Defining Chemical Space Constructively

Chemical space is central to molecular discovery and design, providing a way to organize and explore possible molecular systems. However, accommodating chemically diverse systems within a unified framework that interconnects molecular identity, electronic description, and molecular construction remains challenging. Here, we introduce Constructive Chemical Space (CCS), which organizes these aspects into distinct yet formally connected layers. In CCS, molecular identity at the constitutional level is defined by three features: nuclear identities, direct connections, and total electron count. Alternative electron-allocation forms can remain explicit while mapping to the same constitutional identity. We prove that every finite CCS constitution can be constructed through a finite ordered sequence of three basic operation types. Examples spanning organic, main-group, organometallic, and cluster chemistry demonstrate that CCS can accommodate a wide variety of bonding descriptions. CCS thereby provides a common constructive foundation for a chemical space in which chemically diverse molecular systems can be compared, interpreted, and generated at task-dependent levels of description.