"""Vibrational modes.""" import os import os.path as op import pickle import sys from math import sin, pi, sqrt, log import numpy as np import ase.units as units from ase.io.trajectory import Trajectory from ase.parallel import world, paropen from ase.utils import opencew, pickleload from ase.calculators.singlepoint import SinglePointCalculator class Vibrations: """Class for calculating vibrational modes using finite difference. The vibrational modes are calculated from a finite difference approximation of the Hessian matrix. The *summary()*, *get_energies()* and *get_frequencies()* methods all take an optional *method* keyword. Use method='Frederiksen' to use the method described in: T. Frederiksen, M. Paulsson, M. Brandbyge, A. P. Jauho: "Inelastic transport theory from first-principles: methodology and applications for nanoscale devices", Phys. Rev. B 75, 205413 (2007) atoms: Atoms object The atoms to work on. indices: list of int List of indices of atoms to vibrate. Default behavior is to vibrate all atoms. name: str Name to use for files. delta: float Magnitude of displacements. nfree: int Number of displacements per atom and cartesian coordinate, 2 and 4 are supported. Default is 2 which will displace each atom +delta and -delta for each cartesian coordinate. Example: >>> from ase import Atoms >>> from ase.calculators.emt import EMT >>> from ase.optimize import BFGS >>> from ase.vibrations import Vibrations >>> n2 = Atoms('N2', [(0, 0, 0), (0, 0, 1.1)], ... calculator=EMT()) >>> BFGS(n2).run(fmax=0.01) BFGS: 0 16:01:21 0.440339 3.2518 BFGS: 1 16:01:21 0.271928 0.8211 BFGS: 2 16:01:21 0.263278 0.1994 BFGS: 3 16:01:21 0.262777 0.0088 >>> vib = Vibrations(n2) >>> vib.run() Writing vib.eq.pckl Writing vib.0x-.pckl Writing vib.0x+.pckl Writing vib.0y-.pckl Writing vib.0y+.pckl Writing vib.0z-.pckl Writing vib.0z+.pckl Writing vib.1x-.pckl Writing vib.1x+.pckl Writing vib.1y-.pckl Writing vib.1y+.pckl Writing vib.1z-.pckl Writing vib.1z+.pckl >>> vib.summary() --------------------- # meV cm^-1 --------------------- 0 0.0 0.0 1 0.0 0.0 2 0.0 0.0 3 2.5 20.4 4 2.5 20.4 5 152.6 1230.8 --------------------- Zero-point energy: 0.079 eV >>> vib.write_mode(-1) # write last mode to trajectory file """ def __init__(self, atoms, indices=None, name='vib', delta=0.01, nfree=2): assert nfree in [2, 4] self.atoms = atoms self.calc = atoms.calc if indices is None: indices = range(len(atoms)) self.indices = np.asarray(indices) self.name = name self.delta = delta self.nfree = nfree self.H = None self.ir = None def run(self): """Run the vibration calculations. This will calculate the forces for 6 displacements per atom +/-x, +/-y, +/-z. Only those calculations that are not already done will be started. Be aware that an interrupted calculation may produce an empty file (ending with .pckl), which must be deleted before restarting the job. Otherwise the forces will not be calculated for that displacement. Note that the calculations for the different displacements can be done simultaneously by several independent processes. This feature relies on the existence of files and the subsequent creation of the file in case it is not found. If the program you want to use does not have a calculator in ASE, use ``iterdisplace`` to get all displaced structures and calculate the forces on your own. """ if op.isfile(self.name + '.all.pckl'): raise RuntimeError( 'Cannot run calculation. ' + self.name + '.all.pckl must be removed or split in order ' + 'to have only one sort of data structure at a time.') for dispName, atoms in self.iterdisplace(inplace=True): filename = dispName + '.pckl' fd = opencew(filename) if fd is not None: self.calculate(atoms, filename, fd) def iterdisplace(self, inplace=False): """Yield name and atoms