Sample-based quantum diagonalization approach for open-shell transition-metal complexes in gas and implicit-solvent

Abstract

Open-shell $3d$ transition-metal complexes pose a stringent challenge for correlated electronic-structure methods because near-degenerate metal $d$ orbitals give rise to competing spin states and oxidation-state-dependent charge transfer, while solvation can reshape the relative stability of the resulting electronic configurations. Building on prior demonstrations of open-shell sample-based quantum diagonalization (SQD) for light-atom systems and, separately, closed-shell SQD coupled to the integral-equation-formalism polarizable continuum model (IEF-PCM), we combine these capabilities through an open-shell SQD--IEF-PCM framework and apply it to the octahedrally coordinated $\mathrm{[Co(H_2O)_5CO_2]^{2+/3+}}$ complex, spanning the Co(III) singlet and quintet and Co(II) doublet and quartet states along a metal--ligand dissociation coordinate. Using quantum samples collected on an IBM Heron processor and active spaces of up to 50 qubits, SQD closely reproduces coupled-cluster and heat-bath configuration-interaction benchmarks within the same active spaces in both gas phase and implicit solvent; for high-spin quintet $\mathrm{[Co(H_2O)_5CO_2]^{3+}}$, it additionally resolves an avoided crossing associated with internal charge transfer that is absent in the corresponding singlet and in the lower oxidation state, while IEF-PCM suppresses this crossover by preferentially stabilizing the dissociation channel leading to neutral CO$_2$. To our knowledge, this work provides the first hardware demonstration of SQD for an open-shell 3d transition-metal complex with discrete metal-centered d-orbital chemistry, and the first application of open-shell SQD in a dielectric continuum, establishing a quantum-centric framework for transition-metal chemistry in regimes where spin-state energetics, charge transfer, and environmental response are strongly coupled.