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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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Maitra A, Sarkar S, Leitner DM, Dawlaty JM. Electric Fields Influence Intramolecular Vibrational Energy Relaxation and Line Widths. J Phys Chem Lett 2021; 12:7818-7825. [PMID: 34378946 DOI: 10.1021/acs.jpclett.1c02238] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
Intramolecular vibrational energy relaxation (IVR) is fundamentally important to chemical dynamics. We show that externally applied electric fields affect IVR and vibrational line widths by changing the anharmonic couplings and frequency detunings between modes. We demonstrate this effect in benzonitrile for which prior experimental results show a decrease in vibrational line width as a function of applied electric field. We identify three major channels for IVR that depend on electric field. In the dominant channel, the electric field affects the frequency detuning, while in the other two channels, variation of anharmonic couplings as a function of field is the underlying mechanism. Consistent with experimental results, we show that the combination of all channels gives rise to reduced line widths with increasing electric field in benzonitrile. Our results are relevant for controlling IVR with external or internal fields and for gaining a more complete interpretation of line widths of vibrational Stark probes.
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Affiliation(s)
- Anwesha Maitra
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0001, United States
| | - Sohini Sarkar
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0001, United States
| | - David M Leitner
- Department of Chemistry, University of Nevada Reno, Reno, Nevada 89519, United States
| | - Jahan M Dawlaty
- Department of Chemistry, University of Southern California, Los Angeles, California 90089-0001, United States
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Cole-Filipiak NC, Knepper R, Wood M, Ramasesha K. Sub-picosecond to Sub-nanosecond Vibrational Energy Transfer Dynamics in Pentaerythritol Tetranitrate. J Phys Chem Lett 2020; 11:6664-6669. [PMID: 32787226 DOI: 10.1021/acs.jpclett.0c01780] [Citation(s) in RCA: 4] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The time scale associated with shock-induced detonation is a key property of energetic materials that remains poorly understood. Herein, we test aspects of one potential mechanism, the phonon up-pumping mechanism, where shock compression excites lattice phonon modes, transferring energy to intramolecular vibrations leading to chemical bond cleavage and reaction. Using ultrafast infrared pump-probe spectroscopy on pentaerythritol tetranitrate (PETN), we reveal sub-picosecond vibrational energy transfer (VET) from the photoexcited band at 1660 cm-1 into every other infrared-active mode in the probed frequency range 800-1800 cm-1. Energy transfer processes remain incomplete at 150 ps. Computational predictions from density functional theory are used in tandem to elucidate VET pathways in PETN.
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Affiliation(s)
- Neil C Cole-Filipiak
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551, United States
| | - Robert Knepper
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Mitchell Wood
- Sandia National Laboratories, Albuquerque, New Mexico 87185, United States
| | - Krupa Ramasesha
- Combustion Research Facility, Sandia National Laboratories, Livermore, California 94551, United States
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Stable chaos and delayed onset of statisticality in unimolecular dissociation reactions. Commun Chem 2020; 3:4. [PMID: 36703308 PMCID: PMC9814671 DOI: 10.1038/s42004-019-0252-y] [Citation(s) in RCA: 13] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/03/2019] [Accepted: 12/10/2019] [Indexed: 01/29/2023] Open
Abstract
Statistical models provide a powerful and useful class of approximations for calculating reaction rates by bypassing the need for detailed, and often difficult, dynamical considerations. Such approaches invariably invoke specific assumptions about the extent of intramolecular vibrational energy flow in the system. However, the nature of the transition to the statistical regime as a function of the molecular parameters is far from being completely understood. Here, we use tools from nonlinear dynamics to study the transition to statisticality in a model unimolecular reaction by explicitly visualizing the high dimensional classical phase space. We identify generic features in the phase space involving the intersection of two or more independent anharmonic resonances and show that the presence of correlated, but chaotic, intramolecular dynamics near such junctions leads to nonstatisticality. Interestingly, akin to the stability of asteroids in the Solar System, molecules can stay protected from dissociation at the junctions for several picoseconds due to the phenomenon of stable chaos.