object for initial and displaced structures. Use this to export the structures for each single-point calculation to an external program instead of using ``run()``. Then save the calculated gradients to .pckl and continue using this instance. """ atoms = self.atoms if inplace else self.atoms.copy() yield self.name + '.eq', atoms for dispName, a, i, disp in self.displacements(): if not inplace: atoms = self.atoms.copy() pos0 = atoms.positions[a, i] atoms.positions[a, i] += disp yield dispName, atoms if inplace: atoms.positions[a, i] = pos0 def iterimages(self): """Yield initial and displaced structures.""" for name, atoms in self.iterdisplace(): yield atoms def displacements(self): for a in self.indices: for i in range(3): for sign in [-1, 1]: for ndis in range(1, self.nfree // 2 + 1): dispName = ('%s.%d%s%s' % (self.name, a, 'xyz'[i], ndis * ' +-'[sign])) disp = ndis * sign * self.delta yield dispName, a, i, disp def calculate(self, atoms, filename, fd): forces = self.calc.get_forces(atoms) if self.ir: dipole = self.calc.get_dipole_moment(atoms) if world.rank == 0: if self.ir: pickle.dump([forces, dipole], fd, protocol=2) sys.stdout.write( 'Writing %s, dipole moment = (%.6f %.6f %.6f)\n' % (filename, dipole[0], dipole[1], dipole[2])) else: pickle.dump(forces, fd, protocol=2) sys.stdout.write('Writing %s\n' % filename) fd.close() sys.stdout.flush() def clean(self, empty_files=False, combined=True): """Remove pickle-files. Use empty_files=True to remove only empty files and combined=False to not remove the combined file. """ if world.rank != 0: return 0 n = 0 filenames = [self.name + '.eq.pckl'] if combined: filenames.append(self.name + '.all.pckl') for dispName, a, i, disp in self.displacements(): filename = dispName + '.pckl' filenames.append(filename) for name in filenames: if op.isfile(name): if not empty_files or op.getsize(name) == 0: os.remove(name) n += 1 return n def combine(self): """Combine pickle-files to one file ending with '.all.pckl'. The other pickle-files will be removed in order to have only one sort of data structure at a time. """ if world.rank != 0: return 0 filenames = [self.name + '.eq.pckl'] for dispName, a, i, disp in self.displacements(): filename = dispName + '.pckl' filenames.append(filename) combined_data = {} for name in filenames: if not op.isfile(name) or op.getsize(name) == 0: raise RuntimeError('Calculation is not complete. ' + name + ' is missing or empty.') with open(name, 'rb') as fl: f = pickleload(fl) combined_data.update({op.basename(name): f}) filename = self.name + '.all.pckl' fd = opencew(filename) if fd is None: raise RuntimeError( 'Cannot write file ' + filename + '. Remove old file if it exists.') else: pickle.dump(combined_data, fd, protocol=2) fd.close() return self.clean(combined=False) def split(self): """Split combined pickle-file. The combined pickle-file will be removed in order to have only one sort of data structure at a time. """ if world.rank != 0: return 0 combined_name = self.name + '.all.pckl' if not op.isfile(combined_name): raise RuntimeError('Cannot find combined file: ' + combined_name + '.') with open(combined_name, 'rb') as fl: combined_data = pickleload(fl) filenames = [self.name + '.eq.pckl'] for dispName, a, i, disp in self.displacements(): filename = dispName + '.pckl' filenames.append(filename) if op.isfile(filename): raise RuntimeError( 'Cannot split. File ' + filename + 'already exists.') for name in filenames: fd = opencew(name) try: pickle.dump(combined_data[op.basename(name)], fd, protocol=2) except KeyError: pickle.dump(combined_data[name], fd, protocol=2) # Old version fd.close() os.remove(combined_name) return 1 # One file removed def read(self, method='standard', direction='central'): self.method = method.lower() self.direction = direction.lower() assert self.method in ['standard', 'frederiksen'] assert self.direction in ['central', 'forward', 'backward'] def load(fname, combined_data=None): if combined_data is None: with open(fname, 'rb') as fl: f = pickleload(fl) else: try: f = combined_data[op.basename(fname)] except KeyError: f = combined_data[fname] # Old version if not hasattr(f, 'shape') and not hasattr(f, 'keys'): # output from InfraRed return f[0] return f n = 3 * len(self.indices) H = np.empty((n, n)) r = 0 if op.isfile(self.name + '.all.pckl'): # Open the combined pickle-file combined_data = load(self.name + '.all.pckl') else: combined_data = None if direction != 'central': feq = load(self.name + '.eq.pckl', combined_data) for a in self.indices: for i in 'xyz': name = '%s.%d%s' % (self.name, a, i) fminus = load(name + '-.pckl', combined_data) fplus = load(name + '+.pckl', combined_data) if self.method == 'frederiksen': fminus[a] -= fminus.sum(0) fplus[a] -= fplus.sum(0) if self.nfree == 4: fminusminus = load(name + '--.pckl', combined_data) fplusplus = load(name + '++.pckl', combined_data) if self.method == 'frederiksen': fminusminus[a] -= fminusminus.sum(0) fplusplus[a] -= fplusplus.sum(0) if self.direction == 'central': if self.nfree == 2: H[r] = .5 * (fminus - fplus)[self.indices].ravel() else: H[r] = H[r] = (-fminusminus + 8 * fminus - 8 * fplus + fplusplus)[self.indices].ravel() / 12.0 elif self.direction == 'forward': H[r] = (feq - fplus)[self.indices].ravel() else: assert self.direction == 'backward' H[r] = (fminus - feq)[self.indices].ravel() H[r] /= 2 * self.delta r += 1 H += H.copy().T self.H = H m = self.atoms.get_masses() if 0 in [m[index] for index in self.indices]: raise RuntimeError('Zero mass encountered in one or more of ' 'the vibrated atoms. Use Atoms.set_masses()' ' to set all masses to non-zero values.') self.im = np.repeat(m[self.indices]**-0.5, 3) omega2, modes = np.linalg.eigh(self.im[:, None] * H * self.im) self.modes = modes.T.copy() # Conversion factor: s = units._hbar * 1e10 / sqrt(units._e * units._amu) self.hnu = s * omega2.astype(complex)**0.5 def get_energies(self, method='standard', direction='central', **kw): """Get vibration energies in eV.""" if (self.H is None or method.lower() != self.method or direction.lower() != self.direction): self.read(method, direction, **kw) return self.hnu def get_frequencies(self, method='standard', direction='central'): """Get vibration frequencies in cm^-1.""" s = 1. / units.invcm return s * self.get_energies(method, direction) def summary(self, method='standard', direction='central', freq=None, log=sys.stdout): """Print a summary of the vibrational frequencies. Parameters: method : string Can be 'standard'(default) or 'Frederiksen'. direction: string Direction for finite differences. Can be one of 'central' (default), 'forward', 'backward'. freq : numpy array Optional. Can be used to create a summary on a set of known frequencies. log : if specified, write output to a different location than stdout. Can be an object with a write() method or the name of a file to create. """ if isinstance(log, str): log = paropen(log, 'a') write = log.write s = 0.01 * units._e / units._c / units._hplanck if freq is not None: hnu = freq / s else: hnu = self.get_energies(method, direction) write('---------------------\n') write(' # meV cm^-1\n') write('---------------------\n') for n, e in enumerate(hnu): if e.imag != 0: c = 'i' e = e.imag else: c = ' ' e = e.real write('%3d %6.1f%s %7.1f%s\n' % (n, 1000 * e, c, s * e, c)) write('---------------------\n') write('Zero-point energy: %.3f eV\n' % self.get_zero_point_energy(freq=freq)) def get_zero_point_energy(self, freq=None): if freq is None: return 0.5 * self.hnu.real.sum() else: s = 