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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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2
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Polley K, Loring RF. Two-dimensional vibronic spectroscopy with semiclassical thermofield dynamics. J Chem Phys 2022; 156:124108. [DOI: 10.1063/5.0083868] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/01/2023] Open
Abstract
Thermofield dynamics is an exactly correct formulation of quantum mechanics at finite temperature in which a wavefunction is governed by an effective temperature-dependent quantum Hamiltonian. The optimized mean trajectory (OMT) approximation allows the calculation of spectroscopic response functions from trajectories produced by the classical limit of a mapping Hamiltonian that includes physical nuclear degrees of freedom and other effective degrees of freedom representing discrete vibronic states. Here, we develop a thermofield OMT (TF-OMT) approach in which the OMT procedure is applied to a temperature-dependent classical Hamiltonian determined from the thermofield-transformed quantum mapping Hamiltonian. Initial conditions for bath nuclear degrees of freedom are sampled from a zero-temperature distribution. Calculations of two-dimensional electronic spectra and two-dimensional vibrational–electronic spectra are performed for models that include excitonically coupled electronic states. The TF-OMT calculations agree very closely with the corresponding OMT results, which, in turn, represent well benchmark calculations with the hierarchical equations of motion method.
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Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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3
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Abstract
Multidimensional optical spectra are measured from the response of a material system to a sequence of laser pulses and have the capacity to elucidate specific molecular interactions and dynamics whose influences are absent or obscured in a conventional linear absorption spectrum. Interpretation of complex spectra is supported by theoretical modeling of the spectroscopic observable, requiring implementation of quantum dynamics for coupled electrons and nuclei. Performing numerically correct quantum dynamics in this context may pose computational challenges, particularly in the condensed phase. Semiclassical methods based on calculating classical trajectories offer a practical alternative. Here I review the recent application of some semiclassical, trajectory-based methods to nonlinear molecular vibrational and electronic spectra. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.
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Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York, USA
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4
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Polley K, Loring RF. One and Two Dimensional Vibronic Spectra for an Exciton Dimer from Classical Trajectories. J Phys Chem B 2020; 124:9913-9920. [DOI: 10.1021/acs.jpcb.0c07078] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Kritanjan Polley
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
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5
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Reppert M, Brumer P. Classical coherent two-dimensional vibrational spectroscopy. J Chem Phys 2018; 148:064101. [DOI: 10.1063/1.5017985] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Mike Reppert
- Chemical Physics Theory Group, Department of Chemistry, University of Toronto, Toronto, Ontario M5S 3H6, Canada
| | - Paul Brumer
- Chemical Physics Theory Group, Department of Chemistry, and Center for Quantum Information and Quantum Control, University of Toronto, Toronto, Ontario M5S 3H6, Canada
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6
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Ramesh P, Loring RF. Thermal Population Fluctuations in Two-Dimensional Infrared Spectroscopy Captured with Semiclassical Mechanics. J Phys Chem B 2018; 122:3647-3654. [DOI: 10.1021/acs.jpcb.7b12122] [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)
- Prashanth Ramesh
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, United States
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7
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Loring RF. Mean-trajectory approximation for electronic and vibrational-electronic nonlinear spectroscopy. J Chem Phys 2017; 146:144106. [DOI: 10.1063/1.4979621] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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8
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Moberg DR, Alemi M, Loring RF. Thermal weights for semiclassical vibrational response functions. J Chem Phys 2015; 143:084101. [PMID: 26328812 DOI: 10.1063/1.4929377] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Semiclassical approximations to response functions can allow the calculation of linear and nonlinear spectroscopic observables from classical dynamics. Evaluating a canonical response function requires the related tasks of determining thermal weights for initial states and computing the dynamics of these states. A class of approximations for vibrational response functions employs classical trajectories at quantized values of action variables and represents the effects of the radiation-matter interaction by discontinuous transitions. Here, we evaluate choices for a thermal weight function which are consistent with this dynamical approximation. Weight functions associated with different semiclassical approximations are compared, and two forms are constructed which yield the correct linear response function for a harmonic potential at any temperature and are also correct for anharmonic potentials in the classical mechanical limit of high temperature. Approximations to the vibrational linear response function with quantized classical trajectories and proposed thermal weight functions are assessed for ensembles of one-dimensional anharmonic oscillators. This approach is shown to perform well for an anharmonic potential that is not locally harmonic over a temperature range encompassing the quantum limit of a two-level system and the limit of classical dynamics.
