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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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2
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Houston PL, Van Hoozen BL, Qu C, Yu Q, Bowman JM. Teaching vibrational spectra to assign themselves. Faraday Discuss 2018; 212:65-82. [PMID: 30259026 DOI: 10.1039/c8fd00075a] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
A new paradigm for assigning vibrational spectra is described. Instead of proceeding from potential to Hamiltonian to eigenvalues/eigenvectors/intensities to spectrum, the new method goes "backwards" directly from spectrum to eigenvectors. The eigenvectors then "assign" the spectrum, in that they identify the basis states that contribute to each eigenvalue. To start, we demonstrate an algorithm that can obtain useful estimates of the eigenvectors connecting a real, symmetric Hamiltonian to its eigenvalues even if the only available information about the Hamiltonian is its diagonal elements. When this algorithm is augmented with information about transition intensities, it can be used to assign a complex vibrational spectrum using only information about (1) eigenvalues (the peak centers of the spectrum) and (2) a harmonic basis set (taken to be the diagonal elements of the Hamiltonian). Examples will be discussed, including application to the vibrationally complex spectral region of the formic acid dimer.
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Affiliation(s)
- Paul L Houston
- Department of Chemistry and Chemical Biology, Cornell Universtiy, Ithaca, NY 14853, USA. and School of Chemistry and Biochemistry, Georgia Inst. of Technology, Atlanta, GA 30332-0400, USA
| | - Brian L Van Hoozen
- Department of Chemistry, Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Chen Qu
- Department of Chemistry, Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Qi Yu
- Department of Chemistry, Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
| | - Joel M Bowman
- Department of Chemistry, Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, USA
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Johnson BA, Sibert EL. Assigning the low lying vibronic states of CH 3O and CD 3O. J Chem Phys 2017; 146:174112. [PMID: 28477600 DOI: 10.1063/1.4981795] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/20/2023] Open
Abstract
The assignment of lines in vibrational spectra in strongly mixing systems is considered. Several low lying vibrational states of the ground electronic X∼2E state of the CH3O and CD3O radicals are assigned. Jahn-Teller, spin-orbit, and Fermi couplings mix the normal mode states. The mixing complicates the assignment of the infrared spectra using a zero-order normal mode representation. Alternative zero-order representations, which include specific Jahn-Teller couplings, are explored. These representations allow for definitive assignments. In many instances it is possible to plot the wavefunctions on which the assignments are based. The plots, which are shown in the adiabatic representation, allow one to visualize the effects of various higher order couplings. The plots also enable one to visualize the conical seam and its effect on the wavefunctions. The first and the second order Jahn-Teller couplings in the rocking motion dominate the spectral features in CH3O, while first order and modulated first order couplings dominate the spectral features in CD3O. The methods described here are general and can be applied to other Jahn-Teller systems.
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Affiliation(s)
- Britta A Johnson
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
| | - Edwin L Sibert
- Department of Chemistry and Theoretical Chemistry Institute, University of Wisconsin-Madison, Madison, Wisconsin 53706, USA
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Rashev S, Moule DC. Large scale vibrational calculations on IVR in S0 thiophosgene. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2016. [DOI: 10.1142/s021963361650005x] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
In this work, using a recently derived refined potential energy surface for [Formula: see text] thiophosgene, we perform large scale vibrational calculations to explore the IVR characteristics and vibrational mixing at very high vibrational excitation energies, ranging up to the dissociation limit (at [Formula: see text]20,000[Formula: see text]cm[Formula: see text]). The results from our calculations have been compared to the conclusions based on the available experimentally measured dataset (obtained from SEP and LIF spectra) as well as to the conclusions from the analyses by other authors using local coupling models.
