from __future__ import division, print_function from math import sqrt from ase.geometry import find_mic import numpy as np __all__ = ['FixCartesian', 'FixBondLength', 'FixedMode', 'FixConstraintSingle', 'FixAtoms', 'UnitCellFilter', 'FixScaled', 'StrainFilter', 'FixedPlane', 'Filter', 'FixConstraint', 'FixedLine', 'FixBondLengths', 'FixInternals', 'Hookean', 'ExternalForce'] def dict2constraint(dct): if dct['name'] not in __all__: raise ValueError return globals()[dct['name']](**dct['kwargs']) def slice2enlist(s, n): """Convert a slice object into a list of (new, old) tuples.""" if isinstance(s, slice): return enumerate(range(*s.indices(n))) return enumerate(s) def constrained_indices(atoms, only_include=None): """Returns a list of indices for the atoms that are constrained by a constraint that is applied. By setting only_include to a specific type of constraint you can make it only look for that given constraint. """ indices = [] for constraint in atoms.constraints: if only_include is not None: if not isinstance(constraint, only_include): continue indices.extend(np.array(constraint.get_indices())) return np.array(np.unique(indices)) class FixConstraint: """Base class for classes that fix one or more atoms in some way.""" def index_shuffle(self, atoms, ind): """Change the indices. When the ordering of the atoms in the Atoms object changes, this method can be called to shuffle the indices of the constraints. ind -- List or tuple of indices. """ raise NotImplementedError def repeat(self, m, n): """ basic method to multiply by m, needs to know the length of the underlying atoms object for the assignment of multiplied constraints to work. """ msg = ("Repeat is not compatible with your atoms' constraints." ' Use atoms.set_constraint() before calling repeat to ' 'remove your constraints.') raise NotImplementedError(msg) def adjust_momenta(self, atoms, momenta): """Adjusts momenta in identical manner to forces.""" self.adjust_forces(atoms, momenta) def copy(self): return dict2constraint(self.todict().copy()) class FixConstraintSingle(FixConstraint): """Base class for classes that fix a single atom.""" def __init__(self, a): self.a = a def index_shuffle(self, atoms, ind): """The atom index must be stored as self.a.""" newa = -1 # Signal error for new, old in slice2enlist(ind, len(atoms)): if old == self.a: newa = new break if newa == -1: raise IndexError('Constraint not part of slice') self.a = newa def get_indices(self): return [self.a] class FixAtoms(FixConstraint): """Constraint object for fixing some chosen atoms.""" def __init__(self, indices=None, mask=None): """Constrain chosen atoms. Parameters ---------- indices : list of int Indices for those atoms that should be constrained. mask : list of bool One boolean per atom indicating if the atom should be constrained or not. Examples -------- Fix all Copper atoms: >>> mask = [s == 'Cu' for s in atoms.get_chemical_symbols()] >>> c = FixAtoms(mask=mask) >>> atoms.set_constraint(c) Fix all atoms with z-coordinate less than 1.0 Angstrom: >>> c = FixAtoms(mask=atoms.positions[:, 2] < 1.0) >>> atoms.set_constraint(c) """ if indices is None and mask is None: raise ValueError('Use "indices" or "mask".') if indices is not None and mask is not None: raise ValueError('Use only one of "indices" and "mask".') if mask is not None: indices = np.arange(len(mask))[np.asarray(mask, bool)] else: # Check for duplicates: srt = np.sort(indices) if (np.diff(srt) == 0).any(): raise ValueError( 'FixAtoms: The indices array contained duplicates. ' 'Perhaps you wanted to specify a mask instead, but ' 'forgot the mask= keyword.') self.index = np.asarray(indices, int) if self.index.ndim != 1: raise ValueError('Wrong argument to FixAtoms class!') self.removed_dof = 3 * len(self.index) def adjust_positions(self, atoms, new): new[self.index] = atoms.positions[self.index] def adjust_forces(self, atoms, forces): forces[self.index] = 0.0 def index_shuffle(self, atoms, ind): # See docstring of superclass index = [] for new, old in slice2enlist(ind, len(atoms)): if old in self.index: index.append(new) if len(index) == 0: raise IndexError('All indices in FixAtoms not part of slice') self.index = np.asarray(index, int) def get_indices(self): return self.index def __repr__(self): return 'FixAtoms(indices=%s)' % ints2string(self.index) def todict(self): return {'name': 'FixAtoms', 'kwargs': {'indices': self.index}} def repeat(self, m, n): i0 = 0 natoms = 0 if isinstance(m, int): m = (m, m, m) index_new = [] for m2 in range(m[2]): for m1 in range(m[1]): for m0 in range(m[0]): i1 = i0 + n index_new += [i + natoms for i in self.index] i0 = i1 natoms += n self.index = np.asarray(index_new, int) return self def delete_atoms(self, indices, natoms): """Removes atom number ind from the index array, if present. Required for removing atoms with existing FixAtoms constraints. """ i = np.zeros(natoms, int) - 1 new = np.delete(np.arange(natoms), indices) i[new] = np.arange(len(new)) index = i[self.index] self.index = index[index >= 0] if len(self.index) == 0: return None return self def ints2string(x, threshold=None): """Convert ndarray of ints to string.""" if threshold is None or len(x) <= threshold: return str(x.tolist()) return