Using the small alignment index chaos indicator to characterize the vibrational dynamics of a molecular system: LiNC-LiCN

Abstract

A study of the dynamical characteristics of the phase space corresponding to the vibrations of the LiNC-LiCN molecule using an analysis based on the small alignment index (SALI) is presented. SALI is a good indicator of chaos that can easily determine whether a given trajectory is regular or chaotic regardless of the dimensionality of the system, and can also provide a wealth of dynamical information when conveniently implemented. In two-dimensional (2D) systems SALI maps are computed as 2D phase space representations, where the SALI asymptotic values are represented in color scale. We show here how these maps provide full information on the dynamical phase space structure of the LiNC-LiCN system, even quantifying numerically the volume of the different zones of chaos and regularity as a function of the molecule excitation energy.

Above Saddle-Point Regions of Order in a Sea of Chaos in the Vibrational Dynamics of KCN

“…These structures and processes can be studied by using composite surfaces of sections in two-dimensional systems and in general by using frequency map analysis 14 or other chaotic indicators maps. 15,16 Similar studies can be performed in a full quantum setup, 17,18 by using, for example, suitable quasiprobability density distributions in phase space, such as the Wigner 19 or the Husimi functions, 20 which correspond to different (averaged) transforms of the usual quantum wave function giving joint quasiprobability distributions in phase space, which accurately include all quantum effects, or even plain quantum wavepacket propagations. 21,22 Concerning this type of classical-quantum correspondence studies in realistic models for the vibrations of molecular systems, 23 we presented in a previous paper 24 an accurate global analytic potential energy surface (PES) for the KCN isomerizing system, based on accurate ab initio quantum chemistry calculations at the QCISD(T)/6-311+G(2d) level of calculation, which has greatly updated the previous studies existing in the literature, which were performed either at a very low level of calculation, incorrectly predicting the existence of only one minimum, or restricted to the calculation only of the different equilibrium points in the PES, not being then suitable for dynamical studies like ours.…”

“…In the center of the islands of stability one finds the corresponding stable periodic orbit (PO), and between those centers the corresponding unstable one generates the mentioned homoclinic tangle. These structures and processes can be studied by using composite surfaces of sections in two-dimensional systems and in general by using frequency map analysis or other chaotic indicators maps. , …”

A control approach to complexity : from molecular vibrational dynamics to competition games on networks

“…Indeed, even the existing PB structures are clearly delineated by the existence of darker tones. The areas of chaos, also appear in darker colors, but even here a tonality variation is found, this indicating the existence of different types of chaotic behaviour in the system [Beni15]. Furthermore, Figure 6.3(b) shows the corresponding diffusion coefficient map.…”

“…where L 1 and L 2 are the two largest LCE's. Thus, in the case of a chaotic trajectory, this indicator exponentially decreases in time towards zero, while for regular orbits it remains close to a fixed value [Beni15]. The efficiency of SALI as a chaos indicator is analysed in [Sko04].…”