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Reppert M, Reppert D. Equivalence of quantum and classical third order response for weakly anharmonic coupled oscillators. J Chem Phys 2023; 158:114114. [PMID: 36948800 DOI: 10.1063/5.0135260] [Citation(s) in RCA: 1] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/25/2023] Open
Abstract
Two-dimensional (2D) infrared (IR) spectra are commonly interpreted using a quantum diagrammatic expansion that describes the changes to the density matrix of quantum systems in response to light-matter interactions. Although classical response functions (based on Newtonian dynamics) have shown promise in computational 2D IR modeling studies, a simple diagrammatic description has so far been lacking. Recently, we introduced a diagrammatic representation for the 2D IR response functions of a single, weakly anharmonic oscillator and showed that the classical and quantum 2D IR response functions for this system are identical. Here, we extend this result to systems with an arbitrary number of bilinearly coupled, weakly anharmonic oscillators. As in the single-oscillator case, quantum and classical response functions are found to be identical in the weakly anharmonic limit or, in experimental terms, when the anharmonicity is small relative to the optical linewidth. The final form of the weakly anharmonic response function is surprisingly simple and offers potential computational advantages for application to large, multi-oscillator systems.
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Affiliation(s)
- Mike Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
| | - Deborah Reppert
- Department of Chemistry, Purdue University, West Lafayette, Indiana 47907, USA
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Hanna G, Geva E. Computational study of the signature of hydrogen-bond strength on the infrared spectra of a hydrogen-bonded complex dissolved in a polar liquid. Chem Phys 2010. [DOI: 10.1016/j.chemphys.2010.01.013] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/24/2022]
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Kryvohuz M, Cao J. The influence of dissipation on the quantum-classical correspondence: Stability of stochastic trajectories. J Chem Phys 2009; 130:234107. [PMID: 19548711 DOI: 10.1063/1.3154142] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Kim YS, Hochstrasser RM. Applications of 2D IR spectroscopy to peptides, proteins, and hydrogen-bond dynamics. J Phys Chem B 2009; 113:8231-51. [PMID: 19351162 PMCID: PMC2845308 DOI: 10.1021/jp8113978] [Citation(s) in RCA: 245] [Impact Index Per Article: 16.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/17/2022]
Abstract
Following a survey of 2D IR principles, this article describes recent experiments on the hydrogen-bond dynamics of small ions, amide-I modes, nitrile probes, peptides, reverse transcriptase inhibitors, and amyloid fibrils.
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Affiliation(s)
- Yung Sam Kim
- Department of Chemistry, University of Pennsylvania Philadelphia, Pennsylvania 19104-6323, U.S.A
| | - Robin M. Hochstrasser
- Department of Chemistry, University of Pennsylvania Philadelphia, Pennsylvania 19104-6323, U.S.A
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Hanna G, Geva E. Multidimensional Spectra via the Mixed Quantum-Classical Liouville Method: Signatures of Nonequilibrium Dynamics. J Phys Chem B 2009; 113:9278-88. [DOI: 10.1021/jp902797z] [Citation(s) in RCA: 39] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry, University of Michigan, Ann Arbor, Michigan 48109-1055
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Kryvohuz M, Cao J, Mukamel S. Suppression of photon-echo as a signature of chaos. J Phys Chem B 2008; 112:15999-6007. [PMID: 19367874 PMCID: PMC2905168 DOI: 10.1021/jp804604h] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Abstract
The paper discusses the effect of quantum chaos on photon-echo signals of two-electronic-state molecular systems. The temporal profile of photon-echo signals is shown to reveal key information about nuclear dynamics on the excited electronic state surface. Specifically, the suppression of echo signals at a particular value of the delay time tau1 between the first and second excitation pulses is demonstrated as a signature of quantum level statistics that corresponds to the classically chaotic nuclear motion in the excited electronic state surface.
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Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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Hanna G, Geva E. Computational Study of the One and Two Dimensional Infrared Spectra of a Vibrational Mode Strongly Coupled to Its Environment: Beyond the Cumulant and Condon Approximations. J Phys Chem B 2008; 112:12991-3004. [DOI: 10.1021/jp804120v] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Gabriel Hanna
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
| | - Eitan Geva
- Department of Chemistry and FOCUS center, University of Michigan, Ann Arbor, Michigan 48109-1055
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Malinin SV, Chernyak VY. Classical nonlinear response of a chaotic system. I. Collective resonances. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056201. [PMID: 18643136 DOI: 10.1103/physreve.77.056201] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
We develop a general semiquantitative picture of nonlinear classical response in strongly chaotic systems. In contrast to behavior in integrable or almost integrable systems, the nonlinear classical response in chaotic systems vanishes at long times. The exponential decay of the response functions in the case of strong chaos is attributed to both exponentially decaying and growing elements in the stability matrices. We calculate the linear and second-order response in one of the simplest chaotic systems: free classical motion on a compact surface of constant negative curvature. The response reveals certain features of collective resonances which do not correspond to any periodic classical trajectories. We demonstrate the relevance of the model for the interpretation of spectroscopic experiments.
