Molecular Shape Analysis

Classify and visualize molecular shape using the principal moments of inertia

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Consider three molecules with different shapes:

In[1]:=

{rod,disk,sphere}={Molecule["Buta-1,3-diyne"],Molecule["benzene"],Molecule["adamantane"]};Map[MoleculePlot3D,{rod,disk,sphere}]

Out[1]=

Compute 3D coordinates for the molecules and find the principal moments of inertia:

In[2]:=

MoleculeValue[{rod,disk,sphere},"PrincipalMoments"]

Out[2]=



5.46402×

-12

126.042

,

88.7257

88.7259

177.452

,

300.033

300.034



The principal moments are normalized by dividing the two smaller moments by the largest moment:

In[3]:=

MoleculeValue[{rod,disk,sphere},"NormalizedPrincipalMomentRatios"]

Out[3]=

{{4.33507×

-14

,1.},{0.499999,0.500001},{0.999999,1.}}

Using the principal moment ratios as coordinates, these shapes form the corners of a triangle:

In[4]:=

insets=Map[Inset[MoleculePlot3D[#],#["NormalizedPrincipalMomentRatios"],Center,.3]&,{rod,disk,sphere}];triangle={FaceForm@None,EdgeForm[Gray],Triangle[{{0,1},{1/2,1/2},{1,1}}]};background=Graphics[{triangle,insets},ImagePadding45,AspectRatio3/4,ImageSize400]

Out[4]=

Compare the shape for a collection of molecules, using the principal moment ratios for coordinates and 3D plots for tooltips:

In[5]:=

mols=MapMolecule,

300 SMILES strings

;tooltips=Map[Tooltip[#["NormalizedPrincipalMomentRatios"],MoleculePlot3D[#]]&,mols];Show[background,ListPlot[tooltips]]

Out[5]=

Related Symbols

Molecule
MoleculePlot3D
MoleculeValue

Publisher Information

Contributed by: Wolfram Staff