def evolve(self, points, t):
# Given points at time 0, return points at time t.
lats = geometry.points_to_latitudes(points/self.radius, self.axis)
vels = physics.fluid_rotation(self.eq_angvel, self.polar_angvel, lats)
result = np.zeros(points.shape)
mat = geometry.rotation_matrix(-vels * t, self.axis)
return np.dot( points, mat.transpose() )
def generate_lead_halide(halide, ion="Pb"):
PbX = structures.Molecule([structures.Atom(ion, 0, 0, 0)])
if type(halide) is str:
halide = [halide, halide, halide]
def vdw(y):
return PERIODIC_TABLE[units.elem_s2i(y)]['vdw_r']
for x in halide:
v = vdw(x)
PbX.atoms.append(structures.Atom(x, v, 0, 0.5 * v))
R = geometry.rotation_matrix([0, 0, 1], 120, units="deg")
PbX.rotate(R)
return PbX
def spot(self, theta, phase, fracarea):
# Given spherical coords, get absolute coords
# Convention: theta is a latitude in degrees: 0 = equator, +90 = north pole
# Phase is in periods: 0 = transit, 0.5 = opposition, 1 = next transit
# find axis with z projection removed
w = self.axis[0:2] / np.sqrt(self.axis[0]**2 + self.axis[1]**2)
# apply inclination
theta *= math.pi/180.0
theta -= math.asin(self.axis[2])
# get location at phase 0 (latitude only)
c, s = math.cos(theta), math.sin(theta)
p = self.radius * np.array( [s*w[0], s*w[1], c] )
# rotate to phase
mat = geometry.rotation_matrix(-2.0 * math.pi * phase, self.axis)
p = np.dot(p, mat.transpose())
return (p, fracarea)
def generate_lead_halide_cation(halide, cation, ion="Pb", run_opt=True):
cml_path = fpl_constants.cml_dir
# Check if system exists
fname = reduce_to_name(ion, halide, cation)
if not cml_path.endswith("/"):
cml_path += "/"
if os.path.exists(cml_path + fname + ".cml"):
print("Found system in cml folder, returning system")
system = structures.Molecule(
files.read_cml(cml_path + fname + ".cml",
test_charges=False,
allow_errors=True)[0])
return system
def vdw(y):
return PERIODIC_TABLE[units.elem_s2i(y)]['vdw_r']
# Get the PbX3 system
PbX3 = generate_lead_halide(halide, ion=ion)
# Get the cation from the cml file
atoms, bonds, _, _ = files.read_cml(cml_path + cation + ".cml",
test_charges=False,
allow_errors=True)
system = structures.Molecule(atoms)
# Align along X axis
system.atoms = geometry.align_centroid(system.atoms)[0]
# Rotate to Z axis
# NOTE! In case of FA, we want flat so only translate to origin instead
# NOTE! We have exactly 3 cations we observe: Cs, MA, FA. If 2 N, then FA
elems = [a.element for a in system.atoms]
if elems.count("N") == 2:
system.translate(system.get_center_of_mass())
else:
R = geometry.rotation_matrix([0, 1, 0], 90, units="deg")
system.rotate(R)
# If N and C in system, ensure N is below C (closer to Pb)
if "N" in elems and "C" in elems:
N_index = [i for i, a in enumerate(system.atoms)
if a.element == "N"][0]
C_index = [i for i, a in enumerate(system.atoms)
if a.element == "C"][0]
if system.atoms[N_index].z > system.atoms[C_index].z:
# Flip if needed
R = geometry.rotation_matrix([0, 1, 0], 180, units="deg")
system.rotate(R)
# Offset system so lowest point is at 0 in the z dir
z_offset = min([a.z for a in system.atoms]) * -1
system.translate([0, 0, z_offset])
# Add to the PbX3 system with an offset of vdw(Pb)
system.translate([0, 0, vdw(ion)])
system.atoms += PbX3.atoms
# Run a geometry optimization of this system
if run_opt:
PbXY = orca.job(fname,
fpl_constants.default_routes[0],
atoms=system.atoms,
extra_section=fpl_constants.extra_section,
queue="batch",
procs=2)
PbXY.wait()
new_pos = orca.read(fname).atoms
for a, b in zip(system.atoms, new_pos):
a.x, a.y, a.z = [b.x, b.y, b.z]
# Set OPLS types
for a in system.atoms:
if a.element in [ion, "Cl", "Br", "I"]:
a.type = fpl_constants.atom_types[a.element]
a.type_index = a.type["index"]
# Write cml file so we don't re-generate, and return system
files.write_cml(system, bonds=bonds, name=cml_path + fname + ".cml")
return system
def evolve(self, points, t):
# Given points at time 0, return points at time t.
mat = geometry.rotation_matrix(-self.scalar_angvel * t, self.axis)
return np.dot( points, mat.transpose() )