from __future__ import print_function
import numpy as np
from ase.calculators.calculator import Calculator
from ase.data import atomic_numbers
from ase.utils import convert_string_to_fd
[docs]class SimpleQMMM(Calculator):
"""Simple QMMM calculator."""
implemented_properties = ['energy', 'forces']
def __init__(self, selection, qmcalc, mmcalc1, mmcalc2, vacuum=None):
"""SimpleQMMM object.
The energy is calculated as::
_ _ _
E = E (R ) - E (R ) + E (R )
QM QM MM QM MM all
parameters:
selection: list of int, slice object or list of bool
Selection out of all the atoms that belong to the QM part.
qmcalc: Calculator object
QM-calculator.
mmcalc1: Calculator object
MM-calculator used for QM region.
mmcalc2: Calculator object
MM-calculator used for everything.
vacuum: float or None
Amount of vacuum to add around QM atoms. Use None if QM
calculator doesn't need a box.
"""
self.selection = selection
self.qmcalc = qmcalc
self.mmcalc1 = mmcalc1
self.mmcalc2 = mmcalc2
self.vacuum = vacuum
self.qmatoms = None
self.center = None
self.name = '{0}-{1}+{1}'.format(qmcalc.name, mmcalc1.name)
Calculator.__init__(self)
def initialize_qm(self, atoms):
constraints = atoms.constraints
atoms.constraints = []
self.qmatoms = atoms[self.selection]
atoms.constraints = constraints
self.qmatoms.pbc = False
if self.vacuum:
self.qmatoms.center(vacuum=self.vacuum)
self.center = self.qmatoms.positions.mean(axis=0)
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
if self.qmatoms is None:
self.initialize_qm(atoms)
self.qmatoms.positions = atoms.positions[self.selection]
if self.vacuum:
self.qmatoms.positions += (self.center -
self.qmatoms.positions.mean(axis=0))
energy = self.qmcalc.get_potential_energy(self.qmatoms)
qmforces = self.qmcalc.get_forces(self.qmatoms)
energy += self.mmcalc2.get_potential_energy(atoms)
forces = self.mmcalc2.get_forces(atoms)
if self.vacuum:
qmforces -= qmforces.mean(axis=0)
forces[self.selection] += qmforces
energy -= self.mmcalc1.get_potential_energy(self.qmatoms)
forces[self.selection] -= self.mmcalc1.get_forces(self.qmatoms)
self.results['energy'] = energy
self.results['forces'] = forces
[docs]class EIQMMM(Calculator):
"""Explicit interaction QMMM calculator."""
implemented_properties = ['energy', 'forces']
def __init__(self, selection, qmcalc, mmcalc, interaction,
vacuum=None, embedding=None, output=None):
"""EIQMMM object.
The energy is calculated as::
_ _ _ _
E = E (R ) + E (R ) + E (R , R )
QM QM MM MM I QM MM
parameters:
selection: list of int, slice object or list of bool
Selection out of all the atoms that belong to the QM part.
qmcalc: Calculator object
QM-calculator.
mmcalc: Calculator object
MM-calculator.
interaction: Interaction object
Interaction between QM and MM regions.
vacuum: float or None
Amount of vacuum to add around QM atoms. Use None if QM
calculator doesn't need a box.
embedding: Embedding object or None
Specialized embedding object. Use None in order to use the
default one.
output: None, '-', str or file-descriptor.
File for logging information - default is no logging (None).
