Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Makri, Nancy

doi:10.1039/c0cp02374d

Cited by 24 publications

(23 citation statements)

References 126 publications

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“…III, the third-order response function is formulated as a sum of OMT diagrams whose structure explicitly reflects the possibility of energy transfer among vibrational modes. In a previous treatment of an anharmonic oscillator coupled to a dissipative bath, 45 we proposed an implementation of the OMT employing forward-backward dynamics [50][51][52][53] which greatly enhanced the efficiency of the calculation. The possibility of significant time variation of the approximate action variables poses challenges to this implementation which are addressed in Sec.…”

Section: Introductionmentioning

confidence: 99%

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

Alemi

Loring

2015

The Journal of Chemical Physics

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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. C 2015 AIP Publishing LLC. [http://dx

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Section: Introductionmentioning

confidence: 99%

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

Alemi

Loring

2015

The Journal of Chemical Physics

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“…This approach may find application in situations where the classical mechanical limit is physically relevant so that a semiclassical treatment may be viewed as correcting the well-defined zeroth order case of a classical mechanical system. [15][16][17]22 Semiclassical approximations [40][41][42][43][44][45][46] to the quantum propagator have been applied to time-dependent wavefunctions, [47][48][49][50] to thermal time-correlation functions, [51][52][53][54][55][56][57] and to linear and nonlinear response functions. 21,22,[58][59][60][61] It is useful to categorize qualitatively these time-dependent quantities according to the importance of the cancellation of quantum phases in determining time-dependence.…”

Section: Introductionmentioning

confidence: 99%

An optimized semiclassical approximation for vibrational response functions

Gerace

Loring

2013

The Journal of Chemical Physics

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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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“…To suppress the divergence of the amplitude, several researchers derived different IVR formalisms using a coherent state (Gaussian wave packet) . Moreover, a forward–backward initial value representation (FB‐IVR), which minimizes phase cancelation, was formulated to evaluate time‐correlation functions (see a review article for details). Owing to the phase cancelation, numerical stability of FB‐IVR becomes high in comparison with that of the original IVR.…”

Section: Introductionmentioning

confidence: 99%

Quantal cumulant dynamics for real‐time simulations of quantum many‐body systems

Shigeta

Harada

Kayanuma

2014

Int J of Quantum Chemistry

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] and Mitsuo Shoji [a] With recent progress in theoretical and computational developments, real-time quantum many-body dynamics has become feasible. We first review the quantum dynamics researches including semiclassical treatments by quantum chemists. As one of the latest topics, we introduce the quantal cumulant dynamics (QCD) method, which solves hierarchical equations of motion for cumulant variables together with classical coordinates and momenta, as a natural extension of classical mechanics. We then demonstrate the applications of realtime QCD for molecular vibrations, dynamic isotope effects on proton transfer reactions, and quantum effects on dynamic structures of a quantum Morse cluster. V C 2014 Wiley Periodicals, Inc.

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Forward–backward semiclassical and quantum trajectory methods for time correlation functions

Cited by 24 publications

References 126 publications

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

Vibrational coherence and energy transfer in two-dimensional spectra with the optimized mean-trajectory approximation

An optimized semiclassical approximation for vibrational response functions

Quantal cumulant dynamics for real‐time simulations of quantum many‐body systems

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