Source code for quantum_mechanics

'''
    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
[docs] 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]
[docs] 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]
[docs] def molarmass_to_kilogram(molarmass_gmol): """Convert molar mass [g/mol] to [kg].""" return molarmass_gmol * 1E-3 / s_consts.N_A
[docs] 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]
[docs] 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
[docs] 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
[docs] 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
[docs] 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)
[docs] 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
[docs] 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)
[docs] 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
[docs] 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]
[docs] 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]
[docs] 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]
[docs] 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
[docs] def tranlational_energy(principal_number_x, principal_number_y, principal_number_z): print("TODO: Missing implementation of this function")