"""
self.selection = selection
self.qmcalc = qmcalc
self.mmcalc = mmcalc
self.interaction = interaction
self.vacuum = vacuum
self.embedding = embedding
self.qmatoms = None
self.mmatoms = None
self.mask = None
self.center = None # center of QM atoms in QM-box
self.name = '{0}+{1}+{2}'.format(qmcalc.name,
interaction.name,
mmcalc.name)
self.output = convert_string_to_fd(output)
Calculator.__init__(self)
def initialize(self, atoms):
self.mask = np.zeros(len(atoms), bool)
self.mask[self.selection] = True
constraints = atoms.constraints
atoms.constraints = [] # avoid slicing of constraints
self.qmatoms = atoms[self.mask]
self.mmatoms = atoms[~self.mask]
atoms.constraints = constraints
self.qmatoms.pbc = False
if self.vacuum:
self.qmatoms.center(vacuum=self.vacuum)
self.center = self.qmatoms.positions.mean(axis=0)
print('Size of QM-cell after centering:',
self.qmatoms.cell.diagonal(), file=self.output)
self.qmatoms.calc = self.qmcalc
self.mmatoms.calc = self.mmcalc
if self.embedding is None:
self.embedding = Embedding()
self.embedding.initialize(self.qmatoms, self.mmatoms)
print('Embedding:', self.embedding, file=self.output)
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
if self.qmatoms is None:
self.initialize(atoms)
self.mmatoms.set_positions(atoms.positions[~self.mask])
self.qmatoms.set_positions(atoms.positions[self.mask])
if self.vacuum:
shift = self.center - self.qmatoms.positions.mean(axis=0)
self.qmatoms.positions += shift
else:
shift = (0, 0, 0)
self.embedding.update(shift)
ienergy, iqmforces, immforces = self.interaction.calculate(
self.qmatoms, self.mmatoms, shift)
qmenergy = self.qmatoms.get_potential_energy()
mmenergy = self.mmatoms.get_potential_energy()
energy = ienergy + qmenergy + mmenergy
print('Energies: {0:12.3f} {1:+12.3f} {2:+12.3f} = {3:12.3f}'
.format(ienergy, qmenergy, mmenergy, energy), file=self.output)
qmforces = self.qmatoms.get_forces()
mmforces = self.mmatoms.get_forces()
mmforces += self.embedding.get_mm_forces()
forces = np.empty((len(atoms), 3))
forces[self.mask] = qmforces + iqmforces
forces[~self.mask] = mmforces + immforces
self.results['energy'] = energy
self.results['forces'] = forces
def wrap(D, cell, pbc):
"""Wrap distances to nearest neighbor (minimum image convention)."""
for i, periodic in enumerate(pbc):
if periodic:
d = D[:, i]
L = cell[i]
d[:] = (d + L / 2) % L - L / 2 # modify D inplace
[docs]class Embedding:
def __init__(self, molecule_size=3, **parameters):
"""Point-charge embedding."""
self.qmatoms = None
self.mmatoms = None
self.molecule_size = molecule_size
self.virtual_molecule_size = None
self.parameters = parameters
def __repr__(self):
return 'Embedding(molecule_size={0})'.format(self.molecule_size)
def initialize(self, qmatoms, mmatoms):
"""Hook up embedding object to QM and MM atoms objects."""
self.qmatoms = qmatoms
self.mmatoms = mmatoms
charges = mmatoms.calc.get_virtual_charges(mmatoms)
self.pcpot = qmatoms.calc.embed(charges, **self.parameters)
self.virtual_molecule_size = (self.molecule_size *
len(charges) // len(mmatoms))
def update(self, shift):
"""Update point-charge positions."""
# Wrap point-charge positions to the MM-cell closest to the
# center of the the QM box, but avoid ripping molecules apart:
qmcenter = self.qmatoms.cell.diagonal() / 2
n = self.molecule_size
positions = self.mmatoms.positions.reshape((-1, n, 3)) + shift
# Distances from the center of the QM box to the first atom of
# each molecule:
distances = positions[:, 0] - qmcenter
wrap(distances, self.mmatoms.cell.diagonal(), self.mmatoms.pbc)
offsets = distances - positions[:, 0]
positions += offsets[:, np.newaxis] + qmcenter
# Geometric center positions for each mm mol for LR cut
com = np.array([p.mean(axis=0) for p in positions])
# Need per atom for C-code:
com_pv = np.repeat(com, self.virtual_molecule_size, axis=0)
positions.shape = (-1, 3)
positions = self.mmatoms.calc.add_virtual_sites(positions)
# compatibility with gpaw versions w/o LR cut in PointChargePotential
if 'rc2' in self.parameters:
self.pcpot.set_positions(positions, com_pv=com_pv)
else:
self.pcpot.set_positions(positions)
def get_mm_forces(self):
"""Calculate the forces on the MM-atoms from the QM-part."""
