For designing the electronic devices using molecular wires, it is important to understand the electronic properties at the molecular level. In this paper, the simulation methodology for analyzing the electrical conductivity of anthracene conjugated molecule sandwich between Au atoms via linker Sulfur atom, is proposed. This theoretical analysis is carried out for different applied electric field ranges from 0 to 0.26 VÅ-1 to metal electrode Au atom using density functional theory (DFT). The effect of external applied electric field towards the structural variation of metal attached anthracene molecule [WH] is well explored and compared the results with that of hetero atoms [N, S, and O] substituted heterocyclic systems [HAA, HTA and HOA]. Further, the ability of electron flow through these systems were explored from the analysis frontier molecular orbitals and density of states (DOS). The bonding nature of the studied molecules were well described from the QTAIM analysis and finally the reactive sites for electrophilic and nucleophilic attack was identified from the simulation of molecular electrostatic potential surface. Non-covalent interaction (NCI-RDG) analysis is addressed to characterize the interactions in heteroatom substituted anthracene based molecular nanowires. In our overall study, the outcomes are exposing that the significates feature and importance of electrical conductivity nature and transport characteristic of hetero-atoms (N, S, O) substituted anthracene based molecular nanowires.