Radical-Fragment Many-Body Expansion for Linear Alkane Quantum Chemistry

Abstract

We introduce a radical-fragment many-body expansion at the two-body level (MBE2) for quantum chemistry of linear alkanes. Instead of heterolytic bond cleavage with hydrogen capping atoms and electrostatic embedding like in Fragment Molecular Orbital (FMO), we perform homolytic C-C bond cleavage to produce open-shell radical fragments (CH3, CH2) treated with restricted open-shell Hartree-Fock (ROHF) in isolation. The two-body MBE2 assembly formula reconstructs total alkane energies from only four unique fragment calculations regardless of chain length, reducing the maximum qubit requirement. We benchmark this framework against five energy solvers (RHF, CCSD, VQE, ADAPT-VQE, and SQD) across 11 linear alkanes from butane (C4H10) to hexacosane (C26H54). The MBE2 decomposition achieves a 12.3x qubit reduction for C26H54 (from 368 to 30 qubits) and a 12.8x reduction in unique calculations via symmetry exploitation. MBE2-VQE and MBE2-SQD (executed on IBM quantum hardware) closely track their respective classical MBE2 references, demonstrating that fragmentation-based quantum chemistry is viable for scaling quantum solvers to large molecular systems.