Quantum Assembly Theory: Bridging QTAIM and Molecular Complexity via Electron Density Topology

Quantifying molecular complexity from first principles remains an open challenge in theoretical chemistry.Here we introduce Quantum Assembly Theory (QAT) and the Quantum Assembly Index A , a dimensionless, parameterfree descriptor derived from first principles of information theory, graph theory, and quantum chemical topology, that encodes bond traversal cost, ring topology, cage topology, and rotational symmetry without empirical fitting parameters.Benchmarked across 37 molecules spanning inorganic, organic, biological, framework, and cluster chemistry, A reveals a natural threshold A * = 3.5 separating randomly assembled from selectively assembled chemistry, with a lower bound of A 75.2423 for the polyoxometalate {Mo 154 }, the highest value in the benchmark.Analysis demonstrates that randomly assembled chemistry cannot simultaneously satisfy the topological and electronic conditions required to exceed this threshold, which is crossed exclusively by molecules produced through Darwinian selection, deliberate synthesis, or extreme conditions.The complementarity of QAT with Assembly Theory, combined with its experimental accessibility via high-resolution X-ray diffraction and cryo-electron microscopy, positions A as a rigorous quantum mechanical foundation for detecting and quantifying molecular selection across all domains of chemistry.