• Asok K Mukherjee

      Articles written in Journal of Chemical Sciences

    • A graph-theoretical method for stepwise factorisation of symmetric graphs for simultaneous determination of eigenvectors and eigenvalues

      Kali Kinkar Datta Asok K Mukherjee

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      A simple pictorial algorithm for factorisation of symmetric chemical graphs (weighted and unweighted) leading to simultaneous determination of their eigenvalues and eigenvectors has been devised. The method does not require group-theoretical techniques (viz. identification of the point group of the species under study, formation of symmetryadopted linear combinations using character tables etc.). It requires consideration of only one symmetry element, e.g., a reflection plane and is based on elementary row and column operations which keep the secular determinant of the adjacency matrix unchanged (except possibly for a multiplicative constant).

    • Inductive effect of methyl group in a series of methylated indoles: A graph theoretical analysis in the light of density functional theory and correlation with experimental charge transfer transition energies

      Amit S Tiwary Asok K Mukherjee

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      The inductive effect of methyl group has been quantified by expressing highest occupied molecular orbital (HOMO) and HOMO-1 energies of indole and a series of methylated indoles using a combination of graph theory (GT) and the Coulson-Longuett-Higgins perturbation method. By correlating these expressions with the corresponding Kohn-Sham orbital energies of the indoles obtained by density functional theory (DFT) calculation at the B3LYP/6-31++G(d,p) and M06-2X/6-31++G(d,p) levels of theory, the inductive effect parameter $h_{Me}$ has been estimated; the Coulomb integral 𝛼 of 𝜋-conjugated carbon atom also comes out from the analysis. A correlation of the GT results with the HOMO and HOMO-1 energies obtained by the HF/STO-3G method yield almost the same values of $h_{Me}$ and 𝛼. Finally, when these estimated $h_{Me}$ and 𝛼 are used to calculate the vertical ionization potentials of the methylated indoles in the series, an excellent correlation with experimental charge transfer transition energies of their molecular complexes with tetracyanoethylene is obtained which complies with Mulliken’s theory of charge transfer.

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