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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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Karmakar S, Keshavamurthy S. Relevance of the Resonance Junctions on the Arnold Web to Dynamical Tunneling and Eigenstate Delocalization. J Phys Chem A 2018; 122:8636-8649. [PMID: 30289718 DOI: 10.1021/acs.jpca.8b08626] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
We study the competition and correspondence between the classical and quantum routes to intramolecular vibrational energy redistribution (IVR) in a three degrees of freedom model effective Hamiltonian. Specifically, we focus on the classical and the quantum dynamics near the resonance junctions on the Arnold web that are formed by an intersection of independent resonances. The regime of interest models the IVR dynamics from highly excited initial states near dissociation thresholds of molecular systems wherein both classical and purely quantum, involving dynamical tunneling, routes to IVR coexist. In the vicinity of a resonance junction, classical chaos is inevitably present, and hence one expects the quantum IVR pathways to have a strong classical component as well. We show that with increasing resonant coupling strengths the classical component of IVR leads to a transition from coherent dynamical tunneling to incoherent dynamical tunneling. Furthermore, we establish that the quantum IVR dynamics can be predicted based on the structures on the classical Arnold web. In addition, we investigate the nature of the highly excited eigenstates to identify the quantum signatures of the multiplicity-2 junctions. For the parameter regimes studies herein, by projecting the eigenstates onto the Arnold web, we find that eigenstates in the vicinity of the junctions are primarily delocalized due to dynamical tunneling.
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Affiliation(s)
- Sourav Karmakar
- Department of Chemistry , Indian Institute of Technology , Kanpur , Uttar Pradesh 208 016 , India
| | - Srihari Keshavamurthy
- Department of Chemistry , Indian Institute of Technology , Kanpur , Uttar Pradesh 208 016 , India
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Leitner DM. Molecules and the Eigenstate Thermalization Hypothesis. ENTROPY 2018; 20:e20090673. [PMID: 33265762 PMCID: PMC7513195 DOI: 10.3390/e20090673] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/03/2018] [Revised: 09/02/2018] [Accepted: 09/03/2018] [Indexed: 11/18/2022]
Abstract
We review a theory that predicts the onset of thermalization in a quantum mechanical coupled non-linear oscillator system, which models the vibrational degrees of freedom of a molecule. A system of N non-linear oscillators perturbed by cubic anharmonic interactions exhibits a many-body localization (MBL) transition in the vibrational state space (VSS) of the molecule. This transition can occur at rather high energy in a sizable molecule because the density of states coupled by cubic anharmonic terms scales as N3, in marked contrast to the total density of states, which scales as exp(aN), where a is a constant. The emergence of a MBL transition in the VSS is seen by analysis of a random matrix ensemble that captures the locality of coupling in the VSS, referred to as local random matrix theory (LRMT). Upon introducing higher order anharmonicity, the location of the MBL transition of even a sizable molecule, such as an organic molecule with tens of atoms, still lies at an energy that may exceed the energy to surmount a barrier to reaction, such as a barrier to conformational change. Illustrative calculations are provided, and some recent work on the influence of thermalization on thermal conduction in molecular junctions is also discussed.
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Affiliation(s)
- David M Leitner
- Department of Chemistry, University of Nevada, Reno, NV 89557, USA
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Pandey HD, Leitner DM. Vibrational States and Nitrile Lifetimes of Cyanophenylalanine Isotopomers in Solution. J Phys Chem A 2018; 122:6856-6863. [DOI: 10.1021/acs.jpca.8b06300] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Hari Datt Pandey
- Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557, United States
| | - David M. Leitner
- Department of Chemistry and Chemical Physics Program, University of Nevada, Reno, Nevada 89557, United States
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Classical-quantum correspondence in a model for conformational dynamics: Connecting phase space reactive islands with rare events sampling. Chem Phys Lett 2015. [DOI: 10.1016/j.cplett.2015.05.011] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
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