Polar antiferromagnetic metals have recently attracted increasing interest due to their combined traits of both ferromagnets (with spin polarization) and antiferromagnets (absence of net magnetization) for spintronic applications. However, the inherently incompatible nature of antiferromagnetism, metallicity, and polarity pose a significant challenge in designing these materials. Herein we propose that charge disproportionation can lead to this novel state in the negative charge transfer gap regime in molecular orbital crystals. As a proof of concept, this proposal is demonstrated by molecular orbital analyses of first-principles density functional theory plus $U$ electronic band structures for the representative Ruddlesden-Popper bilayer perovskite oxide ${\mathrm{Sr}}_3{\mathrm{Co}}_2{\mathrm{O}}_7$, corroborated by density matrix renormalization group calculations. Due to the negative charge transfer nature of ${\mathrm{Co}}^{4+}$ and strong interlayer coupling, localized molecular orbitals stemming from the hybridization of Co $d_{z^2}$ and $d_{xz/yz}$ orbitals through the apical oxygen $p$ orbitals preferentially emerge within each bilayer unit and develop antiferromagnetic ordering by invoking Hubbard repulsion. Charge disproportionation driven by Hund's physics causes an occupation imbalance (with broken inversion symmetry) in the remaining $d_{xy}$ and $d_{x^2-y^2}$ orbitals from distinct Co atoms within the bilayer unit, resulting in the polar metallicity. Meanwhile, this charge disproportionation scenario allows consequent conducting carriers to couple with interlayer local spins via Hund's coupling, giving rise to in-plane double-exchange ferromagnetism. Our molecular orbital formulation further provides a guide towards an effective Hamiltonian for modeling the unconventional synergy of metallicity, polarity, and antiferromagnetism in ${\mathrm{Sr}}_3{\mathrm{Co}}_2{\mathrm{O}}_7$, which may be a unified framework widely applicable to double-layer Ruddlesden-Popper perovskite oxides.

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• Electronic structure
• Cobaltates
• Synthetic antiferromagnetic multilayers