'''
Date: 11/26/2024
Author: Martin E. Liza
File: quantum_mechanics.py
Def: Contains Quantum Mechanics functions.
'''
import molmass
import numpy as np
import scipy.constants as s_consts
from haot.src import aerodynamic_functions as aero
from haot.src import constants_tables
# Unit Conversions
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def wavenumber_to_electronvolt(wavenumber_cm):
"""Convert wavenumber [cm^-1] to energy in Joules [J]."""
return wavenumber_to_joules(wavenumber_cm) / s_consts.eV #[eV]
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def wavenumber_to_joules(wavenumber_cm):
"""Convert wavenumber [cm^-1] to energy in electron volts [eV]."""
return wavenumber_cm * s_consts.c * 100 * s_consts.h #[J]
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def molarmass_to_kilogram(molarmass_gmol):
"""Convert molar mass [g/mol] to [kg]."""
return molarmass_gmol * 1E-3 / s_consts.N_A
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def zero_point_energy(molecule):
"""Calculate zero-point energy based on spectroscopy constants.
(Ref: Irikura https://doi.org/10.1063/1.2436891)"""
spectroscopy_const = constants_tables.spectroscopy_constants(molecule)
scope_var = (spectroscopy_const['alpha_e'] *
spectroscopy_const['omega_e'] /
spectroscopy_const['B_e'])
zpe = spectroscopy_const['omega_e'] / 2
zpe -= spectroscopy_const['omega_xe'] / 2
zpe += spectroscopy_const['omega_ye'] / 8
zpe += spectroscopy_const['B_e'] / 4
zpe += scope_var / 12
zpe += scope_var**2 / (144 * spectroscopy_const['B_e'])
return zpe #[1/cm]
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def vibrational_partition_function(vibrational_number, temperature_K, molecule):
"""Calculates the vibrational partition function, (harmonic terms only)"""
z_vib = 0.0
for v in range(vibrational_number + 1):
z_vib += boltzman_factor(temperature_K, molecule, vibrational_number=v)
return z_vib
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def rotational_partition_function(rotational_number, temperature_K, molecule):
"""Calculates the rotational partition function, (harmonic terms only)"""
z_rot = 0.0
for j in range(rotational_number + 1):
z_rot += boltzman_factor(temperature_K, molecule, rotational_number=j)
return z_rot
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def born_oppenheimer_partition_function(vibrational_number,
rotational_number,
temperature_K,
molecule):
"""Calculates the partition function using the Born-Oppenheimer
approximation"""
z_bo = 0.0
for j in range(rotational_number + 1):
for v in range(vibrational_number + 1):
z_bo += boltzman_factor(temperature_K, molecule,
vibrational_number=v,
rotational_number=j,
born_opp_flag=True)
return z_bo
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def potential_dunham_coef_012(molecule):
"""Calculates the 0th, 1st, and 2nd Dunham potential coefficients.
Using: Ogilvie (https://doi.org/10.1016/0022-2852(76)90323-4)
and Herschbach (https://doi.org/10.1063/1.1731952)."""
spectroscopy_const = constants_tables.spectroscopy_constants(molecule)
a_0 = (spectroscopy_const['omega_e']**2 /
(4 * spectroscopy_const['B_e']))
a_1 = -(spectroscopy_const['alpha_e'] * spectroscopy_const['omega_e'] /
(6 * spectroscopy_const['B_e']**2) + 1)
a_2 = ((5/4) * a_1**2 - (2/3) *
(spectroscopy_const['omega_xe'] / spectroscopy_const['B_e']))
return (a_0, a_1, a_2)
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def potential_dunham_coeff_m(a_1, a_2, m):
"""Calculates the higher order Dunham potential coefficients, using
Morizadeh work (https://doi.org/10.1016/j.theochem.2003.12.003)."""
