Periodic Table of Alkane Isomers

Build the periodic table for all the constitutional isomers of any alkane according to partial ordering theory

Retrieve all the isomers of hexane alongside their molecular name:

In[1]:=

alkaneisomers=FindIsomers[Molecule[Entity["Chemical","Hexane"]]];alkanenames=MoleculeName/@alkaneisomers

Out[1]=

{hexane,isohexane,3-methylpentane,2,2-dimethylbutane,2,3-dimethylbutane}

Drop all stereoisomers (if any) and store only constitutional isomers:

In[2]:=

alkconstisomers=Delete[alkaneisomers,Position[StringContainsQ[alkanenames,{"S","R"}],True]]

Out[2]=

Molecule

Formula:

Atoms:

Bonds:

,Molecule

Formula:

Atoms:

Bonds:

,Molecule

Formula:

Atoms:

Bonds:

,Molecule

Formula:

Atoms:

Bonds:

,Molecule

Formula:

Atoms:

Bonds:



Retrieve data for any property (e.g. boiling point) for each constitutional alkane isomer:

In[3]:=

boilpointalkaneisom=Map[ChemicalData[Entity["Chemical",ToString[MoleculeName[#]]],"BoilingPoint"]&,alkconstisomers]

Out[3]=

{68.73,69.},

62.

°C

64.

°C

50.

°C

58.

°C



For each isomer enumerate all paths in each isomer graph (i.e the total number of single bonds, two adjacent bonds and so on) according to the Randić definition:

In[4]:=

nC=AtomCount[alkaneisomers〚1〛,"C"];g=MoleculeGraph[alkconstisomers,IncludeHydrogensNone,ImageSizeTiny];alkanepaths=Map[Table[Length@DeleteDuplicates[Flatten[Table[FindPath[#,i,j,{nn}(*wherenngoesthrough1forsinglebond,2foradjacentbonds,3forthreeadjacentbonds,4forfouradjacentbondsandsoon*)],{i,1,nC},{j,1,nC}],2],(#1Reverse[#2])&],{nn,1,nC-1,1}]&,g]

Out[4]=

{{5,4,3,2,1},{5,5,3,2,0},{5,5,4,1,0},{5,7,3,0,0},{5,6,4,0,0}}

The numbers of two and three consecutive adjacent bonds (paths with index

and

) are needed for unveiling the hidden order behind all isomers:

In[5]:=

alkanepaths23=Map[Table[Length@DeleteDuplicates[Flatten[Table[FindPath[#,i,j,{nn}],{i,1,nC},{j,1,nC}],2],(#1Reverse[#2])&],{nn,2,3,1}]&,g]

Out[5]=

{{4,3},{5,3},{5,4},{7,3},{6,4}}

Associate each molecule name to its corresponding

(

) pair, molecule graph and boiling point:

In[6]:=

assocname=AssociationThread[MoleculeName/@alkconstisomersalkanepaths23]

Out[6]=

hexane{4,3},isohexane{5,3},3-methylpentane{5,4},2,2-dimethylbutane{7,3},2,3-dimethylbutane{6,4}

In[7]:=

assocmolgraph=AssociationThread[MoleculeName/@alkconstisomersg]

Out[7]=

hexane

,isohexane

,3-methylpentane

,2,2-dimethylbutane

,2,3-dimethylbutane



In[8]:=

assocboil=AssociationThread[MoleculeName/@alkconstisomersboilpointalkaneisom]

Out[8]=

hexane{68.73,69.},isohexane

62.

°C

,3-methylpentane

64.

°C

,2,2-dimethylbutane

50.

°C

,2,3-dimethylbutane

58.

°C



Build a function to plot the periodic table of all constitutional isomers of the chosen alkane:

In[9]:=

alkanetableplot[obj_]:=ShowListPlotGatherBy[alkanepaths23,#〚2〛&],PlotRange{{Min[alkanepaths23〚;;,1〛]-1,Max[alkanepaths23〚;;,1〛]},{Min[alkanepaths23〚;;,2〛],Max[alkanepaths23〚;;,2〛]}},

,ListPlotGatherBy[alkanepaths23,#〚1〛&],LabelingFunction(Callout[Framed[Column[{IntegerPart@#,Column[{Column[(ii=Extract[Position[assocname,IntegerPart@#],{All,1,1}];ii),Center],Row[Table[(*physicalpropertyorgraph*)obj〚ii〛〚jj〛,{jj,1,Length[ii]}],","]},Center]},Center],BackgroundYellow],Center]&),

,



Obtain the alkane isomer periodic table with the corresponding values of the boiling point, ordered according to the

(

) indices:

In[10]:=

alkanetableplot[assocboil]

Out[10]=

Obtain the periodic table of all constitutional isomers of the chosen alkane with the corresponding molecule graph ordered according to the

(

) indices:

In[11]:=

alkanetableplot[assocmolgraph]

Out[11]=

External Links

https://community.wolfram.com/groups/-/m/t/3416635

Source Metadata

Citation:
- Book chapter nr. 7 "Partial Ordering" and references therein in "Solved and Unsolved Problems of Structural Chemistry" by Milan Randić, Marjana Novič and Dejan Plavšić, CRC Press (2016), https://doi.org/10.1201/b19046
- On intramolecular average 13C chemical shift in nonanes" by Milan Randić, Marjana Novič and Dejan Plavšić, International Journal of Quantum Chemistry (Wiley), https://doi.org/10.1002/qua.22116

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Contributed by: Jessica Alfonsi

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Periodic Table of Alkane Isomers

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Periodic Table of Alkane Isomers

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