!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! !!!!! !!!!! !!!!! 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_2008PairMorse_PdAgH__MO_108983864770_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)) = 2.21984804376 2^p V(r_1,...,r_N) = 2.21984804376 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 -8.08720200e+00 -1.13150605e+01 -1.26083026e+01 | -8.08720200e+00 -1.13150605e+01 -1.26083026e+01 1 6.19160331e+00 4.22633056e+00 -4.06045476e+00 | 6.19160331e+00 4.22633056e+00 -4.06045476e+00 2 6.71145559e+00 -5.62103164e+00 7.63839333e+00 | 6.71145559e+00 -5.62103164e+00 7.63839333e+00 3 -4.81585690e+00 1.27097615e+01 9.03036407e+00 | -4.81585690e+00 1.27097615e+01 9.03036407e+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)) = 5.20904987815 2^p V(r_1,...,r_N) = 5.20904987815 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 -1.10645585e+01 -7.96341683e+00 -7.16115990e+00 | -1.10645585e+01 -7.96341683e+00 -7.16115990e+00 1 8.39954219e+00 6.49293206e+00 -1.02889924e+01 | 8.39954219e+00 6.49293206e+00 -1.02889924e+01 2 1.23568449e+01 -1.31196420e+01 1.22378430e+01 | 1.23568449e+01 -1.31196420e+01 1.22378430e+01 3 -9.69182851e+00 1.45901268e+01 5.21230929e+00 | -9.69182851e+00 1.45901268e+01 5.21230929e+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)) = 8.8989017478 2^p V(r_1,...,r_N) = 8.8989017478 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 -8.41051720e+00 | 1.42564339e+01 1.40497913e+01 -8.41051720e+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)) = 18.7121974329 2^p V(r_1,...,r_N) = 18.7121974329 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)) = 8.41637821907 2^p V(r_1,...,r_N) = 8.41637821907 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 -1.36990361e+01 | -1.44390358e+01 -1.04508104e+01 -1.36990361e+01 1 1.03522351e+01 1.27207689e+01 -1.10432647e+01 | 1.03522351e+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 -9.55742622e+00 1.21390617e+01 1.23459233e+01 | -9.55742622e+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)) = 2.4196844442 2^p V(r_1,...,r_N) = 2.4196844442 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 -9.99369517e+00 -7.43343202e+00 | -1.15234472e+01 -9.99369517e+00 -7.43343202e+00 1 7.13779395e+00 9.64686840e+00 -8.25909019e+00 | 7.13779395e+00 9.64686840e+00 -8.25909019e+00 2 8.89285351e+00 -4.97660608e+00 1.22036686e+01 | 8.89285351e+00 -4.97660608e+00 1.22036686e+01 3 -4.50720026e+00 5.32343285e+00 3.48885362e+00 | -4.50720026e+00 5.32343285e+00 3.48885362e+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)) = 16.0385134972 2^p V(r_1,...,r_N) = 16.0385134972 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 -2.29356074e+01 1.99366686e+01 1.04834206e+01 | -2.29356074e+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)) = -2.16391756657 2^p V(r_1,...,r_N) = -2.16391756657 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 -2.15054118e+00 -3.01760087e+00 -7.35062481e-01 | -2.15054118e+00 -3.01760087e+00 -7.35062481e-01 1 6.50819083e+00 1.39406102e+00 -5.19830515e+00 | 6.50819083e+00 1.39406102e+00 -5.19830515e+00 2 -6.67815932e-01 7.84659193e-01 4.04728326e-01 | -6.67815932e-01 7.84659193e-01 4.04728326e-01 3 -3.68983371e+00 8.38880653e-01 5.52863931e+00 | -3.68983371e+00 8.38880653e-01 5.52863931e+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)) = 3.8931364606 2^p V(r_1,...,r_N) = 3.8931364606 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 -1.39163952e+01 -1.73253678e+01 -6.08721217e+00 | -1.39163952e+01 -1.73253678e+01 -6.08721217e+00 1 1.82258542e+01 1.16256730e+01 -3.44305498e+00 | 1.82258542e+01 1.16256730e+01 -3.44305498e+00 2 5.29304456e-01 5.47017475e-01 -4.65618744e-01 | 5.29304456e-01 5.47017475e-01 -4.65618744e-01 3 -4.83876345e+00 5.15267737e+00 9.99588590e+00 | -4.83876345e+00 5.15267737e+00 9.99588590e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = 4.93274743163 2^p V(r_1,...,r_N) = 4.93274743163 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 -1.19703437e+01 -2.67044513e+00 -1.70327087e+01 | -1.19703437e+01 -2.67044513e+00 -1.70327087e+01 1 -1.44857092e-01 1.69477663e+00 3.33022701e-01 | -1.44857092e-01 1.69477663e+00 3.33022701e-01 2 1.52160035e+01 -6.50072505e+00 1.58199247e+01 | 1.52160035e+01 -6.50072505e+00 1.58199247e+01 3 -3.10080267e+00 7.47639355e+00 8.79761314e-01 | -3.10080267e+00 7.47639355e+00 8.79761314e-01 ------------------------------------------------------------------------------------------------------------------------ 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)) = -2.29912196606 2^p V(r_1,...,r_N) = -2.29912196606 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 4.16928668e-01 7.19496110e-01 -5.27214378e-01 | 4.16928668e-01 7.19496110e-01 -5.27214378e-01 1 3.35072719e-01 1.89133755e+00 -4.10728393e+00 | 3.35072719e-01 1.89133755e+00 -4.10728393e+00 2 3.20949150e+00 -5.61794818e+00 2.81089114e+00 | 3.20949150e+00 -5.61794818e+00 2.81089114e+00 3 -3.96149289e+00 3.00711452e+00 1.82360717e+00 | -3.96149289e+00 3.00711452e+00 1.82360717e+00 ------------------------------------------------------------------------------------------------------------------------ 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)) = -1.9882344755 2^p V(r_1,...,r_N) = -1.9882344755 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 -2.44805001e+00 -5.37144769e+00 -5.39667074e+00 | -2.44805001e+00 -5.37144769e+00 -5.39667074e+00 1 -2.81149782e-01 6.46175427e-01 6.28727701e-01 | -2.81149782e-01 6.46175427e-01 6.28727701e-01 2 2.75175700e+00 -2.05509870e+00 1.70396634e+00 | 2.75175700e+00 -2.05509870e+00 1.70396634e+00 3 -2.25572078e-02 6.78037097e+00 3.06397670e+00 | -2.25572078e-02 6.78037097e+00 3.06397670e+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)) = 3.62102841803 2^p V(r_1,...,r_N) = 3.62102841803 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 8.86293013e-01 -1.68349760e+00 2.37632600e-02 | 8.86293013e-01 -1.68349760e+00 2.37632600e-02 1 1.07019813e+01 7.89572633e+00 -1.43763806e+01 | 1.07019813e+01 7.89572633e+00 -1.43763806e+01 2 4.82169389e+00 -1.01437682e+01 4.48831471e+00 | 4.82169389e+00 -1.01437682e+01 4.48831471e+00 3 -1.64099682e+01 3.93153949e+00 9.86430259e+00 | -1.64099682e+01 3.93153949e+00 9.86430259e+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)) = -2.28782381381 2^p V(r_1,...,r_N) = -2.28782381381 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 -1.53705465e+00 -3.14080486e+00 -4.36113199e-01 | -1.53705465e+00 -3.14080486e+00 -4.36113199e-01 1 4.62148992e+00 2.85568481e+00 -4.23943604e+00 | 4.62148992e+00 2.85568481e+00 -4.23943604e+00 2 -7.49290210e-01 -1.89178767e+00 1.07346026e+00 | -7.49290210e-01 -1.89178767e+00 1.07346026e+00 3 -2.33514506e+00 2.17690772e+00 3.60208898e+00 | -2.33514506e+00 2.17690772e+00 3.60208898e+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.