str(x[:threshold].tolist())[:-1] + ', ...]' class FixBondLengths(FixConstraint): maxiter = 500 def __init__(self, pairs, tolerance=1e-13, iterations=None): """iterations: Ignored""" self.pairs = np.asarray(pairs) self.tolerance = tolerance self.removed_dof = len(pairs) def adjust_positions(self, atoms, new): old = atoms.positions masses = atoms.get_masses() for i in range(self.maxiter): converged = True for a, b in self.pairs: r0 = old[a] - old[b] d0 = find_mic([r0], atoms.cell, atoms._pbc)[0][0] d1 = new[a] - new[b] - r0 + d0 m = 1 / (1 / masses[a] + 1 / masses[b]) x = 0.5 * (np.dot(d0, d0) - np.dot(d1, d1)) / np.dot(d0, d1) if abs(x) > self.tolerance: new[a] += x * m / masses[a] * d0 new[b] -= x * m / masses[b] * d0 converged = False if converged: break else: raise RuntimeError('Did not converge') def adjust_momenta(self, atoms, p): old = atoms.positions masses = atoms.get_masses() for i in range(self.maxiter): converged = True for a, b in self.pairs: d = old[a] - old[b] d = find_mic([d], atoms.cell, atoms._pbc)[0][0] dv = p[a] / masses[a] - p[b] / masses[b] m = 1 / (1 / masses[a] + 1 / masses[b]) x = -np.dot(dv, d) / np.dot(d, d) if abs(x) > self.tolerance: p[a] += x * m * d p[b] -= x * m * d converged = False if converged: break else: raise RuntimeError('Did not converge') def adjust_forces(self, atoms, forces): self.constraint_forces = -forces self.adjust_momenta(atoms, forces) self.constraint_forces += forces def get_indices(self): return np.unique(self.pairs.ravel()) def todict(self): return {'name': 'FixBondLengths', 'kwargs': {'pairs': self.pairs, 'tolerance': self.tolerance}} def index_shuffle(self, atoms, ind): """Shuffle the indices of the two atoms in this constraint""" map = np.zeros(len(atoms), int) map[ind] = 1 n = map.sum() map[:] = -1 map[ind] = range(n) pairs = map[self.pairs] self.pairs = pairs[(pairs != -1).all(1)] if len(self.pairs) == 0: raise IndexError('Constraint not part of slice') def FixBondLength(a1, a2): """Fix distance between atoms with indices a1 and a2.""" return FixBondLengths([(a1, a2)]) class FixedMode(FixConstraint): """Constrain atoms to move along directions orthogonal to a given mode only.""" def __init__(self, mode): self.mode = (np.asarray(mode) / np.sqrt((mode**2).sum())).reshape(-1) def adjust_positions(self, atoms, newpositions): newpositions = newpositions.ravel() oldpositions = atoms.positions.ravel() step = newpositions - oldpositions newpositions -= self.mode * np.dot(step, self.mode) def adjust_forces(self, atoms, forces): forces = forces.ravel() forces -= self.mode * np.dot(forces, self.mode) def index_shuffle(self, atoms, ind): eps = 1e-12 mode = self.mode.reshape(-1, 3) excluded = np.ones(len(mode), dtype=bool) excluded[ind] = False if (abs(mode[excluded]) > eps).any(): raise IndexError('All nonzero parts of mode not in slice') self.mode = mode[ind].ravel() def get_indices(self): # This function will never properly work because it works on all # atoms and it has no idea how to tell how many atoms it is # attached to. If it is being used, surely the user knows # everything is being constrained. return [] def todict(self): return {'name': 'FixedMode', 'kwargs': {'mode': self.mode}} def __repr__(self): return 'FixedMode(%s)' % self.mode.tolist() class FixedPlane(FixConstraintSingle): """Constrain an atom index *a* to move in a given plane only. The plane is defined by its normal vector *direction*.""" removed_dof = 1 def __init__(self, a, direction): self.a = a self.dir = np.asarray(direction) / sqrt(np.dot(direction, direction)) def adjust_positions(self, atoms, newpositions): step = newpositions[self.a] - atoms.positions[self.a] newpositions[self.a] -= self.dir * np.dot(step, self.dir) def adjust_forces(self, atoms, forces): forces[self.a] -= self.dir * np.dot(forces[self.a], self.dir) def todict(self): return {'name': 'FixedPlane', 'kwargs': {'a': self.a, 'direction': self.dir}} def __repr__(self): return 'FixedPlane(%d, %s)' % (self.a, self.dir.tolist()) class FixedLine(FixConstraintSingle): """Constrain an atom index *a* to move on a given line only. The line is defined by its vector *direction*.""" removed_dof = 2 def __init__(self, a, direction): self.a = a self.dir = np.asarray(direction) / sqrt(np.dot(direction, direction)) def adjust_positions(self, atoms, newpositions): step = newpositions[self.a] - atoms.positions[self.a] x = np.dot(step, self.dir) newpositions[self.a] = atoms.positions[self.a] + x * self.dir def adjust_forces(self, atoms, forces): forces[self.a] = self.dir * np.dot(forces[self.a], self.dir) def __repr__(self): return 'FixedLine(%d, %s)' % (self.a, self.dir.tolist()) def todict(self): return {'name': 'FixedLine', 'kwargs': {'a': self.a, 'direction': self.dir}} class FixCartesian(FixConstraintSingle): 'Fix an atom index *a* in the directions of the cartesian coordinates.' def __init__(self, a, mask=(1, 1, 1)): self.a = a self.mask = ~np.asarray(mask, bool) self.removed_dof = 3 - self.mask.sum() def adjust_positions(self, atoms, new): step = new[self.a] - atoms.positions[self.a] step *= self.mask new[self.a] = atoms.positions[self.a] + step def adjust_forces(self, atoms, forces): forces[self.a] *= self.mask def __repr__(self): return 'FixCartesian(a={0}, mask={1})'.format(self.a, list(~self.mask)) def