Abstract :
The eigenstates of a model floppy molecule (i.e. a molecule for which large-amplitude isomerization-like deformations are possible) are variationally calculated. The Hamiltonian operator and the Hamiltonian matrix are established in following the adiabatic weak-mode approach that has been recently proposed. The model consists of a triatomic molecule with two linear isomers, roughly connected with HCN ⇌ CNH: the atomic masses are the appropriate ones, but the isomerization reaction profile does not present the shoulder that is typical of CNH, and the model potential energy surface is a simplified version of the one by Murrell et al. Indeed, the actual high-energy vibrational level distribution of both HCN and CNH turns out to be particularly complicated because of this shoulder and, in order to test new theoretical arguments for analyzing the vibrational eigenstates, using a model with no shoulder is simpler. For zero total angular momentum, the eigenvalues converge up to 20000 cm−1. An adiabatic model, based on the separation of hard (radial) and soft (angular) Jacobi coordinates, is used. The adiabatic representation (in which the analytical radial basis functions parametrically depend on the angle) is interesting from the physical viewpoint: it allows discriminating between various types of eigenstates, depending on (i) the angular distribution of the amplitude and (ii) the value of the projection of the state over the subspace corresponding to a given couple of adiabatic stretching quantum numbers. Many spectroscopic states (both energetically low- and high-lying) are localizated on one isomer side. Several other states are quantally delocalized on both sides, i.e. are linear combinations (interference pattern) of two or more contributions (at least one for each isomer), separated from each other by an angular range where the eigenfunction is very small. We call these states “composite”. Finally, high-lying states (for energies equal to or higher than well identified adiabatic isomerization barriers) are intrinsically delocalized, i.e. with noticeable amplitude almost everywhere. They are very well described within the framework of the adiabatic approach: large-amplitude bending motion of the light atom around the strongly bound diatomic core takes place. Only these states we term “floppy”. The adiabatic weak-mode description allows obtaining quasi-automatically a spectroscopic assignment (as far as it is meaningful) of the molecular states, by means of adiabatic quantum numbers, consistently from the low-lying levels (where the adiabatic quantum numbers are equivalent to standard normal-mode quantum numbers) up to the floppy states, for which normal-mode quantum numbers would be meaningless. The adiabatic quantum numbers appropriately indicate what part of the dynamics can be described as quasi-regular in the molecular states (basically the adiabatic stretching vibrations, and, in localized and floppy states, also the bending motion) and what other part (if any) can be deeply perturbed.