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Affiliation(s)
- Svetoslav Rashev
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradsko Chaussee 72, 1784 Sofia, Bulgaria
| | - David C. Moule
- Department of Chemistry, Brock University, St. Catharines, ON, L2S3A1, Canada
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Rashev S, Moule DC. A refined quartic potential energy surface and large scale vibrational calculations for S0 thiophosgene. SPECTROCHIMICA ACTA. PART A, MOLECULAR AND BIOMOLECULAR SPECTROSCOPY 2015; 140:305-310. [PMID: 25615683 DOI: 10.1016/j.saa.2014.12.101] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/13/2014] [Revised: 12/08/2014] [Accepted: 12/28/2014] [Indexed: 06/04/2023]
Abstract
In this work we present a full 6D quartic potential energy surface (PES) for S0 thiophosgene in curvilinear symmetrized bond-angle coordinates. The PES was refined starting from an ab initio field derived from acc-pVTZ basis set with CCSD(T) corrections for electron correlation. In the present calculations we used our variational method that was recently tested on formaldehyde and some of its isotopomers, along with additional improvements. The lower experimentally known vibrational levels for 35Cl2CS were reproduced quite well in the calculations, which can be regarded as a test for the feasibility of the obtained quartic PES.
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Affiliation(s)
- Svetoslav Rashev
- Institute of Solid State Physics, Bulgarian Academy of Sciences, Tsarigradskochaussee 72, 1784 Sofia, Bulgaria.
| | - David C Moule
- Department of Chemistry, Brock University, St. Catharines, ON L2S3A1, Canada
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Manikandan P, Keshavamurthy S. Dynamical traps lead to the slowing down of intramolecular vibrational energy flow. Proc Natl Acad Sci U S A 2014; 111:14354-9. [PMID: 25246538 PMCID: PMC4209979 DOI: 10.1073/pnas.1406630111] [Citation(s) in RCA: 30] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/18/2022] Open
Abstract
The phenomenon of intramolecular vibrational energy redistribution (IVR) is at the heart of chemical reaction dynamics. Statistical rate theories, assuming instantaneous IVR, predict exponential decay of the population with the properties of the transition state essentially determining the mechanism. However, there is growing evidence that IVR competes with the reaction timescales, resulting in deviations from the exponential rate law. Dynamics cannot be ignored in such cases for understanding the reaction mechanisms. Significant insights in this context have come from the state space model of IVR, which predicts power law behavior for the rates with the power law exponent, an effective state space dimensionality, being a measure of the nature and extent of the IVR dynamics. However, whether the effective IVR dimensionality can vary with time and whether the mechanism for the variation is of purely quantum or classical origins are issues that remain unresolved. Such multiple power law scalings can lead to surprising mode specificity in the system, even above the threshold for facile IVR. In this work, choosing the well-studied thiophosgene molecule as an example, we establish the anisotropic and anomalous nature of the quantum IVR dynamics and show that multiple power law scalings do manifest in the system. More importantly, we show that the mechanism of the observed multiple power law scaling has classical origins due to a combination of trapping near resonance junctions in the network of classical nonlinear resonances at short to intermediate times and the influence of weak higher-order resonances at relatively longer times.