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Affiliation(s)
- Daniel R Moberg
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Mallory Alemi
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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9
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Alemi M, Loring RF. Two-Dimensional Vibrational Spectroscopy of a Dissipative System with the Optimized Mean-Trajectory Approximation. J Phys Chem B 2015; 119:8950-9. [PMID: 25275943 PMCID: PMC4383732 DOI: 10.1021/jp5076884] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.9] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/30/2014] [Revised: 09/10/2014] [Indexed: 11/30/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions representing radiation-matter interactions. Here we apply this method to an anharmonic chromophore coupled to a harmonic bath. A forward-backward trajectory implementation of the OMT method is described that addresses the numerical challenges of applying the OMT to large systems with disparate frequency scales. The OMT is shown to well reproduce line shapes and waiting time dynamics in the pure dephasing limit of weak coupling to an off-resonant bath. The OMT is also shown to describe a case where energy transfer is the predominant source of line broadening.
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Affiliation(s)
- Mallory Alemi
- Department
of Chemistry and
Chemical Biology, Baker Laboratory, Cornell
University, Ithaca, New York 14853, United
States
| | - Roger F. Loring
- Department
of Chemistry and
Chemical Biology, Baker Laboratory, Cornell
University, Ithaca, New York 14853, United
States
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10
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Alemi M, Loring RF. Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation. J Chem Phys 2015; 142:212417. [PMID: 26049437 DOI: 10.1063/1.4916644] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical method for computing vibrational response functions from action-quantized classical trajectories connected by discrete transitions that represent radiation-matter interactions. Here, we extend the OMT to include additional vibrational coherence and energy transfer processes. This generalized approximation is applied to a pair of anharmonic chromophores coupled to a bath. The resulting 2D spectra are shown to reflect coherence transfer between normal modes.
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Affiliation(s)
- Mallory Alemi
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Roger F Loring
- Baker Laboratory, Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
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11
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Gerace M, Loring RF. Two-dimensional spectroscopy of coupled vibrations with the optimized mean-trajectory approximation. J Phys Chem B 2013; 117:15452-61. [PMID: 23924378 PMCID: PMC3865215 DOI: 10.1021/jp405225g] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
The optimized mean-trajectory (OMT) approximation is a semiclassical representation of the nonlinear vibrational response function used to compute multidimensional infrared spectra. In this method, response functions are calculated from a sequence of classical trajectories linked by discontinuities representing the effects of radiation-matter interactions, thus providing an approximation to quantum dynamics using classical inputs. This approach was previously formulated and assessed numerically for a single anharmonic degree of freedom. Our previous work is generalized here in two respects. First, the derivation of the OMT is extended to any number of coupled anharmonic vibrations by determining semiclassical approximations for pairs of double-sided Feynman diagrams. Second, an efficient numerical procedure is developed for calculating two-dimensional infrared spectra of coupled anharmonic vibrations in the OMT approximation. The OMT approximation is shown to reproduce the fundamental features of the quantum response function including both coherence and population dynamics.
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Affiliation(s)
- Mallory Gerace
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York, 14853, USA
| | - Roger F. Loring
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York, 14853, USA
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12
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Gerace M, Loring RF. An optimized semiclassical approximation for vibrational response functions. J Chem Phys 2013; 138:124104. [PMID: 23556706 DOI: 10.1063/1.4795941] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
The observables of multidimensional infrared spectroscopy may be calculated from nonlinear vibrational response functions. Fully quantum dynamical calculations of vibrational response functions are generally impractical, while completely classical calculations are qualitatively incorrect at long times. These challenges motivate the development of semiclassical approximations to quantum mechanics, which use classical mechanical information to reconstruct quantum effects. The mean-trajectory (MT) approximation is a semiclassical approach to quantum vibrational response functions employing classical trajectories linked by deterministic transitions representing the effects of the radiation-matter interaction. Previous application of the MT approximation to the third-order response function R(3)(t3, t2, t1) demonstrated that the method quantitatively describes the coherence dynamics of the t3 and t1 evolution times, but is qualitatively incorrect for the waiting-time t2 period. Here we develop an optimized version of the MT approximation by elucidating the connection between this semiclassical approach and the double-sided Feynman diagrams (2FD) that represent the quantum response. Establishing the direct connection between 2FD and semiclassical paths motivates a systematic derivation of an optimized MT approximation (OMT). The OMT uses classical mechanical inputs to accurately reproduce quantum dynamics associated with all three propagation times of the third-order vibrational response function.
