coordinate set. The inversion path develops along the θ coordinate from the $^{4}$C$_{1}$ conformer at θ = 0 to the $^{1}$C$_{4}$ one at θ = π , while the pseudo-rotation one develops along φ , at θ = π/ 2. Notice that φ is a 2 π − periodic coordinate, meaning that points at φ = 0 or φ = 2 π (at a given value of θ ) represent the same conformer. This is not true for θ , which is not periodic. In this sense, the spherical set ( Q, θ, φ ) has the advantage that only the two angular variables are needed as collective variables in order to perform a proper – that is, ergodic and unbiased – exploration of the puckered conformations space of typical six-membered rings. This is because along the radial direction no meta-stabilities occur, and the radial coordinate Q relaxes fast enough to be ergodic for every reasonable set of potential (that is, when the bond lengths are rigid or quasi-rigid). As we showed in a previous work $^{77}$, not every representation of the Cremer–Pople coordinates is equivalent to the end of being used as collective variables for a conformational search. In particular, any two-dimensional subset of Cremer–Pople coordinates whose functional form involves also biasing forces along the direction of Q might suffer from lack of ergodicity and, therefore, lead to biased sampling $^{84}$. In this work we make only use of the angular variables of the spherical coordinate set as collective variables for the metadynamics run. Alternative generalized coordinates can be in principle employed to characterize the puck- ered conformers of six-membered rings, such as the three out-of-plane dihedrals introduced by Strauss and Pickett $^{88}$, or other definitions based on three internal dihedral angles$^{89–91}$. All these alternative schemes produce good puckering coordinates, in the sense that they allow to uniquely map the complete puckering conformational space. However, in the context of conformational search using accelerated methods, oppositely to Cremer–Pople coordinates, (a) they require the exploration of the complete three-dimensional space, being therefore less convenient than a two dimensional phase space search, and (b) the set of micro-states cor- responding to the different conformers generally define less simple surfaces which, as it will be discussed later, might affect the determination of the relative populations of conformers. The metadynamics and equilibrium simulations have been performed using a version of the grometa simulation package $^{92–95}$, previously modified to allow the usage of the θ and φ angular coordinates of Cremer and Pople, as described in Ref. 77. For each of the 16 C. Simulation Details 11