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Affiliation(s)
- Paranjothy Manikandan
- Department of Chemistry, Indian Institute of Technology, Kanpur (U.P.) 208016, India
| | - Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur (U.P.) 208016, India
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Tyuterev V, Tashkun S, Rey M, Kochanov R, Nikitin A, Delahaye T. Accurate Spectroscopic Models for Methane Polyads Derived from a Potential Energy Surface Using High-Order Contact Transformations. J Phys Chem A 2013; 117:13779-805. [DOI: 10.1021/jp408116j] [Citation(s) in RCA: 107] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Vladimir Tyuterev
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
| | - Sergei Tashkun
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Michael Rey
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
| | - Roman Kochanov
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Andrei Nikitin
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
- LTS, V.E. Zuev Institute of Atmospheric Optics, Academician Zuev square 1, 634021, Tomsk, Russia
| | - Thibault Delahaye
- GSMA,
UMR CNRS 7331, University of Reims, BP 1039, 51687 Reims Cedex 2, France
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Krasnoshchekov SV, Stepanov NF. Polyad quantum numbers and multiple resonances in anharmonic vibrational studies of polyatomic molecules. J Chem Phys 2013; 139:184101. [DOI: 10.1063/1.4829143] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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9
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Berrios E, Pratt S, Tripathi P, Gruebele M. More Protected Vibrational States at the Dissociation Limit of SCCl2. J Phys Chem A 2013; 117:12082-90. [DOI: 10.1021/jp404834y] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Eduardo Berrios
- Department of Chemistry, ‡Department of Physics, and §Center for Biophysics
and Computational
Biology, University of Illinois, Urbana, Illinois 61801, United States
| | - Susan Pratt
- Department of Chemistry, ‡Department of Physics, and §Center for Biophysics
and Computational
Biology, University of Illinois, Urbana, Illinois 61801, United States
| | - Prabhat Tripathi
- Department of Chemistry, ‡Department of Physics, and §Center for Biophysics
and Computational
Biology, University of Illinois, Urbana, Illinois 61801, United States
| | - Martin Gruebele
- Department of Chemistry, ‡Department of Physics, and §Center for Biophysics
and Computational
Biology, University of Illinois, Urbana, Illinois 61801, United States
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Keshavamurthy S. Eigenstates of Thiophosgene Near the Dissociation Threshold: Deviations From Ergodicity. J Phys Chem A 2013; 117:8729-36. [DOI: 10.1021/jp4033386] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Srihari Keshavamurthy
- Department
of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India
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12
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Abstract
A reformulation of a semiclassical theory that presently seems uniquely capable of interpreting generic complex multiresonant vibrational spectra is presented. Once given the spectroscopic Hamiltonian which reveals the set of possible resonant couplings and its eigenstates, the new and old formulations both yield without any further computation level by level dynamical assignments for the spectra. Computing a simple trajectory in phase space reveals the motions that when quantized yield the assigned levels. The reformulation introduces two new projected representations of the wave functions. The first is in action space and the second in angle space. The projected representations often allow the reduced angle space, where nodal searches are made, to be of lower dimension than formally occurred. In addition the action representation is a similarly lower dimension lattice representation whose discreteness and regularity allow higher reduced dimensions to be studied. The lattice representation is used to produce a significantly more complete and detailed assignment of the thiophosgene spectrum than previously published.
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Affiliation(s)
- Christof Jung
- Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Av. Universidad s/n, 62251 Cuernavaca, Mexico
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13
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Farantos SC, Schinke R, Guo H, Joyeux M. Energy Localization in Molecules, Bifurcation Phenomena, and Their Spectroscopic Signatures: The Global View. Chem Rev 2009; 109:4248-71. [DOI: 10.1021/cr900069m] [Citation(s) in RCA: 64] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Stavros C. Farantos
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Reinhard Schinke
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Hua Guo
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
| | - Marc Joyeux
- Institute of Electronic Structure and Laser, Foundation for Research and Technology—Hellas, and Department of Chemistry, University of Crete, Iraklion 711 10, Crete, Greece, Max-Planck-Institut für Dynamik und Selbstorganisation, D-37073 Göttingen, Germany, Department of Chemistry and Chemical Biology, University of New Mexico, Albuquerque, New Mexico 87131, and Laboratoire de Spectrométrie Physique, Université Joseph Fourier—Grenoble I, BP 87, F-38402, St. Martin d’Heres Cedex, France