0.01 * units._e / units._c / units._hplanck return 0.5 * freq.real.sum() / s def get_mode(self, n): """Get mode number .""" mode = np.zeros((len(self.atoms), 3)) mode[self.indices] = (self.modes[n] * self.im).reshape((-1, 3)) return mode def write_mode(self, n=None, kT=units.kB * 300, nimages=30): """Write mode number n to trajectory file. If n is not specified, writes all non-zero modes.""" if n is None: for index, energy in enumerate(self.get_energies()): if abs(energy) > 1e-5: self.write_mode(n=index, kT=kT, nimages=nimages) return mode = self.get_mode(n) * sqrt(kT / abs(self.hnu[n])) pos0 = self.atoms.get_positions() n %= 3 * len(self.indices) atoms = self.atoms.copy() with Trajectory('%s.%d.traj' % (self.name, n), 'w') as traj: for x in np.linspace(0, 2 * pi, nimages, endpoint=False): atoms.set_positions(pos0 + sin(x) * mode) traj.write(atoms) def show_as_force(self, n, scale=0.2): mode = self.get_mode(n) * len(self.hnu) * scale calc = SinglePointCalculator(self.atoms, forces=mode) self.atoms.calc = calc self.atoms.edit() def write_jmol(self): """Writes file for viewing of the modes with jmol.""" with open(self.name + '.xyz', 'w') as fd: self._write_jmol(fd) def _write_jmol(self, fd): symbols = self.atoms.get_chemical_symbols() freq = self.get_frequencies() for n in range(3 * len(self.indices)): fd.write('%6d\n' % len(self.atoms)) if freq[n].imag != 0: c = 'i' freq[n] = freq[n].imag else: c = ' ' fd.write('Mode #%d, f = %.1f%s cm^-1' % (n, freq[n], c)) if self.ir: fd.write(', I = %.4f (D/Å)^2 amu^-1.\n' % self.intensities[n]) else: fd.write('.\n') mode = self.get_mode(n) for i, pos in enumerate(self.atoms.positions): fd.write('%2s %12.5f %12.5f %12.5f %12.5f %12.5f %12.5f \n' % (symbols[i], pos[0], pos[1], pos[2], mode[i, 0], mode[i, 1], mode[i, 2])) def fold(self, frequencies, intensities, start=800.0, end=4000.0, npts=None, width=4.0, type='Gaussian', normalize=False): """Fold frequencies and intensities within the given range and folding method (Gaussian/Lorentzian). The energy unit is cm^-1. normalize=True ensures the integral over the peaks to give the intensity. """ lctype = type.lower() assert lctype in ['gaussian', 'lorentzian'] if not npts: npts = int((end - start) / width * 10 + 1) prefactor = 1 if lctype == 'lorentzian': intensities = intensities * width * pi / 2. if normalize: prefactor = 2. / width / pi else: sigma = width / 2. / sqrt(2. * log(2.)) if normalize: prefactor = 1. / sigma / sqrt(2 * pi) # Make array with spectrum data spectrum = np.empty(npts) energies = np.linspace(start, end, npts) for i, energy in enumerate(energies): energies[i] = energy if lctype == 'lorentzian': spectrum[i] = (intensities * 0.5 * width / pi / ((frequencies - energy)**2 + 0.25 * width**2)).sum() else: spectrum[i] = (intensities * np.exp(-(frequencies - energy)**2 / 2. / sigma**2)).sum() return [energies, prefactor * spectrum] def write_dos(self, out='vib-dos.dat', start=800, end=4000, npts=None, width=10, type='Gaussian', method='standard', direction='central'): """Write out the vibrational density of states to file. First column is the wavenumber in cm^-1, the second column the folded vibrational density of states. Start and end points, and width of the Gaussian/Lorentzian should be given in cm^-1.""" frequencies = self.get_frequencies(method, direction).real intensities = np.ones(len(frequencies)) energies, spectrum = self.fold(frequencies, intensities, start, end, npts, width, type) # Write out spectrum in file. outdata = np.empty([len(energies), 2]) outdata.T[0] = energies outdata.T[1] = spectrum with open(out, 'w') as fd: fd.write('# %s folded, width=%g cm^-1\n' % (type.title(), width)) fd.write('# [cm^-1] arbitrary\n') for row in outdata: fd.write('%.3f %15.5e\n' % (row[0], row[1]))