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ChemRxivA Free Energy Decomposition Analysis: Insight into Binding Thermodynamics from Absolutely Localized Molecular OrbitalsFree energies of association determine chemical equilibria and thus control noncovalent binding. While traditional energy decomposition analysis (EDA) methods can provide a chemically or physically interpretive decomposition of noncovalent electronic binding energies, by definition they neglect entropic effects (and nuclear contributions to the enthalpy). With the objective of revealing the chemical origins of trends in free energies of binding, we introduce the concept of a free energy or Gibbs decomposition analysis (GDA), by coupling the absolutely localized molecular orbital (ALMO) treatment of electrons in non-covalent interactions with the simplest possible quantum treatment of nuclear motion at finite temperature, which is the rigid rotor-harmonic oscillator (RR-HO) model. The resulting pilot GDA is employed to decompose enthalpic and entropic contributions to the free energy of association of the water dimer, fluoride-water dimer, and the binding of water to an open metal site in a recently synthesized metal-organic framework (Cu(I)-MFU-4l). The results show enthalpic trends that generally track the energy of binding (i.e. EDA results), and entropic trends that reveal the increasing price of loss of translational and rotational degrees freedom with temperature. The GDA approach can be generalized to more sophisticated treatment of quantum nuclei, as well as to semiclassical or classical nuclear motion.