Complexes of three aromatic diols, catechol, naphthalene‐1,8‐diol, and fluorene‐4,5‐diol, with a series of hydrogen bond acceptors (HBAs) that have oxygen, nitrogen, and sulfur acceptor atoms, have been studied by density functional theory (DFT) at the B3LYP/6‐311+G(d,p) level. Binding energies, geometries, infrared spectroscopic (IR) frequencies, nuclear magnetic resonance (NMR) shifts, and measures of the electron density distribution from the Quantum Theory of Atoms in Molecules (QTAIM) are evaluated and compared with data for the corresponding monohydroxy compounds (monols), phenol, naphth‐1‐ol, and fluorene‐4‐ol, in order to assess the importance of cooperativity between intramolecular and intermolecular hydrogen bonding. All measures for all complexes show positive cooperativity whereby both the intermolecular and intramolecular hydrogen bonds are strengthened upon complexation. Cooperativity is weak for catechol and strong for the other two diols and, for all diols, increases with the hydrogen bond basicity of the acceptor. Correlations of IR and NMR metrics against binding energies for a single HBA and all six monols and diols are excellent, but attempts to correlate the same metrics for all HBAs and a single donor are frustrated by differences in intermolecular hydrogen bonding, depending notably on the identity of the acceptor atom in the HBA. Atom–atom interaction energies, calculated by the Interacting Quantum Atoms approach, are used to discuss the covalency of both types of hydrogen bond.