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Affiliation(s)
- Mallory Gerace
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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13
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Gruenbaum SM, Loring RF. Semiclassical quantization in Liouville space for vibrational dynamics. J Phys Chem B 2011; 115:5148-56. [PMID: 21375227 DOI: 10.1021/jp104872r] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
Semiclassical approximations to quantum mechanics can include quantum coherence effects in dynamical calculations based on classical mechanics. The Herman-Kluk (HK) semiclassical propagator has been demonstrated to reproduce quantum effects in nonlinear vibrational response functions of anharmonic oscillators but does not provide a practical numerical route to calculations for multiple degrees of freedom. In an HK calculation of a response function, quantum coherence effects enter through interference between pairs of classical trajectories. We have previously elucidated the mechanism by which the HK approximation reproduces quantum effects in response functions in the regime of quasiperiodic dynamics. We have applied this understanding to significantly simplify the semiclassical calculation of response functions in this dynamical regime. The phase space difference between trajectories is treated perturbatively in anharmonicity, allowing integration over these differences to be performed analytically and leaving integration over mean trajectories to be performed numerically. This mean-trajectory (MT) approximation has been applied to linear and nonlinear vibrational response functions for isolated and coupled anharmonic motions. Here, we derive an MT approximation for the Liouville space time evolution operator or superoperator that propagates the density operator. This analysis provides a form of the MT approximation that is readily applicable to other dynamical quantities besides response functions and clarifies the connection between semiclassical quantization of propagators for the wave function and for the density operator.
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Affiliation(s)
- Scott M Gruenbaum
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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14
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Sakurai A, Tanimura Y. Does ℏ Play a Role in Multidimensional Spectroscopy? Reduced Hierarchy Equations of Motion Approach to Molecular Vibrations. J Phys Chem A 2011; 115:4009-22. [DOI: 10.1021/jp1095618] [Citation(s) in RCA: 56] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Atsunori Sakurai
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto Universiy, Kyoto 606-8502, Japan
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15
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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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16
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Sahrapour MM, Makri N. Multitime response functions and nonlinear spectra for model quantum dissipative systems. J Chem Phys 2010; 132:134506. [DOI: 10.1063/1.3336463] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
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17
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Gruenbaum SM, Loring RF. Semiclassical nonlinear response functions for coupled anharmonic vibrations. J Chem Phys 2009; 131:204504. [PMID: 19947691 DOI: 10.1063/1.3266566] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Observables in linear and nonlinear infrared spectroscopy may be computed from vibrational response functions describing nuclear dynamics on a single electronic surface. We demonstrate that the Herman-Kluk (HK) semiclassical approximation to the quantum propagator yields an accurate representation of quantum coherence effects in linear and nonlinear response functions for coupled anharmonic oscillators. A considerable numerical price is paid for this accuracy; the calculation requires a multidimensional integral over a highly oscillatory integrand that also grows without bound as a function of evolution times. The interference among classical trajectories in the HK approximation produces quantization of good action variables. By treating this interference analytically, we develop a mean-trajectory (MT) approximation that requires only the propagation of classical trajectories linked by transitions in action. The MT approximation accurately reproduces coherence effects in response functions of coupled anharmonic oscillators in a regime in which the observables are strongly influenced by these interactions among vibrations.
