Two-dimensional hypersurfaces for the inversion process of the group 15 fluorides MF(3) (M = N, P, As, Sb, Bi) involving the MF(3) umbrella motion and the symmetric F-M-F bending mode have been calculated at the Hartree-Fock level. The MO scheme of NF3 shows an a(2)" HOMO and a(1)’ LUMO in accordance with the frontier orbitals of the group 15 hydrides, and therefore it inverts through the expected trigonal planar D-3h transition state. For PFS, AsF3, SbF3, and BiF3, however, the HOMO-LUMO sequence is inverted and the HOMO is of a(1)’ symmetry. This results in an a(1)’(xe)(HOMO)’(LUMO) mixing at the trigonal planar D-3h structure causing a second-order Jahn-Teller symmetry breaking (distortion Hamiltonian is of e’ symmetry) toward the T-shaped C-2v arrangement. The minimum energy inversion path is of C-s symmetry starting from the pyramidal C-3v minimum structure by distorting immediately toward the T-shaped C-2v first-order transition state. Moller-Plesset second-order results (MP2) are compared with local density functional approximation (LDA) methods including nonlocal corrections and several semiempirical (AM1, PM3, and MNDO) calculations. The performance of different exchange and correlation functionals within LDA including gradient corrections is discussed in detail. Because of the a(1)’(xe)(HOMO)’(LUMO) mixing, electron correlation contributions become very important and Freed’s theorem is not valid for the fluorides of the heavier elements P, As, Sb, and Bi. Hence, to assess the validity of a single-determinant MP2 approach we performed complete active space MP2 calculations (CASPT2) for the minimum and inversion structures of NF3 and PF3. These calculations show that for PF3 a multireference scheme is necessary to describe the energetics of the D-3h to C-2v Jahn-Teller distortion accurately. The inversion barrier from the C-3v minimum structure to the C-2v inversion point is, however, satisfactorily described by a single-reference MP2 procedure. Vibrational frequencies and structure are predicted for gas-phase BiF3 at the MP2 level. The relativistic change in the F-Bi-F bond angle is large (alpha(NR) - alpha(R) = -1.5 degrees at the MP2 level), resulting in an anomaly in the trend of F-M-F bond angles along the group 15 fluorides. When the vibrational frequencies are considered, MP2 of all the methods performs the best while, somewhat surprisingly, the Becke correction to the LDA exchange functional leads to large errors. Despite this, the LDA inversion barriers seem to be more accurate than the single-reference MP2 values, and in the case of PF3 both the LDA (using the Vosko-Wilk-Nusair (VWN) parametrization) and the CASPT2 method are in close agreement. For BiF3 at the relativistic level, LDA/VWN and PM3 predict a trigonal planar inversion structure contradicting MP2 and coupled cluster results. However, if relativistic effects are neglected, both LDA and MP2 yield a T-shaped inversion state.