isotope: Isotopic masses and relative abundances.

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Dependencies base (>=4.7 && <5), containers (==0.5.*), megaparsec (==4.*), template-haskell, th-lift [details]
License GPL-3.0-only
Copyright 2015 Michael Thomas
Author Michael Thomas
Category Chemistry
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Uploaded by Michaelt293 at 2016-08-28T02:09:04Z
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Isotope is a chemistry library for calculating masses of elements and molecules. The main focus of the Isotope library is mass spectrometry, an area where the masses and relative abundances of isotopes and isotopologues is of central importance.


The Isotope library designed with type safety and flexibility in mind. Key features will be described below.

Isotopic, integer, monoisotopic, nominal and average masses

In mass spectrometry and general chemistry, there are several different ways in which to describe mass. This can lead to some confusion since more than one term can exist to describe the same unit of measurement. In the Isotope library, the following conventions are used:

Mass | Description --- | --- Isotopic mass | The mass of an isotope for an element. Integer mass | The mass of an isotope rounded to the nearest integer value. Monoisotopic mass | The mass of the most abundant isotope for an element or the sum of the masses of the most abundant isotope of each element for a molecule. Nominal mass | The integer mass of the most abundant isotope for an element or the sum of integer masses of the most abundant isotope of each element for a molecule. Average mass | The average mass of an element or molecule based on naturally-occurring abundances. In the isotopes library, average mass is used in place of atomic mass and molecular mass.

For more detailed discussion regarding the concept of mass in mass spectrometry, please refer to "Molecular Weight and the Nominal Mass, Monoisotopic Mass and Average Molar Mass" by Prof. O. David Sparkman [1].

Element symbols

In Isotope, element symbols are represented by the enumeration type, ElementSymbol, i.e. data ElementSymbol = H | He | Li | Be ...... This is advantageous over the use of strings to represent element symbols (i.e. type ElementSymbol = String) since it increases type safety. Moreover, values of type ElementSymbol can be used as keys within maps as an intuitive way to map elements to their properties. Isotope presently contains information on the isotopic masses and relative abundances for all elements from Hydrogen to Bismuth and Thorium and Uranium.

Molecular, condensed and empirical formulae

In the Isotope library, a distinction between molecular, condensed and empirical formulae is made. Molecular formulae contain the total number of atoms for each element of a molecule while condensed formulae give information on the connectivity of atoms within molecules. For example, the molecule trimethylamine has a molecular formula of C3H9N and a condensed formula of N(CH3)3. Here the molecular formula indicates trimethyelamine has a total of 3 carbon atoms, 9 hydrogen atoms and 1 nitrogen whereas the condensed formula indicates trimethylamine has 3 methyl groups bonded to a central nitrogen. Conversely, an empirical formula is the simplest integer ratio for the atoms of a compound. For example, the molecular formula of benzene is C6H6 whereas the empirical formula of benzene is simply CH.

Molecular, condensed and empirical formula QuasiQuoters

The QuasiQuoters, mol, con and emp, are provided for MolecularFormula, CondensedFormula and EmpiricalFormula data types, respectively. Therefore, shorthand notation can be used when working with molecular, condensed and empirical formulae. The use of molecular, condensed and empirical formulae QuasiQuoters requires the use of the QuasiQuotes language extension (:set -XQuasiQuotes can be added to the .ghci file when working in GHCi).

GHCi> [mol|CH4|]
MolecularFormula {getMolecularFormula = fromList [(H,4),(C,1)]}

Importantly, errors in formulae will be detected at compile-time and give informative error messages! (Note the example below is from a GHCi session.)

GHCi> [mol|Ch4|]

    Could not parse formula: 1:2:
unexpected 'h'
expecting "Ag", "Al", "Ar", "As", "Au", "Ba", "Be", "Bi", "Br", "Ca", "Cd", "Ce", "Cl", "Co", "Cr", "Cs", "Cu", "Dy", "Er", "Eu", "Fe", "Ga", "Gd", "Ge", "He", "Hf", "Hg", "Ho", "In", "Ir", "Kr", "La", "Li", "Lu", "Mg", "Mn", "Mo", "Na", "Nb", "Nd", "Ne", "Ni", "Os", "Pa", "Pb", "Pd", "Pm", "Pr", "Pt", "Rb", "Re", "Rh", "Ru", "Sb", "Sc", "Se", "Si", "Sm", "Sn", "Sr", "Ta", "Tb", "Tc", "Te", "Th", "Ti", "Tl", "Tm", "Xe", "Yb", "Zn", "Zr", '(', 'B', 'C', 'F', 'H', 'I', 'K', 'N', 'O', 'P', 'S', 'U', 'V', 'W', 'Y', or end of input

Conversion between CondensedFormula, MolecularFormula and EmpiricalFormula data types

A condensed formula can be converted to a molecular or empirical formula and a molecular formula can be converted to an empirical formula. In Isotope, this functionality is provided by two type classes, ToMolecularFormula and ToEmpiricalFormula, which contain the methods, toMolecularFormula and toEmpiricalFormula, respectively.

