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This paper introduces a self-consistent field framework for finite embedded quantum-chemical clusters that employs constant potential boundary conditions through an energy-independent self-energy. By deriving an analytic expression for the one-particle density matrix update, the authors integrate this approach into conventional Hartree鈥揊ock and density functional theory, solving the resulting non-Hermitian equations with adapted Pulay-type mixing schemes. The method accurately captures the polarization response of a quasi-periodic hydrogen ring and demonstrates effective charge transfer in a lithium cluster, establishing a new foundation for quantum embedding methods in electrochemical systems.
A novel self-consistent field framework reveals that finite quantum-chemical clusters can effectively model polarization and charge transfer under constant potential boundary conditions.
We present a self-consistent field framework for finite embedded quantum-chemical clusters with constant potential boundary conditions. The coupling is realized through an energy-independent self-energy commonly employed in quantum-transport calculations within the wide-band approximation. Starting from the corresponding non-equilibrium Green's function formalism, we derive an analytic expression for the one-particle density matrix update that can be incorporated into conventional Hartree--Fock and density functional theory. The resulting non-Hermitian self-consistent field equations are solved using adapted Pulay-type mixing schemes. Applications to a quasi-periodic hydrogen ring demonstrate that a finite fragment coupled through an optimized self-energy accurately reproduces the polarization response of the extended system, while calculations on a lithium cluster capture metallic charge transfer and fractional occupations under open-boundary conditions. The proposed framework establishes practical grand-canonical boundary conditions for finite quantum-chemical clusters and lays the methodological foundation for quantum embedding methods for electrochemical systems.
