ChemPy

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.. contents::

About ChemPy

ChemPy is a Python <https://www.python.org>_ package useful for chemistry (mainly physical/inorganic/analytical chemistry). Currently it includes:

• Numerical integration routines for chemical kinetics (ODE solver front-end)

• Integrated rate expressions (and convenience fitting routines)

• Solver for equilibria (including multiphase systems)

• Relations in physical chemistry:

  • Debye-Hückel expressions
  • Arrhenius & Eyring equation
  • Einstein-Smoluchowski equation

• Properties (pure python implementations from the literature)

  • water density <https://github.com/bjodah/chempy/blob/master/chempy/properties/water_density_tanaka_2001.py>_ as function of temperature
  • water permittivity <https://github.com/bjodah/chempy/blob/master/chempy/properties/water_permittivity_bradley_pitzer_1979.py>_ as function of temperature and pressure
  • water diffusivity <https://github.com/bjodah/chempy/blob/master/chempy/properties/water_diffusivity_holz_2000.py>_ as function of temperature
  • water viscosity <https://github.com/bjodah/chempy/blob/master/chempy/properties/water_viscosity_korson_1969.py>_ as function of temperature
  • sulfuric acid density <https://github.com/bjodah/chempy/blob/master/chempy/properties/sulfuric_acid_density_myhre_1998.py>_ as function of temperature & weight fraction H₂SO₄
  • More <https://github.com/bjodah/chempy/tree/master/chempy/properties>_ to come... (and contributions are most welcome!)

Documentation

The easiest way to get started is to have a look at the examples in this README, and also the jupyter notebooks_. In addition there is auto-generated API documentation for the latest stable release here <https://bjodah.github.io/chempy/latest>_.

.. _notebooks: https://github.com/bjodah/chempy/tree/master/examples

Installation

Simplest way to install ChemPy and its (optional) dependencies is to use the conda package manager <https://conda.pydata.org/docs/>_::

$ conda install -c conda-forge chempy pytest $ pytest -rs -W ignore::chempy.ChemPyDeprecationWarning --pyargs chempy

currently conda packages are only provided for Linux. On Windows and OS X you will need to use pip instead::

$ python3 -m pip install chempy pytest $ python3 -m pytest -rs -W ignore::chempy.ChemPyDeprecationWarning --pyargs chempy

there will a few tests which will be skipped due to some missing optional backends in addition to those in SciPy (used for solving systems of non-linear equations and ordinary differential equations).

Optional dependencies

If you used ``conda`` to install ChemPy you can skip this section.
But if you use ``pip`` the default installation is achieved by writing::

   $ python3 -m pip install --user --upgrade chempy pytest
   $ python3 -m pytest -rs --pyargs chempy

you can skip the ``--user`` flag if you have got root permissions.
You may be interested in using additional backends (in addition to those provided by SciPy)
for solving ODE-systems and non-linear optimization problems::

   $ python3 -m pip install chempy[all]

Note that this option will install the following libraries
(some of which require additional libraries to be present on your system):

- `pygslodeiv2 <https://github.com/bjodah/pygslodeiv2>`_: solving initial value problems, requires GSL_. (>=1.16).
- `pyodeint <https://github.com/bjodah/pyodeint>`_: solving initial value problems, requires boost_ (>=1.65.0).
- `pycvodes <https://github.com/bjodah/pycvodes>`_: solving initial value problems, requires SUNDIALS_ (>=5.3.0).
- `pykinsol <https://github.com/bjodah/pykinsol>`_: solving non-linear root-finding, requires SUNDIALS_ (>=5.3.0).
- `pycompilation <https://github.com/bjodah/pycompilation>`_: python front-end for calling compilers, requires gcc/clang/icpc.
- `pycodeexport <https://github.com/bjodah/pycodeexport>`_: package for code-generation, used when generating C++ code.

.. _GSL: https://www.gnu.org/software/gsl/
.. _boost: http://www.boost.org/
.. _SUNDIALS: https://computation.llnl.gov/projects/sundials

if you want to see what packages need to be installed on a Debian based system you may look at this
`Dockerfile <scripts/environment/Dockerfile>`_.