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Affiliation(s)
- Sergey V Malinin
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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Malinin SV, Chernyak VY. Classical nonlinear response of a chaotic system. II. Langevin dynamics and spectral decomposition. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2008; 77:056202. [PMID: 18643137 DOI: 10.1103/physreve.77.056202] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/30/2008] [Indexed: 05/26/2023]
Abstract
The spectrum of a strongly chaotic system consists of discrete complex Ruelle-Pollicott (RP) resonances. We interpret the RP resonances as eigenstates and eigenvalues of the Fokker-Planck operator obtained by adding an infinitesimal diffusion term to the first-order Liouville operator. We demonstrate how the deterministic expression for the linear response is reproduced in the limit of vanishing noise. For the second-order response function we establish an equivalence of the spectral decomposition in the limit of vanishing noise and the long-time asymptotic expansion in the deterministic case.
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Affiliation(s)
- Sergey V Malinin
- Department of Chemistry, Wayne State University, 5101 Cass Avenue, Detroit, Michigan 48202, USA
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Saito S, Ohmine I. Fifth-order two-dimensional Raman spectroscopy of liquid water, crystalline ice Ih and amorphous ices: Sensitivity to anharmonic dynamics and local hydrogen bond network structure. J Chem Phys 2006; 125:084506. [PMID: 16965028 DOI: 10.1063/1.2232254] [Citation(s) in RCA: 30] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/14/2023] Open
Abstract
The theoretical study of off-resonant fifth-order two-dimensional (2D)-Raman spectroscopy is made to analyze the intermolecular dynamics of liquid and solid water. The 2D-Raman spectroscopy is susceptible to the nonlinear anharmonic dynamics and local hydrogen bond structure in water. It is found that the distinct 2D-Raman response appears as the negative signal near the t(2) axis. The origin of this negative signal for t(2)<15 fs is from the nonlinear polarizability in the librational motions, whereas that for 30 fs<t(2)<150 fs is attributed to the anharmonic translational motions. It is found that the mechanical anharmonicity and nonlinear polarizability couplings among modes clearly can be observed as the sum- and difference-frequency peaks in the 2D-Raman spectrum (i.e., Fourier transforms of the response). The 2D-Raman spectroscopies of ice Ih and amorphous ices, i.e., low density, high density, and very high density amorphous ices, are also investigated. It is found that the 2D-Raman spectroscopy is very sensitive to the anisotropy of the structure of ice Ih. The strong hydrogen bond stretching band is seen in the 2D-Raman spectroscopy of the polarization directions parallel to the c axis, whereas the contributions of the librational motion can be also seen in the spectrum with the polarization directions parallel to the a axis. The 2D-Raman spectroscopy is also found to be also very sensitive to the differences in local hydrogen bond network structures in various amorphous phases.
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Affiliation(s)
- Shinji Saito
- Department of Computational Molecular Science, Institute for Molecular Science, Myodaiji, Okazaki, Aichi 444-8585, Japan.
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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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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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Kryvohuz M, Cao J. Quantum-classical correspondence in response theory. PHYSICAL REVIEW LETTERS 2005; 95:180405. [PMID: 16383881 DOI: 10.1103/physrevlett.95.180405] [Citation(s) in RCA: 43] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/20/2005] [Indexed: 05/05/2023]
Abstract
The correspondence principle between the quantum commutator [A, B] and the classical Poisson brackets iota h{A, B} is examined in the context of response theory. The classical response function is obtained as the leading term of the expansion of the phase space representation of the response function in terms of Weyl-Wigner transformations and is shown to increase without bound at long times as a result of ignoring divergent higher-order contributions. Systematical inclusion of higher-order contributions improves the accuracy of the h expansion at finite times. Resummation of all the higher-order terms establishes the classical-quantum correspondence <v + n|alpha(t)v> <--> alpha n e iota n omega t|Jv + nh/2. The time interval of the validity of the simple classical limit [A(t), B(0)] --> iota h{A(t), B(0)} is estimated for quasiperiodic dynamics and is shown to be inversely proportional to anharmonicity.
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Affiliation(s)
- Maksym Kryvohuz
- Department of Chemistry, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
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