GHCi> let butane = [con|CH3(CH2)2CH3|]
GHCi> toMolecularFormula butane
MolecularFormula {getMolecularFormula = fromList [(H,10),(C,4)]}
GHCi> toEmpiricalFormula butane
EmpiricalFormula {getEmpiricalFormula = fromList [(H,5),(C,2)]}

When using condensed, molecular or empirical formula QuasiQuoters, it is possible to this implicitly. For example, the QuasiQuoter emp could be applied to the condensed formula "CH3(CH2)2CH3" used above to yield a value of type EmpiricalFormula.

GHCi> [emp|CH3(CH2)2CH3|]
EmpiricalFormula {getEmpiricalFormula = fromList [(H,5),(C,2)]}

Operators for working with molecular formulae

The Isotope library comes with three operators for working with molecular formulae; |+|, |-| and |*|. These operators have the same fixity and associativity as +, - and *, respectively. This allows us to the |+|, |-| and |*| operators in an intuitive manner (i.e., like basic arithmetic). For example, we could define the molecule formula of propane in terms of its building blocks; that is, 2 methyl groups and 1 methylene group.

GHCi> let methyl = [mol|CH3|]
GHCi> let methylene = [mol|CH2|]
GHCi> let propane = 2 |*| methyl |+| methylene
GHCi> propane
MolecularFormula {getMolecularFormula = fromList [(H,8),(C,3)]}

We could then go one step further and define propene to be propane minus molecular hydrogen.

GHCi> let propene = propane |-| [mol|H2|]
GHCi> propene
MolecularFormula {getMolecularFormula = fromList [(H,6),(C,3)]}

ChemicalMass type class

The ChemicalMass type class has four methods; toElementalComposition, monoisotopicMass, nominalMass and averageMass, where toElementalComposition is the minimal complete definition. ElementSymbol, EmpiricalFormula, MolecularFormula and CondensedFormula are instances of ChemicalMass. This provides a uniform approach to working with elements, empirical formulae, molecular formulae and condensed formulae.

GHCi> nominalMass C
GHCi> averageMass [mol|CH4|]
GHCi> monoisotopicMass [mol|N(CH3)3|]

Additional functions accepting an ElementSymbol as input

Isotope also provides a range of addition functions which accepts an ElementSymbol as input. For example, to get the masses of all isotopes for titanium, we simply have to pass the element symbol Ti to the function isotopicMasses.

GHCi> isotopicMasses Ti

Comparison to other chemistry libraries

In addition to Isotope, there are two other open-source chemistry libraries written in Haskell; Radium [2] and Ouch [3].


Radium is a Haskell library written by klangner and has been uploaded to Hackage [3]. Radium is also under active development with the last commit occurring 15 hours before the time of writing (27/03/16). In comparison to Isotope, the main difference is that Radium does not provide information on the masses and relative abundances of elemental isotopes. Consequently, Radium could not be used for calculating the monoisotopic masses of molecules and ions. Conversely, Radium provides information on electron negativities, ionisation energies and electron configurations and support for SMILES strings which are not provided by Isotope.


Ouch is a chemistry informatics toolkit written in Haskell by Orion Jankowski (Note: Ouch is not on Hackage). Unfortunately, Ouch is no longer under active development with the last commit occurring three years ago. Similar to Radium, Ouch does not provide information on the masses and relative abundances of elemental isotopes making it unsuitable for mass spectrometry. On the otherhand, Ouch provides support for SMILES strings and molecular structure. More information on Ouch can be found on Orion Jankowski's blog [4].

Future directions

Isotopic profiles currently cannot be calculated for molecular formulae. This is a major limitation since isotopic profiles are important in mass spectrometry. Therefore, this functionality should be added to Isotope in a future version. Since calculating isotopic profiles is computationally expensive, this feature could be introduced using Rust if performance is an issue using pure Haskell code. (Rust is a modern systems programming language with a strong type system and memory safety [6].)

To increase compile-time checks, refinement types could be introduced using LiquidHaskell [7]. For example, not all elements have naturally-occurring isotopes and such elements therefore do not have an average mass. Using LiquidHaskell, the function averageMass could be refined to only accept elements with naturally-occurring isotopes. If such a direction is taken, two separate libraries may be maintained; one using LiquidHaskell and the other using only conventional Haskell code.


Please report bugs and feature suggestions using the issue tracker. Pull requests are welcome and will be merged provided they improve Isotope. Suggestions or questions about Isotope can also be directed towards the Gitter room.


The Isotope library is authored and maintained by Michael Thomas. Isotope logo was designed by Ben Jerrems.


Copyright © 2015–2016 Michael Thomas