Chimie Théorique » QMX

#!/usr/bin/env python

"""Modules for calculating thermochemical information from computational

outputs."""

import os

import sys

import numpy as np

from ase import units

def rotationalinertia(atoms):

    """Calculates the three principle moments of inertia for an ASE atoms

    object. This uses the atomic masses from ASE, which (if not explicitly

    specified by the user) gives an inexact approximation of an isotopically

    averaged result. Units are in amu*angstroms**2."""

    # Calculate the center of mass.

    xcm, ycm, zcm = atoms.get_center_of_mass()

    masses = atoms.get_masses()

    # Calculate moments of inertia in the current frame of reference.

    Ixx = 0.

    Iyy = 0.

    Izz = 0.

    Ixy = 0.

    Ixz = 0.

    Iyz = 0.

    for index, atom in enumerate(atoms):

        m = masses[index]

        x = atom.get_x() - xcm

        y = atom.get_y() - ycm

        z = atom.get_z() - zcm

        Ixx += m * (y**2. + z**2.)

        Iyy += m * (x**2. + z**2.)

        Izz += m * (x**2. + y**2.)

        Ixy += m * x * y

        Ixz += m * x * z

        Iyz += m * y * z

    # Create the inertia tensor in the current frame of reference.

    I_ = np.matrix([[ Ixx, -Ixy, -Ixz],

                    [-Ixy,  Iyy, -Iyz],

                    [-Ixz, -Iyz,  Izz]])

    # Find the eigenvalues, which are the principle moments of inertia.

    I = np.linalg.eigvals(I_)

    return I

class ThermoChem:

    """Base class containing common methods used in thermochemistry

    calculations."""

    def get_ZPE_correction(self):

        """Returns the zero-point vibrational energy correction in eV."""

        zpe = 0.

        for energy in self.vib_energies:

            zpe += 0.5 * energy

        return zpe

    def _vibrational_energy_contribution(self, temperature):

        """Calculates the change in internal energy due to vibrations from

        0K to the specified temperature for a set of vibrations given in

        inverse centimeters and a temperature given in Kelvin. Returns the

        energy change in eV."""

        kT = units.kB * temperature

        dU = 0.

        for energy in self.vib_energies:

            dU += energy / (np.exp(energy/kT) - 1.)

        return dU

    def _vibrational_entropy_contribution(self, temperature):

        """Calculates the entropy due to vibrations for a set of vibrations

        given in inverse centimeters and a temperature given in Kelvin.

        Returns the entropy in eV/K."""

        kT = units.kB * temperature

        S_v = 0.

        for energy in self.vib_energies:

            x = energy / kT

            S_v += x / (np.exp(x)-1.) - np.log(1-np.exp(-x))

        S_v *= units.kB

        return S_v

    def _vprint(self, text):

        """Print output if verbose flag True."""

        if self.verbose:

            sys.stdout.write(text + os.linesep)

class HarmonicThermo(ThermoChem):

    """Class for calculating thermodynamic properties in the approximation

    that all degrees of freedom are treated harmonically. Often used for

    adsorbates.

    Inputs:

    vib_energies : list

        a list of the harmonic energies of the adsorbate (e.g., from

        ase.vibrations.Vibrations.get_energies). The number of

        energies should match the number of degrees of freedom of the

        adsorbate; i.e., 3*n, where n is the number of atoms. Note that

        this class does not check that the user has supplied the correct

        number of energies. Units of energies are eV.

    electronicenergy : float

        the electronic energy in eV

        (If the electronicenergy is unspecified, then the methods of this

        class can be interpreted as the energy corrections.)

    """

    def __init__(self, vib_energies, electronicenergy=None):

        self.vib_energies = vib_energies

        # Check for imaginary frequencies.

        if sum(np.iscomplex(self.vib_energies)):

            raise ValueError('Imaginary vibrational energies are present.')

        else:

            self.vib_energies = np.real(self.vib_energies) # clear +0.j

        if electronicenergy:

            self.electronicenergy = electronicenergy

        else:

            self.electronicenergy = 0.

    def get_internal_energy(self, temperature, verbose=True):

        """Returns the internal energy, in eV, in the harmonic approximation

        at a specified temperature (K)."""

        self.verbose = verbose

        write = self._vprint

        fmt = '%-15s%13.3f eV'

        write('Internal energy components at T = %.2f K:' % temperature)

        write('='*31)

        U = 0.

        write(fmt % ('E_elec', self.electronicenergy))

        U += self.electronicenergy

        zpe = self.get_ZPE_correction()

        write(fmt % ('E_ZPE', zpe))

        U += zpe

        dU_v = self._vibrational_energy_contribution(temperature)

        write(fmt % ('Cv_harm (0->T)', dU_v))

        U += dU_v

        write('-'*31)

        write(fmt % ('U', U))

        write('='*31)

        return U

    def get_entropy(self, temperature, verbose=True):

        """Returns the entropy, in eV/K, in the harmonic approximation

        at a specified temperature (K)."""

        self.verbose = verbose

        write = self._vprint

        fmt = '%-15s%13.7f eV/K%13.3f eV'

        write('Entropy components at T = %.2f K:' % temperature)

        write('='*49)

        write('%15s%13s     %13s'%('', 'S', 'T*S'))

        S = 0.