f = self.pcpot.get_forces(self.qmatoms.calc)
return self.mmatoms.calc.redistribute_forces(f)
def combine_lj_lorenz_berthelot(sigmaqm, sigmamm,
epsilonqm, epsilonmm):
"""Combine LJ parameters according to the Lorenz-Berthelot rule"""
sigma_c = np.zeros((len(sigmaqm), len(sigmamm)))
epsilon_c = np.zeros_like(sigma_c)
for ii in range(len(sigmaqm)):
sigma_c[ii, :] = (sigmaqm[ii] + sigmamm) / 2
epsilon_c[ii, :] = (epsilonqm[ii] * epsilonmm)**0.5
return sigma_c, epsilon_c
class LJInteractionsGeneral:
name = 'LJ-general'
def __init__(self, sigmaqm, epsilonqm, sigmamm,
epsilonmm, molecule_size=3):
self.sigmaqm = sigmaqm
self.epsilonqm = epsilonqm
self.sigmamm = sigmamm
self.epsilonmm = epsilonmm
self.molecule_size = molecule_size
self.combine_lj()
def combine_lj(self):
self.sigma, self.epsilon = combine_lj_lorenz_berthelot(
self.sigmaqm, self.sigmamm, self.epsilonqm, self.epsilonmm)
def calculate(self, qmatoms, mmatoms, shift):
mmpositions = self.update(qmatoms, mmatoms, shift)
qmforces = np.zeros_like(qmatoms.positions)
mmforces = np.zeros_like(mmatoms.positions)
energy = 0.0
for qmi in range(len(qmatoms)):
if ~np.any(self.epsilon[qmi, :]):
continue
D = mmpositions - qmatoms.positions[qmi, :]
d2 = (D**2).sum(2)
c6 = (self.sigma[qmi, :]**2 / d2)**3
c12 = c6**2
e = 4 * self.epsilon[qmi, :] * (c12 - c6)
energy += e.sum()
f = (24 * self.epsilon[qmi, :] *
(2 * c12 - c6) / d2)[:, :, np.newaxis] * D
mmforces += f.reshape((-1, 3))
qmforces[qmi, :] -= f.sum(0).sum(0)
return energy, qmforces, mmforces
def update(self, qmatoms, mmatoms, shift):
"""Update point-charge positions."""
# Wrap point-charge positions to the MM-cell closest to the
# center of the the QM box, but avoid ripping molecules apart:
qmcenter = qmatoms.cell.diagonal() / 2
n = self.molecule_size
positions = mmatoms.positions.reshape((-1, n, 3)) + shift
# Distances from the center of the QM box to the first atom of
# each molecule:
distances = positions[:, 0] - qmcenter
wrap(distances, mmatoms.cell.diagonal(), mmatoms.pbc)
offsets = distances - positions[:, 0]
positions += offsets[:, np.newaxis] + qmcenter
return positions
[docs]class LJInteractions:
name = 'LJ'
def __init__(self, parameters):
"""Lennard-Jones type explicit interaction.
parameters: dict
Mapping from pair of atoms to tuple containing epsilon and sigma
for that pair.
