60591330e+01 1.84559738e+01 1.52406723e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTT (Configuration in file "config-Ag-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)) = 8.41637821914 2^p V(r_1,...,r_N) = 8.41637821914 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 -1.44390358e+01 -1.04508104e+01 -1.36990362e+01 | -1.44390358e+01 -1.04508104e+01 -1.36990362e+01 1 1.03522350e+01 1.27207689e+01 -1.10432647e+01 | 1.03522350e+01 1.27207689e+01 -1.10432647e+01 2 1.36442269e+01 -1.44090201e+01 1.23963775e+01 | 1.36442269e+01 -1.44090201e+01 1.23963775e+01 3 -9.55742621e+00 1.21390617e+01 1.23459233e+01 | -9.55742621e+00 1.21390617e+01 1.23459233e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FTF (Configuration in file "config-Ag-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)) = 2.41968444476 2^p V(r_1,...,r_N) = 2.41968444476 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 -1.15234472e+01 -9.99369516e+00 -7.43343200e+00 | -1.15234472e+01 -9.99369516e+00 -7.43343200e+00 1 7.13779395e+00 9.64686842e+00 -8.25909020e+00 | 7.13779395e+00 9.64686842e+00 -8.25909020e+00 2 8.89285351e+00 -4.97660608e+00 1.22036686e+01 | 8.89285351e+00 -4.97660608e+00 1.22036686e+01 3 -4.50720023e+00 5.32343282e+00 3.48885360e+00 | -4.50720023e+00 5.32343282e+00 3.48885360e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Ag, PBC = FFT (Configuration in file "config-Ag-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)) = 16.0385134974 2^p V(r_1,...,r_N) = 16.0385134974 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 -1.17283254e+01 -1.08653131e+01 -1.48685424e+01 | -1.17283254e+01 -1.08653131e+01 -1.48685424e+01 1 1.52174592e+01 1.41794748e+01 -1.19800402e+01 | 1.52174592e+01 1.41794748e+01 -1.19800402e+01 2 1.94464735e+01 -2.32508303e+01 1.63651620e+01 | 1.94464735e+01 -2.32508303e+01 1.63651620e+01 3 -2.29356073e+01 1.99366686e+01 1.04834206e+01 | -2.29356073e+01 1.99366686e+01 1.04834206e+01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTT (Configuration in file "config-H-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)) = 0.447221170635 2^p V(r_1,...,r_N) = 0.447221170635 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 -2.75698378e+00 -1.33759053e+00 -3.18498712e+00 | -2.75698378e+00 -1.33759053e+00 -3.18498712e+00 1 1.05174291e+00 2.02796942e+00 -1.49920707e+00 | 1.05174291e+00 2.02796942e+00 -1.49920707e+00 2 3.88005329e+00 -2.94717620e+00 3.38325663e+00 | 3.88005329e+00 -2.94717620e+00 3.38325663e+00 3 -2.17481242e+00 2.25679731e+00 1.30093757e+00 | -2.17481242e+00 2.25679731e+00 1.30093757e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TTF (Configuration in file "config-H-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)) = 0.841319268037 2^p V(r_1,...,r_N) = 0.841319268037 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 -2.21335770e+00 -1.50663336e+00 -1.67768904e+00 | -2.21335770e+00 -1.50663336e+00 -1.67768904e+00 1 1.50579893e+00 2.54195517e+00 -1.97420764e+00 | 1.50579893e+00 2.54195517e+00 -1.97420764e+00 2 4.89953772e+00 -4.52504293e+00 2.52082319e+00 | 4.89953772e+00 -4.52504293e+00 2.52082319e+00 3 -4.19197895e+00 3.48972112e+00 1.13107350e+00 | -4.19197895e+00 3.48972112e+00 1.13107350e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFT (Configuration in file "config-H-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)) = -0.445312378197 2^p V(r_1,...,r_N) = -0.445312378197 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 -2.54512056e-01 -4.67591677e-01 -3.58998367e-01 | -2.54512056e-01 -4.67591677e-01 -3.58998367e-01 1 6.19859061e-01 1.46726004e+00 -2.57760374e+00 | 6.19859061e-01 1.46726004e+00 -2.57760374e+00 2 7.82838987e-01 -2.31058079e+00 2.57519158e+00 | 7.82838987e-01 -2.31058079e+00 2.57519158e+00 3 -1.14818599e+00 1.31091243e+00 3.61410531e-01 | -1.14818599e+00 1.31091243e+00 3.61410531e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = TFF (Configuration in file "config-H-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)) = -0.538021272385 2^p V(r_1,...,r_N) = -0.538021272385 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 -1.32316312e+00 -1.48707856e+00 -2.44762760e+00 | -1.32316312e+00 -1.48707856e+00 -2.44762760e+00 1 8.48767030e-01 1.04333342e+00 -3.04822443e-01 | 8.48767030e-01 1.04333342e+00 -3.04822443e-01 2 1.35472050e+00 -7.60048329e-01 1.32568239e+00 | 1.35472050e+00 -7.60048329e-01 1.32568239e+00 3 -8.80324413e-01 1.20379346e+00 1.42676765e+00 | -8.80324413e-01 1.20379346e+00 1.42676765e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTT (Configuration in file "config-H-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)) = -0.290919742026 2^p V(r_1,...,r_N) = -0.290919742026 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 -1.97712992e+00 -1.02906268e+00 -1.70106605e+00 | -1.97712992e+00 -1.02906268e+00 -1.70106605e+00 1 1.50115097e+00 1.19190792e+00 -2.02285615e+00 | 1.50115097e+00 1.19190792e+00 -2.02285615e+00 2 1.87663131e+00 -6.16379397e-01 2.63533285e+00 | 1.87663131e+00 -6.16379397e-01 2.63533285e+00 3 -1.40065237e+00 4.53534153e-01 1.08858934e+00 | -1.40065237e+00 4.53534153e-01 1.08858934e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FTF (Configuration in file "config-H-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)) = -0.592866835583 2^p V(r_1,...,r_N) = -0.592866835583 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 -1.14569955e+00 -1.81157840e+00 -4.16773999e-01 | -1.14569955e+00 -1.81157840e+00 -4.16773999e-01 1 2.07134822e+00 1.36790582e+00 -1.34890240e+00 | 2.07134822e+00 1.36790582e+00 -1.34890240e+00 2 3.12259680e-01 -5.09351153e-01 5.41363563e-01 | 3.12259680e-01 -5.09351153e-01 5.41363563e-01 3 -1.23790835e+00 9.53023736e-01 1.22431283e+00 | -1.23790835e+00 9.53023736e-01 1.22431283e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = H, PBC = FFT (Configuration in file "config-H-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)) = 2.25571092271 2^p V(r_1,...,r_N) = 2.25571092271 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 -7.09592059e+00 -4.41532236e+00 -6.53257016e+00 | -7.09592059e+00 -4.41532236e+00 -6.53257016e+00 1 1.34914895e+00 2.27439124e+00 -2.43539556e+00 | 1.34914895e+00 2.27439124e+00 -2.43539556e+00 2 8.69966944e+00 -1.79746481e+00 7.35660057e+00 | 8.69966944e+00 -1.79746481e+00 7.35660057e+00 3 -2.95289780e+00 3.93839593e+00 1.61136515e+00 | -2.95289780e+00 3.93839593e+00 1.61136515e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTT (Configuration in file "config-Pd-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)) = -1.19524173815 2^p V(r_1,...,r_N) = -1.19524173815 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 -6.33147179e-01 -1.85967678e-01 -2.90183000e-01 | -6.33147179e-01 -1.85967678e-01 -2.90183000e-01 1 2.75005721e-01 4.94287447e-01 -3.91057298e-01 | 2.75005721e-01 4.94287447e-01 -3.91057298e-01 2 4.18842621e-01 -1.92630614e-01 6.49079649e-01 | 4.18842621e-01 -1.92630614e-01 6.49079649e-01 3 -6.07011629e-02 -1.15689154e-01 3.21606486e-02 | -6.07011629e-02 -1.15689154e-01 3.21606486e-02 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TTF (Configuration in file "config-Pd-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)) = -0.244325653067 2^p V(r_1,...,r_N) = -0.244325653067 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 -2.26954553e+00 -1.67645617e+00 -2.05413119e+00 | -2.26954553e+00 -1.67645617e+00 -2.05413119e+00 1 1.80758219e+00 2.13068307e+00 -1.51511471e+00 | 1.80758219e+00 2.13068307e+00 -1.51511471e+00 2 1.47116705e+00 -1.98736876e+00 2.09133999e+00 | 1.47116705e+00 -1.98736876e+00 2.09133999e+00 3 -1.00920371e+00 1.53314186e+00 1.47790592e+00 | -1.00920371e+00 1.53314186e+00 1.47790592e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFT (Configuration in file "config-Pd-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)) = 2.75207745794 2^p V(r_1,...,r_N) = 2.75207745794 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 -5.32471150e+00 -5.34583343e+00 -5.66594068e+00 | -5.32471150e+00 -5.34583343e+00 -5.66594068e+00 1 4.17772502e+00 4.28144896e+00 -4.28567496e+00 | 4.17772502e+00 4.28144896e+00 -4.28567496e+00 2 5.91778241e+00 -4.57301544e+00 4.29647494e+00 | 5.91778241e+00 -4.57301544e+00 4.29647494e+00 3 -4.77079593e+00 5.63739991e+00 5.65514071e+00 | -4.77079593e+00 5.63739991e+00 5.65514071e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = TFF (Configuration in file "config-Pd-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)) = 0.059740448748 2^p V(r_1,...,r_N) = 0.059740448748 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 -2.48917504e+00 -1.05672751e+00 -3.13299341e+00 | -2.48917504e+00 -1.05672751e+00 -3.13299341e+00 1 1.26367304e+00 1.57404134e+00 -7.64611626e-01 | 1.26367304e+00 1.57404134e+00 -7.64611626e-01 2 2.94942741e+00 -3.17210443e+00 2.72717181e+00 | 2.94942741e+00 -3.17210443e+00 2.72717181e+00 3 -1.72392542e+00 2.65479059e+00 1.17043322e+00 | -1.72392542e+00 2.65479059e+00 1.17043322e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTT (Configuration in file "config-Pd-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)) = 0.824283005789 2^p V(r_1,...,r_N) = 0.824283005789 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 -3.69957136e+00 -4.56815192e+00 -3.27188604e+00 | -3.69957136e+00 -4.56815192e+00 -3.27188604e+00 1 3.76346333e+00 3.21596237e+00 -3.04749341e+00 | 3.76346333e+00 3.21596237e+00 -3.04749341e+00 2 1.78689337e+00 -1.99389925e+00 2.25760746e+00 | 1.78689337e+00 -1.99389925e+00 2.25760746e+00 3 -1.85078534e+00 3.34608881e+00 4.06177200e+00 | -1.85078534e+00 3.34608881e+00 4.06177200e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FTF (Configuration in file "config-Pd-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)) = 0.768956343405 2^p V(r_1,...,r_N) = 0.768956343405 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 -2.99133917e+00 -2.78835744e+00 -1.70504612e+00 | -2.99133917e+00 -2.78835744e+00 -1.70504612e+00 1 3.21198382e+00 3.28405873e+00 -5.32291750e+00 | 3.21198382e+00 3.28405873e+00 -5.32291750e+00 2 3.17270932e+00 -3.14527248e+00 4.94505710e+00 | 3.17270932e+00 -3.14527248e+00 4.94505710e+00 3 -3.39335397e+00 2.64957119e+00 2.08290653e+00 | -3.39335397e+00 2.64957119e+00 2.08290653e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MONOATOMIC STRUCTURE -- Species = Pd, PBC = FFT (Configuration in file "config-Pd-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)) = 1.4835694137 2^p V(r_1,...,r_N) = 1.4835694137 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 -4.32308346e+00 -1.69985635e+00 -3.65759734e+00 | -4.32308346e+00 -1.69985635e+00 -3.65759734e+00 1 3.27483541e+00 4.41147418e+00 -3.10268110e+00 | 3.27483541e+00 4.41147418e+00 -3.10268110e+00 2 2.47655635e+00 -4.09345390e+00 6.08060839e+00 | 2.47655635e+00 -4.09345390e+00 6.08060839e+00 3 -1.42830829e+00 1.38183607e+00 6.79670056e-01 | -1.42830829e+00 1.38183607e+00 6.79670056e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = TTT (Configuration in file "config-AgHPd-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)) = -3.44341258005 2^p V(r_1,...,r_N) = -3.44341258005 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 -2.10498038e+00 -3.27921903e+00 -1.07913209e+00 | -2.10498038e+00 -3.27921903e+00 -1.07913209e+00 1 4.65684781e+00 1.86791089e+00 -3.41609045e+00 | 4.65684781e+00 1.86791089e+00 -3.41609045e+00 2 -6.35139103e-01 6.70061480e-01 4.07753936e-01 | -6.35139103e-01 6.70061480e-01 4.07753936e-01 3 -1.91672833e+00 7.41246666e-01 4.08746861e+00 | -1.91672833e+00 7.41246666e-01 4.08746861e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = TTF (Configuration in file "config-AgHPd-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)) = -3.1141148099 2^p V(r_1,...,r_N) = -3.1141148099 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 -3.45804121e+00 -2.47584702e+00 -1.46756957e+00 | -3.45804121e+00 -2.47584702e+00 -1.46756957e+00 1 