Intramolecular energy transfer and the driving mechanisms for large-amplitude collective motions of clusters

Abstract

This paper uncovers novel and specific dynamical mechanisms that initiate large-amplitude collective motions in polyatomic molecules. These mechanisms are understood in terms of intramolecular energy transfer between modes and driving forces. Structural transition dynamics of a six-atom cluster between a symmetric and an elongated isomer is highlighted as an illustrative example of what is a general message. First, we introduce a general method of hyperspherical mode analysis to analyze the energy transfer among internal modes of polyatomic molecules. In this method, the ͑3n −6͒ internal modes of an n-atom molecule are classified generally into three coarse level gyration-radius modes, three fine level twisting modes, and ͑3n −12͒ fine level shearing modes. We show that a large amount of kinetic energy flows into the gyration-radius modes when the cluster undergoes structural transitions by changing its mass distribution. Based on this fact, we construct a reactive mode as a linear combination of the three gyration-radius modes. It is shown that before the reactive mode acquires a large amount of kinetic energy, activation or inactivation of the twisting modes, depending on the geometry of the isomer, plays crucial roles for the onset of a structural transition. Specifically, in a symmetric isomer with a spherical mass distribution, activation of specific twisting modes drives the structural transition into an elongated isomer by inducing a strong internal centrifugal force, which has the effect of elongating the mass distribution of the system. On the other hand, in an elongated isomer, inactivation of specific twisting modes initiates the structural transition into a symmetric isomer with lower potential energy by suppressing the elongation effect of the internal centrifugal force and making the effects of the potential force dominant. This driving mechanism for reactions as well as the present method of hyperspherical mode analysis should be widely applicable to molecular reactions in which a system changes its overall mass distribution in a significant way.

Roles of dynamical symmetry breaking in driving oblate-prolate transitions of atomic clusters

“…Moreover, recent studies 75,[77][78][79] have suggested that one can utilize these pathways of energy transfer to induce molecular reactions by selectively activating specific degrees of freedom. Since the hyperspherical coordinates give a concise and universal expression for the kinetic energy of many-atom systems, [48][49][50][51][52][53][54][55][56][57][58]70,71 our present approach is indeed suitable to the study of energy transfer among internal degrees of freedom. By taking this advantage, we identify characteristic pathways of energy transfer that are responsible for the onset of structural transitions of the cluster between oblate and prolate isomers.…”

“…Three of the hyperangular degrees of freedom correspond to twisting motions, and the remaining 3n − 12 hyperangular degrees of freedom correspond to shearing motions. 71 Activations of the twisting and shearing motions induce dynamical forces called the internal centrifugal forces. 70,71 The internal centrifugal force originating from the twisting motions has an effect of breaking the symmetry between two of the gyration radii.…”

“…71 Activations of the twisting and shearing motions induce dynamical forces called the internal centrifugal forces. 70,71 The internal centrifugal force originating from the twisting motions has an effect of breaking the symmetry between two of the gyration radii. While the potential forces generally play the role of restoring the symmetry of mass distribution of a molecule, the internal centrifugal forces can be a driving force for structural transitions by breaking the symmetry of molecular mass distribution.…”

“…Recently, the authors have been utilizing these hyperspherical coordinates with the framework of geometric mechanics, [59][60][61][62][63][64][65][66][67] which gives a rigorous treatment of the coupling between molecular vibrations and rotations, to study structural transitions of molecular systems. [68][69][70][71][72] The hyperspherical coordinates consist of three gyration radii and 3n − 9 hyperangular degrees of freedom. While the three gyration radii characterize the instantaneous mass distributions of the system along the three instantaneous principal axes, the 3n − 9 hyperangular degrees of freedom characterize the internal shape changes.…”

Control of a model of DNA division via parametric resonance

“…The coarse variable of the (approximate) 0th mode, which is the average angle of the pendula, corresponds to the angle of the frame defined by the radius of gyration in our molecular studies. [40][41][42] This variable is a global and slow variable and it plays an important role as the reactive coordinate for our DNA work. Moreover, this reactive mode forms a nearly 0:1 resonance with any other mode, each of which has an O(1) frequency.…”