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Chowdary PD, Gruebele M. An effective Hamiltonian survey of the anharmonic vibrational state space of SCCl2 up to the dissociation energy. J Chem Phys 2009; 130:134310. [DOI: 10.1063/1.3105989] [Citation(s) in RCA: 13] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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15
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Manikandan P, Semparithi A, Keshavamurthy S. Decoding the Dynamical Information Embedded in Highly Excited Vibrational Eigenstates: State Space and Phase Space Viewpoints. J Phys Chem A 2009; 113:1717-30. [DOI: 10.1021/jp807231p] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Paranjothy Manikandan
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India
| | - Aravindan Semparithi
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India
| | - Srihari Keshavamurthy
- Department of Chemistry, Indian Institute of Technology, Kanpur, Uttar Pradesh 208016, India
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16
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Chowdary PD, Gruebele M. Regular vibrational state progressions at the dissociation limit of SCCl2. J Chem Phys 2009; 130:024305. [DOI: 10.1063/1.3038019] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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Diaz A, Jung C. Analytic perturbative classification and assignment of eigenstates of algebraic vibrational Hamiltonians. Mol Phys 2008. [DOI: 10.1080/00268970801961021] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
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18
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Rashev S, Moule DC, Djambova ST. On the T1→S0 intersystem crossing rate constant in thiophosgene. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.04.093] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Rashev S, Bivas I, Moule DC. Large scale vibrational Hamiltonian calculations on thiophosgene. Chem Phys Lett 2007. [DOI: 10.1016/j.cplett.2007.02.067] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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Jung C, Taylor HS. Assignment and Extracting Dynamics from Experimentally and Theoretically Obtained Spectroscopic Hamiltonians in the Complex Spectral and Classically Chaotic Regions. J Phys Chem A 2007; 111:3047-68. [PMID: 17388400 DOI: 10.1021/jp066741p] [Citation(s) in RCA: 23] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
An analysis of existing algebraic multiresonance spectroscopic Hamiltonians, derived by fitting to experimental data or from classical canonical or quantum Van Vleck perturbation theory, allows without any significant further classical or quantum calculation the assignment of quantum numbers and motions to states observed in spectra that were previously thought to be irregular or just unassignable. In such cases, inspection of the amplitude and phase of eigenfunctions previously calculated in the Hamiltonians derivation process but now transformed to a reduced dimension semiclassical action-angle representation reveals extremely simple albeit unfamiliar topologies that give quantum numbers by simply counting nodes and phase advances. The topology allows these simple wave functions to be sorted into dynamically different excitation ladders or classes of states which are associated with different regions of phase space. The rungs of these ladders or the states in the classes intersperse in energy causing the spectral complexity. No experimental procedure allows such sorting. The success of the work stems from (1) the qualitative insights of nonlinear dynamics, (2) the conversion of the quantum problem in full dimension to a semiclassical one in reduced dimension by use of a canonical transform that takes advantage of the polyad and other constants of the motion, and (3) the judicious choice of the reduced angle variables to reflect rational ratio resonance frequency conditions. This leads to localization of those semiclassical wave functions, which are affected by the particular resonance. In reverse, the localized appearance of the reduced dimension wave function reveals which resonances govern it and makes sorting visually simple. The success of the work also stems from (4) the revealing use of plots of phase advances as well as the usual densities of the eigenstates for sorting and assignment purposes. Even in classically chaotic regions, organizing trajectories, which correspond to averages over regional phase space structures that need not be computed, can easily be drawn as the structure about which eigenfunction localization takes place. The organizing trajectories when transformed back to the full dimensional configuration space reveal the internal molecular motions. The complexity of the usual quantum stationary and propagated wave functions and associated classical trajectories forbids most often such assignments and sorting. This procedure brings the ability to interpret complex vibrational spectra to a degree previously thought possible only for lower excitations. The new methodology replaces and extends the computationally more difficult parts of a procedure used by the authors that was applied successfully to several molecules during the past few years. The new methodology is applied to DCO, CHBrClF, and the bending of acetylene.
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Affiliation(s)
- Christof Jung
- Instituto de Ciencias Fisicas, Universidad Nacional Autonoma de Mexico, Av. Universidad s/n, 62251 Cuernavaca, Mexico
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