Orbital Entanglement from the Topology of Bond Breaking

Bond breaking in molecules is accompanied by a fundamental restructuring of orbital entanglement. Here, we formulate a deterministic, unitary resource theory for this process, establishing a rigorous connection between quantum entanglement and the topology of chemical bonding. Within this framework, bond dissociation is interpreted as a trajectory in orbital entanglement space, generated by fermionic unitaries that redistribute correlations among orbitals. The free operations are identified with particle-number–preserving Givens rotations, which implement all possible one-body orbital transformations and preserve the separable structure of single-determinant wavefunctions. In contrast, resource-generating operations correspond to two-body unitaries or equivalent interactions with a maximally entangled ancilla, which are required to produce one-particle reduced density matrices (1-RDMs) with partial occupation. These operations thus define the cost of creating electron correlation and, by extension, of breaking a bond. Using this formalism, the evolution of a molecular density matrix under constrained unitary maps reproduces the characteristic growth of orbital entropy observed in ab-initio bond-stretching calculations. The resulting unitary resource topology provides a minimal, CPTP-consistent description of bond breaking as the controlled activation of orbital entanglement, unifying concepts from quantum chemistry and quantum resource theory under a common operational framework.