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Zaccone A. General theory of the viscosity of liquids and solids from nonaffine particle motions. Phys Rev E 2023; 108:044101. [PMID: 37978701 DOI: 10.1103/physreve.108.044101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2023] [Accepted: 09/08/2023] [Indexed: 11/19/2023]
Abstract
A microscopic formula for the viscosity of liquids and solids is derived rigorously from a first-principles (microscopically reversible) Hamiltonian for particle-bath atomistic motion. The derivation is done within the framework of nonaffine linear response theory. This formula may lead to a valid alternative to the Green-Kubo approach to describe the viscosity of condensed matter systems from molecular simulations without having to fit long-time tails. Furthermore, it provides a direct link between the viscosity, the vibrational density of states of the system, and the zero-frequency limit of the memory kernel. Finally, it provides a microscopic solution to Maxwell's interpolation problem of viscoelasticity by naturally recovering Newton's law of viscous flow and Hooke's law of elastic solids in two opposite limits.
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Affiliation(s)
- Alessio Zaccone
- Department of Physics "A. Pontremoli," University of Milan, via Celoria 16, 20133 Milan, Italy
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2
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Pelargonio S, Zaccone A. Generalized Langevin equation with shear flow and its fluctuation-dissipation theorems derived from a Caldeira-Leggett Hamiltonian. Phys Rev E 2023; 107:064102. [PMID: 37464636 DOI: 10.1103/physreve.107.064102] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/27/2022] [Accepted: 04/26/2023] [Indexed: 07/20/2023]
Abstract
We provide a first-principles derivation of the Langevin equation with shear flow and its corresponding fluctuation-dissipation theorems. Shear flow of simple fluids has been widely investigated by numerical simulations. Most studies postulate a Markovian Langevin equation with a simple shear drag term in the manner of Stokes. However, this choice has never been justified from first principles. We start from a particle-bath system described by a classical Caldeira-Leggett Hamiltonian modified by adding a term proportional to the strain-rate tensor according to Hoover's DOLLS method, and we derive a generalized Langevin equation for the sheared system. We then compute, analytically, the noise time-correlation functions in different regimes. Based on the intensity of the shear rate, we can distinguish between close-to-equilibrium and far-from-equilibrium states. According to the results presented here, the standard, simple, and Markovian form of the Langevin equation with shear flow postulated in the literature is valid only in the limit of extremely weak shear rates compared to the effective vibrational temperature of the bath. For even marginally higher shear rates, the (generalized) Langevin equation is strongly non-Markovian, and nontrivial fluctuation-dissipation theorems are derived.
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Affiliation(s)
- Sara Pelargonio
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
- Complex Systems and Statistical Mechanics, Department of Physics and Materials Science, University of Luxembourg, L-1511 Luxembourg
| | - Alessio Zaccone
- Department of Physics "A. Pontremoli", University of Milan, via Celoria 16, 20133 Milan, Italy
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Takahashi H, Tanimura Y. Discretized hierarchical equations of motion in mixed Liouville-Wigner space for two-dimensional vibrational spectroscopies of liquid water. J Chem Phys 2023; 158:044115. [PMID: 36725520 DOI: 10.1063/5.0135725] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
Abstract
A model of a bulk water system describing the vibrational motion of intramolecular and intermolecular modes is constructed, enabling analysis of its linear and nonlinear vibrational spectra as well as the energy transfer processes between the vibrational modes. The model is described as a system of four interacting anharmonic oscillators nonlinearly coupled to their respective heat baths. To perform a rigorous numerical investigation of the non-Markovian and nonperturbative quantum dissipative dynamics of the model, we derive discretized hierarchical equations of motion in mixed Liouville-Wigner space, with Lagrange-Hermite mesh discretization being employed in the Liouville space of the intramolecular modes and Lagrange-Hermite mesh discretization and Hermite discretization in the Wigner space of the intermolecular modes. One-dimensional infrared and Raman spectra and two-dimensional terahertz-infrared-visible and infrared-infrared-Raman spectra are computed as demonstrations of the quantum dissipative description provided by our model.
