Dynamical tunnelling in molecules: quantum routes to energy flow

Keshavamurthy, Srihari

doi:10.1080/01442350701462288

Cited by 54 publications

(59 citation statements)

References 228 publications

(401 reference statements)

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“…Illustrative examples of this can be found in Refs. [11] and [12], respectively. On the other hand, the analysis of the quantum counterpart has produced many fewer results [13][14][15].…”

mentioning

confidence: 99%

Poincaré-Birkhoff theorem in quantum mechanics

Wisniacki¹,

Saraceno

Arranz

et al. 2011

Phys. Rev. E

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Quantum manifestations of the dynamics around resonant tori in perturbed Hamiltonian systems, dictated by the Poincaré-Birkhoff theorem, are shown to exist. They are embedded in the interactions involving states which differ in a number of quanta equal to the order of the classical resonance. Moreover, the associated classical phase space structures are mimicked in the quasiprobability density functions and their zeros. The quantum manifestations of classical chaos, or quantum chaos, have received much attention in the recent past [1]. Besides random matrix theory, which describes universal properties, Gutzwiller's trace formula describes the dual relationship between coherent sums over periodic orbits with sums over quantized states [2]. The appearance of scars of periodic orbits in individual eigenfunctions and the associated scar theory are results that deserve special mention [3][4][5]. These results are by now routinely applied in a variety of important technological applications [6]. At the other extreme, for integrable systems, this dual relationship is more precise and collective sums over the degenerate periodic orbits on rational tori give rise to individual states on quantized tori [7].For systems close to integrable, the classical behavior is completely understood in terms of the celebrated KolmogorovArnold-Moser (KAM) and the Poincaré-Birkhoff (PB) theorems [8,9]. The first one deals with quasiperiodic motion and the persistence of sufficiently irrational tori under perturbations. The second considers the fate of the (unperturbed) resonant tori, from which an even number of periodic orbits (POs) survive. In their vicinity, chains of islands of regularity surrounded by a chaotic separatrix organized by a homoclinic tangle are formed. This structure and the associated transport are well described by the universal pendulum model of Chirikov [10], where the (slow) Arnold diffusion [8] is the controlling mechanism of transport. Classical resonances are crucial in the control of many relevant processes, such as intramolecular vibrational relaxation in chemistry or directional laser emission in nano-optics. Illustrative examples of this can be found in Refs. [11] and [12], respectively. On the other hand, the analysis of the quantum counterpart has produced many fewer results [13][14][15].In this paper, we explore the quantum implications of the classical PB theorem. We find that they exist and can be unveiled by studying the mechanism by which two quantized tori of the unperturbed system interact to form the beginning of an island chain on a resonant rational torus. The subtle mechanism by which the quantum numbers of the unperturbed tori are exchanged in a quasicrossing is illustrated by the exchange of zeros of the stellar representation [16]. The splitting of a series of avoided crossings (ACs) ruled by a PB resonance in the correlation diagram is explained semiclassically.The model that we have chosen to study is the Harper map in the unit square, with N = (2πh) −1 . The simplicity of this model allow...

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“…Illustrative examples of this can be found in Refs. [11] and [12], respectively. On the other hand, the analysis of the quantum counterpart has produced many fewer results [13][14][15].…”

mentioning

confidence: 99%

Poincaré-Birkhoff theorem in quantum mechanics

Wisniacki¹,

Saraceno

Arranz

et al. 2011

Phys. Rev. E

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“…Thirdly, the various sequences "collide" near E ∼ 7800 cm −1 leading to significant disruption of the regularity of the sequences. Small level velocities and energy spacings in this region imply several multistate avoided crossings and suggest that the state mixing could be due to dynamical tunneling [19]. Dynamical assignments of the states in this complicated transition region are difficult if not impossible.…”