Example:
lj = LJInteractions({('O', 'O'): (eps, sigma)})
"""
self.parameters = {}
for (symbol1, symbol2), (epsilon, sigma) in parameters.items():
Z1 = atomic_numbers[symbol1]
Z2 = atomic_numbers[symbol2]
self.parameters[(Z1, Z2)] = epsilon, sigma
self.parameters[(Z2, Z1)] = epsilon, sigma
def calculate(self, qmatoms, mmatoms, shift):
qmforces = np.zeros_like(qmatoms.positions)
mmforces = np.zeros_like(mmatoms.positions)
species = set(mmatoms.numbers)
energy = 0.0
for R1, Z1, F1 in zip(qmatoms.positions, qmatoms.numbers, qmforces):
for Z2 in species:
if (Z1, Z2) not in self.parameters:
continue
epsilon, sigma = self.parameters[(Z1, Z2)]
mask = (mmatoms.numbers == Z2)
D = mmatoms.positions[mask] + shift - R1
wrap(D, mmatoms.cell.diagonal(), mmatoms.pbc)
d2 = (D**2).sum(1)
c6 = (sigma**2 / d2)**3
c12 = c6**2
energy += 4 * epsilon * (c12 - c6).sum()
f = 24 * epsilon * ((2 * c12 - c6) / d2)[:, np.newaxis] * D
F1 -= f.sum(0)
mmforces[mask] += f
return energy, qmforces, mmforces
class RescaledCalculator(Calculator):
"""Rescales length and energy of a calculators to match given
lattice constant and bulk modulus
Useful for MM calculator used within a :class:`ForceQMMM` model.
See T. D. Swinburne and J. R. Kermode, Phys. Rev. B 96, 144102 (2017)
for a derivation of the scaling constants.
"""
implemented_properties = ['forces', 'energy', 'stress']
def __init__(self, mm_calc,
qm_lattice_constant, qm_bulk_modulus,
mm_lattice_constant, mm_bulk_modulus):
Calculator.__init__(self)
self.mm_calc = mm_calc
self.alpha = qm_lattice_constant / mm_lattice_constant
self.beta = mm_bulk_modulus / qm_bulk_modulus / (self.alpha**3)
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
# mm_pos = atoms.get_positions()
scaled_atoms = atoms.copy()
# scaled_atoms.positions = mm_pos/self.alpha
mm_cell = atoms.get_cell()
scaled_atoms.set_cell(mm_cell / self.alpha, scale_atoms=True)
forces = self.mm_calc.get_forces(scaled_atoms)
energy = self.mm_calc.get_potential_energy(scaled_atoms)
stress = self.mm_calc.get_stress(scaled_atoms)
self.results = {'energy': energy / self.beta,
'forces': forces / (self.beta * self.alpha),
'stress': stress / (self.beta * self.alpha**3)}
class ForceConstantCalculator(Calculator):
"""
Compute forces based on provided force-constant matrix
Useful with `ForceQMMM` to do harmonic QM/MM using force constants
of QM method.
"""
implemented_properties = ['forces', 'energy']
def __init__(self, D, ref, f0):
"""
Parameters:
D: matrix or sparse matrix, shape `(3*len(ref), 3*len(ref))`
Force constant matrix.
Sign convention is `D_ij = d^2E/(dx_i dx_j), so
`force = -D.dot(displacement)`
ref: ase.atoms.Atoms
Atoms object for reference configuration
f0: array, shape `(len(ref), 3)`
Value of forces at reference configuration
"""
assert D.shape[0] == D.shape[1]
assert D.shape[0] // 3 == len(ref)
self.D = D
self.ref = ref
self.f0 = f0
self.size = len(ref)
Calculator.__init__(self)
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
u = atoms.positions - self.ref.positions
f = -self.D.dot(u.reshape(3 * self.size))
forces = np.zeros((len(atoms), 3))
forces[:, :] = f.reshape(self.size, 3)
self.results['forces'] = forces + self.f0
self.results['energy'] = 0.0
[docs]class ForceQMMM(Calculator):
"""
Force-based QM/MM calculator
QM forces are computed using a buffer region and then mixed abruptly
with MM forces:
F^i_QMMM = { F^i_QM if i in QM region
{ F^i_MM otherwise
cf. N. Bernstein, J. R. Kermode, and G. Csanyi,
Rep. Prog. Phys. 72, 026501 (2009)
and T. D. Swinburne and J. R. Kermode, Phys. Rev. B 96, 144102 (2017).
