Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction

Martinez, Franz; Rekik, Najeh; Hanna, Gabriel

doi:10.1016/j.cplett.2013.04.018

Cited by 14 publications

(26 citation statements)

References 49 publications

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“…First, we review the results of these methods for a simple model of a photo-induced condensed-phase ET reaction, previously studied by our group in Refs [39,40]. Second, we present and discuss new results of the PBME method for a realistic model of a PT reaction in a hydrogen-bonded complex dissolved in a nanocluster of polar solvent molecules.…”

Section: Applicationsmentioning

confidence: 98%

“…For the full details of this methodology, we would like to direct the reader to Ref. [40]. Here, we only present the equations needed to calculate a polarisation component of interest, P k , resulting from a three-pulse experiment:…”

Section: Computation Of Donor State Population and Timeintegrated Ta mentioning

confidence: 99%

“…The coupling constants and frequencies are given by c j ¼ ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi l D tan 21 ðv max =v D Þ=ðpNÞ p v j and v j ¼ tanðjtan 21 ðv max =v D Þ=NÞv D , respectively, where v max is the maximum frequency of the spectral density and N is the number of oscillators. [51,52,54] All of the model parameters are provided in Refs [39,40]. …”

Section: Modelmentioning

confidence: 99%

“…[40], we formulated a general approach for computing any N p -pulse induced signal, which combines the EOM phase-matching approach (EOM-PMA) [57,58] and the PBME/FBTS approach. For the full details of this methodology, we would like to direct the reader to Ref.…”

Section: Computation Of Donor State Population and Timeintegrated Ta mentioning

confidence: 99%

“…Specifically, we review the results for the dynamics of a three-state model of a laser-induced electron transfer (ET) reaction in a harmonic oscillator bath, previously studied by our group in Refs [39,40], and present new results for the dynamics of a realistic, atomistic model of a proton transfer (PT) complex in a nanocluster of polar molecules. It should be noted that this is the first time that any of these approximate methods have been applied to a realistic system.…”

Section: Introductionmentioning

confidence: 99%

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Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Martinez

Hanna

2014

Molecular Simulation

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The quantum-classical Liouville equation (QCLE) provides a rigorous approach for modelling the dynamics of systems that can be effectively partitioned into a quantum subsystem and a classical environment. Several surface-hopping algorithms have been developed for solving the QCLE and successfully applied to simple model systems, but simulating the long-time dynamics of complex, realistic systems using these schemes has proven to be computationally demanding. Motivated by the need for computationally efficient algorithms, two approximate solutions of the QCLE, the Poisson bracket mapping equation (PBME) solution and the forward-backward trajectory solution (FBTS), were developed. These solutions involve simple algorithms in which both the quantum and classical degrees of freedom are described in terms of continuous variables and evolve according to classical-like equations of motion. However, since these schemes are approximate, they must be benchmarked against the exact quantum and QCLE surface-hopping solutions for a variety of simple and complex systems to determine the conditions under which they are valid. To illustrate the validity of the PBME and FBTS approaches, we review the results of a simple model for a condensed-phase photo-induced electron transfer and present new results for a realistic model for a proton transfer in a hydrogen-bonded complex dissolved in a polar nanocluster. Overall, the results demonstrate that caution must be taken when applying these approximate methods, since they can manifest nonphysical behaviour for systems where a mean-field-like description is not valid.

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Section: Applicationsmentioning

confidence: 98%

Section: Computation Of Donor State Population and Timeintegrated Ta mentioning

confidence: 99%

Section: Modelmentioning

confidence: 99%

Section: Computation Of Donor State Population and Timeintegrated Ta mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Martinez

Hanna

2014

Molecular Simulation

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Two‐dimensional electronic spectrum simulation of simple photosynthetic complex models with semi‐classical Poisson bracket mapping equation

Kim

Rhee

2022

Bulletin Korean Chem Soc

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As understanding experimentally observed two-dimensional electronic spectroscopy (2DES) signals usually requires theoretical modeling, various approaches have been applied to simulating the spectra. It will be desirable to develop a method that is free from parameters that are adjusted based on spectroscopic outcomes. Often, such parameters without any a priori known information come from quantum chemical calculations that can only be achieved at the atomistic resolution, and a necessity arises for designing a scheme that can be readily used for generating 2DES spectra even for atomistic models of complex systems. Here, we present such an approach based on mixed quantum-classical Poisson bracket mapping equation formalism, which can be extended to all-atom simulations. We check its performance by adopting a two-state toy model and show that we can efficiently construct 2D spectra. We show that our scheme can yield reasonable 2D spectra even when high-frequency vibrations modulate the population dynamics.

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Mixed quantum–classical Liouville simulation of vibrational energy transfer in a model α-helix at 300 K

Freedman

Hanna

2016

Chemical Physics

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Simulation of nonlinear optical signals via approximate solutions of the quantum–classical Liouville equation: Application to the pump–probe spectroscopy of a condensed phase electron transfer reaction

Cited by 14 publications

References 49 publications

Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Assessment of approximate solutions of the quantum–classical Liouville equation for dynamics simulations of quantum subsystems embedded in classical environments

Two‐dimensional electronic spectrum simulation of simple photosynthetic complex models with semi‐classical Poisson bracket mapping equation

Mixed quantum–classical Liouville simulation of vibrational energy transfer in a model α-helix at 300 K

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