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A new reference state for density functional theory (DFT), termed the independent atom ansatz, is introduced in this work. This ansatz allows for the formally exact representation of electron density in terms of atom-localized orbitals. Self-consistent equations for such states are derived in general and asymptotic forms. The resultant total energy functional is found to closely resemble tight-binding theory. The independent atom ansatz facilitates partial cancellation of inter-atomic electron–electron and nucleus–electron interactions, which allows for the derivation of analytical tight-binding Hamiltonian matrix elements in a weak interaction limit. The formalism provides energy decomposition and charge analyses at no additional cost and links tight-binding, localized orbital, and electronegativity concepts. Numerical accuracy of the total energy functional has been previously reported for hydrogenic systems [Mironenko, J. Phys. Chem. A 127, 7836 (2023)] and is demonstrated here for He2, Li2, Be2, B2, N2, O2, F2, and Ne2. The method accurately reproduces the shapes of potential energy curves, capturing large-basis CCSD(T)-level bond lengths and bond dissociation energies for N2, O2, and F2 using only a minimal basis set. It outperforms both CCSD(T) and some mainstream approximate restricted Kohn–Sham DFT functionals in describing bond dissociation behavior away from equilibrium geometries.