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Keshavamurthy S. Dynamical Tunneling in More than Two Degrees of Freedom. ENTROPY (BASEL, SWITZERLAND) 2024; 26:333. [PMID: 38667887 PMCID: PMC11049088 DOI: 10.3390/e26040333] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/11/2024] [Revised: 04/08/2024] [Accepted: 04/10/2024] [Indexed: 04/28/2024]
Abstract
Recent progress towards understanding the mechanism of dynamical tunneling in Hamiltonian systems with three or more degrees of freedom (DoF) is reviewed. In contrast to systems with two degrees of freedom, the three or more degrees of freedom case presents several challenges. Specifically, in higher-dimensional phase spaces, multiple mechanisms for classical transport have significant implications for the evolution of initial quantum states. In this review, the importance of features on the Arnold web, a signature of systems with three or more DoF, to the mechanism of resonance-assisted tunneling is illustrated using select examples. These examples represent relevant models for phenomena such as intramolecular vibrational energy redistribution in isolated molecules and the dynamics of Bose-Einstein condensates trapped in optical lattices.
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Affiliation(s)
- Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur 208016, Uttar Pradesh, India
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Rashmi R, Yadav PK, Seal A, Paranjothy M, Lourderaj U. E-Z Isomerization in Guanidine: Second-order Saddle Dynamics, Non-statisticality, and Time-frequency Analysis. Chemphyschem 2023; 24:e202200640. [PMID: 36205532 DOI: 10.1002/cphc.202200640] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/25/2022] [Revised: 10/06/2022] [Indexed: 01/20/2023]
Abstract
Our recent work on the E-Z isomerization reaction of guanidine using ab initio chemical dynamics simulations [Rashmi et al., Regul. Chaotic Dyn. 2021, 26, 119] emphasized the role of second-order saddle (SOS) in the isomerization reaction; however, we could not unequivocally establish the non-statistical nature of the dynamics followed in the reaction. In the present study, we performed thousands of on-the-fly trajectories using forces computed at the MNDO level to investigate the influence of second-order saddle in the E-Z isomerization reaction of guanidine and the role of intramolecular vibrational energy redistribution (IVR) on the reaction dynamics. The simulations reveal that while majority of the trajectories follow the traditional transition state pathways, 15 % of the trajectories follow the SOS path. The dynamics was found to be highly non-statistical with the survival probabilities of the reactants showing large deviations from those obtained within the RRKM assumptions. In addition, a detailed analysis of the dynamics using time-dependent frequencies and the frequency ratio spaces reveal the existence of multiple resonance junctions that indicate the existence of regular dynamics and long-lived quasi-periodic trajectories in the phase space associated with non-RRKM behavior.
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Affiliation(s)
- Richa Rashmi
- National Insitute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute P. O. Jatni, Khurdha, Odisha, 752050, India
| | - Pankaj Kumar Yadav
- National Insitute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute P. O. Jatni, Khurdha, Odisha, 752050, India
| | - Aniruddha Seal
- National Insitute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute P. O. Jatni, Khurdha, Odisha, 752050, India
| | - Manikandan Paranjothy
- Department of Chemistry, Indian Institute of Technology Jodhpur, Jodhpur, Rajasthan, India
| | - Upakarasamy Lourderaj
- National Insitute of Science Education and Research (NISER) Bhubaneswar, An OCC of Homi Bhabha National Institute P. O. Jatni, Khurdha, Odisha, 752050, India
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Takatsuka K. Quantum Chaos in the Dynamics of Molecules. ENTROPY (BASEL, SWITZERLAND) 2022; 25:63. [PMID: 36673204 PMCID: PMC9857761 DOI: 10.3390/e25010063] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 11/07/2022] [Revised: 12/22/2022] [Accepted: 12/22/2022] [Indexed: 06/17/2023]
Abstract
Quantum chaos is reviewed from the viewpoint of "what is molecule?", particularly placing emphasis on their dynamics. Molecules are composed of heavy nuclei and light electrons, and thereby the very basic molecular theory due to Born and Oppenheimer gives a view that quantum electronic states provide potential functions working on nuclei, which in turn are often treated classically or semiclassically. Therefore, the classic study of chaos in molecular science began with those nuclear dynamics particularly about the vibrational energy randomization within a molecule. Statistical laws in probabilities and rates of chemical reactions even for small molecules of several atoms are among the chemical phenomena requiring the notion of chaos. Particularly the dynamics behind unimolecular decomposition are referred to as Intra-molecular Vibrational energy Redistribution (IVR). Semiclassical mechanics is also one of the main research fields of quantum chaos. We herein demonstrate chaos that appears only in semiclassical and full quantum dynamics. A fundamental phenomenon possibly giving birth to quantum chaos is "bifurcation and merging" of quantum wavepackets, rather than "stretching and folding" of the baker's transformation and the horseshoe map as a geometrical foundation of classical chaos. Such wavepacket bifurcation and merging are indeed experimentally measurable as we showed before in the series of studies on real-time probing of nonadiabatic chemical reactions. After tracking these aspects of molecular chaos, we will explore quantum chaos found in nonadiabatic electron wavepacket dynamics, which emerges in the realm far beyond the Born-Oppenheimer paradigm. In this class of chaos, we propose a notion of Intra-molecular Nonadiabatic Electronic Energy Redistribution (INEER), which is a consequence of the chaotic fluxes of electrons and energy within a molecule.