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Affiliation(s)
- Hideaki Takahashi
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
| | - Yoshitaka Tanimura
- Department of Chemistry, Graduate School of Science, Kyoto University, Kyoto 606-8502, Japan
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Abstract
Protein-folding kinetics is often described as Markovian (i.e., memoryless) diffusion in a one-dimensional free energy landscape, governed by an instantaneous friction coefficient that is fitted to reproduce experimental or simulated folding times. For the α-helix forming polypeptide alanine9 and a specific reaction coordinate that consists of the summed native hydrogen-bond lengths, we demonstrate that the friction extracted from molecular dynamics simulations exhibits significant memory with a decay time that is in the nanosecond range and thus, of the same order as the folding and unfolding times. Our non-Markovian modeling not only reproduces the molecular dynamics simulations accurately but also demonstrates that memory friction effects lead to anomalous and drastically accelerated protein kinetics. We extract the folding free energy landscape and the time-dependent friction function, the two ingredients of the generalized Langevin equation (GLE), from explicit-water molecular dynamics (MD) simulations of the α-helix forming polypeptide alanine9 for a one-dimensional reaction coordinate based on the sum of the native H-bond distances. Folding and unfolding times from numerical integration of the GLE agree accurately with MD results, which demonstrate the robustness of our GLE-based non-Markovian model. In contrast, Markovian models do not accurately describe the peptide kinetics and in particular, cannot reproduce the folding and unfolding kinetics simultaneously, even if a spatially dependent friction profile is used. Analysis of the GLE demonstrates that memory effects in the friction significantly speed up peptide folding and unfolding kinetics, as predicted by the Grote–Hynes theory, and are the cause of anomalous diffusion in configuration space. Our methods are applicable to any reaction coordinate and in principle, also to experimental trajectories from single-molecule experiments. Our results demonstrate that a consistent description of protein-folding dynamics must account for memory friction effects.
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Rognoni A, Conte R, Ceotto M. Caldeira-Leggett model vs ab initio potential: A vibrational spectroscopy test of water solvation. J Chem Phys 2021; 154:094106. [PMID: 33685187 DOI: 10.1063/5.0040494] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We present a semiclassically approximate quantum treatment of solvation with the purpose of investigating the accuracy of the Caldeira-Leggett model. We do that by simulating the vibrational features of water solvation by means of two different approaches. One is entirely based on the adoption of an accurate ab initio potential to describe water clusters of increasing dimensionality. The other one consists of a model made of a central water molecule coupled to a high-dimensional Caldeira-Leggett harmonic bath. We demonstrate the role of quantum effects in the detection of water solvation and show that the computationally cheap approach based on the Caldeira-Leggett bath is only partially effective. The main conclusion of the study is that quantum methods associated with high-level potential energy surfaces are necessary to correctly study solvation features, while simplified models, even if attractive owing to their reduced computational cost, can provide some useful insights but are not able to come up with a comprehensive description of the solvation phenomenon.
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Affiliation(s)
- Alessandro Rognoni
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Riccardo Conte
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Universitá degli Studi di Milano, via Golgi 19, 20133 Milano, Italy
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Clear C, Schofield RC, Major KD, Iles-Smith J, Clark AS, McCutcheon DPS. Phonon-Induced Optical Dephasing in Single Organic Molecules. PHYSICAL REVIEW LETTERS 2020; 124:153602. [PMID: 32357066 DOI: 10.1103/physrevlett.124.153602] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/20/2019] [Accepted: 03/18/2020] [Indexed: 05/23/2023]
Abstract
We present a joint experiment-theory analysis of the temperature-dependent emission spectra, zero-phonon linewidth, and second-order correlation function of light emitted from a single organic molecule. We observe spectra with a zero-phonon line together with several additional sharp peaks, broad phonon sidebands, and a strongly temperature dependent homogeneous broadening. Our model includes both localized vibrational modes of the molecule and a thermal phonon bath, which we include nonperturbatively, and is able to capture all observed features. For resonant driving we measure Rabi oscillations that become increasingly damped with temperature, which our model naturally reproduces. Our results constitute an essential characterization of the photon coherence of molecules, paving the way to their use in future quantum information applications.
