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Sanrey M, Joyeux M. Slow periodic oscillations in time domain dynamics of NO2. J Chem Phys 2007; 126:074301. [PMID: 17328599 DOI: 10.1063/1.2446920] [Citation(s) in RCA: 16] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The authors investigated the time domain nonadiabatic dynamics of NO2 on the coupled X 2A1 and A 2B2 electronic states by launching wave packets on the excited electronic state and focused on the evolution at long times (t>200 fs), which has received little attention up to now. The authors showed that the initial fast spreading of the wave packets is followed at all energies by slow periodic intramolecular vibronic energy redistribution (IVER) with periods in the range of 0.3 to several tens of picoseconds. These energy transfers lead to oscillations with the same periods in the population of each electronic state. Propagation of wave packets indicates that IVER frequencies also dominate the fluctuations of the squared modulus of the autocorrelation function |A(t)|2 at energies not too high above the bottom of the conical intersection, but this is no longer the case at higher energies. For example, for initial wave packets prepared by almost vertical excitation of the vibrational ground state of the ground electronic surface, the oscillations of |A(t)|2 essentially reflect the detuning from 1:2 resonance between the frequency of the bend and that of the symmetric stretch in the excited electronic state. These theoretical results were used to discuss the possible origin of the low-frequency oscillations which were recently observed in time domain experimental spectra of NO2.
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Affiliation(s)
- Michaël Sanrey
- Laboratoire de Spectrométrie Physique (CNRS UMR5588), Université Joseph Fourier, BP 87, 38402 St. Martin d'Hères, France
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Noid WG, Loring RF. Classical and quantum mechanical infrared echoes from resonantly coupled molecular vibrations. J Chem Phys 2007; 122:174507. [PMID: 15910045 DOI: 10.1063/1.1888485] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The nonlinear response function associated with the infrared vibrational echo is calculated for a quantum mechanical model of resonantly coupled, anharmonic oscillators at zero temperature. The classical mechanical response function is determined from the quantum response function by setting variant Planck's over 2pi-->0, permitting the comparison of the effects of resonant vibrational coupling among an arbitrary number of anharmonic oscillators on quantum and classical vibrational echoes. The quantum response function displays a time dependence that reflects both anharmonicity and resonant coupling, while the classical response function depends on anharmonicity only through a time-independent amplitude, and shows a time dependence controlled only by the resonant coupling. In addition, the classical response function grows without bound in time, a phenomenon associated with the nonlinearity of classical mechanics, and absent in quantum mechanics. This unbounded growth was previously identified in the response function for a system without resonant vibrational energy transfer, and is observed to persist in the presence of resonant coupling among vibrations. Quantitative agreement between classical and quantum response functions is limited to a time scale of duration inversely proportional to the anharmonicity.
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Affiliation(s)
- W G Noid
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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Goj A, Loring RF. Effect of noise on the classical and quantum mechanical nonlinear response of resonantly coupled anharmonic oscillators. J Chem Phys 2006; 124:194101. [PMID: 16729797 DOI: 10.1063/1.2198203] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Multidimensional infrared spectroscopy probes coupled molecular vibrations in complex, condensed phase systems. Recent theoretical studies have focused on the analytic structure of the nonlinear response functions required to calculate experimental observables in a perturbative treatment of the radiation-matter interaction. Classical mechanical nonlinear response functions have been shown to exhibit unbounded growth for anharmonic, integrable systems, as a consequence of the nonlinearity of classical mechanics, a feature that is absent in a quantum mechanical treatment. We explore the analytic structure of the third-order vibrational response function for an exactly solvable quantum mechanical model that includes some of the important and theoretically challenging aspects of realistic models of condensed phase systems: anharmonicity, resonant coupling, fluctuations, and a well-defined classical mechanical limit.
