The theoretical parameters such as optimized geometrical parameters (bond lengths, bond angles, and dihedral angles), vibrational assignments, non-linear optical property, natural population analysis, and global chemical descriptors were calculated using the density functional theory with Becke, 3-parameter, Lee-Yang-Parr functional and Coulomb-attenuating method. Spectroscopic characterization of (E)-N '-((1H-Indol-3-yl)methylene)-4-bromobenzohydrazide was investigated by the Fourier transform infrared analysis with the potential energy distribution, proton nuclear magnetic resonance, and ultraviolet-visible techniques. The intermolecular interactions of the title molecule in the crystal structure were visualized by the three-dimensional Hirshfeld surface and associated two-dimensional fingerprint plots. In order to understand molecular stability, global reactive properties calculated at the time-dependent density functional theory have been investigated by visualization of frontier molecular orbitals. In addition, the first-order hyperpolarizability has been investigated to understand the non-linear optical activity of the molecule. Molecular docking studies supporting the antibacterial activity of the title molecule give a high-binding energy value of -5.20 kcal/mol due to the interaction of the carbonyl group with the target protein.