Fluorinated organic compounds are ubiquitous in the pharmaceutical and agricultural industries. To better discern the mode of action of these compounds, it is critical to understand the strengths of hydrogen bonds involving fluorine. There are only a few published examples of the strengths of these bonds. This study provides a high level ab initio study of inter-and intramolecular hydrogen bonds between RF and R'OH, where R and R' are aryl, vinyl, alkyl, and cycloalkyl. Intermolecular binding energies average near 5 kcal/mol, while intramolecular binding energies average about 3 kcal/mol. Inclusion of zero-point energies and applying a counterpoise correction lessen the difference. In both series, modest increases in binding energies are seen with increased acidity of R'OH and increased electron donation of R in RF. In the intramolecular compounds, binding energy increases with the rigidity of the F-(C)(n)-OH ring. Inclusion of free energy corrections at 298 K results in exoergic binding energies for the intramolecular compounds and endoergic binding energies for the intermolecular compounds. Parameters such as bond lengths, vibrational frequencies, and atomic populations are consistent with formation of a hydrogen bond and with slightly stronger binding in the intermolecular cases over the intramolecular cases. However, these parameters correlated poorly with binding energies.