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Affiliation(s)
- Anne Goj
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, NY 14853, USA
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Sanrey M, Joyeux M, Sadovskii DA. Classical and quantum-mechanical plane switching in CO2. J Chem Phys 2006; 124:74318. [PMID: 16497047 DOI: 10.1063/1.2167747] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Classical plane switching takes place in systems with a pronounced 1:2 resonance, where the degree of freedom with the lowest frequency is doubly degenerate. Under appropriate conditions, one observes a periodic and abrupt precession of the plane in which the doubly degenerate motion takes place. In this article, we show that quantum plane switching exists in CO(2). Based on our analytical solutions of classical Hamilton's equations of motion, we describe the dependence on vibrational angular momentum and energy of the frequency of switches and the plane switching angle. Using these results, we find optimal initial wave-packet conditions for CO(2) and show, through quantum-mechanical propagation, that such a wave packet indeed displays plane switching at energies around 10 000 cm(-1) above the ground state on time scales of about 100 fs.
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Affiliation(s)
- Michaël Sanrey
- Laboratoire de Spectrométrie Physique (CNRS UMR 5588), Université Joseph Fourier--Grenoble 1, St. Martin d'Hères, France
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Noid WG, Loring * RF. Nonlinear spectroscopy of resonantly coupled classical mechanical molecular vibrations. Mol Phys 2005. [DOI: 10.1080/00268970500245999] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Kellman ME, Dow MW, Tyng V. Dressed basis for highly excited molecular vibrations. J Chem Phys 2003. [DOI: 10.1063/1.1569908] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022] Open
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Svitak JF, Tyng V, Kellman ME. Bifurcation Analysis of Higher m:n Resonance Spectroscopic Hamiltonian†. J Phys Chem A 2002. [DOI: 10.1021/jp0263976] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/16/2022]
Affiliation(s)
- John F. Svitak
- Department of Chemistry, University of Oregon, Eugene, Oregon 97403-1253
| | - Vivian Tyng
- Department of Chemistry, University of Oregon, Eugene, Oregon 97403-1253
| | - Michael E. Kellman
- Department of Chemistry, University of Oregon, Eugene, Oregon 97403-1253
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Joyeux M, Farantos SC, Schinke R. Highly Excited Motion in Molecules: Saddle-Node Bifurcations and Their Fingerprints in Vibrational Spectra. J Phys Chem A 2002. [DOI: 10.1021/jp0131065] [Citation(s) in RCA: 77] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- M. Joyeux
- Laboratoire de Spectrométrie Physique, Université Joseph Fourier-Grenoble I, BP 87, F-38402 St Martin d'Heres Cedex, France
| | - S. C. Farantos
- Institute of Electronic Struture and Laser Foundation for Research and Technology−Hellas, Greece, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece
| | - R. Schinke
- Max-Planck-Institut für Strömungsforschung, D-37073 Göttingen, Germany
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Zhou C, Xie D, Chen R, Yan G, Guo H, Tyng V, Kellman ME. Quantum calculation of highly excited vibrational energy levels of CS2(X) on a new empirical potential energy surface and semiclassical analysis of 1:2 Fermi resonance. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2002; 58:727-746. [PMID: 11991492 DOI: 10.1016/s1386-1425(01)00666-7] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 05/23/2023]
Abstract
We report a refined potential energy function for the ground electronic state of CS2 based on a least-squares fitting to several low-lying experimental vibrational frequencies. Energy levels up to 20,000 cm(-1) have been obtained on this empirical potential using the Lanczos algorithm and potential optimized discrete variable representation. Among them, 329 levels below 10,000 cm(-1) are assigned with approximate normal mode quantum numbers (n1, n(0)2, n3), based on expectation values of one-dimensional (1D) reference Hamiltonians. An effective Hamiltonian is extracted from these assigned levels. The agreement with experimental data, including those of several isotopically substituted species, is excellent. In addition, some Fermi and anharmonic resonances are analyzed. The nearest neighbor level spacing and delta3 distributions indicated that the vibrational spectrum of CS2 is largely regular in the energy range up to 20,000 cm(-1). Semiclassical phase space analysis, including bifurcation analysis of the spectroscopic Hamiltonian, is used to interpret subtle anomalies signaled by expectation values used in normal mode assignments. The meaning of Fermi resonance is clarified by contrasting the semiclassical analysis of CS2 and CO2.
