Phase space geometry of dynamics passing through saddle coupled with spatial rotation

Abstract

Nonlinear reaction dynamics through a rank-one saddle is investigated for many-particle system with spatial rotation. Based on the recently developed theories of the phase space geometry in the saddle region, we present a theoretical framework to incorporate the spatial rotation which is dynamically coupled with the internal vibrational motions through centrifugal and Coriolis interactions. As an illustrative simple example, we apply it to isomerization reaction of HCN with some nonzero total angular momenta. It is found that no-return transition state (TS) and a set of impenetrable reaction boundaries to separate the "past" and "future" of trajectories can be identified analytically under rovibrational couplings. The three components of the angular momentum are found to have distinct effects on the migration of the "anchor" of the TS and the reaction boundaries through rovibrational couplings and anharmonicities in vibrational degrees of freedom. This method provides new insights in understanding the origin of a wide class of reactions with nonzero angular momentum.

Reactivity boundaries for chemical reactions associated with higher-index and multiple saddles

“…Quantum effects must also be considered for the complete treatment of this system. We here briefly mention that the concept of reactivity boundaries around the index 1 saddle point has recently been extended to incorporate ro-vibrational couplings [47,48] and quantum effects [45,46]. It will be an important future work to combine these studies with the generalized reactivity boundaries proposed in the present paper.…”

“…The definition of the reactivity boundary (the destination-or the origin-dividing set) can be applied to systems with multiple states, since the definition of the reactivity boundaries are only based on a single state. This definition of the reactivity boundaries and their seed is a generalization of the previous invariant objects (the stable and unstable manifolds of NHIM, and the NHIM, respectively) studied in the literature [27,28,[38][39][40][41][42][43][44][45][46][47][48][49][50][51] and summarized in Sec. II A.…”

“…The theory has been applied and developed to elucidate the mechanism of several reaction dynamics about a decade [27,28,[38][39][40][41][42][43][44][45][46][47][48][49][50][51]. For practical applications the Lie canonical perturbation theory, developed by a Japanese astrophysicist, Gen-Ichiro Hori [74,75] (and equivalent theory was independently developed by Deprit [76,77]), has been frequently used.…”

“…The scope of the dynamical reaction theory [51] is not limited to only chemical reactions but also includes, for example, ionization of a hydrogen atom under electromagnetic fields [27,40], isomerization of clusters [38,39], orbit designs in solar systems [55], and so forth. Recently, these approaches have been generalized to dissipative multidimensional Langevin equations [41,43,44] based on a seminal work by Martens [53], laser-controlled chemical reactions with quantum effects [45,46], and systems with rovibrational couplings [47,48] and showed the robust existence of reactivity boundaries even while a no-return TS ceases to exist [28].…”

“…The dynamics around the saddle point have been recently investigated extensively in terms of nonlinear dynamics [26][27][28]35,[38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] in the context of TS theory [29,30] in molecular science. Among them, particularly relevant to the present work, is the finding of the "tube" [26] structures in phase space to conduct the reacting trajectories from the reactant to the product across an index 1 saddle.…”