todict(self): return {'name': 'FixCartesian', 'kwargs': {'a': self.a, 'mask': ~self.mask}} class FixScaled(FixConstraintSingle): 'Fix an atom index *a* in the directions of the unit vectors.' def __init__(self, cell, a, mask=(1, 1, 1)): self.cell = np.asarray(cell) self.a = a self.mask = np.array(mask, bool) self.removed_dof = self.mask.sum() def adjust_positions(self, atoms, new): scaled_old = np.linalg.solve(self.cell.T, atoms.positions.T).T scaled_new = np.linalg.solve(self.cell.T, new.T).T for n in range(3): if self.mask[n]: scaled_new[self.a, n] = scaled_old[self.a, n] new[self.a] = np.dot(scaled_new, self.cell)[self.a] def adjust_forces(self, atoms, forces): scaled_forces = np.linalg.solve(self.cell.T, forces.T).T scaled_forces[self.a] *= -(self.mask - 1) forces[self.a] = np.dot(scaled_forces, self.cell)[self.a] def todict(self): return {'name': 'FixScaled', 'kwargs': {'a': self.a, 'cell': self.cell, 'mask': self.mask}} def __repr__(self): return 'FixScaled(%s, %d, %s)' % (repr(self.cell), self.a, repr(self.mask)) # TODO: Better interface might be to use dictionaries in place of very # nested lists/tuples class FixInternals(FixConstraint): """Constraint object for fixing multiple internal coordinates. Allows fixing bonds, angles, and dihedrals.""" def __init__(self, bonds=None, angles=None, dihedrals=None, epsilon=1.e-7): self.bonds = bonds or [] self.angles = angles or [] self.dihedrals = dihedrals or [] # Initialize these at run-time: self.n = 0 self.constraints = [] self.epsilon = epsilon self.initialized = False self.removed_dof = (len(self.bonds) + len(self.angles) + len(self.dihedrals)) def initialize(self, atoms): if self.initialized: return masses = atoms.get_masses() self.n = len(self.bonds) + len(self.angles) + len(self.dihedrals) self.constraints = [] for bond in self.bonds: masses_bond = masses.take(bond[1]) self.constraints.append(self.FixBondLengthAlt(bond[0], bond[1], masses_bond)) for angle in self.angles: masses_angle = masses.take(angle[1]) self.constraints.append(self.FixAngle(angle[0], angle[1], masses_angle)) for dihedral in self.dihedrals: masses_dihedral = masses.take(dihedral[1]) self.constraints.append(self.FixDihedral(dihedral[0], dihedral[1], masses_dihedral)) self.initialized = True def get_indices(self): cons = self.bonds + self.dihedrals + self.angles return np.unique(np.ravel([constraint[1] for constraint in cons])) def todict(self): return {'name': 'FixInternals', 'kwargs': {'bonds': self.bonds, 'angles': self.angles, 'dihedrals': self.dihedrals, 'epsilon': self.epsilon}} def adjust_positions(self, atoms, new): self.initialize(atoms) for constraint in self.constraints: constraint.set_h_vectors(atoms.positions) for j in range(50): maxerr = 0.0 for constraint in self.constraints: constraint.adjust_positions(atoms.positions, new) maxerr = max(abs(constraint.sigma), maxerr) if maxerr < self.epsilon: return raise ValueError('Shake did not converge.') def adjust_forces(self, atoms, forces): """Project out translations and rotations and all other constraints""" self.initialize(atoms) positions = atoms.positions N = len(forces) list2_constraints = list(np.zeros((6, N, 3))) tx, ty, tz, rx, ry, rz = list2_constraints list_constraints = [r.ravel() for r in list2_constraints] tx[:, 0] = 1.0 ty[:, 1] = 1.0 tz[:, 2] = 1.0 ff = forces.ravel() # Calculate the center of mass center = positions.sum(axis=0) / N rx[:, 1] = -(positions[:, 2] - center[2]) rx[:, 2] = positions[:, 1] - center[1] ry[:, 0] = positions[:, 2] - center[2] ry[:, 2] = -(positions[:, 0] - center[0]) rz[:, 0] = -(positions[:, 1] - center[1]) rz[:, 1] = positions[:, 0] - center[0] # Normalizing transl., rotat. constraints for r in list2_constraints: r /= np.linalg.norm(r.ravel()) # Add all angle, etc. constraint vectors for constraint in self.constraints: constraint.adjust_forces(positions, forces) list_constraints.insert(0, constraint.h) # QR DECOMPOSITION - GRAM SCHMIDT list_constraints = [r.ravel() for r in list_constraints] aa = np.column_stack(list_constraints) (aa, bb) = np.linalg.qr(aa) # Projection hh = [] for i, constraint in enumerate(self.constraints): hh.append(aa[:, i] * np.row_stack(aa[:, i])) txx = aa[:, self.n] * np.row_stack(aa[:, self.n]) tyy = aa[:, self.n + 1] * np.row_stack(aa[:, self.n + 1]) tzz = aa[:, self.n + 2] * np.row_stack(aa[:, self.n + 2]) rxx = aa[:, self.n + 3] * np.row_stack(aa[:, self.n + 3]) ryy = aa[:, self.n + 4] * np.row_stack(aa[:, self.n + 4]) rzz = aa[:, self.n + 5] * np.row_stack(aa[:, self.n + 5]) T = txx + tyy + tzz + rxx + ryy + rzz for vec in hh: T += vec ff = np.dot(T, np.row_stack(ff)) forces[:, :] -= np.dot(T, np.row_stack(ff)).reshape(-1, 3) def __repr__(self): constraints = repr(self.constraints) return 'FixInternals(_copy_init=%s, epsilon=%s)' % (constraints, repr(self.epsilon)) def __str__(self): return '\n'.join([repr(c) for c in self.constraints]) # Classes for internal use in FixInternals class FixBondLengthAlt: """Constraint subobject for fixing bond length within FixInternals.""" def __init__(self, bond, indices, masses, maxstep=0.01): """Fix distance between atoms with indices a1, a2.""" self.indices = indices self.bond = bond self.h1 = None self.h2 = None self.masses = masses