Statistical Thermodynamics Reactor

A python script to calculate reaction data with Statistical Thermodynamics (ΔG, ΔS, ΔH, ΔU, reaction constant); from the lecture of Roberto Marquardt.

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Required package:

• pandas
• matplotlib

Remarks:

• The script works for one reaction only.
• The input parameters are stored in a dictionary called 'data'. The reaction state functions are stored in a dictionary called 'results'.
• The script is meant to be used from python interpreter. Make sure the script is located in the working directory or added to the pythonpath
• To convert cm-1 to Joule: multiply for hc

Required parameters summary:

• U0_value: Internal Energy of the reaction at 0 kelvin at standard pressure [Joule/mol]
• s_c: stoichiometric number, positive for products and negative for reactants
• P: pressure [bar]
• m: molecular mass [dalton]
• B: rotational constant [cm-1]
• o: symmetry number of the compound (The symmetry number of a molecule is the order of the finite rotational sub-group of the point group of the molecule.)
• linear: the molecule is linear ('True'), not linear ('False'), or an atom ('Atom')
• n_mod: list of the vibrational mode frequencies [cm-1]
• n_deg: list of the vibrational mode degeneracies
• gn_list_elec: list of electron levels degeneracies
• En: list of electron level Energies [cm-1]
• spin_list: list of the nuclear spins
• A: other eventual rotational constant [cm-1]
• C: other eventual rotational constant [cm-1]
• T: temperature [Kelvin]

Usage in the python interpreter:

Import the functions:
from stat_thermo import *

Initialize a dictionary with the value of the Internal Energy at 0 Kelvin (U0_value), by typing

data["U0"]= U0_value

Initialize a new compound (compound_name) and set the stoichiometric number:

data["compound_name"]=dict()
data["compound_name"]["s_c"]= stechometric number

Start setting the parameters for each reactant and product. Do not change the keyword 'param'. Use this order:

data['compound_name']["param"]= [P, m, B, o, linear (True, False or 'Atom'), n_mod, n_deg, gn_list_elec, En, spin_list, A, C]

Functions

Low-level functions:

• Partition functions:
  • qt(T, P, m)
  • qro(T, B, linear, o, A=0, C=0)
  • qv(T, n_mod, n_deg)
  • qe(T, gn_list_elec, En)
  • qn(spin_list)
  • Q(name, T, P, m, B, o, linear, n_mod, n_deg, gn_list_elec, En, spin_list, A=0, C=0)
• Internal Energy:
  • Ut(T)
  • Ur(T, linear)
  • Uv(T, n_mod, n_deg)
  • Ue(T, qe, gn_list_elec, En)
  • U(compound_name, T, n_mod, n_deg, linear, qe, gn_list_elec, En)
• Entropy:
  • St(qt)
  • S(T, q, U)
  • S_calc(compound_name, T)

Easy-to-use functions:

• Q_fast(compound_name, T)
• U_fast(name, T)
• S_fast(name, T)
• k_fast(T)

Plotting the state functions:

• plot(Ti, Tf, step, save=False)

Print the results on screen:

• visual()

Save the results:

• save(filename='stat_thermo_results')

Example:

Decomposition of formaldehyde into carbon monoxide and dihydrogen:

1 H2CO ⇌ 1 H2 + 1 CO

# import the functions

from stat_thermo import *

# set up the initial parameters

data["U0"]= -1700
data["H2"]=dict()
data["H2"]["s_c"]= 1
data['H2']['param']=[1, 2.01588, 60.89, 2, True,[4280], [1], [1], [0], [1/2, 1/2], 0, 0]
data["CO"]=dict()
data["CO"]["s_c"]= 1
data["CO"]["param"]=[1, 28.0140, 1.930, 1, True, [2156], [1], [1], [0], [0, 0], 0, 0]
data["H2CO"]=dict()
data["H2CO"]["s_c"]= -1
data["H2CO"]["param"]=[1, 30.02628, 9.405, 2, False, [2843, 2766, 1746, 1501, 1247, 1164],[1,1,1,1,1,1], [1], [0], [1/2, 1/2, 0, 0], 1.295, 1.134 ]

# Calculate the results

Q_fast("H2",300) #calculate all q for H2
data["H2"][300]["qt"] #to see the values of qt
U_fast("H2",300)
S_fast("H2",300)
k_fast(300)
k_fast(100)
visual()
plot(100,300,20, save= "example")
visual()
save("reaction_data")

Help

In the python interpreter type:

import stat_thermo
help(stat_thermo)