1
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Althorpe SC. Path Integral Simulations of Condensed-Phase Vibrational Spectroscopy. Annu Rev Phys Chem 2024; 75:397-420. [PMID: 38941531 DOI: 10.1146/annurev-physchem-090722-124705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/30/2024]
Abstract
Recent theoretical and algorithmic developments have improved the accuracy with which path integral dynamics methods can include nuclear quantum effects in simulations of condensed-phase vibrational spectra. Such methods are now understood to be approximations to the delocalized classical Matsubara dynamics of smooth Feynman paths, which dominate the dynamics of systems such as liquid water at room temperature. Focusing mainly on simulations of liquid water and hexagonal ice, we explain how the recently developed quasicentroid molecular dynamics (QCMD), fast-QCMD, and temperature-elevated path integral coarse-graining simulations (Te PIGS) methods generate classical dynamics on potentials of mean force obtained by averaging over quantum thermal fluctuations. These new methods give very close agreement with one another, and the Te PIGS method has recently yielded excellent agreement with experimentally measured vibrational spectra for liquid water, ice, and the liquid-air interface. We also discuss the limitations of such methods.
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Affiliation(s)
- Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Cambridge, United Kingdom;
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2
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LaCour RA, Heindel JP, Head-Gordon T. Predicting the Raman Spectra of Liquid Water with a Monomer-Field Model. J Phys Chem Lett 2023; 14:11742-11749. [PMID: 38116782 DOI: 10.1021/acs.jpclett.3c02873] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/21/2023]
Abstract
The Raman spectrum of liquid water is quite complex, reflecting its strong sensitivity to the local environment of the individual waters. The OH-stretch region of the spectrum, which captures the influence of hydrogen bonding, has only just begun to be unraveled. Here we develop a model for predicting the Raman spectra of the OH-stretch region by considering how local electric fields distort the energy surface of each water monomer. We find that our model is capable of reproducing the bimodal nature of the main peak, with the shoulder at 3250 cm-1 resulting almost entirely from Fermi resonance. Furthermore, we capture the temperature and polarization dependence of the shoulder, which has proven to be difficult to obtain with previous methods, and analyze the origin of this dependence. We expect our model to be generally useful for understanding and predicting how Raman spectra change under different conditions and with different probe reporters beyond water.
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Affiliation(s)
- R Allen LaCour
- Kenneth S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Joseph P Heindel
- Kenneth S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
| | - Teresa Head-Gordon
- Kenneth S. Pitzer Theory Center and Department of Chemistry, University of California, Berkeley, California 94720, United States
- Chemical Sciences Division, Lawrence Berkeley National Laboratory, Berkeley, California 94720, United States
- Departments of Bioengineering and Chemical and Biomolecular Engineering, University of California, Berkeley, California 94720, United States
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3
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Zhang Y, Wang Y, Xu X, Chen Z, Yang Y. Vibrational Spectra of Highly Anharmonic Water Clusters: Molecular Dynamics and Harmonic Analysis Revisited with Constrained Nuclear-Electronic Orbital Methods. J Chem Theory Comput 2023; 19:9358-9368. [PMID: 38096546 DOI: 10.1021/acs.jctc.3c01037] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/27/2023]
Abstract
Vibrational spectroscopy is widely used to gain insights into structural and dynamic properties of chemical, biological, and materials systems. Thus, an efficient and accurate method to simulate vibrational spectra is desired. In this paper, we justify and employ a microcanonical molecular simulation scheme to calculate the vibrational spectra of three challenging water clusters: the neutral water dimer (H4O2), the protonated water trimer (H7O3+), and the protonated water tetramer (H9O4+). We find that with the accurate description of quantum nuclear delocalization effects through the constrained nuclear-electronic orbital framework, including vibrational mode coupling effects through molecular dynamics simulations can additionally improve the vibrational spectrum calculations. In contrast, without the quantum nuclear delocalization picture, conventional ab initio molecular dynamics may even lead to less accurate results than harmonic analysis.