self.h = [] self.sigma = 1. def set_h_vectors(self, pos): dist1 = pos[self.indices[0]] - pos[self.indices[1]] self.h1 = 2 * dist1 self.h2 = -self.h1 def adjust_positions(self, old, new): h1 = self.h1 / self.masses[0] h2 = self.h2 / self.masses[1] dist1 = new[self.indices[0]] - new[self.indices[1]] dist = np.dot(dist1, dist1) self.sigma = dist - self.bond**2 lamda = -self.sigma / (2 * np.dot(dist1, (h1 - h2))) new[self.indices[0]] += lamda * h1 new[self.indices[1]] += lamda * h2 def adjust_forces(self, positions, forces): self.h1 = 2 * (positions[self.indices[0]] - positions[self.indices[1]]) self.h2 = -self.h1 self.h = np.zeros([len(forces) * 3]) self.h[(self.indices[0]) * 3] = self.h1[0] self.h[(self.indices[0]) * 3 + 1] = self.h1[1] self.h[(self.indices[0]) * 3 + 2] = self.h1[2] self.h[(self.indices[1]) * 3] = self.h2[0] self.h[(self.indices[1]) * 3 + 1] = self.h2[1] self.h[(self.indices[1]) * 3 + 2] = self.h2[2] self.h /= np.linalg.norm(self.h) def __repr__(self): return 'FixBondLengthAlt(%s, %d, %d)' % \ (repr(self.bond), self.indices[0], self.indices[1]) class FixAngle: """Constraint object for fixing an angle within FixInternals.""" def __init__(self, angle, indices, masses): """Fix atom movement to construct a constant angle.""" self.indices = indices self.a1m, self.a2m, self.a3m = masses self.angle = np.cos(angle) self.h1 = self.h2 = self.h3 = None self.h = [] self.sigma = 1. def set_h_vectors(self, pos): r21 = pos[self.indices[0]] - pos[self.indices[1]] r21_len = np.linalg.norm(r21) e21 = r21 / r21_len r23 = pos[self.indices[2]] - pos[self.indices[1]] r23_len = np.linalg.norm(r23) e23 = r23 / r23_len angle = np.dot(e21, e23) self.h1 = -2 * angle * ((angle * e21 - e23) / (r21_len)) self.h3 = -2 * angle * ((angle * e23 - e21) / (r23_len)) self.h2 = -(self.h1 + self.h3) def adjust_positions(self, oldpositions, newpositions): r21 = newpositions[self.indices[0]] - newpositions[self.indices[1]] r21_len = np.linalg.norm(r21) e21 = r21 / r21_len r23 = newpositions[self.indices[2]] - newpositions[self.indices[1]] r23_len = np.linalg.norm(r23) e23 = r23 / r23_len angle = np.dot(e21, e23) self.sigma = (angle - self.angle) * (angle + self.angle) h1 = self.h1 / self.a1m h3 = self.h3 / self.a3m h2 = self.h2 / self.a2m h21 = h1 - h2 h23 = h3 - h2 # Calculating new positions deriv = (((np.dot(r21, h23) + np.dot(r23, h21)) / (r21_len * r23_len)) - (np.dot(r21, h21) / (r21_len * r21_len) + np.dot(r23, h23) / (r23_len * r23_len)) * angle) deriv *= 2 * angle lamda = -self.sigma / deriv newpositions[self.indices[0]] += lamda * h1 newpositions[self.indices[1]] += lamda * h2 newpositions[self.indices[2]] += lamda * h3 def adjust_forces(self, positions, forces): r21 = positions[self.indices[0]] - positions[self.indices[1]] r21_len = np.linalg.norm(r21) e21 = r21 / r21_len r23 = positions[self.indices[2]] - positions[self.indices[1]] r23_len = np.linalg.norm(r23) e23 = r23 / r23_len angle = np.dot(e21, e23) self.h1 = -2 * angle * (angle * e21 - e23) / r21_len self.h3 = -2 * angle * (angle * e23 - e21) / r23_len self.h2 = -(self.h1 + self.h3) self.h = np.zeros([len(positions) * 3]) self.h[(self.indices[0]) * 3] = self.h1[0] self.h[(self.indices[0]) * 3 + 1] = self.h1[1] self.h[(self.indices[0]) * 3 + 2] = self.h1[2] self.h[(self.indices[1]) * 3] = self.h2[0] self.h[(self.indices[1]) * 3 + 1] = self.h2[1] self.h[(self.indices[1]) * 3 + 2] = self.h2[2] self.h[(self.indices[2]) * 3] = self.h3[0] self.h[(self.indices[2]) * 3 + 1] = self.h3[1] self.h[(self.indices[2]) * 3 + 2] = self.h3[2] self.h /= np.linalg.norm(self.h) def __repr__(self): return 'FixAngle(%s, %f)' % (tuple(self.indices), np.arccos(self.angle)) class FixDihedral: """Constraint object for fixing an dihedral using the shake algorithm. This one allows also other constraints.""" def __init__(self, angle, indices, masses): """Fix atom movement to construct a constant dihedral angle.""" self.indices = indices self.a1m, self.a2m, self.a3m, self.a4m = masses self.angle = np.cos(angle) self.h1 = self.h2 = self.h3 = self.h4 = None self.h = [] self.sigma = 1. def set_h_vectors(self, pos): r12 = pos[self.indices[1]] - pos[self.indices[0]] r23 = pos[self.indices[2]] - pos[self.indices[1]] r23_len = np.linalg.norm(r23) e23 = r23 / r23_len r34 = pos[self.indices[3]] - pos[self.indices[2]] a = -r12 - np.dot(-r12, e23) * e23 a_len = np.linalg.norm(a) ea = a / a_len b = r34 - np.dot(r34, e23) * e23 b_len = np.linalg.norm(b) eb = b / b_len angle = np.dot(ea, eb).clip(-1.0, 1.0) self.h1 = (eb - angle * ea) / a_len self.h4 = (ea - angle * eb) / b_len self.h2 = self.h1 * (np.dot(-r12, e23) / r23_len - 1) self.h2 += np.dot(r34, e23) / r23_len * self.h4 self.h3 = -self.h4 * (np.dot(r34, e23) / r23_len + 1) self.h3 += np.dot(r12, e23) / r23_len * self.h1 def adjust_positions(self, oldpositions, newpositions): r12 = newpositions[self.indices[1]] - newpositions[self.indices[0]] r23 = newpositions[self.indices[2]] - newpositions[self.indices[1]] r34 = newpositions[self.indices[3]] - newpositions[self.indices[2]] n1 = np.cross(r12, r23) n1_len = np.linalg.norm(n1) n1e = n1 / n1_len n2 = np.cross(r23, r34) n2_len = np.linalg.norm(n2) n2e = n2 / n2_len angle = np.dot(n1e, n2e).clip(-1.0, 1.0) self.sigma = (angle - self.angle) * (angle + self.angle) h1 = self.h1 / self.a1m h2 = self.h2 / self.a2m h3 = self.h3 / self.a3m h4 = self.h4 / self.a4m h12 = h2 - h1 h23 = h3 - h2 h34 = h4 - h3 deriv = ((np.dot(n1, np.cross(r34, h23) + np.cross(h34, r23)) + np.dot(n2, np.cross(r23, h12) + np.cross(h23, r12))) / (n1_len * n2_len)) deriv -= (((np.dot(n1, np.cross(r23, h12) + np.cross(h23, r12)) / n1_len**2) + (np.dot(n2, np.cross(r34, h23) + np.cross(h34, r23)) / n2_len**2)) * angle) deriv *= -2 * angle lamda = -self.sigma / deriv newpositions[self.indices[0]] += lamda * h1 newpositions[self.indices[1]] += lamda * h2 newpositions[self.indices[2]] += lamda * h3 newpositions[self.indices[3]] += lamda * h4 def adjust_forces(self, positions, forces): r12 = positions[self.indices[1]] - positions[self.indices[0]] r23 = positions[self.indices[2]] - positions[self.indices[1]] r23_len = np.linalg.norm(r23) e23 = r23 / r23_len r34 = positions[self.indices[3]] - positions[self.indices[2]] a = -r12 - np.dot(-r12, e23) * e23 a_len = np.linalg.norm(a) ea = a / a_len b = r34 - np.dot(r34, e23) * e23 b_len = np.linalg.norm(b) eb = b / b_len angle = np.dot(ea, eb).clip(-1.0, 1.0) self.h1 = (eb - angle * ea) / a_len self.h4 = (ea - angle * eb) / b_len self.h2 = self.h1 * (np.dot(-r12, e23) / r23_len - 1) self.h2 += np.dot(r34, e23) / r23_len * self.h4 self.h3 = -self.h4 * (np.dot(r34, e23) / r23_len + 1) self.h3 -= np.dot(-r12, e23) / r23_len * self.h1 self.h = np.zeros([len(positions) * 3]) self.h[(self.indices[0]) * 3] = self.h1[0] self.h[(self.indices[0]) * 3 + 1] = self.h1[1] self.h[(self.indices[0]) * 3 + 2] = self.h1[2] self.h[(self.indices[1]) * 3] = self.h2[0] self.h[(self.indices[1]) * 3 + 1] = self.h2[1] self.h[(self.indices[1]) * 3 + 2] = self.h2[2] self.h[(self.indices[2]) * 3] = self.h3[0] self.h[(self.indices[2]) * 3 + 1] = self.h3[1] self.h[(self.indices[2]) * 3 + 2] = self.h3[2] self.h[(self.indices[3]) * 3] = self.h4[0] self.h[(self.indices[3]) * 3 + 1] = self.h4[1] self.h[(self.indices[3]) * 3 + 2] = self.h4[2] self.h /= np.linalg.norm(self.h) def __repr__(self): return 'FixDihedral(%s, %f)' % (tuple(self.indices), self.angle) class Hookean(FixConstraint): """Applies a Hookean restorative force between a pair of atoms, an atom and a point, or an atom and a plane.""" def __init__(self, a1, a2, k, rt=None): """Forces two atoms to stay close together by applying no force if they are below a threshold length, rt, and applying a Hookean restorative force when the distance between them exceeds rt. Can also be used to tether an atom to a fixed point in space or to a distance above a plane. a1 : int Index of atom 1 a2 : one of three options 1) index of atom 2 2) a fixed point in cartesian space to which to tether a1 3) a plane given as (A, B, C, D) in A x + B y + C z + D = 0. k : float Hooke's law (spring) constant to apply when distance exceeds threshold_length. Units of eV A^-2. rt : float The threshold length below which there is no force. The length is 1) between two atoms, 2) between atom and point. This argument is not supplied in case 3. Units of A. If a plane is specified, the Hooke's law force is applied if the atom is on the normal side of the plane. For instance, the plane with (A, B, C, D) = (0, 0, 1, -7) defines a plane in the xy plane with a z intercept of +7 and a normal vector pointing in the +z direction. If the atom has z > 7, then a downward force would be applied of k * (atom.z - 7). The same plane with the normal vector pointing in the -z direction would be given by (A, B, C, D) = (0, 0, -1, 7). """ if isinstance(a2, int): self._type = 'two atoms' self.indices = [a1, a2] elif len(a2) == 3: self._type = 'point' self.index = a1 self.origin = np.array(a2) elif len(a2) == 4: self._type = 'plane' self.index = a1 self.plane = a2 else: raise RuntimeError('Unknown type for a2') self.threshold = rt self.spring = k def todict(self): dct = {'name': 'Hookean'} dct['kwargs'] = {'rt': self.threshold, 'k': self.spring} if self._type == 'two atoms': dct['kwargs']['a1'] = self.indices[0] dct['kwargs']['a2'] = self.indices[1] elif self._type == 'point': dct['kwargs']['a1'] = self.index dct['kwargs']['a2'] = self.origin elif self._type == 'plane': dct['kwargs']['a1'] = self.index dct['kwargs']['a2'] = self.plane else: raise NotImplementedError('Bad type: %s' % self._type) return dct def adjust_positions(self, atoms, newpositions): pass def adjust_momenta(self, atoms, momenta): pass def adjust_forces(self, atoms, forces): positions = atoms.positions if self._type == 'plane': A, B, C, D = self.plane x, y, z = positions[self.index] d = ((A * x + B * y + C * z + D) / np.sqrt(A**2 + B**2 + C**2)) if d < 0: return magnitude = self.spring * d direction = - np.array((A, B, C)) / np.linalg.norm((A, B, C)) forces[self.index] += direction * magnitude return if self._type == 'two atoms': p1, p2 = positions[self.indices] elif self._type == 'point': p1 = positions[self.index] p2 = self.origin displace = p2 - p1 bondlength = np.linalg.norm(displace) if bondlength > self.threshold: magnitude = self.spring * (bondlength - self.threshold) direction = displace / np.linalg.norm(displace) if self._type == 'two atoms': forces[self.indices[0]] += direction * magnitude forces[self.indices[1]] -= direction * magnitude else: forces[self.index] += direction * magnitude def adjust_potential_energy(self, atoms): """Returns the difference to the potential energy due to an active constraint. (That is, the quantity returned is to be added to the potential energy.)""" positions = atoms.positions if self._type == 'plane': A, B, C, D = self.plane x, y, z = positions[self.index] d = ((A * x + B * y + C * z + D) / np.sqrt(A**2 + B**2 + C**2)) if d > 0: return 0.5 * self.spring * d**2 else: return 0. if self._type == 'two atoms': p1, p2 = positions[self.indices] elif self._type == 'point': p1 = positions[self.index] p2 = self.origin displace = p2 - p1 bondlength = np.linalg.norm(displace) if bondlength > self.threshold: return 0.5 * self.spring * (bondlength - self.threshold)**2 else: return 0. def get_indices(self): if self._type == 'two atoms': return self.indices elif self._type == 'point': return self.index elif self._type == 'plane': return self.index def index_shuffle(self, atoms, ind): # See docstring of superclass if self._type == 'two atoms': self.indices = [ind.index(self.indices[0]), ind.index(self.indices[1])] elif self._type == 'point': self.index = ind.index(self.index) elif self._type == 'plane': self.index = ind.index(self.index) def __repr__(self): if self._type == 'two atoms': return 'Hookean(%d, %d)' % tuple(self.indices) elif self._type == 'point': return 'Hookean(%d) to cartesian' % self.index else: return 'Hookean(%d) to plane' % self.index class ExternalForce(FixConstraint): """Constraint object for pulling two atoms apart by an external force. You can combine this constraint for example with FixBondLength but make sure that the ExternalForce-constraint comes first in the list: >>> con1 = ExternalForce(atom1, atom2, f_ext) >>> con2 = FixBondLength(atom3, atom4) >>> atoms.set_constraint([con1, con2]) see ase/test/external_force.py""" def __init__(self, a1, a2, f_ext): self.indices = [a1, a2] self.external_force = f_ext def adjust_positions(self, atoms, new): pass def adjust_forces(self, atoms, forces): dist = np.subtract.reduce(atoms.positions[self.indices]) force = self.external_force * dist / np.linalg.norm(dist) forces[self.indices] += (force, -force) def adjust_potential_energy(self, atoms): dist = np.subtract.reduce(atoms.positions[self.indices]) return -np.linalg.norm(dist) * self.external_force def index_shuffle(self, atoms, ind): """Shuffle the indices of the two atoms in this constraint""" newa = [-1, -1] # Signal error for new, old in slice2enlist(ind, len(atoms)): for i, a in enumerate(self.indices): if old == a: newa[i] = new if newa[0] == -1 or newa[1] == -1: raise IndexError('Constraint not part of slice') self.indices = newa def __repr__(self): return 'ExternalForce(%d, %d, %f)' % (self.indices[0], self.indices[1], self.external_force) def todict(self): return {'name': 'ExternalForce', 'kwargs': {'a1': self.indices[0], 'a2': self.indices[1], 'f_ext': self.external_force}} class Filter: """Subset filter class.""" def __init__(self, atoms, indices=None, mask=None): """Filter atoms. This filter can be used to hide degrees of freedom in an Atoms object. Parameters ---------- indices : list of int Indices for those atoms that should remain visible. mask : list of bool One boolean per atom indicating if the atom should remain visible or not. If a Trajectory tries to save this object, it will instead save the underlying Atoms object. To prevent this, delete the atoms_for_saving attribute. """ self.atoms = atoms self.constraints = [] # Make self.info a reference to the underlying atoms' info dictionary. self.info = self.atoms.info if indices is None and mask is None: raise ValueError('Use "indices" or "mask".') if indices is not None and mask is not None: raise ValueError('Use only one of "indices" and "mask".') if mask is not None: self.index = np.asarray(mask, bool) self.n = self.index.sum() else: self.index = np.asarray(indices, int) self.n = len(self.index) # Present the real atoms object to Trajectory and friends self.atoms_for_saving = self.atoms def get_cell(self): """Returns the computational cell. The computational cell is the same as for the original system. """ return self.atoms.get_cell() def get_pbc(self): """Returns the periodic boundary conditions. The boundary conditions are the same as for the original system. """ return self.atoms.get_pbc() def get_positions(self): 'Return the positions of the visible atoms.' return self.atoms.get_positions()[self.index] def set_positions(self, positions): 'Set the positions of the visible atoms.' pos = self.atoms.get_positions() pos[self.index] = positions self.atoms.set_positions(pos) positions = property(get_positions, set_positions, doc='Positions of the atoms') def get_momenta(self): 'Return the momenta of the visible atoms.' return self.atoms.get_momenta()[self.index] def set_momenta(self, momenta, **kwargs): 'Set the momenta of the visible atoms.' mom = self.atoms.get_momenta() mom[self.index] = momenta self.atoms.set_momenta(mom, **kwargs) def get_atomic_numbers(self): 'Return the atomic numbers of the visible atoms.' return self.atoms.get_atomic_numbers()[self.index] def set_atomic_numbers(self, atomic_numbers): 'Set the atomic numbers of the visible atoms.' z = self.atoms.get_atomic_numbers() z[self.index] = atomic_numbers self.atoms.set_atomic_numbers(z) def get_tags(self): 'Return the tags of the visible atoms.' return self.atoms.get_tags()[self.index] def set_tags(self, tags): 'Set the tags of the visible atoms.' tg = self.atoms.get_tags() tg[self.index] = tags self.atoms.set_tags(tg) def get_forces(self, *args, **kwargs): return self.atoms.get_forces(*args, **kwargs)[self.index] def get_stress(self): return self.atoms.get_stress() def get_stresses(self): return self.atoms.get_stresses()[self.index] def get_masses(self): return self.atoms.get_masses()[self.index] def get_potential_energy(self, **kwargs): """Calculate potential energy. Returns the potential energy of the full system. """ return self.atoms.get_potential_energy(**kwargs) def get_chemical_symbols(self): return self.atoms.get_chemical_symbols() def get_initial_magnetic_moments(self): return self.atoms.get_initial_magnetic_moments() def get_calculator(self): """Returns the calculator. WARNING: The calculator is unaware of this filter, and sees a different number of atoms. """ return self.atoms.get_calculator() def get_celldisp(self): return self.atoms.get_celldisp() def has(self, name): 'Check for existence of array.' return self.atoms.has(name) def __len__(self): 'Return the number of movable atoms.' return self.n def __getitem__(self, i): 'Return an atom.' return self.atoms[self.index[i]] class StrainFilter(Filter): """Modify the supercell while keeping the scaled positions fixed. Presents the strain of the supercell as the generalized positions, and the global stress tensor (times the volume) as the generalized force. This filter can be used to relax the unit cell until the stress is zero. If MDMin is used for this, the timestep (dt) to be used depends on the system size. 0.01/x where x is a typical dimension seems like a good choice. The stress and strain are presented as 6-vectors, the order of the components follow the standard engingeering practice: xx, yy, zz, yz, xz, xy. """ def __init__(self, atoms, mask=None): """Create a filter applying a homogeneous strain to a list of atoms. The first argument, atoms, is the atoms object. The optional second argument, mask, is a list of six booleans, indicating which of the six independent components of the strain that are allowed to become non-zero. It defaults to [1,1,1,1,1,1]. """ self.atoms = atoms self.strain = np.zeros(6) if mask is None: self.mask = np.ones(6) else: self.mask = np.array(mask) self.index = np.arange(len(atoms)) self.n = self.index.sum() self.origcell = atoms.get_cell() def get_positions(self): return self.strain.reshape((2, 3)).copy() def set_positions(self, new): new = new.ravel() * self.mask eps = np.array([[1.0 + new[0], 0.5 * new[5], 0.5 * new[4]], [0.5 * new[5], 1.0 + new[1], 0.5 * new[3]], [0.5 * new[4], 0.5 * new[3], 1.0 + new[2]]]) self.atoms.set_cell(np.dot(self.origcell, eps), scale_atoms=True) self.strain[:] = new def get_forces(self): stress = self.atoms.get_stress() return -self.atoms.get_volume() * (stress * self.mask).reshape((2, 3)) def get_potential_energy(self): return self.atoms.get_potential_energy() def has(self, x): return self.atoms.has(x) def __len__(self): return 2 # The indices of the full stiffness matrix of (orthorhombic) interest voigt_notation = [(0, 0), (1, 1), (2, 2), (1, 2), (0, 2), (0, 1)] def full_3x3_to_voigt_6_index(i, j): if i == j: return i return 6 - i - j def voigt_6_to_full_3x3_strain(strain_vector): """ Form a 3x3 strain matrix from a 6 component vector in Voigt notation """ e1, e2, e3, e4, e5, e6 = np.transpose(strain_vector) return np.transpose([[1.0 + e1, 0.5 * e6, 0.5 * e5], [0.5 * e6, 1.0 + e2, 0.5 * e4], [0.5 * e5, 0.5 * e4, 1.0 + e3]]) def voigt_6_to_full_3x3_stress(stress_vector): """ Form a 3x3 stress matrix from a 6 component vector in Voigt notation """ s1, s2, s3, s4, s5, s6 = np.transpose(stress_vector) return np.transpose([[s1, s6, s5], [s6, s2, s4], [s5, s4, s3]]) def full_3x3_to_voigt_6_strain(strain_matrix): """ Form a 6 component strain vector in Voigt notation from a 3x3 matrix """ strain_matrix = np.asarray(strain_matrix) return np.transpose([strain_matrix[..., 0, 0] - 1.0, strain_matrix[..., 1, 1] - 1.0, strain_matrix[..., 2, 2] - 1.0, strain_matrix[..., 1, 2] + strain_matrix[..., 2, 1], strain_matrix[..., 0, 2] + strain_matrix[..., 2, 0], strain_matrix[..., 0, 1] + strain_matrix[..., 1, 0]]) def full_3x3_to_voigt_6_stress(stress_matrix): """ Form a 6 component stress vector in Voigt notation from a 3x3 matrix """ stress_matrix = np.asarray(stress_matrix) return np.transpose([stress_matrix[..., 0, 0], stress_matrix[..., 1, 1], stress_matrix[..., 2, 2], (stress_matrix[..., 1, 2] + stress_matrix[..., 1, 2]) / 2, (stress_matrix[..., 0, 2] + stress_matrix[..., 0, 2]) / 2, (stress_matrix[..., 0, 1] + stress_matrix[..., 0, 1]) / 2]) class UnitCellFilter(Filter): """Modify the supercell and the atom positions. """ def __init__(self, atoms, mask=None, cell_factor=None, hydrostatic_strain=False, constant_volume=False): """Create a filter that returns the atomic forces and unit cell stresses together, so they can simultaneously be minimized. The first argument, atoms, is the atoms object. The optional second argument, mask, is