In Stadler et al (2003 Nanotechnology 14 138), a scheme for a molecular memory was presented. It was based on the influence of the positions of chemical side-groups attached to aromatic molecules on the paths for electrons propagating through these molecules in the ballistic and tunnelling transport regimes. Here we extend this concept in the following ways. (i) A graphical method is derived from an electron scattering formalism based on a topological Hückel description, which allows us to estimate whether the electron transport between two electrodes attached to specific atomic sites in an arbitrary molecule is finite or zero at the Fermi level. (ii) The same scheme that was used for the implementation of the molecular memory is extended to logic functions, in particular a half-adder. (iii) A more realistic description of the chemical nature of the proposed intra-molecular circuits is achieved by using the elastic scattering quantum chemistry (ESQC) technique in an extended Hückel implementation and by specifying the side-groups as nitro-groups, which are rotated in order to feed the signal inputs into the computational circuit.