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Affiliation(s)
- Chloe Clear
- Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, BS8 1FD, United Kingdom
| | - Ross C Schofield
- Centre for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ London, United Kingdom
| | - Kyle D Major
- Centre for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ London, United Kingdom
| | - Jake Iles-Smith
- Department of Physics and Astronomy, University of Sheffield, Sheffield, S3 7RH, United Kingdom
| | - Alex S Clark
- Centre for Cold Matter, Blackett Laboratory, Imperial College London, Prince Consort Road, SW7 2AZ London, United Kingdom
| | - Dara P S McCutcheon
- Quantum Engineering Technology Labs, H. H. Wills Physics Laboratory and Department of Electrical and Electronic Engineering, University of Bristol, BS8 1FD, United Kingdom
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Gottwald F, Ivanov SD, Kühn O. On computing spectral densities from classical, semiclassical, and quantum simulations. J Chem Phys 2019; 150:084109. [DOI: 10.1063/1.5045293] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Fabian Gottwald
- Institute of Physics, University of Rostock, Albert Einstein Straße 23-24, 18059 Rostock, Germany
| | - Sergei D. Ivanov
- Institute of Physics, University of Rostock, Albert Einstein Straße 23-24, 18059 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert Einstein Straße 23-24, 18059 Rostock, Germany
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Picconi D, Cina JA, Burghardt I. Quantum dynamics and spectroscopy of dihalogens in solid matrices. I. Efficient simulation of the photodynamics of the embedded I 2Kr 18 cluster using the G-MCTDH method. J Chem Phys 2019; 150:064111. [PMID: 30770011 DOI: 10.1063/1.5082650] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/12/2023] Open
Abstract
The molecular dynamics following the electronic BΠu30+⟵XΣg+1 photoexcitation of the iodine molecule embedded in solid krypton are studied quantum mechanically using the Gaussian variant of the multiconfigurational time-dependent Hartree method (G-MCTDH). The accuracy of the Gaussian wave packet approximation is validated against numerically exact MCTDH simulations for a fully anharmonic seven-dimensional model of the I2Kr18 cluster in a crystal Kr cage. The linear absorption spectrum, time-evolving vibrational probability densities, and I2 energy expectation value are accurately reproduced by the numerically efficient G-MCTDH approach. The reduced density matrix of the chromophore is analyzed in the coordinate, Wigner and energy representations, so as to obtain a multifaceted dynamical view of the guest-host interactions. Vibrational coherences extending over the bond distance range 2.7 Å < RI-I < 4.0 Å are found to survive for several vibrational periods, despite extensive dissipation. The present results prepare the ground for the simulation of time-resolved coherent Raman spectroscopy of the I2-krypton system addressed in Paper II.
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Affiliation(s)
- David Picconi
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
| | - Jeffrey A Cina
- Department of Chemistry and Biochemistry, and Oregon Center for Optical, Molecular, and Quantum Science, University of Oregon, Eugene, Oregon 97403, USA
| | - Irene Burghardt
- Institute of Physical and Theoretical Chemistry, Goethe University Frankfurt, Max-von-Laue-Straße 7, D-60438 Frankfurt am Main, Germany
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Gottwald F, Bonfanti M, Martinazzo R, Ivanov SD, Kühn O. Note: Caldeira-Leggett model describes dynamics of hydrogen atoms on graphene. J Chem Phys 2016; 145:126101. [PMID: 27782622 DOI: 10.1063/1.4963737] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Fabian Gottwald
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Matteo Bonfanti
- Dipartimento di Chimica, Universitá degli Studi di Milano, v. Golgi 19, 20133 Milano, Italy
| | - Rocco Martinazzo
- Dipartimento di Chimica, Universitá degli Studi di Milano, v. Golgi 19, 20133 Milano, Italy
| | - Sergei D Ivanov
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
| | - Oliver Kühn
- Institute of Physics, University of Rostock, Albert-Einstein-Str. 23-24, 18059 Rostock, Germany
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