Contemporary pre-clinical drug discovery is complemented by the combinatorial use of numerous computational techniques linked to computer-aided drug design and discovery. We combined inherently different computational analyses derived from multi-scale conventional, steered and umbrella sampling simulations to identify potential drug candidates for the first bromodomain of the human bromodomain containing protein 4 (BRD4-BD1). The BRD4-BD1 protein is a recognized therapeutic target for various diseases including cancer, neurological disorders, inflammation, and obesity. The in-house synthesized benzosuberene-sulfone (BSS) molecules were assessed for their potential to act as inhibitors against the BRD4-BD1 protein. We compared the molecular interactions and docking scores of BSS analogues with six different co-crystal inhibitors of the BRD4-BD1 protein. Further, the thermodynamic free energy of binding for each complex was estimated by the end-state Molecular Mechanics Poisson-Boltzmann Surface Area (MM/PBSA) approach. Moreover, umbrella sampling simulations were utilized to validate the results obtained from MM/PBSA analyses and to demonstrate the unbinding/binding process of the most potent BSS analogue from the binding pocket of BRD4-BD1 protein. Our results show the potential of organosulfur molecules to be developed as inhibitors of the BRD4-BD1 protein and endorse their evaluation by suitable in-vitro and in-vivo studies.