tmp = (12 / a_1)**(m - 2)
tmp *= (2**(m + 1) - 1)
tmp *= (a_2 / 7)**(m - 1)
for i in range(m - 2):
tmp *= (1 / (m + 2 - i))
return tmp
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def boltzman_factor(temperature_K, molecule, vibrational_number=None,
rotational_number=None, born_opp_flag=False):
"""Calculates the Boltzman factor at a given vibrational_number and/or
rotational_number. If the born_opp_flag is provided, it will calculate the
total energy using the Born-Oppenheimer approximation"""
# Initialize energy terms, degeneracy and thermal beta
energy_vib_k = 0
energy_rot_k = 0
degeneracy_rotation = 1
thermal_beta = 1 / (s_consts.k * temperature_K)
# Calculates Energy levels
if not born_opp_flag:
if vibrational_number is not None:
energy_vib_k = vibrational_energy_k(vibrational_number, molecule)
if rotational_number is not None:
energy_rot_k = rotational_energy_k(rotational_number, molecule)
degeneracy_rotation = 2 * rotational_number + 1
tot_energy = wavenumber_to_joules(energy_vib_k + energy_rot_k)
else:
degeneracy_rotation = 2 * rotational_number + 1
tot_energy = wavenumber_to_joules(born_oppenheimer_approximation(vibrational_number,
rotational_number,molecule))
return degeneracy_rotation * np.exp(-tot_energy * thermal_beta)
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def distribution_function(temperature_K, molecule, vibrational_number=None,
rotational_number=None, born_opp_flag=False):
"""Compute the population distribution function."""
# Calculates partition functions if vibrational or rotational numbers are provided
if not born_opp_flag:
z_rot = 1
z_vib = 1
if vibrational_number is not None:
z_vib = vibrational_partition_function(vibrational_number, temperature_K,
molecule)
if rotational_number is not None:
z_rot = rotational_partition_function(rotational_number, temperature_K,
molecule)
z_tot = z_rot * z_vib
else:
z_tot = born_oppenheimer_partition_function(vibrational_number,
rotational_number, temperature_K,
molecule)
# Create the distribution array based on the inputs provided
if vibrational_number and rotational_number:
tmp = np.zeros([vibrational_number + 1, rotational_number + 1])
for j in range(rotational_number + 1):
for v in range(vibrational_number + 1):
tmp[v][j] = boltzman_factor(temperature_K=temperature_K,
molecule=molecule,
vibrational_number=v,
rotational_number=j,
born_opp_flag=born_opp_flag)
elif vibrational_number:
tmp = np.zeros(vibrational_number + 1)
for v in range(vibrational_number + 1):
tmp[v] = boltzman_factor(temperature_K=temperature_K,
molecule=molecule,
vibrational_number=v)
elif rotational_number:
tmp = np.zeros(rotational_number + 1)
for j in range(rotational_number + 1):
tmp[j] = boltzman_factor(temperature_K=temperature_K,
molecule=molecule,
rotational_number=j)
return tmp / z_tot
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def born_oppenheimer_approximation(vibrational_number, rotational_number,
molecule):
"""Calculates the energy at a rotational and vibrational quantum number,
using the Born-Oppenheimer approximation."""
spectroscopy_constants = constants_tables.spectroscopy_constants(molecule)
vib_levels = vibrational_number + 1/2
rot_levels = rotational_number * (rotational_number + 1)
# Harmonic vibration and rotation terms
harmonic = spectroscopy_constants['omega_e'] * vib_levels
harmonic += spectroscopy_constants['B_e'] * rot_levels
# Anharmonic vibration and rotation terms
anharmonic = spectroscopy_constants['omega_xe'] * vib_levels**2
anharmonic += spectroscopy_constants['D_e'] * rot_levels**2
# Interaction between vibration and rotation modes
interaction = spectroscopy_constants['alpha_e'] * vib_levels * rot_levels
return harmonic - anharmonic - interaction #[cm^1]
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def vibrational_energy_k(vibrational_number, molecule):
"""Calculates the vibrational energy at a given vibrational quantum number,
using for the harmonic terms"""
spectroscopy_constants = constants_tables.spectroscopy_constants(molecule)
# Calculates the vibrational energy in units of wave number
vib_levels = vibrational_number + 1/2
return spectroscopy_constants['omega_e'] * vib_levels #[cm^-1]
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def rotational_energy_k(rotational_number, molecule):
"""Calculates the rotational energy at a given rotational quantum number,
using for the harmonic terms"""
spectroscopy_constants = constants_tables.spectroscopy_constants(molecule)
# Calculates the rotational energy in units of wave number
rot_levels = rotational_number * (rotational_number + 1)
return spectroscopy_constants['B_e'] * rot_levels #[cm^-1]
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def reduced_mass_kg(molecule_1, molecule_2):
"""Calculates the molar reduced mass and returns it in kg of two
elements"""
m_1 = molmass.Formula(molecule_1).mass
m_2 = molmass.Formula(molecule_2).mass
mu = m_1 * m_2 / (m_1 + m_2)
return molarmass_to_kilogram(mu)
# TODO: Missing Translational Energy
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def tranlational_energy(principal_number_x, principal_number_y,
principal_number_z):
print("TODO: Missing implementation of this function")