        S_v = self._vibrational_entropy_contribution(temperature)

        write(fmt%('S_harm', S_v, S_v*temperature))

        S += S_v

        write('-'*49)

        write(fmt%('S', S, S*temperature))

        write('='*49)

        return S

    def get_free_energy(self, temperature, verbose=True):

        """Returns the free energy, in eV, in the harmonic approximation

        at a specified temperature (K)."""

        self.verbose = True

        write = self._vprint

        U = self.get_internal_energy(temperature, verbose=verbose)

        write('')

        S = self.get_entropy(temperature, verbose=verbose)

        G = U - temperature * S

        write('')

        write('Free energy components at T = %.2f K:' % temperature)

        write('='*23)

        fmt = '%5s%15.3f eV'

        write(fmt % ('U', U))

        write(fmt % ('-T*S', -temperature * S))

        write('-'*23)

        write(fmt % ('G', G))

        write('='*23)

        return G

class IdealGasThermo(ThermoChem):

    """Class for calculating thermodynamic properties of a molecule

    based on statistical mechanical treatments in the ideal gas

    approximation.

    Inputs for enthalpy calculations:

    vib_energies : list

        a list of the vibrational energies of the molecule (e.g., from

        ase.vibrations.Vibrations.get_energies). The number of vibrations

        used is automatically calculated by the geometry and the number of

        atoms. If more are specified than are needed, then the lowest

        numbered vibrations are neglected. If either atoms or natoms is

        unspecified, then uses the entire list. Units are eV.

    geometry : 'monatomic', 'linear', or 'nonlinear'

        geometry of the molecule

    electronicenergy : float

        the electronic energy in eV

        (If electronicenergy is unspecified, then the methods of this

        class can be interpreted as the enthalpy and free energy

        corrections.)

    natoms : integer

        the number of atoms, used along with 'geometry' to determine how

        many vibrations to use. (Not needed if an atoms object is supplied

        in 'atoms' or if the user desires the entire list of vibrations

        to be used.)

    Extra inputs needed for for entropy / free energy calculations:

    atoms : an ASE atoms object

        used to calculate rotational moments of inertia and molecular mass

    symmetrynumber : integer

        symmetry number of the molecule. See, for example, Table 10.1 and

        Appendix B of C. Cramer "Essentials of Computational Chemistry",

        2nd Ed.

    spin : float

        the total electronic spin. (0 for molecules in which all electrons

        are paired, 0.5 for a free radical with a single unpaired electron,

        1.0 for a triplet with two unpaired electrons, such as O_2.)

    """

    def __init__(self, vib_energies, geometry, electronicenergy=None,

                 atoms=None, symmetrynumber=None, spin=None, natoms=None):

        if electronicenergy == None:

            self.electronicenergy = 0.

        else:

            self.electronicenergy = electronicenergy

        self.geometry = geometry

        self.atoms = atoms

        self.sigma = symmetrynumber

        self.spin = spin

        if natoms == None:

            if atoms:

                natoms = len(atoms)

        # Cut the vibrations to those needed from the geometry.

        if natoms:

            if geometry == 'nonlinear':

                self.vib_energies = vib_energies[-(3*natoms-6):]

            elif geometry == 'linear':

                self.vib_energies = vib_energies[-(3*natoms-5):]

            elif geometry == 'monatomic':

                self.vib_energies = []

        else:

            self.vib_energies = vib_energies

        # Make sure no imaginary frequencies remain.

        if sum(np.iscomplex(self.vib_energies)):

            raise ValueError('Imaginary frequencies are present.')

        else:

            self.vib_energies = np.real(self.vib_energies) # clear +0.j

        self.referencepressure = 101325. # Pa

    def get_enthalpy(self, temperature, verbose=True):

        """Returns the enthalpy, in eV, in the ideal gas approximation

        at a specified temperature (K)."""

        self.verbose = verbose

        write = self._vprint

        fmt = '%-15s%13.3f eV'

        write('Enthalpy components at T = %.2f K:' % temperature)

        write('='*31)

        H = 0.

        write(fmt % ('E_elec', self.electronicenergy))

