edgeMol =
ImportString[
"C1(C=CC2=CC=C3)=CC=CC4=C1C2=C3C=C4", {"SMILES", "EdgeRules", 1}];
From edgeMol, get hamiltMol with some code, then:
evalMol = N[Eigenvalues[hamiltMol]];
evecMol =
Orthogonalize[N[Eigenvectors[hamiltMol]]];
AdjacencyGraph[adjMol, GraphStyle -> "SpringEmbedding",
EdgeShapeFunction -> (Line[#1] &),
VertexShapeFunction -> ({{Opacity[0], Disk[#1, #3]}, {Orange,
Disk[#1, Abs[evecMol[[1, #2]]]^2]}} &), VertexSize -> 4/3,
ImageSize -> Full]