Using Docker
~~~~~~~~~~~~
If you have `Docker <https://www.docker.com>`_ installed, you may use it to host a jupyter
notebook server::

  $ ./scripts/host-jupyter-using-docker.sh . 8888

the first time you run the command, some dependencies will be downloaded. When the installation
is complete there will be a link visible which you can open in your browser. You can also run
the test suite using the same docker-image::

  $ ./scripts/host-jupyter-using-docker.sh . 0

there will be a few skipped test (due to some dependencies not being installed by default) and
quite a few warnings.


Examples
--------
See demonstration scripts in `examples/ <https://github.com/bjodah/chempy/tree/master/examples>`_,
and some rendered jupyter notebooks_.
You may also browse the documentation for more examples. Below you will find a few code snippets:

Parsing formulae
~~~~~~~~~~~~~~~~
.. code:: python

   >>> from chempy import Substance
   >>> ferricyanide = Substance.from_formula('Fe(CN)6-3')
   >>> ferricyanide.composition == {0: -3, 26: 1, 6: 6, 7: 6}  # 0 for charge
   True
   >>> print(ferricyanide.unicode_name)
   Fe(CN)₆³⁻
   >>> print(ferricyanide.latex_name + ", " + ferricyanide.html_name)
   Fe(CN)_{6}^{3-}, Fe(CN)<sub>6</sub><sup>3-</sup>
   >>> print('%.3f' % ferricyanide.mass)
   211.955


as you see, in composition, the atomic numbers (and 0 for charge) is used as
keys and the count of each kind became respective value.

Balancing stoichiometry of a chemical reaction

.. code:: python

from chempy import balance_stoichiometry # Main reaction in NASA's booster rockets: reac, prod = balance_stoichiometry({'NH4ClO4', 'Al'}, {'Al2O3', 'HCl', 'H2O', 'N2'}) from pprint import pprint pprint(dict(reac)) {'Al': 10, 'NH4ClO4': 6} pprint(dict(prod)) {'Al2O3': 5, 'H2O': 9, 'HCl': 6, 'N2': 3} from chempy import mass_fractions for fractions in map(mass_fractions, [reac, prod]): ... pprint({k: '{0:.3g} wt%'.format(v*100) for k, v in fractions.items()}) ... {'Al': '27.7 wt%', 'NH4ClO4': '72.3 wt%'} {'Al2O3': '52.3 wt%', 'H2O': '16.6 wt%', 'HCl': '22.4 wt%', 'N2': '8.62 wt%'}

ChemPy can also balance reactions where the reacting species are more complex and are better described in other terms than their molecular formula. A silly, yet illustrative example would be how to make pancakes without any partially used packages:

.. code:: python

substances = {s.name: s for s in [ ... Substance('pancake', composition=dict(eggs=1, spoons_of_flour=2, cups_of_milk=1)), ... Substance('eggs_6pack', composition=dict(eggs=6)), ... Substance('milk_carton', composition=dict(cups_of_milk=4)), ... Substance('flour_bag', composition=dict(spoons_of_flour=60)) ... ]} pprint([dict(_) for _ in balance_stoichiometry({'eggs_6pack', 'milk_carton', 'flour_bag'}, ... {'pancake'}, substances=substances)]) [{'eggs_6pack': 10, 'flour_bag': 2, 'milk_carton': 15}, {'pancake': 60}]

ChemPy can even handle reactions with linear dependencies (underdetermined systems), e.g.:

.. code:: python

pprint([dict(_) for _ in balance_stoichiometry({'C', 'O2'}, {'CO2', 'CO'})]) # doctest: +SKIP [{'C': x1 + 2, 'O2': x1 + 1}, {'CO': 2, 'CO2': x1}]

the x1 object above is an instance of SymPy's Symbol_. If we prefer to get a solution with minimal (non-zero) integer coefficients we can pass underdetermined=None:

.. code:: python

pprint([dict(_) for _ in balance_stoichiometry({'C', 'O2'}, {'CO2', 'CO'}, underdetermined=None)]) [{'C': 3, 'O2': 2}, {'CO': 2, 'CO2': 1}]

note however that even though this solution is in some sense "canonical", it is merely one of an infinite number of solutions (x1 from earlier may be any integer).