Section: B Breaking the Goodness Of V2mentioning

confidence: 99%

On the nature of highly vibrationally excited states of thiophosgene#

Keshavamurthy

2012

J Chem Sci

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In this work an analysis of the highly vibrationally excited states of thiophosgene (SCCl2) is made in order to gain insights into some of the experimental observations and spectral features. The states analyzed herein lie in a spectrally complex region where strong mode mixings are expected due to the overlap of several strong anharmonic Fermi resonances. Two recent techniques, a semiclassical angle space representation of the eigenstates and the parametric variation of the eigenvalues (levelvelocities) are used to identify eigenstate sequences exhibiting common localization characteristics. Preliminary results on the influence of highly excited out-of-plane bending modes on the nature of the eigenstates suggest a possible bifurcation in the system. I. INTRODUCIONUnderstanding the nature of the highly excited molecular eigenstates is equivalent to deciphering the mechanism of intramolecular vibrational energy redistribution (IVR) occuring in the molecule [1]. However, the assignment of eigenstates is far from simple. The existence of and interplay of several strong anharmonic resonances result in complicated spectral patterns and highly mixed states. Nevertheless, eigenstates of molecular systems rarely exhibit the extreme scenario of being completely ergodic or completely regular [2]. A generic situation, even at fairly high energies, is the coexistence of several classes of eigenstates with differing degree of mixing being interspersed among each other [3,4]. More interestingly, the interspersed states can show several sequences associated with certain identifiable common localization characteristics. In other words, although a full set of quantum numbers do not exist for labeling such states, there are reasons to believe that a sufficient number of approximate quantum numbers do exist to understand, and hence assign, the eigenstates. Since the approximate quantum numbers arise out of the local dynamics due to specific resonances, relevant at the energies of interest, the assignment is inherently dynamical in nature. In a nutshell, several decades of work have shown that dynamical assignments can be done reliably only if the structure of the corresponding classical phase space is well understood [5].This work is concerned with the dynamical assignment of the eigenstates of thiophosgene SCCl 2 . The Hamiltonian of interest is a highly accurate spectroscopic Hamiltonian obtained [6] by Gruebele and Sibert via a canonical Van Vleck perturbation analysis of the experimentally derived normal mode potential surface [7]. The Hamiltonian can be expressed as H = H 0 + V res withThe zeroth-order anharmonic Hamiltonian is H 0 , whose eigenstates are the feature states and V res accounts for the important anharmonic resonances responsible for the IVR dynamics. In the rest of the paper the various resonances will be refered to by simply indicating the modes. For instance, the first resonance term in V res above will be refered to as the 526-resonance. The hermitian adjoints of the operators are denoted by c.c., and the op...

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“…In the work presented here the intrinsic non-RRKM N(t) is represented by the above multi-exponential function, but it should be noted that both power law [12][13][14][15][16][17] and stretched exponential [18] expressions have also been used to describe non-exponential unimolecular decomposition. RRKM theory requires chaotic intramolecular dynamics, with ergodic behavior on the time-scale of the unimolecular reaction, and there is considerable interest in characterizing the type(s) of classical motions and resulting phase space structure(s) which give rise to intrinsic non-RRKM behavior [19][20][21][22][23][24][25][26][27][28].…”

Section: P(t) = I F I K I Ementioning

confidence: 99%

Models for Intrinsic Non-RRKM Dynamics. Decomposition of the SN2 Intermediate Cl––CH3Br

Paranjothy

Sun

Paul

et al. 2013

Zeitschrift Für Physikalische Chemie

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Chemical dynamics simulations, based on both an analytic potential energy surface (PES) and direct dynamics, were used to investigate the intrinsic non-RRKM dynamics of the Cl products were fit with multi-exponential functions. The intrinsic non-RRKM dynamics is more pronounced for the simulations with the analytic PES than by direct dynamics, with the populations for the former and latter primarily represented by tri-and bi-exponential functions, respectively. For the analytic PES and direct dynamics simulations, the intrinsic non-RRKM dynamics is more important for the isomerization pathway to form ClCH 3 -Br − than for dissociation to Cl − + CH 3 Br. Since the decomposition probability of Cl − -CH 3 Br is non-exponential, the Cl − -CH 3 Br unimolecular rate constant depends on pressure, with both high and low pressure limits. The high pressure limit is the RRKM rate constant and for the simulations with the analytic PES the rate constant decreased by a factor of 3.0, 5.6, and 4.3 in going from the high to low pressure limit for total energies of 40, 60, and 80 kcal/mol. For the direct dynamics simulations these respective factors are 2.4, 1.4, and 1.2. A separable phase space model with intermolecular and intramolecular complexes describes some of the simulation results, but overall models advanced for intrinsic non-RRKM dynamics give incomplete representations of the intermediate and product populations vs. time determined from the simulations.

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Dynamical tunnelling in molecules: quantum routes to energy flow

Cited by 54 publications

References 228 publications

Poincaré-Birkhoff theorem in quantum mechanics

Poincaré-Birkhoff theorem in quantum mechanics

On the nature of highly vibrationally excited states of thiophosgene#

Models for Intrinsic Non-RRKM Dynamics. Decomposition of the SN2 Intermediate Cl––CH3Br

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