Constraint geometry homogeneous catalysts, such as ansa-metallocenes, are powerful and versatile systems to control the tacticity of polypropylene (PP). Among such systems, CMe2[Flu–μ–3-R-Cp]ZrCl2 with R=H, Me, t-Bu groups cover the full range of tacticities from iso- to syndio-, through hemiisoselectivity with very good stereocontrol. The series of increasing substituent size and the loss of Cs symmetry correlate elegantly with the progressive shift from a full chain-migratory to a chain-stationary mechanism accounting for the change of PP tacticity. Unfortunately, the introduction of a bulkier SiMe3 substituent disrupts the trend by producing a less isotactic polymer containing small syndioblocks. Supported by indirect experimental evidences, a mechanism based on a reversible haptotropic shift of the catalyst structure, leading to the alternation of iso- and syndioselective conformations has been proposed. Using classical Molecular Mechanics (including topological analysis of the potential energy hypersurface and statistical mechanics) and ab initio Quantum Mechanics (including NBO and AIM wavefunction analysis schemes at both RHF and DFT levels of theory), the molecular properties of the non-activated, activated, resting, and monomer-complex forms of the four systems with R=H, Me, t-Bu, and SiMe3 are computed. From these properties, four hypothetical mechanisms are proposed for the CMe2[Flu–μ–3- SiMe3-Cp]ZrCl2 catalyst: i) a regular two-sites model with altered stereoselectivity, ii) a model with a degenerated active site enabling both Front-Side and Back-Side attacks, iii) the haptotropic shift model, and iv) a SiMe3 group sigmatropic shift model. Using a new formulation of an existing statistical method relating the control mechanism to the PP microstructure and its generalization in the form of a (possibly time-varying) Hidden Markov Model, together with Genetic Algorithm and Monte Carlo fitting methods, the observed 13C NMR pentad fractions of the PP produced by the catalyst are reproduced to evaluate the hypotheses. The four mechanisms enable reproducing the observed polymer microstructures with good agreement. The best fits were found for the haptotropic and sigmatropic shift models. The later receives however better direct support from the calculated molecular properties together with dynamic experimental data regarding the rates of SiMe3 shift and monomer insertion. This result bears similar features with the prevalent mechanism of the existing and well-studied Waymouth oscillating catalyst.