"""
implemented_properties = ['forces', 'energy']
def __init__(self,
atoms,
qm_selection_mask,
qm_calc,
mm_calc,
buffer_width,
vacuum=5.,
zero_mean=True):
"""
ForceQMMM calculator
Parameters:
qm_selection_mask: list of ints, slice object or bool list/array
Selection out of atoms that belong to the QM region.
qm_calc: Calculator object
QM-calculator.
mm_calc: Calculator object
MM-calculator (should be scaled, see :class:`RescaledCalculator`)
Can use `ForceConstantCalculator` based on QM force constants, if
available.
vacuum: float or None
Amount of vacuum to add around QM atoms.
zero_mean: bool
If True, add a correction to zero the mean force in each direction
"""
if len(atoms[qm_selection_mask]) == 0:
raise ValueError("no QM atoms selected!")
self.qm_selection_mask = qm_selection_mask
self.qm_calc = qm_calc
self.mm_calc = mm_calc
self.vacuum = vacuum
self.buffer_width = buffer_width
self.zero_mean = zero_mean
self.qm_buffer_mask = None
self.cell = None
self.qm_shift = None
Calculator.__init__(self)
def initialize_qm_buffer_mask(self, atoms):
"""
Initialises system to perform qm calculation
"""
# get the radius of the qm_selection in non periodic directions
qm_positions = atoms[self.qm_selection_mask].get_positions()
# identify qm radius as an larges distance from the center
# of the cluster (overestimation)
qm_center = qm_positions.mean(axis=0)
non_pbc_directions = np.logical_not(self.atoms.pbc)
centered_positions = atoms.get_positions()
for i, non_pbc in enumerate(non_pbc_directions):
if non_pbc:
qm_positions.T[i] -= qm_center[i]
centered_positions.T[i] -= qm_center[i]
qm_radius = np.linalg.norm(qm_positions.T, axis=1).max()
self.cell = self.atoms.cell.copy()
for i, non_pbc in enumerate(non_pbc_directions):
if non_pbc:
self.cell[i][i] = 2.0 * (qm_radius +
self.buffer_width +
self.vacuum)
# identify atoms in region < qm_radius + buffer
distances_from_center = np.linalg.norm(
centered_positions.T[non_pbc_directions].T, axis=1)
self.qm_buffer_mask = (distances_from_center <
qm_radius + self.buffer_width)
# exclude atoms that are too far (in case of non spherical region)
for i, buffer_atom in enumerate(self.qm_buffer_mask &
np.logical_not(self.qm_selection_mask)):
if buffer_atom:
distance = np.linalg.norm(
(qm_positions -
centered_positions[i]).T[non_pbc_directions].T, axis=1)
if distance.min() > self.buffer_width:
self.qm_buffer_mask[i] = False
def calculate(self, atoms, properties, system_changes):
Calculator.calculate(self, atoms, properties, system_changes)
if self.qm_buffer_mask is None:
self.initialize_qm_buffer_mask(atoms)
# initialize the object
# qm_buffer_atoms = atoms.copy()
qm_buffer_atoms = atoms[self.qm_buffer_mask]
del qm_buffer_atoms.constraints
qm_buffer_atoms.set_cell(self.cell)
qm_shift = (0.5 * qm_buffer_atoms.cell.diagonal() -
qm_buffer_atoms.positions.mean(axis=0))
qm_buffer_atoms.set_cell(self.cell)
qm_buffer_atoms.positions += qm_shift
forces = self.mm_calc.get_forces(atoms)
qm_forces = self.qm_calc.get_forces(qm_buffer_atoms)
forces[self.qm_selection_mask] = \
qm_forces[self.qm_selection_mask[self.qm_buffer_mask]]
if self.zero_mean:
# Target is that: forces.sum(axis=1) == [0., 0., 0.]
forces[:] -= forces.mean(axis=0)
self.results['forces'] = forces
self.results['energy'] = 0.0