.. _Symbol: http://docs.sympy.org/latest/modules/core.html#sympy.core.symbol.Symbol

Balancing reactions

.. code:: python

   >>> from chempy import Equilibrium
   >>> from sympy import symbols
   >>> K1, K2, Kw = symbols('K1 K2 Kw')
   >>> e1 = Equilibrium({'MnO4-': 1, 'H+': 8, 'e-': 5}, {'Mn+2': 1, 'H2O': 4}, K1)
   >>> e2 = Equilibrium({'O2': 1, 'H2O': 2, 'e-': 4}, {'OH-': 4}, K2)
   >>> coeff = Equilibrium.eliminate([e1, e2], 'e-')
   >>> coeff
   [4, -5]
   >>> redox = e1*coeff[0] + e2*coeff[1]
   >>> print(redox)
   32 H+ + 4 MnO4- + 20 OH- = 26 H2O + 4 Mn+2 + 5 O2; K1**4/K2**5
   >>> autoprot = Equilibrium({'H2O': 1}, {'H+': 1, 'OH-': 1}, Kw)
   >>> n = redox.cancel(autoprot)
   >>> n
   20
   >>> redox2 = redox + n*autoprot
   >>> print(redox2)
   12 H+ + 4 MnO4- = 6 H2O + 4 Mn+2 + 5 O2; K1**4*Kw**20/K2**5

