# -*- coding: utf-8 -*- """Vibrational modes.""" from __future__ import division 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 rank, paropen from ase.utils import opencew 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 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 self.ram = 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. """ filename = self.name + '.eq.pckl' fd = opencew(filename) if fd is not None: self.calculate(filename, fd) p = self.atoms.positions.copy() for filename, a, i, disp in self.displacements(): fd = opencew(filename) if fd is not None: self.atoms.positions[a, i] = p[a, i] + disp self.calculate(filename, fd) self.atoms.positions[a, i] = p[a, i] 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): filename = ('%s.%d%s%s.pckl' % (self.name, a, 'xyz'[i], ndis * ' +-'[sign])) disp = ndis * sign * self.delta yield filename, a, i, disp def calculate(self, filename, fd): forces = self.atoms.get_forces() if self.ir: dipole = self.calc.get_dipole_moment(self.atoms) if self.ram: freq, pol = self.get_polarizability() if rank == 0: if self.ir and self.ram: pickle.dump([forces, dipole, freq, pol], fd) sys.stdout.write( 'Writing %s, dipole moment = (%.6f %.6f %.6f)\n' % (filename, dipole[0], dipole[1], dipole[2])) elif self.ir and not self.ram: pickle.dump([forces, dipole], fd) sys.stdout.write( 'Writing %s, dipole moment = (%.6f %.6f %.6f)\n' % (filename, dipole[0], dipole[1], dipole[2])) else: pickle.dump(forces, fd) sys.stdout.write('Writing %s\n' % filename) fd.close() sys.stdout.flush() def clean(self, empty_files=False): """Remove pickle-files. Use empty_files=True to remove only empty files.""" if rank != 0: return 0 n = 0 filenames = [self.name + '.eq.pckl'] for filename, a, i, disp in self.displacements(): 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 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): f = pickle.load(open(fname, 'rb')) if not hasattr(f, 'shape'): # output from InfraRed return f[0] return f n = 3 * len(self.indices) H = np.empty((n, n)) r = 0 if direction != 'central': feq = load(self.name + '.eq.pckl') for a in self.indices: for i in 'xyz': name = '%s.%d%s' % (self.name, a, i) fminus = load(name + '-.pckl') fplus = load(name + '+.pckl') if self.method == 'frederiksen': fminus[a] -= fminus.sum(0) fplus[a] -= fplus.sum(0) if self.nfree == 4: fminusminus = load(name + '--.pckl') fplusplus = load(name + '++.pckl') 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'): """Get vibration energies in eV.""" if (self.H is None or method.lower() != self.method or direction.lower() != self.direction): self.read(method, direction) 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])) p = self.atoms.positions.copy() n %= 3 * len(self.indices) traj = Trajectory('%s.%d.traj' % (self.name, n), 'w') calc = self.atoms.get_calculator() self.atoms.set_calculator() for x in np.linspace(0, 2 * pi, nimages, endpoint=False): self.atoms.set_positions(p + sin(x) * mode) traj.write(self.atoms) self.atoms.set_positions(p) self.atoms.set_calculator(calc) traj.close() def write_jmol(self): """Writes file for viewing of the modes with jmol.""" fd = open(self.name + '.xyz', 'w') symbols = self.atoms.get_chemical_symbols() f = self.get_frequencies() for n in range(3 * len(self.indices)): fd.write('%6d\n' % len(self.atoms)) if f[n].imag != 0: c = 'i' f[n] = f[n].imag else: c = ' ' fd.write('Mode #%d, f = %.1f%s cm^-1' % (n, f[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])) fd.close() 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. """ self.type = type.lower() assert self.type in ['gaussian', 'lorentzian'] if not npts: npts = int((end - start) / width * 10 + 1) prefactor = 1 if type == '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 type == '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 fd = open(out, 'w') 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])) fd.close()