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Affiliation(s)
- Cheng Zhou
- Department of Chemistry, University of New Mexico, Albuquerque 87111, USA
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Bredenbeck J, Beck C, Schinke R, Koput J, Stamatiadis S, Farantos SC, Joyeux M. The vibrational spectrum of deuterated phosphaethyne: A quantum mechanical, classical, and semiclassical analysis. J Chem Phys 2000. [DOI: 10.1063/1.481500] [Citation(s) in RCA: 12] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Joyeux M, Sugny D, Tyng V, Kellman ME, Ishikawa H, Field RW, Beck C, Schinke R. Semiclassical study of the isomerization states of HCP. J Chem Phys 2000. [DOI: 10.1063/1.481001] [Citation(s) in RCA: 49] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Weiß J, Hauschildt J, Grebenshchikov SY, Düren R, Schinke R, Koput J, Stamatiadis S, Farantos SC. Saddle-node bifurcations in the spectrum of HOCl. J Chem Phys 2000. [DOI: 10.1063/1.480563] [Citation(s) in RCA: 45] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Jost R, Joyeux M, Skokov S, Bowman J. Vibrational analysis of HOCl up to 98% of the dissociation energy with a Fermi resonance Hamiltonian. J Chem Phys 1999. [DOI: 10.1063/1.479974] [Citation(s) in RCA: 41] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Ishikawa H, Field RW, Farantos SC, Joyeux M, Koput J, Beck C, Schinke R. HCP CPH ISOMERIZATION: Caught in the Act. Annu Rev Phys Chem 1999; 50:443-84. [PMID: 15012419 DOI: 10.1146/annurev.physchem.50.1.443] [Citation(s) in RCA: 108] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/09/2022]
Abstract
▪ Abstract In this overview we discuss the vibrational spectrum of phosphaethyne, HCP, in its electronic ground state, as revealed by complementary experimental and theoretical examinations. The main focus is the evolution of specific spectral patterns from the bottom of the potential well up to excitation energies of approximately 25,000 cm−1, where large-amplitude, isomerization-type motion from H–CP to CP–H is prominent. Distinct structural and dynamical changes, caused by an abrupt transformation from essentially HC bonding to mainly PH bonding, set in around 13,000 cm−1. They reflect saddle-node bifurcations in the classical phase space—a phenomenon well known in the nonlinear dynamics literature—and result in characteristic patterns in the spectrum and the quantum-number dependence of the vibrational fine-structure constants. Two polar opposites are employed to elucidate the spectral patterns: the exact solution of the Schrödinger equation, using an accurate potential energy surface and an effective or resonance Hamiltonian (expressed in a harmonic oscillator basis set and block diagonalized into polyads), which is defined by parameters adjusted to fit either the measured or the calculated vibrational energies. The combination of both approaches—together with classical mechanics and semiclassical analyses—provides a detailed spectroscopic picture of the breaking of one bond and the formation of a new one.
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Affiliation(s)
- H Ishikawa
- Department of Chemistry, Graduate School of Science, Tohoku University, Sendai 980-8578, Japan
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Joyeux M. Classical dynamics of a non-integrable Hamiltonian near coupling-induced resonance islands. ACTA ACUST UNITED AC 1999. [DOI: 10.1088/0305-4470/29/18/025] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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Joyeux M, Grebenshchikov SY, Schinke R. Analysis of the highly excited vibrational dynamics of HCP using a high-order Fermi resonance Hamiltonian. J Chem Phys 1998. [DOI: 10.1063/1.477497] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022] Open
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Assigning vibrational spectra of highly excited molecules: classical and quantum vibrational dynamics of the H2O molecule. Chem Phys Lett 1996. [DOI: 10.1016/0009-2614(96)00727-0] [Citation(s) in RCA: 21] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/22/2022]
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