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IRC.py
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IRC.py
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from ase.optimize.optimize import Optimizer
import numpy as np
import numpy.linalg as la
from hessian import get_hessian
from ase.io.trajectory import Trajectory
def vnorm(vector):
"""normalized vector
"""
return vector / la.norm(vector)
def calc_angle(a, b, c):
ba = a.flatten() - b.flatten()
bc = c.flatten() - b.flatten()
cosine_angle = np.dot(ba, bc) / (np.linalg.norm(ba) * np.linalg.norm(bc))
angle = np.arccos(cosine_angle)
return angle
class IRC(Optimizer):
class IRCError(Exception):
pass
_dump_attr = ('stride', 'mw', 'M', 'Mi', 'sv', 'forward', 'H', 'S')
def __init__(self, atoms, stride=0.1, hessian=None, search_vector=None, forward=True, mw=True,
restart=None, logfile='-', trajectory=None, master=None):
"""IRC with Gonsalez-Schlegel method
Parameters:
atoms: Atoms object
stride: step radius
hessian: Hessian matrix in cartesian coordinates. Will be calculates if not given,
or search_vector will be used instead.
Will use first eigenvector of hessian, should be negative
search_vector: initial step direction, in cartesian coordinates
forward: positive or negative direction along search vector
mw: do search in mass-weighted (IRC) or cartesian (MEP) coordinates
"""
self.stride = stride
self.H = hessian
self.sv = search_vector
self.forward = forward
self.maxstep = 0.3
self.S = None
self._s_prev = None
self._g_prev = None
self.is_converged = False
# mass weighing
if mw:
self.M = np.sqrt(atoms.get_masses()).reshape(-1, 1)
else:
self.M = np.ones(len(atoms)).reshape(-1, 1)
self.Mi = 1 / self.M
Optimizer.__init__(self, atoms, restart, logfile, trajectory, master)
self.trajectory = Trajectory(trajectory, 'w')
def initialize(self):
# path taken so far
self.S = 0
# search vector
if self.sv is not None:
assert len(self.sv.flat) == 3 * len(self.atoms), "search_vector is in bad shape"
self.sv = self.sv * (1 if self.forward else -1) * self.M.repeat(3)
else:
self.H = self.H or get_hessian(self.atoms, mass_weighted=False)
v = self.Mi.repeat(3).reshape(-1, 1)
self.H *= v.dot(v.T)
assert self.H.shape == (3 * len(self.atoms), 3 * len(self.atoms)), "hessian is in bad shape"
eval, evec = la.eigh(self.H)
assert (eval[0] < -0.1).all(), "Hessian doesn't have imaginary eigenvalues!"
self.sv = evec[:, 0] * (1 if self.forward else -1)
self.sv = vnorm(self.sv.reshape(-1, 3))
# TODO: will use unit initial hessian until figure out how to project out rotations
self.H = 70 * np.eye(3 * len(self.atoms))
v = self.Mi.repeat(3).reshape(-1, 1)
self.H *= v.dot(v.T)
def todoct(self):
d = Optimizer.todict()
for attr in self._dump_attr:
if hasattr(self, attr):
d.update(attr, getattr(self, attr))
return d
def read(self):
data = self.load()
for attr in self._dump_attr:
setattr(self, data[attr])
def run(self, fmax=0.05, steps=1000, maxmicro=1000):
self.fmax = fmax
step = 0
pass_high_grad = False
e0 = self.atoms.get_potential_energy()
while step < steps:
p0 = self.atoms.get_positions() * self.M
p1 = self.do_step_forward(self.stride)
conv = self.do_sg2_search(p1, maxmicro)
if not conv:
raise self.IRCError("SG2 iterations not converged! Terminating.")
