def metric(point):
# Update molecular configuration based on given configuration
molecule.set_positions(convert_vector_to_atoms(point))
# Evaluate the value of sqrt(2(E-V)), replacing E-V with 1E-9 if V > E.
cf = math.sqrt(max([2*(energy - molecule.get_potential_energy()), 1E-9]))
# Return sqrt(2(E-V)) and it's gradient
return [cf, molecule.get_forces().flatten()/cf]
def integrand(t, x_1, x_2):
x = np.add(np.subtract(x_2, x_1) * t, x_1)
curve.configuration['molecule'].set_positions(
convert_vector_to_atoms(x))
metric_cf = 1 / math.sqrt(
2 * (curve.energy -
curve.configuration['molecule'].get_potential_energy()))
return metric_cf * math.sqrt(
np.inner(np.subtract(x_2, x_1),
mass_matrix.dot(np.subtract(x_2, x_1))))
def write_xyz_animation(curve_pickle, filename):
""" This function takes a curve object that has been pickled and writes out an XYZ animation file to use with JMol.
Args:
curve_pickle (str): The location of a pickled curve object.
filename (str): The location of where to write the XYZ animation.
"""
# Unpickle the curve object
curve = pickle.load(open(curve_pickle, "rb"))
# Extract the trajectories points
trajectory = curve.get_points()
# Reparameterise to determine physical times
times = get_times(curve)
# Index to determine correct time
i = 0
# Extract the curves molecular configuration as described by an ASE atoms object
molecule = curve.configuration['molecule']
# Create a new file for the animation to be stored
animation_file = open(filename, 'w')
# For each node along the curve...
for state in trajectory:
# Determine the molecular configuration in ASE
molecule.set_positions(convert_vector_to_atoms(state))
# Produce a snapshot XYZ file of the configuration at that point in time
write('current_state.xyz',
molecule,
format='xyz')
# Increase index
i += 1
# Open the newly produced XYZ file
current_state = open('current_state.xyz', 'r')
# Append the snapshot XYZ file into the animation file
for line in current_state:
animation_file.write(line)
current_state.close()
# Once finished close the file so that other programs can access it
animation_file.close()
# Delete the temporary file used to store current snapshots
os.remove('current_state.xyz')
def write_xyz_animation(curve_pickle, filename):
""" This function takes a curve object that has been pickled and writes out an XYZ animation file to use with JMol.
Args:
curve_pickle (str): The location of a pickled curve object.
filename (str): The location of where to write the XYZ animation.
"""
# Unpickle the curve object
curve = pickle.load(open(curve_pickle, "rb"))
# Extract the trajectories points
trajectory = curve.get_points()
# Reparameterise to determine physical times
times = get_times(curve)
# Index to determine correct time
i = 0
# Extract the curves molecular configuration as described by an ASE atoms object
molecule = curve.configuration['molecule']
# Create a new file for the animation to be stored
animation_file = open(filename, 'w')
# For each node along the curve...
for state in trajectory:
# Determine the molecular configuration in ASE
molecule.set_positions(convert_vector_to_atoms(state))
# Produce a snapshot XYZ file of the configuration at that point in time
write('current_state.xyz', molecule, format='xyz')
# Increase index
i += 1
# Open the newly produced XYZ file
current_state = open('current_state.xyz', 'r')
# Append the snapshot XYZ file into the animation file
for line in current_state:
animation_file.write(line)
current_state.close()
# Once finished close the file so that other programs can access it
animation_file.close()
# Delete the temporary file used to store current snapshots
os.remove('current_state.xyz')
def metric(point):
# Update molecular configuration based on given configuration
molecule.set_positions(convert_vector_to_atoms(point[:-9]))
# Compute -grad(V)
minus_grad_V = molecule.get_forces().flatten()
# Extract cell information from the point
cell = np.reshape(convert_vector_to_atoms(point[-9:]), (3, 3))
# Compute the cell volume scaled by pressure
cell_volume = pressure * abs(np.linalg.det(cell))
# Compute gradient of the volume
grad_cell_volume = -cell_volume * np.linalg.inv(cell).transpose().flatten()
# Update the molecule's cell
molecule.set_cell(cell)
# Evaluate the value of sqrt(2(E-V)), replacing E-V with 1E-9 if V > E.
cf = math.sqrt(max([2*(energy - molecule.get_potential_energy() - cell_volume), 1E-9]))
return [cf, np.hstack((minus_grad_V, grad_cell_volume))/cf]
def metric(point, Q_I_matrix, x_k):
# Update molecular configuration based on given configuration
molecule.set_positions(convert_vector_to_atoms(point))
# Evaluate the value of sqrt(2(E-V)), replacing E-V with 1E-9 if V > E.
x_k = np.asarray(x_k)
Q_I_matrix = np.asarray(Q_I_matrix)
# print Q_I_matrix
b = Q_I_matrix.dot(x_k)
# print b
c = np.absolute(np.inner(x_k, b))
# print c
cf = math.sqrt(max([c, 1E-9]))
# Return sqrt(2(E-V)) and it's gradient
return [cf, molecule.get_forces().flatten() / cf]
def metric(point, Q_I_matrix, x_k):
# Update molecular configuration based on given configuration
molecule.set_positions(convert_vector_to_atoms(point))
# Evaluate the value of sqrt(2(E-V)), replacing E-V with 1E-9 if V > E.
x_k = np.asarray(x_k)
Q_I_matrix = np.asarray(Q_I_matrix)
# print Q_I_matrix
b = Q_I_matrix.dot(x_k)
# print b
c = np.absolute(np.inner(x_k, b))
# print c
cf = math.sqrt(max([c, 1E-9]))
# Return sqrt(2(E-V)) and it's gradient
return [cf, molecule.get_forces().flatten()/cf]
def integrand(t, x_1, x_2):
x = np.add(np.subtract(x_2, x_1)*t, x_1)
curve.configuration['molecule'].set_positions(convert_vector_to_atoms(x))
metric_cf = 1/math.sqrt(2*(curve.energy - curve.configuration['molecule'].get_potential_energy()))
return metric_cf * math.sqrt(np.inner(np.subtract(x_2, x_1), mass_matrix.dot(np.subtract(x_2, x_1))))