Structures and vibrational frequencies of group 17 fluorides EF3 (E = I, At, and element 117) are calculated at the density functional theory (DFT) level of theory using relativistic effective core potentials (RECPs) with and without spin-orbit terms in order to investigate the effects of spin-orbit interactions and electron correlations on the structures and vibrational frequencies of EF3. Various tests imply that spin-orbit and electron correlation effects estimated presently from Hartree-Fock (HF) and DFT calculations with RECPs with and without spin-orbit terms are quite reasonable. Spin-orbit and electron correlation effects generally increase bond lengths and/or angles in both C-2v and D-3h structures. For IF3, the C-2v structure is a global minimum, and the D-3h structure is a second-order saddle point in both HF and DFT calculations with and without spin-orbit interactions. Spin-orbit effects for IF3 are negligible in comparison to electron correlation effects. The D-3h global minimum is the only minimum structure for (117)F-3 in all RECP calculations, and the C-2v structure is neither a local minimum nor a saddle point. In the case of AtF3, the C-2v structure is found to be a local minimum in all RECP calculations without spin-orbit terms, and the D-3v structure becomes a local minimum at the DFT level of theory with and without spin-orbit interactions. In the HF calculation with spin-orbit terms, the D-3h structure of AtF3 is a second-order saddle point. AtF3 is a borderline case between the valence-shell-electron-pair-repulsion (VSEPR) structure of IF3 and the non-VSEPR structure of (117)F-3. Relativistic effects, including scalar relativistic and spin-orbit effects, and electron correlation effects together or separately stabilize the D-3h structures more than the C-2v structures. As a result, one may suggest that the VSEPR predictions agree very well with the structures optimized by the nonrelativistic HF level of theory even for heavy-atom molecules but not so well with those from more elaborate theoretical methods. Vibrational frequencies of AtF3 and (117)F-3 are modified substantially and nonadditively by spin-orbit and electron correlation contributions. This is one of those rare cases for which vibrational frequencies of the closed-shell molecules are significantly affected by spin-orbit interactions. Spin-orbit interactions decrease all vibrational frequencies of EF3 molecules considered.