Density Functional Theory of Bose–Einstein Condensation: Road to Chemical Bonding Quantum Condensate

Abstract

The marriage of the celebrated fermionic and bosonic theories of matter that are Density Functional Theory and Bose–Einstein Condensation, respectively, is presented at the conceptual level of the Hohenberg–Kohn–Sham equations and energy functionals. Particular attention is given to the general formulation of the exchange-correlation within the context of perturbation theory at finite temperature, then specialized to the analytical exchange functional in terms of ordering parameter dependency by employing the Bogoliubov transformation (or the first-order main-field expansion); this further provides the appropriate framework within which the celebrated Gross–Pitaevsky BEC equation is recovered. This nonlinear generalization of the Schrödinger equation was then employed in first providing the DFT–BEC connection at the level of the Thomas–Fermi approximation; such connections were further used in generalizing the classical Heitler–London formalism and bonding–antibonding equations of homopolar chemical bonding with the aid of the mass quantification of the quantum particle of the chemical bonding field—the bondons. Actually, two branches of bosonic–bondonic condensate were identified as physical and chemical bonding BEC, both with bonding and antibonding features. The paradigmatic DFT–BEC application to the bonding interaction in hydrogen and helium molecular systems confirms both the physical and chemical forbidden bindings in He–He interactions, while allowing only the chemical interaction in the H–H system, though with bonding and antibonding quantum condensates below the “normal” ground-state potential of H₂. Further exciting perspectives at both physical and chemical levels, for conceptual and practical realizations of DFT–BEC systems, are in this review opened toward searching for unified fermionic–bosonic manifestations in nature.