An Ontology of the Periodic Table Using electronic structure of the atom

I’ve been doing an experiment on inferring the groups of the periodic table from their physicochemical properties. It is hard and only sort of works.

Mendeleev’s Periodic Table also reflects the electronic structure of the atom that was revealed decades after the first version of the Periodic table was published. The light metals of the alkaline earths and alkali metals correspond to atoms with valence electrons in the S-shell; the transition metals are those with valence electrons in the D-shell and the non-metals have valence electrons in the P-shell.

It is much easier, of course, to define classes representing the groups of the Periodic Table using electronic structure. For example, a definition of an alkali metal atom is:

Class: AlkaliMetalAtom

    EquivalentTo: [in atoms]
        * AlkaliMetalAtom,
        Atom
         and (hasValenceElectronShell some
            (SShell
             and (contains exactly 1 Electron)
             and (hasOrder some integer[>= 2])))
         and (hasValenceElectronShell only
            (SShell
             and (contains exactly 1 Electron)
             and (hasOrder some integer[>= 2])))

Here I’ve said that any atom that has a valence shell that is an S-shell and that this electron shell contains exactly one elecgtron is to be recognised as an alkali earth atom. Note that I’ve put in a grubby fix to deal with the first S-shell. We nubmer electron shells; S1, S2, S3, S4, and so on are the S-shells that occur each time we start a new period. The first S-shell gives us hydrogen and helium; neither of which count as alkali metals or alkaline earths. So, I’ve put an index number on the shell. Each instance of S-shell doesn’t have an index. Also note that my modelling of valence shell is bad; I’ve done the usual thing of conflating a class into a property. I should really have something on the shell indicating that its role ifs valence or that it is outer rather than inner. However, I did it a quick and grubby way.

I’ve also put an atomic number on each atom class, and this is, of course, not “real”.the atomic number may correspond to the number of protons, but atomic numbers don’t exist. If anything, they are second order things; they belong to the class and not to the individuals themselves.

Anyway, that axiomisation all basically works. Here are a few more examples:

Class: HalogenAtom

    EquivalentTo: [in atoms]
        * HalogenAtom,
        Atom
         and (hasValenceElectronShell some
            (PShell
             and (contains exactly 5 Electron)))

for the noble, or inert, gases below, note the use of the index on shell to incorporate helium into the group:

Class: NobleGasAtom

    EquivalentTo: [in atoms]
        * NobleGasAtom,
        Atom
         and ((hasValenceElectronShell some
            (PShell
             and (contains exactly 6 Electron)))
         or (hasValenceElectronShell some
            (SShell
             and (contains exactly 2 Electron)
             and (hasOrder value 1))))

For some of the groups or families within the transition elements the story becomes slightly more complex. take as an example the nikel family:

Class: NickelFamilyAtom

    EquivalentTo: [in atoms]
        * NickelFamilyAtom,
        (Atom
         and (hasValenceElectronShell some
            (DShell
             and (contains exactly 8 Electron)))
         and (hasValenceElectronShell some
            (SShell
             and (contains exactly 2 Electron)))
         and (hasValenceElectronShell only
            (DShell
             or FShell
             or SShell)))
         or (Atom
         and (hasValenceElectronShell some
            (DShell
             and (contains exactly 9 Electron)))
         and (hasValenceElectronShell some
            (SShell
             and (contains exactly 1 Electron)))
         and (hasValenceElectronShell only
            (DShell
             or FShell
             or SShell)))
         or ((hasValenceElectronShell some
            (DShell
             and (contains exactly 10 Electron)))
         and (hasValenceElectronShell only
            (DShell
             and (contains exactly 10 Electron))))

Elements in this family have 8 electrons in the D-shell and 2 electrons in their outermost S-shell. Platinum atoms, however, have 9 electrons in their outermost D-shell and 1 in their outermost S-shell. an alternative modelling style would allow me to “add up” electrons and avoid this clumsiness.

Class: PlatinumAtom

    SubClassOf: [in atoms]
        * NickelFamilyAtom,
        Atom
         and (hasValenceElectronShell some
            (DShell
             and (contains exactly 9 Electron)
             and (hasOrder value 5)))
         and (hasValenceElectronShell some
            (FShell
             and (contains exactly 14 Electron)
             and (hasOrder value 4)))
         and (hasValenceElectronShell some
            (SShell
             and (contains exactly 1 Electron)
             and (hasOrder value 6)))
         and (hasValenceElectronShell only
            ((DShell
             and (contains exactly 9 Electron)
             and (hasOrder value 5))
             or (FShell
             and (contains exactly 14 Electron)
             and (hasOrder value 4))
             or (SShell
             and (contains exactly 1 Electron)
             and (hasOrder value 6))))
         and (hasAtomicNumber value 78)

Not the most exciting ontology I’ve ever built, but it does touch quite a lot of nice modelling points. There is another way to build the same ontology that allows less clumsy modelling and to simply state the number of electrons in the valence shell and “distribute” them around different shells to achieve the same effect. I’ll do this way and show it at a later date.

This version of the Periodic Table ontology is available.

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One Response to “An Ontology of the Periodic Table Using electronic structure of the atom”

  1. Putting an ontology of the atoms in order | Robert Stevens' Blog Says:

    […] the Periodic table of the Elements – thanks to an excellent third year project by Ionica Durchi. I’ve already written about an ontology of the atoms, where each atom is described according to its electronic configuration; then the atom families are […]

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