Selected Drug-Likeness Properties of 2-Arylidene-indan-1,3-dione Derivatives—Chemical Compounds with Potential Anti-Cancer Activity

2-Arylidene-indan-1,3-done derivatives have very different properties, thanks to which they find various applications in science, medicine, and industry. Selected derivatives show antiviral, antibacterial, and anti-inflammatory activity. This paper presents a procedure for the synthesis of a series of indan-1,3-dione derivatives that present antiproliferative activity. The aim of the work was to develop a method of simple synthesis and purification, evaluate the fulfillment of the Lipiński’s and Veber’s rule, and determine the potential scope of application of the obtained series of compounds. The structure of the synthesized compounds was confirmed, and their lipophilicity was determined using experimental and computational methods. Their antiproliferative activity against selected cell lines was tested in accordance with the MTT protocol; the ability to bind to albumin was tested, and the parameters related to the toxicity of substances in silico were determined. The selected compounds which showed antiproliferative activity were strongly bound to albumin and, in most cases, met the Lipiński’s and Veber’s rule. Thus, the obtained results suggest that 2-arylidene-indan-1,3-done derivatives appear to be good candidates for drugs with a potential leading structure for further development.