        H += self.electronicenergy

        zpe = self.get_ZPE_correction()

        write(fmt % ('E_ZPE', zpe))

        H += zpe

        Cv_t = 3./2. * units.kB # translational heat capacity (3-d gas)

        write(fmt % ('Cv_trans (0->T)', Cv_t * temperature))

        H += Cv_t * temperature

        if self.geometry == 'nonlinear': # rotational heat capacity

            Cv_r = 3./2.*units.kB

        elif self.geometry == 'linear':

            Cv_r = units.kB

        elif self.geometry == 'monatomic':

            Cv_r = 0.

        write(fmt % ('Cv_rot (0->T)', Cv_r * temperature))

        H += Cv_r*temperature

        dH_v = self._vibrational_energy_contribution(temperature)

        write(fmt % ('Cv_vib (0->T)', dH_v))

        H += dH_v

        Cp_corr = units.kB * temperature

        write(fmt % ('(C_v -> C_p)', Cp_corr))

        H += Cp_corr

        write('-'*31)

        write(fmt % ('H', H))

        write('='*31)

        return H

    def get_entropy(self, temperature, pressure, verbose=True):

        """Returns the entropy, in eV/K, in the ideal gas approximation

        at a specified temperature (K) and pressure (Pa)."""

        if self.atoms == None or self.sigma == None or self.spin == None:

            raise RuntimeError('atoms, symmetrynumber, and spin must be '

                               'specified for entropy and free energy '

                               'calculations.')

        self.verbose = verbose

        write = self._vprint

        fmt = '%-15s%13.7f eV/K%13.3f eV'

        write('Entropy components at T = %.2f K and P = %.1f Pa:' %

               (temperature, pressure))

        write('='*49)

        write('%15s%13s     %13s' % ('', 'S', 'T*S'))

        S = 0.

        # Translational entropy (term inside the log is in SI units).

        mass = sum(self.atoms.get_masses()) * units._amu # kg/molecule

        S_t = (2*np.pi*mass*units._k*temperature/units._hplanck**2)**(3./2)

        S_t *= units._k * temperature / self.referencepressure

        S_t = units.kB * (np.log(S_t) + 5./2.)

        write(fmt % ('S_trans (1 atm)', S_t, S_t * temperature))

        S += S_t

        # Rotational entropy (term inside the log is in SI units).

        if self.geometry == 'monatomic':

            S_r = 0.

        elif self.geometry == 'nonlinear':

            inertias = (rotationalinertia(self.atoms) * units._amu /

                        (10.**10)**2) # kg m^2

            S_r = np.sqrt(np.pi*np.product(inertias)) / self.sigma

            S_r *= (8. * np.pi**2 * units._k * temperature /

                    units._hplanck**2)**(3./2.)

            S_r = units.kB * (np.log(S_r) + 3./2.)

        elif self.geometry == 'linear':

            inertias = (rotationalinertia(self.atoms) * units._amu /

                        (10.**10)**2) # kg m^2

            inertia = max(inertias) # should be two identical and one zero

            S_r = (8 * np.pi**2 * inertia * units._k * temperature /

                   self.sigma / units._hplanck**2)

            S_r = units.kB * ( np.log(S_r) + 1.)

        write(fmt % ('S_rot', S_r, S_r*temperature))

        S += S_r

        # Electronic entropy.

        S_e = units.kB * np.log(2*self.spin+1)

        write(fmt % ('S_elec', S_e, S_e * temperature))

        S += S_e

        # Vibrational entropy.

        S_v = self._vibrational_entropy_contribution(temperature)

        write(fmt % ('S_vib', S_v, S_v* temperature))

        S += S_v

        # Pressure correction to translational entropy.

        S_p = - units.kB * np.log(pressure/self.referencepressure)

        write(fmt % ('S (1 atm -> P)', S_p, S_p * temperature))

        S += S_p

        write('-'*49)

        write(fmt % ('S', S, S * temperature))

        write('='*49)

        return S

    def get_free_energy(self, temperature, pressure, verbose=True):

        """Returns the free energy, in eV, in the ideal gas approximation

        at a specified temperature (K) and pressure (Pa)."""

        self.verbose = verbose

        write = self._vprint

        H = self.get_enthalpy(temperature, verbose=verbose)

        write('')

        S = self.get_entropy(temperature, pressure, verbose=verbose)

        G = H - temperature * S

        write('')

        write('Free energy components at T = %.2f K and P = %.1f Pa:' %

               (temperature, pressure))

        write('='*23)

        fmt = '%5s%15.3f eV'

        write(fmt % ('H', H))

        write(fmt % ('-T*S', -temperature * S))

        write('-'*23)

        write(fmt % ('G', G))

        write('='*23)

        return G