The characteristic shape of the JT-split APES has specific consequences for the nuclear dynamics, here considered in the fully quantum sense. For sufficiently strong JT coupling, the minimum points are sufficiently far (at least by a few vibrational energy quanta) below the JT intersection. Two different energy regimes are then to be distinguished, those of low and high energy.
* In the low-energy regime the nuclear motion is confined to regions near the "minimum energy points". The distorted configurations sampled impart their geometrical parameters on, for example, the rotational fine structure in a spectrum. Due to the existence of barriers between the various minima in the APES, like those appearing due to the warping of the , motion on the low-energy regime is usually classified as either a static JTE, dynamic JTE or incoherent hopping. Each regime shows particular fingerprints on experimental measurements.
:* Static JTE: In this case, the system is trapped in one of the lowest-energy minima of the APES (usually determined by small perturbations created by the environment of the JT system) and does not have enough energy to cross the barrier towards another minimum during the typical time associated to the measurement. Quantum dynamical effects like tunnelling are negligible, and effectively the molecule or solid displays the low symmetry associated with a single minimum.
:* Dynamic JTE: In this case, the barriers are sufficiently small compared to, for example, the zero-point energy associated to the minima, so that vibronic wavefunctions (and all observables) display the symmetry of the reference (undistorted) system. In the linear E ⊗ e problem, the motion associated to this regime would be around the circular path in the figure. When the barrier is sufficiently small, this is called (free) pseudorotation (not to be confused with the rotation of a rigid body in space, see difference between real and pseudo rotations illustrated [http://www.nottingham.ac.uk/~ppzjld/pseudorotate.htm here] for the fullerene molecule C). When the barrier between the minima and the saddle points on the warped path exceeds a vibrational quantum, pseudorotational motion is slowed down and occurs through tunnelling. This is called hindered pseudorotation. In both free and hindered pseudorotation, the important phenomenon of the geometric (Berry) phase alters the ordering of the levels.
:* Incoherent hopping: Another way in which the system can overcome the barrier is through thermal energy. In this case, while the system moves throughout the minima of the system, the state is not a quantum coherent one but a statistical mixture. This difference can be observed experimentally.
* The dynamics is quite different for high energies, such as occur from an optical transition from a non-degenerate initial state with a high-symmetry (JT undistorted) equilibrium geometry into a JT distorted state. This leads the system to the region near the conical intersection of the JT-split APES in the centre of the figure. Here the nonadiabatic couplings become very large and the behaviour of the system cannot be described within the familiar Born–Oppenheimer (BO) separation between the electronic and nuclear motions. The nuclear motion ceases to be confined to a single, well-defined APES and the transitions between the adiabatic surfaces occur yielding effects like Slonzcewsky resonances. In molecules this is usually a femtosecond timescale, which amounts to ultrafast (femtosecond) internal conversion processes, accompanied by broad spectral bands also under isolated-molecule conditions and highly complex spectral features. Examples for these phenomena will be covered in section .
As already stated above, the distinction of low and high energy regimes is valid only for sufficiently strong JT couplings, that is, when several or many vibrational energy quanta fit into the energy window between the conical intersection and the minimum of the lower JT-split APES. For the many cases of small to intermediate JT couplings this energy window and the corresponding adiabatic low-energy regime does not exist. Rather, the levels on both JT-split APES are intricately mixed for all energies and the nuclear motion always proceeds on both JT split APES simultaneously.