def Energy(self, coordinates3, gradients3=None):
"""Calculate the energy."""
# . Displacements.
v12 = coordinates3.Displacement(self.point1, self.point2)
v32 = coordinates3.Displacement(self.point3, self.point2)
v34 = coordinates3.Displacement(self.point3, self.point4)
# . Get m and n.
m = Clone(v12)
m.Cross(v32)
n = Clone(v32)
n.Cross(v34)
# . Get the sizes of m and n.
msize = m.Norm2()
nsize = n.Norm2()
# . Normalize m and n.
m.Scale(1.0 / msize)
n.Scale(1.0 / nsize)
# . Get the dot-product.
dotfac = m.Dot(n)
if dotfac > 1.0: dotfac = 1.0
elif dotfac < -1.0: dotfac = -1.0
# . Get the sign of the angle.
sgnfac = 1.0
if v12.Dot(n) < 0.0: sgnfac = -1.0
# . Determine the dihedral.
value = sgnfac * math.acos(dotfac) * UNITS_ANGLE_RADIANS_TO_DEGREES
# . Get the energy.
(f, df) = self.energyModel.Energy(value)
# . Derivatives.
if gradients3 is not None:
df *= UNITS_ANGLE_RADIANS_TO_DEGREES
# . Calculate r32.
r32 = v32.Norm2()
# . Calculate dedi and dedl in m and n respectively.
m.Scale(df * r32 / msize)
n.Scale(-df * r32 / nsize)
# . Calculate some additional factors.
fact12 = v12.Dot(v32) / (r32 * r32)
fact34 = v34.Dot(v32) / (r32 * r32)
# . Gradients for i and l.
gradients3.Increment(self.point1, m)
gradients3.Increment(self.point4, n)
# . Calculate dedj and dedk in v12 and v32 respectively.
m.CopyTo(v12)
v12.Scale(fact12 - 1.0)
v12.AddScaledVector3(-fact34, n)
n.CopyTo(v32)
v32.Scale(fact34 - 1.0)
v32.AddScaledVector3(-fact12, m)
# . calculate the gradients.
gradients3.Increment(self.point2, v12)
gradients3.Increment(self.point3, v32)
return (f, value)
def NormalModesTrajectory_SystemGeometry(system,
trajectory,
cycles=10,
frames=21,
mode=0,
state=None,
temperature=300.0):
"""Generate a normal mode trajectory."""
# . Get the state.
if state is None: state = system.configuration.nmState
# . Get state-related information.
if state.freeAtoms == None: freeAtoms = range(len(system.atoms))
else: freeAtoms = state.freeAtoms
frequencies = state.frequencies
modes = state.modes
# . Get the mode frequency.
omega = math.fabs(frequencies[mode])
# . Calculate the number of frames.
total = cycles * frames
# . Check for a calculation.
if (mode >= 0) and (mode < state.dimension) and (
omega > _LOWFREQUENCY) and (total > 0):
# . Calculate the amplitude (in Angstroms).
amplitude = math.sqrt(
2.0 * 1.0e-3 * CONSTANT_AVOGADRO_NUMBER * CONSTANT_BOLTZMANN *
temperature) * (_TO_WAVENUMBERS / omega)
# . Allocate space for the coordinates and mode.
coordinates3 = Clone(system.coordinates3)
displacement = Coordinates3.WithExtent(len(system.atoms))
displacement.Set(0.0)
# . Get the displacement.
for f in freeAtoms:
displacement[f, 0] = modes[mode, 3 * f]
displacement[f, 1] = modes[mode, 3 * f + 1]
displacement[f, 2] = modes[mode, 3 * f + 2]
# . Loop over the cycles and frames.
# . Calculate the displacement prefactor using sine instead of cosine.
trajectory.WriteHeader(temperature=temperature)
for c in range(cycles):
for f in range(frames):
factor = amplitude * math.sin(
2.0 * math.pi * float(f) / float(frames))
coordinates3.CopyTo(system.coordinates3)
system.coordinates3.AddScaledMatrix(factor, displacement)
trajectory.WriteOwnerData()
# . Finish up.
trajectory.WriteFooter()
trajectory.Close()
def Superimpose(self, reference3=None, weights=None):
"""Superimpose the trajectory on a reference structure using the first trajectory frame by default."""
# . Initialization.
coordinates3 = self.owner.coordinates3
# . Save the owner coordinates to restore later.
saved3 = Clone(coordinates3)
# . Get the reference coordinates.
if reference3 is coordinates3:
reference3 = saved3
elif reference3 is None:
self.RestoreOwnerData(index=0)
reference3 = Clone(coordinates3)
# . Loop over trajectory frames.
results = []
for index in range(self.frames):
self.RestoreOwnerData(index=index)
rms0 = coordinates3.RMSDeviation(reference3, weights=weights)
coordinates3.Superimpose(reference3, weights=weights)
rms1 = coordinates3.RMSDeviation(reference3, weights=weights)
self.WriteOwnerData(index=index)
results.append((rms0, rms1))
# . Finish up.
saved3.CopyTo(coordinates3)
return results