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Chemistry Toy BoxDr. Charles R. Denham, U.S. Geological Survey, Woods Hole, MA 02543Send suggestions and comments to cdenham@usgs.gov

Motivation

We present a simple chemical algebra, implemented with some of the object-oriented features ofMatlab-5. The main idea is to use the Periodic Table of the Elements to construct atoms fromfermions (protons, electrons, and neutrons), and then to combine those atoms into compounds. SeveralMatlab operators are overloaded, in order to explore algebraic notation in elementary chemistry.

Elements

The "elements.m" function returns a "cell" or "struct" of the elements through #107, containing atomicsymbol, number, weight, and common valences, one row per element. Because of a notational conflictbetween the Nitrogen +1 ion and Neptunium, the latter is given the symbol "Npt". Symbols for the"unnamed" elements (#104-107) are given in uppercase.

Fermions

Classes known as "proton", "electron" and "neutron" are available for the assembly atoms. Forexample, helium can be constructed as:

helium4 = 2*proton + 2*electron + 2*neutron helium3 = helium4 - neutron

The meaning of "2*proton" here is "two protons", not one proton with a super-charge of 2.

Atoms

The "atom" constructor accepts several arguments, starting with the atomic symbol. Alternatively, onecan add components to an "empty-atom" to construct an atom of any atomic symbol, number, weight,and valence. Thus, for common helium:

He = atom('He', 2, 2, 2) He = atom('He') + 2*proton + 2*electron + 2*neutron He = atom + 'He' + 2*proton + 2*electron + 2*neutron

The "atoms.m" function creates neutral atoms, using the Periodic Table available from the

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"elements.m" function. By default, the atoms are placed in the caller's workspace, named by theiratomic symbol. If an output argument is given, a "struct" is returned, whose fieldnames are the atomicsymbols. Common ions can be returned as well, depending on the calling syntax.

The "atom" class can be interrogated with several methods: atomic "symbol", "number", "weight",and "valence".

Valence

Valence can be imposed on an atom in several ways. To derive bivalent (ferrous) iron from iron, useany of the following:

Fepp = Fe - 2*electron Fepp = Fe(+2) Fepp = Fe + 2

Our notation gives names to ions according to their valence, using "p" for "plus" and "m" for "minus".Only one conflict exists in the Periodic Table: Np could be +1 valence Nitrogen or neutral Neptunium.We have given Neptunium the symbol Npt to resolve the problem.

Note how the Matlab arithmetic operators are overloaded here to accomodate the fact that our objectsare chemical entities, not numbers.

Compounds

Compounds can be assembled from atoms, typically ions, using the "+" operator:

water = 2*(H+1) + (O-2) common_table_salt = (Na+1) + (Cl-1) ammonia_ion = (N-3) + 4*(H+1)

Compounds are automatically created whenever an atom or compound is added to another atom orcompound. Some common compounds are constructed in this fashion and placed in the caller'sworkspace by the "compounds.m" script.

Overloaded Operators

The "+", "-", "*", and "()" operators have been overloaded in "chem", for the purpose of assemblingcomponents and setting valence. These are handled by the "plus", "minus", "mtimes", and "subsref"methods.

fermion = {proton | electron | neutron} fermions = fermion * count % Default count = 1.

atom = 'symbol' + fermions atom = atom {+ | -} fermions atoms = atom * count

ion = atom {+ | -} electron ion = atom {+ | -} valence ion = atom({+ | -} valence) ions = ion * count

compound = {atoms | ions | compounds} + {atoms | ions | compounds} compounds = compound * count

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Any of the Matlab symbolic operators can be overloaded easily, so the syntax of "chem" is not limitedto the above.

The most difficult methods to overload are "subsref" for interpreting indices on the right-hand side of anassignment; "subsasgn" on the left; and "subsindex", to return a value for an object when it is used asan index. The first two methods process ".", "()", and "{}", which typically refer to parts of a "struct", a"double-precision array", and a "cell", respectively. When overloaded, these and other Matlab operatorscan be given whatever meaning the programmer desires.

Future Work

Whether the "Chemistry Toy Box" should be extended depends on the utility of simple algebraicnotation for the representation of meaningful chemistry.

How can chemical expressions be represented for mass and equilibrium balancing? Example: theseawater bicarbonate system.Do we need a "system" object that would incorporate pressure, temperature, and solvent? Itwould seem essential for equilibrium work.Is there an existing, intuitive, "tty" notation for chemical formulas?Is there an analog in nuclear chemistry?Should "2*H" differ from "H*2", the former for concentration and the latter for structure?Organic compounds?Isomers?

Software

Here is chem_install.p for Matlab 5.2/5.3, an installer in the form of a Matlab P-code function. ForMatlab 5.0/5.1, get chem_install.p50, then delete "50" from its name. Execute "chem_install" at theMatlab prompt to unbundle the software into a new or existing local folder called "chem". Then, add"chem" to your Matlab path, restart Matlab, and execute "chem_test".

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