a list of booleans, indicating which of the six independent components of the strain are relaxed. - True = relax to zero - False = fixed, ignore this component Degrees of freedom are the positions in the original undeformed cell, plus the deformation tensor (extra 3 "atoms"). This gives forces consistent with numerical derivatives of the potential energy with respect to the cell degreees of freedom. For full details see: E. B. Tadmor, G. S. Smith, N. Bernstein, and E. Kaxiras, Phys. Rev. B 59, 235 (1999) You can still use constraints on the atoms, e.g. FixAtoms, to control the relaxation of the atoms. >>> # this should be equivalent to the StrainFilter >>> atoms = Atoms(...) >>> atoms.set_constraint(FixAtoms(mask=[True for atom in atoms])) >>> ucf = UnitCellFilter(atoms) You should not attach this UnitCellFilter object to a trajectory. Instead, create a trajectory for the atoms, and attach it to an optimizer like this: >>> atoms = Atoms(...) >>> ucf = UnitCellFilter(atoms) >>> qn = QuasiNewton(ucf) >>> traj = Trajectory('TiO2.traj', 'w', atoms) >>> qn.attach(traj) >>> qn.run(fmax=0.05) Helpful conversion table: - 0.05 eV/A^3 = 8 GPA - 0.003 eV/A^3 = 0.48 GPa - 0.0006 eV/A^3 = 0.096 GPa - 0.0003 eV/A^3 = 0.048 GPa - 0.0001 eV/A^3 = 0.02 GPa Additional optional arguments: cell_factor: float (default float(len(atoms))) Factor by which deformation gradient is multiplied to put it on the same scale as the positions when assembling the combined position/cell vector. The stress contribution to the forces is scaled down by the same factor. This can be thought of as a very simple preconditioners. Default is number of atoms which gives approximately the correct scaling. hydrostatic_strain: bool (default False) Constrain the cell by only allowing hydrostatic deformation. The virial tensor is replaced by np.diag([np.trace(virial)]*3). constant_volume: bool (default False) Project out the diagonal elements of the virial tensor to allow relaxations at constant volume, e.g. for mapping out an energy-volume curve. Note: this only approximately conserves the volume and breaks energy/force consistency so can only be used with optimizers that do require do a line minimisation (e.g. FIRE). """ Filter.__init__(self, atoms, indices=range(len(atoms))) self.atoms = atoms self.deform_grad = np.eye(3) self.atom_positions = atoms.get_positions() self.orig_cell = atoms.get_cell() self.stress = None if mask is None: mask = np.ones(6) mask = np.asarray(mask) if mask.shape == (6,): self.mask = voigt_6_to_full_3x3_stress(mask) elif mask.shape == (3, 3): self.mask = mask else: raise ValueError('shape of mask should be (3,3) or (6,)') if cell_factor is None: cell_factor = float(len(atoms)) self.hydrostatic_strain = hydrostatic_strain self.constant_volume = constant_volume self.cell_factor = cell_factor self.copy = self.atoms.copy self.arrays = self.atoms.arrays def get_positions(self): ''' this returns an array with shape (natoms + 3,3). the first natoms rows are the positions of the atoms, the last three rows are the deformation tensor associated with the unit cell, scaled by self.cell_factor. ''' natoms = len(self.atoms) pos = np.zeros((natoms + 3, 3)) pos[:natoms] = self.atom_positions pos[natoms:] = self.cell_factor * self.deform_grad return pos def set_positions(self, new): ''' new is an array with shape (natoms+3,3). the first natoms rows are the positions of the atoms, the last three rows are the deformation tensor used to change the cell shape. the positions are first set with respect to the original undeformed cell, and then the cell is transformed by the current deformation gradient. ''' natoms = len(self.atoms) self.atom_positions[:] = new[:natoms] self.deform_grad = new[natoms:] / self.cell_factor self.atoms.set_positions(self.atom_positions) self.atoms.set_cell(self.orig_cell, scale_atoms=False) self.atoms.set_cell(np.dot(self.orig_cell, self.deform_grad.T), scale_atoms=True) def get_forces(self, apply_constraint=False): ''' returns an array with shape (natoms+2,3) of the atomic forces and unit cell stresses. the first natoms rows are the forces on the atoms, the last three rows are the forces on the unit cell, which are computed from the stress tensor. ''' atoms_forces = self.atoms.get_forces() stress = self.atoms.get_stress() self.stress = voigt_6_to_full_3x3_stress(stress) * self.mask volume = self.atoms.get_volume() virial = -volume * voigt_6_to_full_3x3_stress(stress) atoms_forces = np.dot(atoms_forces, self.deform_grad) dg_inv = np.linalg.inv(self.deform_grad) virial = np.dot(virial, dg_inv.T) if self.hydrostatic_strain: vtr = virial.trace() virial = np.diag([vtr / 3.0, vtr / 3.0, vtr / 3.0]) # Zero out components corresponding to fixed lattice elements if (self.mask != 1.0).any(): virial *= self.mask if self.constant_volume: vtr = virial.trace() np.fill_diagonal(virial, np.diag(virial) - vtr / 3.0) natoms = len(self.atoms) forces = np.zeros((natoms + 3, 3)) forces[:natoms] = atoms_forces forces[natoms:] = virial / self.cell_factor return forces def get_potential_energy(self): return self.atoms.get_potential_energy() def get_stress(self): raise NotImplementedError def has(self, x): return self.atoms.has(x) def __len__(self): return (len(self.atoms) + 3)