import numpy as np from ase.calculators.calculator import Calculator from ase.data import atomic_numbers from ase.utils import convert_string_to_fd 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 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 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.positions.mean(axis=0) # if counter ions are used, then molecule_size has more than 1 value if self.mmatoms.calc.name == 'combinemm': mask1 = self.mmatoms.calc.mask mask2 = ~mask1 vmask1 = self.mmatoms.calc.virtual_mask vmask2 = ~vmask1 apm1 = self.mmatoms.calc.apm1 apm2 = self.mmatoms.calc.apm2 spm1 = self.mmatoms.calc.atoms1.calc.sites_per_mol spm2 = self.mmatoms.calc.atoms2.calc.sites_per_mol pos = self.mmatoms.positions pos1 = pos[mask1].reshape((-1, apm1, 3)) pos2 = pos[mask2].reshape((-1, apm2, 3)) pos = (pos1, pos2) else: pos = (self.mmatoms.positions, ) apm1 = self.molecule_size apm2 = self.molecule_size # This is only specific to calculators where apm != spm, # i.e. TIP4P. Non-native MM calcs do not have this attr. if hasattr(self.mmatoms.calc, 'sites_per_mol'): spm1 = self.mmatoms.calc.sites_per_mol spm2 = self.mmatoms.calc.sites_per_mol else: spm1 = self.molecule_size spm2 = spm1 mask1 = np.ones(len(self.mmatoms), dtype=bool) mask2 = mask1 wrap_pos = np.zeros_like(self.mmatoms.positions) com_all = [] apm = (apm1, apm2) mask = (mask1, mask2) spm = (spm1, spm2) for p, n, m, vn in zip(pos, apm, mask, spm): positions = p.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, vn, axis=0) com_all.append(com_pv) wrap_pos[m] = positions.reshape((-1, 3)) positions = wrap_pos.copy() positions = self.mmatoms.calc.add_virtual_sites(positions) if self.mmatoms.calc.name == 'combinemm': com_pv = np.zeros_like(positions) for ii, m in enumerate((vmask1, vmask2)): com_pv[m] = com_all[ii] # 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 = [] epsilon = [] # check if input is tuple of vals for more than 1 mm calc, or only for 1. if type(sigmamm) == tuple: numcalcs = len(sigmamm) else: numcalcs = 1 # if only 1 mm calc, eps and sig are simply np arrays sigmamm = (sigmamm, ) epsilonmm = (epsilonmm, ) for cc in range(numcalcs): sigma_c = np.zeros((len(sigmaqm), len(sigmamm[cc]))) epsilon_c = np.zeros_like(sigma_c) for ii in range(len(sigmaqm)): sigma_c[ii, :] = (sigmaqm[ii] + sigmamm[cc]) / 2 epsilon_c[ii, :] = (epsilonqm[ii] * epsilonmm[cc])**0.5 sigma.append(sigma_c) epsilon.append(epsilon_c) if numcalcs == 1: # retain original, 1 calc function sigma = np.array(sigma[0]) epsilon = np.array(epsilon[0]) return sigma, epsilon class LJInteractionsGeneral: name = 'LJ-general' def __init__(self, sigmaqm, epsilonqm, sigmamm, epsilonmm, qm_molecule_size, mm_molecule_size=3, rc=np.Inf, width=1.0): """General Lennard-Jones type explicit interaction. sigmaqm: array Array of sigma-parameters which should have the length of the QM subsystem epsilonqm: array As sigmaqm, but for epsilon-paramaters sigmamm: Either array (A) or tuple (B) A (no counterions): Array of sigma-parameters with the length of the smallest repeating atoms-group (i.e. molecule) of the MM subsystem B (counterions): Tuple: (arr1, arr2), where arr1 is an array of sigmas with the length of counterions in the MM subsystem, and arr2 is the array from A. epsilonmm: array or tuple As sigmamm but for epsilon-parameters. qm_molecule_size: int number of atoms of the smallest repeating atoms-group (i.e. molecule) in the QM subystem (often just the number of atoms in the QM subsystem) mm_molecule_size: int as qm_molecule_size but for the MM subsystem. Will be overwritten if counterions are present in the MM subsystem (via the CombineMM calculator) """ self.sigmaqm = sigmaqm self.epsilonqm = epsilonqm self.sigmamm = sigmamm self.epsilonmm = epsilonmm self.qms = qm_molecule_size self.mms = mm_molecule_size self.rc = rc self.width = width 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): epsilon = self.epsilon sigma = self.sigma # loop over possible multiple mm calculators # currently 1 or 2, but could be generalized in the future... apm1 = self.mms mask1 = np.ones(len(mmatoms), dtype=bool) mask2 = mask1 apm = (apm1, ) sigma = (sigma, ) epsilon = (epsilon, ) if hasattr(mmatoms.calc, 'name'): if mmatoms.calc.name == 'combinemm': mask1 = mmatoms.calc.mask mask2 = ~mask1 apm1 = mmatoms.calc.apm1 apm2 = mmatoms.calc.apm2 apm = (apm1, apm2) sigma = sigma[0] # Was already loopable 2-tuple epsilon = epsilon[0] mask = (mask1, mask2) e_all = 0 qmforces_all = np.zeros_like(qmatoms.positions) mmforces_all = np.zeros_like(mmatoms.positions) # zip stops at shortest tuple so we dont double count # cases of no counter ions. for n, m, eps, sig in zip(apm, mask, epsilon, sigma): mmpositions = self.update(qmatoms, mmatoms[m], n, shift) qmforces = np.zeros_like(qmatoms.positions) mmforces = np.zeros_like(mmatoms[m].positions) energy = 0.0 qmpositions = qmatoms.positions.reshape((-1, self.qms, 3)) for q, qmpos in enumerate(qmpositions): # molwise loop # cutoff from first atom of each mol R00 = mmpositions[:, 0] - qmpos[0, :] d002 = (R00**2).sum(1) d00 = d002**0.5 x1 = d00 > self.rc - self.width x2 = d00 < self.rc x12 = np.logical_and(x1, x2) y = (d00[x12] - self.rc + self.width) / self.width t = np.zeros(len(d00)) t[x2] = 1.0 t[x12] -= y**2 * (3.0 - 2.0 * y) dt = np.zeros(len(d00)) dt[x12] -= 6.0 / self.width * y * (1.0 - y) for qa in range(len(qmpos)): if ~np.any(eps[qa, :]): continue R = mmpositions - qmpos[qa, :] d2 = (R**2).sum(2) c6 = (sig[qa, :]**2 / d2)**3 c12 = c6**2 e = 4 * eps[qa, :] * (c12 - c6) energy += np.dot(e.sum(1), t) f = t[:, None, None] * (24 * eps[qa, :] * (2 * c12 - c6) / d2)[:, :, None] * R f00 = - (e.sum(1) * dt / d00)[:, None] * R00 mmforces += f.reshape((-1, 3)) qmforces[q * self.qms + qa, :] -= f.sum(0).sum(0) qmforces[q * self.qms, :] -= f00.sum(0) mmforces[::n, :] += f00 e_all += energy qmforces_all += qmforces mmforces_all[m] += mmforces return e_all, qmforces_all, mmforces_all def update(self, qmatoms, mmatoms, n, shift): # 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 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 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 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