2.52827466e+00 4.63116288e+00 -1.78380672e+00 | 2.52827466e+00 4.63116288e+00 -1.78380672e+00 2 7.62048000e-01 -1.78298486e+00 2.96131018e+00 | 7.62048000e-01 -1.78298486e+00 2.96131018e+00 3 1.67718551e-01 -3.72331002e-01 2.90066120e-01 | 1.67718551e-01 -3.72331002e-01 2.90066120e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = TFT (Configuration in file "config-AgHPd-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)) = -0.706692964019 2^p V(r_1,...,r_N) = -0.706692964019 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 -5.58638254e+00 -7.60729583e+00 -7.27806009e+00 | -5.58638254e+00 -7.60729583e+00 -7.27806009e+00 1 4.94811161e+00 3.91667979e+00 4.78810568e-01 | 4.94811161e+00 3.91667979e+00 4.78810568e-01 2 2.36628385e+00 -1.24372269e-01 9.47909407e-01 | 2.36628385e+00 -1.24372269e-01 9.47909407e-01 3 -1.72801292e+00 3.81498831e+00 5.85134011e+00 | -1.72801292e+00 3.81498831e+00 5.85134011e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = TFF (Configuration in file "config-AgHPd-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)) = 0.153311214929 2^p V(r_1,...,r_N) = 0.153311214929 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 -9.17755901e-01 2.01147049e-01 -1.92473427e-01 | -9.17755901e-01 2.01147049e-01 -1.92473427e-01 1 1.90770462e+00 7.75018945e+00 -9.35135497e+00 | 1.90770462e+00 7.75018945e+00 -9.35135497e+00 2 2.25340271e+00 -1.05465000e+01 9.09943201e+00 | 2.25340271e+00 -1.05465000e+01 9.09943201e+00 3 -3.24335143e+00 2.59516353e+00 4.44396393e-01 | -3.24335143e+00 2.59516353e+00 4.44396393e-01 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = FTT (Configuration in file "config-AgHPd-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)) = -2.11335867848 2^p V(r_1,...,r_N) = -2.11335867848 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 -5.75836352e+00 -8.26893621e+00 -4.12153859e+00 | -5.75836352e+00 -8.26893621e+00 -4.12153859e+00 1 5.69877532e+00 5.74176525e+00 -3.56194899e+00 | 5.69877532e+00 5.74176525e+00 -3.56194899e+00 2 1.89798128e+00 -5.72595984e-01 2.06464606e+00 | 1.89798128e+00 -5.72595984e-01 2.06464606e+00 3 -1.83839308e+00 3.09976694e+00 5.61884152e+00 | -1.83839308e+00 3.09976694e+00 5.61884152e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = FTF (Configuration in file "config-AgHPd-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)) = -1.58981626311 2^p V(r_1,...,r_N) = -1.58981626311 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 -1.18568834e+00 -2.36210280e+00 -8.23648597e-01 | -1.18568834e+00 -2.36210280e+00 -8.23648597e-01 1 7.75466969e+00 2.87951137e+00 -6.26893818e+00 | 7.75466969e+00 2.87951137e+00 -6.26893818e+00 2 8.51941805e-02 -2.88827831e+00 1.48870921e+00 | 8.51941805e-02 -2.88827831e+00 1.48870921e+00 3 -6.65417553e+00 2.37086974e+00 5.60387757e+00 | -6.65417553e+00 2.37086974e+00 5.60387757e+00 ------------------------------------------------------------------------------------------------------------------------ PASS: Energies and forces are the same to within a relative error of 1e-08 ------------------------------------------------------------------------------------------------------------------------ MIXED STRUCTURE -- Species = Ag H Pd, PBC = FFT (Configuration in file "config-AgHPd-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)) = -3.15525466075 2^p V(r_1,...,r_N) = -3.15525466075 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 -3.37204548e+00 -3.10827708e+00 1.94124783e-01 | -3.37204548e+00 -3.10827708e+00 1.94124783e-01 1 3.48548940e+00 3.85360978e+00 -1.04705939e+00 | 3.48548940e+00 3.85360978e+00 -1.04705939e+00 2 -2.18450433e-01 -1.20809020e-01 6.77990026e-01 | -2.18450433e-01 -1.20809020e-01 6.77990026e-01 3 1.05006516e-01 -6.24523689e-01 1.74944579e-01 | 1.05006516e-01 -6.24523689e-01 1.74944579e-01 ------------------------------------------------------------------------------------------------------------------------ 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.