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Affiliation(s)
- Yuzhe Zhang
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Yiwen Wang
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Xi Xu
- Center for Advanced Materials Research, Beijing Normal University, Zhuhai 519087, China
| | - Zehua Chen
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
| | - Yang Yang
- Theoretical Chemistry Institute and Department of Chemistry, University of Wisconsin-Madison, 1101 University Avenue, Madison, Wisconsin 53706, United States
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4
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Plé T, Lagardère L, Piquemal JP. Force-field-enhanced neural network interactions: from local equivariant embedding to atom-in-molecule properties and long-range effects. Chem Sci 2023; 14:12554-12569. [PMID: 38020379 PMCID: PMC10646944 DOI: 10.1039/d3sc02581k] [Citation(s) in RCA: 2] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/22/2023] [Accepted: 10/03/2023] [Indexed: 12/01/2023] Open
Abstract
We introduce FENNIX (Force-Field-Enhanced Neural Network InteraXions), a hybrid approach between machine-learning and force-fields. We leverage state-of-the-art equivariant neural networks to predict local energy contributions and multiple atom-in-molecule properties that are then used as geometry-dependent parameters for physically-motivated energy terms which account for long-range electrostatics and dispersion. Using high-accuracy ab initio data (small organic molecules/dimers), we trained a first version of the model. Exhibiting accurate gas-phase energy predictions, FENNIX is transferable to the condensed phase. It is able to produce stable Molecular Dynamics simulations, including nuclear quantum effects, for water predicting accurate liquid properties. The extrapolating power of the hybrid physically-driven machine learning FENNIX approach is exemplified by computing: (i) the solvated alanine dipeptide free energy landscape; (ii) the reactive dissociation of small molecules.
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Affiliation(s)
- Thomas Plé
- Sorbonne Université, LCT, UMR 7616 CNRS F-75005 Paris France thomas.ple@sorbonne-université louis.lagardere@sorbonne-université jean-philip.piquemal@sorbonne-université
| | - Louis Lagardère
- Sorbonne Université, LCT, UMR 7616 CNRS F-75005 Paris France thomas.ple@sorbonne-université louis.lagardere@sorbonne-université jean-philip.piquemal@sorbonne-université
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS F-75005 Paris France thomas.ple@sorbonne-université louis.lagardere@sorbonne-université jean-philip.piquemal@sorbonne-université
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5
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Lawrence JE, Lieberherr AZ, Fletcher T, Manolopoulos DE. Fast Quasi-Centroid Molecular Dynamics for Water and Ice. J Phys Chem B 2023; 127:9172-9180. [PMID: 37830934 PMCID: PMC10614180 DOI: 10.1021/acs.jpcb.3c05028] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/26/2023] [Revised: 09/21/2023] [Indexed: 10/14/2023]
Abstract
We describe how the fast quasi-centroid molecular dynamics (f-QCMD) method can be applied to condensed-phase systems by approximating the quasi-centroid potential of mean force as a sum of inter- and intramolecular corrections to the classical interaction potential. The corrections are found by using a regularized iterative Boltzmann inversion procedure to recover the inter- and intramolecular quasi-centroid distribution functions obtained from a path integral molecular dynamics simulation. The resulting methodology is found to give good agreement with a previously published QCMD dipole absorption spectrum for liquid water and satisfactory agreement for ice. It also gives good agreement with spectra from a recent implementation of CMD that uses a precomputed elevated temperature potential of mean force. Modern centroid molecular dynamics methods, therefore, appear to be reaching a consensus regarding the impact of nuclear quantum effects on the vibrational spectra of water and ice.
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Affiliation(s)
| | - Annina Z. Lieberherr
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United
Kingdom
| | - Theo Fletcher
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United
Kingdom
| | - David E. Manolopoulos
- Physical
and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United
Kingdom
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6
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Hasegawa T. Nuclear Quantum Dynamics of Three-Dimensional Condensed-Phase Systems by Constant Uncertainty Molecular Dynamics. J Phys Chem Lett 2023; 14:8043-8049. [PMID: 37651720 DOI: 10.1021/acs.jpclett.3c01254] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 09/02/2023]
Abstract
Constant uncertainty molecular dynamics (CUMD), which was developed to include nuclear quantum effects (NQEs) in molecular dynamics (MD) simulations, is extended to three-dimensional condensed-phase systems. Its applicability was verified via CUMD simulations of bulk water and ice Ih with the q-TIP4P/F potential model. The simulated radial distribution functions, proton momentum distributions, and infrared spectra were compared with those of previous studies in which the simulations were carried out on the basis of the imaginary-time path-integral formalism. We found that CUMD can function as an alternative trajectory-based simulation method for including static and dynamic NQEs in MD simulations of three-dimensional condensed-phase systems.