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Affiliation(s)
- Kazuo Takatsuka
- Fukui Institute for Fundamental Chemistry, Kyoto University, Kyoto 606-8103, Japan
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Mondal S, Wang DS, Keshavamurthy S. Dissociation dynamics of a diatomic molecule in an optical cavity. J Chem Phys 2022; 157:244109. [PMID: 36586980 DOI: 10.1063/5.0124085] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We study the dissociation dynamics of a diatomic molecule, modeled as a Morse oscillator, coupled to an optical cavity. A marked suppression of the dissociation probability, both classical and quantum, is observed for cavity frequencies significantly below the fundamental transition frequency of the molecule. We show that the suppression in the probability is due to the nonlinearity of the dipole function. The effect can be rationalized entirely in terms of the structures in the classical phase space of the model system.
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Affiliation(s)
- Subhadip Mondal
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208 016, India
| | - Derek S Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208 016, India
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Wang DS, Flick J, Yelin SF. Chemical reactivity under collective vibrational strong coupling. J Chem Phys 2022; 157:224304. [DOI: 10.1063/5.0124551] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
Abstract
Recent experiments of chemical reactions in optical cavities have shown great promise to alter and steer chemical reactions, but still remain poorly understood theoretically. In particular, the origin of resonant effects between the cavity and certain vibrational modes in the collective limit is still subject to active research. In this paper, we study the unimolecular dissociation reactions of many molecules, collectively interacting with an infrared cavity mode, through their vibrational dipole moment. We find that the reaction rate can slow down by increasing the number of aligned molecules, if the cavity mode is resonant with a vibrational mode of the molecules. We also discover a simple scaling relation that scales with the collective Rabi splitting, to estimate the onset of reaction rate modification by collective vibrational strong coupling and numerically demonstrate these effects for up to 104 molecules.
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Affiliation(s)
- Derek S. Wang
- Harvard John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, USA
| | - Johannes Flick
- Center for Computational Quantum Physics, Flatiron Institute, New York, New York 10010, USA
- Department of Physics, City College of New York, New York, New York 10031, USA
- Department of Physics, The Graduate Center, City University of New York, New York, New York 10016, USA
| | - Susanne F. Yelin
- Department of Physics, Harvard University, Cambridge, Massachusetts 02138, USA
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Wang DS, Neuman T, Yelin SF, Flick J. Cavity-Modified Unimolecular Dissociation Reactions via Intramolecular Vibrational Energy Redistribution. J Phys Chem Lett 2022; 13:3317-3324. [PMID: 35389664 PMCID: PMC9036583 DOI: 10.1021/acs.jpclett.2c00558] [Citation(s) in RCA: 22] [Impact Index Per Article: 11.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 05/11/2023]
Abstract
While the emerging field of vibrational polariton chemistry has the potential to overcome traditional limitations of synthetic chemistry, the underlying mechanism is not yet well understood. Here, we explore how the dynamics of unimolecular dissociation reactions that are rate-limited by intramolecular vibrational energy redistribution (IVR) can be modified inside an infrared optical cavity. We study a classical model of a bent triatomic molecule, where the two outer atoms are bound by anharmonic Morse potentials to the center atom coupled to a harmonic bending mode. We show that an optical cavity resonantly coupled to particular anharmonic vibrational modes can interfere with IVR and alter unimolecular dissociation reaction rates when the cavity mode acts as a reservoir for vibrational energy. These results lay the foundation for further theoretical work toward understanding the intriguing experimental results of vibrational polaritonic chemistry within the context of IVR.
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Affiliation(s)
- Derek S. Wang
- Harvard
John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, Massachusetts 02138, United States
- E-mail:
| | - Tomáš Neuman
- IPCMS
de Strasbourg, UMR 7504 (CNRS − Université
de Strasbourg), 67034 Strasbourg, France
| | - Susanne F. Yelin
- Department
of Physics, Harvard University, Cambridge, Massachusetts 02138, United States
- E-mail:
| | - Johannes Flick
- Center
for Computational Quantum Physics, Flatiron
Institute, New York, New York 10010, United
States
- E-mail:
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Karmakar S, Keshavamurthy S. Intramolecular vibrational energy redistribution and the quantum ergodicity transition: a phase space perspective. Phys Chem Chem Phys 2020; 22:11139-11173. [DOI: 10.1039/d0cp01413c] [Citation(s) in RCA: 26] [Impact Index Per Article: 6.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022]
Abstract
The onset of facile intramolecular vibrational energy flow can be related to features in the connected network of anharmonic resonances in the classical phase space.
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Affiliation(s)
- Sourav Karmakar
- Department of Chemistry
- Indian Institute of Technology
- Kanpur
- India
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