Working with units
~~~~~~~~~~~~~~~~~~
Functions and objects useful
for working with units are available from the ``chempy.units`` module. Here is an
example of how ChemPy can check consistency of units:

.. code:: python

   >>> from chempy import Reaction
   >>> r = Reaction.from_string("H2O -> H+ + OH-; 1e-4/M/s")
   Traceback (most recent call last):
   ...
   ValueError: Unable to convert between units of "1/M" and "dimensionless"
   >>> r = Reaction.from_string("H2O -> H+ + OH-; 1e-4/s")
   >>> from chempy.units import to_unitless, default_units as u
   >>> to_unitless(r.param, 1/u.minute)
   0.006

right now the ``.units`` module wraps the quantities_ package with some minor
additions and work-arounds. However, there is no guarantee that the underlying
package will not change in a future version of ChemPy (there are many packages
for dealing with units in the scientific Python ecosystem).

.. _quantities: http://python-quantities.readthedocs.io/en/latest/


Chemical equilibria

If we want to predict pH of a bicarbonate solution we simply just need pKa and pKw values:

.. code:: python

from collections import defaultdict from chempy.equilibria import EqSystem eqsys = EqSystem.from_string("""HCO3- = H+ + CO3-2; 10**-10.3 ... H2CO3 = H+ + HCO3-; 10**-6.3 ... H2O = H+ + OH-; 10**-14/55.4 ... """) # pKa1(H2CO3) = 6.3 (implicitly incl. CO2(aq)), pKa2=10.3 & pKw=14 arr, info, sane = eqsys.root(defaultdict(float, {'H2O': 55.4, 'HCO3-': 1e-2})) conc = dict(zip(eqsys.substances, arr)) from math import log10 print("pH: %.2f" % -log10(conc['H+'])) pH: 8.30

here is another example for ammonia:

.. code:: python

from chempy import Equilibrium from chempy.chemistry import Species water_autop = Equilibrium({'H2O'}, {'H+', 'OH-'}, 10**-14) # unit "molar" assumed ammonia_prot = Equilibrium({'NH4+'}, {'NH3', 'H+'}, 10**-9.24) # same here substances = [Species.from_formula(f) for f in 'H2O OH- H+ NH3 NH4+'.split()] eqsys = EqSystem([water_autop, ammonia_prot], substances) print('\n'.join(map(str, eqsys.rxns))) # "rxns" short for "reactions" H2O = H+ + OH-; 1e-14 NH4+ = H+ + NH3; 5.75e-10 init_conc = defaultdict(float, {'H2O': 1, 'NH3': 0.1}) x, sol, sane = eqsys.root(init_conc) assert sol['success'] and sane print(', '.join('%.2g' % v for v in x)) 1, 0.0013, 7.6e-12, 0.099, 0.0013

Concepts

ChemPy collects equations and utility functions for working with
concepts such as `ionic strength <https://en.wikipedia.org/wiki/Ionic_strength>`_:

.. code:: python

   >>> from chempy.electrolytes import ionic_strength
   >>> ionic_strength({'Fe+3': 0.050, 'ClO4-': 0.150}) == .3
   True

note how ChemPy parsed the charges from the names of the substances. There are
also e.g. empirical equations and convenience classes for them available, e.g.:

.. code:: python

   >>> from chempy.henry import Henry
   >>> kH_O2 = Henry(1.2e-3, 1800, ref='carpenter_1966')
   >>> print('%.1e' % kH_O2(298.15))
   1.2e-03

to get more information about e.g. this class, you may can look at the `API documentation`_.

.. _API documentation: https://bjodah.github.io/chempy/latest/chempy.html#module-chempy.henry


Chemical kinetics (system of ordinary differential equations)

A common task when modelling problems in chemistry is to investigate the time dependence of a system. This branch of study is known as chemical kinetics <https://en.wikipedia.org/wiki/Chemical_kinetics>_, and ChemPy has some classes and functions for working with such problems:

.. code:: python

from chempy import ReactionSystem # The rate constants below are arbitrary rsys = ReactionSystem.from_string("""2 Fe+2 + H2O2 -> 2 Fe+3 + 2 OH-; 42 ... 2 Fe+3 + H2O2 -> 2 Fe+2 + O2 + 2 H+; 17 ... H+ + OH- -> H2O; 1e10 ... H2O -> H+ + OH-; 1e-4""") # "[H2O]" = 1.0 (actually 55.4 at RT) from chempy.kinetics.ode import get_odesys odesys, extra = get_odesys(rsys) from collections import defaultdict import numpy as np tout = sorted(np.concatenate((np.linspace(0, 23), np.logspace(-8, 1)))) c0 = defaultdict(float, {'Fe+2': 0.05, 'H2O2': 0.1, 'H2O': 1.0, 'H+': 1e-2, 'OH-': 1e-12}) result = odesys.integrate(tout, c0, atol=1e-12, rtol=1e-14) import matplotlib.pyplot as plt fig, axes = plt.subplots(1, 2, figsize=(12, 5)) for ax in axes: ... _ = result.plot(names=[k for k in rsys.substances if k != 'H2O'], ax=ax) ... _ = ax.legend(loc='best', prop={'size': 9}) ... _ = ax.set_xlabel('Time') ... _ = ax.set_ylabel('Concentration') _ = axes[1].set_ylim([1e-13, 1e-1]) _ = axes[1].set_xscale('log') _ = axes[1].set_yscale('log') _ = fig.tight_layout() _ = fig.savefig('examples/kinetics.png', dpi=72)

.. image:: https://raw.githubusercontent.com/bjodah/chempy/master/examples/kinetics.png

Properties

One of the fundamental tasks in science is the careful collection of data about the world
around us. ChemPy contains a growing collection of parametrizations from the scientific
literature with relevance in chemistry. Here is how you use one of these formulations:

.. code:: python

   >>> from chempy import Substance
   >>> from chempy.properties.water_density_tanaka_2001 import water_density as rho
   >>> from chempy.units import to_unitless, default_units as u
   >>> water = Substance.from_formula('H2O')
   >>> for T_C in (15, 25, 35):
   ...     concentration_H2O = rho(T=(273.15 + T_C)*u.kelvin, units=u)/water.molar_mass(units=u)
   ...     print('[H2O] = %.2f M (at %d °C)' % (to_unitless(concentration_H2O, u.molar), T_C))
   ...
   [H2O] = 55.46 M (at 15 °C)
   [H2O] = 55.35 M (at 25 °C)
   [H2O] = 55.18 M (at 35 °C)


Run notebooks using binder

Using only a web-browser (and an internet connection) it is possible to explore the notebooks here: (by the courtesy of the people behind mybinder)

.. image:: http://mybinder.org/badge.svg :target: https://mybinder.org/v2/gh/bjodah/chempy/f5f2546e79e165ba8fb258fc87d83a7fbdcbad64?filepath=index.ipynb :alt: Binder

Citing

If you make use of ChemPy in e.g. academic work you may cite the following peer-reviewed publication:

.. image:: http://joss.theoj.org/papers/10.21105/joss.00565/status.svg :target: https://doi.org/10.21105/joss.00565 :alt: Journal of Open Source Software DOI

Depending on what underlying solver you are using you should also cite the appropriate paper (you can look at the list of references in the JOSS article). If you need to reference, in addition to the paper, a specific point version of ChemPy (for e.g. reproducibility) you can get per-version DOIs from the zendodo archive:

.. image:: https://zenodo.org/badge/8840/bjodah/chempy.svg :target: https://zenodo.org/badge/latestdoi/8840/bjodah/chempy :alt: Zenodo DOI

Licensing

The source code is Open Source and is released under the very permissive "simplified (2-clause) BSD license" <https://opensource.org/licenses/BSD-2-Clause>. See LICENSE <LICENSE> for further details.

See also

• SymPy <https://github.com/sympy/sympy>_
• pyneqsys <https://github.com/bjodah/pyneqsys>_
• pyodesys <https://github.com/bjodah/pyodesys>_
• thermo <https://github.com/CalebBell/thermo>_

Contributing

Contributors are welcome to suggest improvements at https://github.com/bjodah/chempy (see further details here <CONTRIBUTING.rst>_).

Author

Björn I. Dahlgren, contact:

• gmail address: bjodah