e1 = self.atoms.get_potential_energy()
if e1 > e0:
self.logfile.write(
'Energy is rising. Probably we just passed though a minimum. \n' +
'Signaling convergence now without storing last geometry!\n')
self.is_converged = True
break
self.S += self.calc_path(p0, p1, self.atoms.get_positions() * self.M)
self.trajectory.write(self.atoms)
f = self.atoms.get_forces()
angle = calc_angle(p0, p1, self.atoms.get_positions() * self.M)
self.logfile.write('IRC: step {:3d} path {:.4f} energy {:.5f} unconstrained force {:5f} angle {:.2f}\n'.format(
step, self.S, e1, la.norm(f), angle
))
yield self.S, e1, la.norm(f), angle
if not self.converged(f * 3):
pass_high_grad = True
elif pass_high_grad and self.converged(f / 3):
self.logfile.write('Total gradient is below threshold. Signaling convergence now!\n')
self.is_converged = True
break
e0 = e1
self.sv = vnorm(self.atoms.get_positions() * self.M - p1)
step += 1
def do_step_forward(self, stride):
"""Initial guess for next IRC point
Return circle center
"""
p0 = self.atoms.get_positions() * self.M
p1 = p0 + stride * self.sv
p2 = p1 + stride * self.sv
self.atoms.set_positions(p2 * self.Mi)
return p1
def do_sg2_search(self, c, maxstep):
step = 0
converged = False
while step < maxstep:
p = self.atoms.get_positions() * self.M
r = p - c
rn = vnorm(r)
# calculate force
f = self.atoms.get_forces() * self.Mi
# update hessian
# TODO: Something wrong with H update. skip for now
# self.h_update_dfp(p, ft)
# self.h_update_dfp(p, f)
# tangent force
ft = f - rn * np.vdot(f.reshape(-1, 1), rn.reshape(-1, 1))
if self.converged(ft):
converged = True
break
# scaled unconstrained step
x = self.determine_step(self.nr_step(f) * self.Mi, self.stride / 9.0) * self.M
# constrained displacement
x = la.norm(r) * vnorm(r + x) - r
# update coords
self.atoms.set_positions((p + x) * self.Mi)
self.logfile.write('SG2 step {:3d}: force {:.5f} displ {:.5f} angle {:.3f} energy {:.5f}\n'.format(
step, np.sqrt((ft**2).sum(axis=1)).max(), np.sqrt((x**2).sum(axis=1)).max(),
2 * np.rad2deg(np.arcsin(la.norm(x*0.5) / la.norm(r))),
self.atoms.get_potential_energy()
))
step += 1
# self.trajectory.write(self.atoms)
self.logfile.write('SG2 converged! force: {:.5f} energy {:.5f}\n'.format(
np.sqrt((ft ** 2).sum(axis=1)).max(), self.atoms.get_potential_energy()
))
return converged
@staticmethod
def calc_path(a, b, c):
theta = np.pi - calc_angle(a, b, c)
chord = la.norm(a - c)
r = chord / 2 / np.sin(theta / 2)
s = theta * r
return s
def h_update_bfgs(self, positions, force):
""" Do Hessian update with BFGS formula
"""
positions = positions.reshape(-1, 1)
grad = - force.reshape(-1, 1)
if self._s_prev is not None and self._g_prev is not None:
s = positions - self._s_prev
g = grad - self._g_prev
if (s < 1e-4).all() or (g < 1e-5).all():
return None
a = np.vdot(s, g)
v = np.dot(self.H, s)
b = np.dot(s.T, v)
self.H += np.dot(g, g.T) / a - np.dot(v, v.T) / b
self._s_prev = positions
self._g_prev = grad
def h_update_dfp(self, positions, force):
""" Do Hessian update with DFP formula
"""
positions = positions.reshape(-1, 1)
grad = - force.reshape(-1, 1)
if self._s_prev is not None and self._g_prev is not None:
s = positions - self._s_prev
g = grad - self._g_prev
if (s < 1e-4).all() or (g < 1e-5).all():
return None
self.H += - self.H.dot(g).dot(g.T).dot(self.H) / g.T.dot(self.H).dot(g) + s.dot(s.T) / g.T.dot(s)
self._s_prev = positions
self._g_prev = grad
def nr_step(self, f):
f = f.flatten()
val, vec = la.eigh(self.H)
return np.dot(vec, np.dot(f, vec) / np.abs(val)).reshape(-1, 3)
def determine_step(self, dr, maxstep):
"""Determine step to take according to maxstep
Normalize all steps as the largest step. This way
we still move along the eigendirection.
"""
maxsteplength = np.sqrt((dr * dr).sum(axis=1)).max()
if maxsteplength >= maxstep:
dr *= maxstep / maxsteplength
return dr
if __name__ == '__main__':
import os
import numpy as np
import numpy.linalg as la
from ase.calculators import mopac
from ase import Atoms
import pybel
os.chdir('../test')
MOPAC = os.path.join(os.getcwd(), 'MOPAC')
os.environ['MOPAC_LICENSE'] = MOPAC
os.environ['LD_LIBRARY_PATH'] = MOPAC
mopac_calc = mopac.MOPAC()
mopac_calc.command = 'MOPAC/MOPAC2016.exe PREFIX.mop 2> /dev/null'
mopac_calc.set(method='pm3')
mol = next(pybel.readfile('xyz', 'ts2.xyz'))
atoms = Atoms(numbers=[a.atomicnum for a in mol.atoms],
positions=[a.coords for a in mol.atoms])
atoms.set_positions(atoms.positions - atoms.get_center_of_mass())
atoms.set_calculator(mopac_calc)
irccalc = IRC(atoms, stride=0.15, mw=True, forward=True, trajectory='ts1.traj')
for _ in irccalc.run():
pass