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Affiliation(s)
- Scott M Gruenbaum
- Department of Chemistry and Chemical Biology, Baker Laboratory, Cornell University, Ithaca, New York 14853, USA
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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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19
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Gruenbaum SM, Loring RF. Semiclassical mean-trajectory approximation for nonlinear spectroscopic response functions. J Chem Phys 2008; 129:124510. [DOI: 10.1063/1.2978167] [Citation(s) in RCA: 20] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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20
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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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21
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Gruenbaum SM, Loring RF. Interference and quantization in semiclassical response functions. J Chem Phys 2008; 128:124106. [DOI: 10.1063/1.2841943] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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22
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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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23
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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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25
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Nagata Y, Tanimura Y. Two-dimensional Raman spectra of atomic solids and liquids. J Chem Phys 2006; 124:024508. [PMID: 16422612 DOI: 10.1063/1.2131053] [Citation(s) in RCA: 26] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We calculate third- and fifth-order Raman spectra of simple atoms interacting through a soft-core potential by means of molecular-dynamics (MD) simulations. The total polarizability of molecules is treated by the dipole-induced dipole model. Two- and three-body correlation functions of the polarizability at various temperatures are evaluated from equilibrium MD simulations based on a stability matrix formulation. To analyze the processes involved in the spectroscopic measurements, we divide the fifth-order response functions into symmetric and antisymmetric integrated response functions; the symmetric one is written as a simple three-body correlation function, while the antisymmetric one depends on a stability matrix. This analysis leads to a better understanding of the time scales and molecular motions that govern the two-dimensional (2D) signal. The 2D Raman spectra show novel differences between the solid and liquid phases, which are associated with the decay rates of coherent motions. On the other hand, these differences are not observed in the linear Raman spectra.
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Affiliation(s)
- Yuki Nagata
- Department of Chemistry, Kyoto University, Oiwakecho, Kitashirakawa, Sakyoku, Kyoto 606-8502, Japan.
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26
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Hyeon-Deuk K, Hyeon-Deuk K, Tanimura Y. Multidimensional infrared spectroscopy for molecular vibrational modes with dipolar interactions, anharmonicity, and nonlinearity of dipole moments and polarizability. J Chem Phys 2005; 123:224310. [PMID: 16375479 DOI: 10.1063/1.2134702] [Citation(s) in RCA: 11] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
Abstract
We present an analytical expression for the linear and nonlinear infrared spectra of interacting molecular vibrational motions. Each of the molecular modes is explicitly represented by a classical damped oscillator on an anharmonic multidimensional potential-energy surface. The two essential interactions, the dipole-dipole (DD) and the dipole-induced-dipole (DID) interactions, are taken into account, and each dipole moment and polarizability are expanded to nonlinear order with respect to the nuclear vibrational coordinate. Our analytical treatment leads to expressions for the contributions of anharmonicity, DD and DID interactions, and the nonlinearity of dipole moments and polarizability elements to the one-, two-, and three-dimensional spectra as separated terms, which allows us to discuss the relative importance of these respective contributions. We can calculate multidimensional signals for various configurations of molecules interacting through DD and DID interactions for different material parameters over the whole range of frequencies. We demonstrate that contributions from the DD and DID interactions and anharmonicity are separately detectable through the third-order three-dimensional IR spectroscopy, whereas they cannot be distinguished from each other in either the linear or the second-order IR spectroscopies. The possibility of obtaining the intra- or intermolecular structural information from multidimensional spectra is also discussed.
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Affiliation(s)
- Kim Hyeon-Deuk
- Department of Chemistry, Kyoto University, Kyoto 606-8502, Japan.
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27
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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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28
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Noid WG, Loring RF. Interpreting nonlinear vibrational spectroscopy with the classical mechanical analogs of double-sided Feynman diagrams. J Chem Phys 2004; 121:7057-69. [PMID: 15473771 DOI: 10.1063/1.1792211] [Citation(s) in RCA: 14] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/31/2022] Open
Abstract
Observables in coherent, multiple-pulse infrared spectroscopy may be computed from a vibrational nonlinear response function. This response function is conventionally calculated quantum-mechanically, but the challenges in applying quantum mechanics to large, anharmonic systems motivate the examination of classical mechanical vibrational nonlinear response functions. We present an approximate formulation of the classical mechanical third-order vibrational response function for an anharmonic solute oscillator interacting with a harmonic solvent, which establishes a clear connection between classical and quantum mechanical treatments. This formalism permits the identification of the classical mechanical analog of the pure dephasing of a quantum mechanical degree of freedom, and suggests the construction of classical mechanical analogs of the double-sided Feynman diagrams of quantum mechanics, which are widely applied to nonlinear spectroscopy. Application of a rotating wave approximation permits the analytic extraction of signals obeying particular spatial phase matching conditions from a classical-mechanical response function. Calculations of the third-order response function for an anharmonic oscillator coupled to a harmonic solvent are compared to numerically correct classical mechanical results.
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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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