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Affiliation(s)
- Taisuke Hasegawa
- Center for Computational Sciences, University of Tsukuba, 1-1-1 Tennodai, Tsukuba 305-8577, Japan
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7
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Litman Y, Lan J, Nagata Y, Wilkins DM. Fully First-Principles Surface Spectroscopy with Machine Learning. J Phys Chem Lett 2023; 14:8175-8182. [PMID: 37671886 PMCID: PMC10510433 DOI: 10.1021/acs.jpclett.3c01989] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/18/2023] [Accepted: 08/29/2023] [Indexed: 09/07/2023]
Abstract
Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially due to the continuous development of surface-specific spectroscopies, such as vibrational sum-frequency generation (VSFG). As in other vibrational spectroscopies, we must turn to atomistic simulations to extract all of the information encoded in the VSFG spectra. The high computational cost associated with existing methods means that they have limitations in representing systems with complex electronic structure or in achieving statistical convergence. In this work, we combine high-dimensional neural network interatomic potentials and symmetry-adapted Gaussian process regression to overcome these constraints. We show that it is possible to model VSFG signals with fully ab initio accuracy using machine learning and illustrate the versatility of our approach on the water/air interface. Our strategy allows us to identify the main sources of theoretical inaccuracy and establish a clear pathway toward the modeling of surface-sensitive spectroscopy of complex interfaces.
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Affiliation(s)
- Yair Litman
- Yusuf
Hamied Department of Chemistry, University
of Cambridge, Lensfield Road, Cambridge CB2 1EW, U.K.
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - Jinggang Lan
- Department
of Chemistry, New York University, New York, New York 10003, United States
- Simons
Center for Computational Physical Chemistry at New York University, New York, New York 10003, United States
| | - Yuki Nagata
- Max
Planck Institute for Polymer Research, Ackermannweg 10, 55128 Mainz, Germany
| | - David M. Wilkins
- Centre
for Quantum Materials and Technologies School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, Northern Ireland, United Kingdom
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8
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Lieberherr AZ, Furniss STE, Lawrence JE, Manolopoulos DE. Vibrational strong coupling in liquid water from cavity molecular dynamics. J Chem Phys 2023; 158:234106. [PMID: 37326163 DOI: 10.1063/5.0156808] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Accepted: 05/30/2023] [Indexed: 06/17/2023] Open
Abstract
We assess the cavity molecular dynamics method for the calculation of vibrational polariton spectra using liquid water as a specific example. We begin by disputing a recent suggestion that nuclear quantum effects may lead to a broadening of polariton bands, finding instead that they merely result in anharmonic red shifts in the polariton frequencies. We go on to show that our simulated cavity spectra can be reproduced to graphical accuracy with a harmonic model that uses just the cavity-free spectrum and the geometry of the cavity as input. We end by showing that this harmonic model can be combined with the experimental cavity-free spectrum to give results in good agreement with optical cavity measurements. Since the input to our harmonic model is equivalent to the input to the transfer matrix method of applied optics, we conclude that cavity molecular dynamics cannot provide any more insight into the effect of vibrational strong coupling on the absorption spectrum than this transfer matrix method, which is already widely used by experimentalists to corroborate their cavity results.
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Affiliation(s)
- Annina Z Lieberherr
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Seth T E Furniss
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Joseph E Lawrence
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - David E Manolopoulos
- Department of Chemistry, University of Oxford, Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, United Kingdom
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9
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Videla PE, Batista VS. Matsubara dynamics approximation for generalized multi-time correlation functions. J Chem Phys 2023; 158:2889027. [PMID: 37154285 DOI: 10.1063/5.0146654] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2023] [Accepted: 04/21/2023] [Indexed: 05/10/2023] Open
Abstract
We introduce a semi-classical approximation for calculating generalized multi-time correlation functions based on Matsubara dynamics, a classical dynamics approach that conserves the quantum Boltzmann distribution. This method is exact for the zero time and harmonic limits and reduces to classical dynamics when only one Matsubara mode is considered (i.e., the centroid). Generalized multi-time correlation functions can be expressed as canonical phase-space integrals, involving classically evolved observables coupled through Poisson brackets in a smooth Matsubara space. Numerical tests on a simple potential show that the Matsubara approximation exhibits better agreement with exact results than classical dynamics, providing a bridge between the purely quantum and classical descriptions of multi-time correlation functions. Despite the phase problem that prevents practical applications of Matsubara dynamics, the reported work provides a benchmark theory for the future development of quantum-Boltzmann-preserving semi-classical approximations for studies of chemical dynamics in condensed phase systems.
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Affiliation(s)
- Pablo E Videla
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
| | - Victor S Batista
- Department of Chemistry, Yale University, 225 Prospect Street, New Haven, Connecticut 06520-8107, USA
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10
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Begušić T, Blake GA. Two-dimensional infrared-Raman spectroscopy as a probe of water's tetrahedrality. Nat Commun 2023; 14:1950. [PMID: 37029146 PMCID: PMC10082090 DOI: 10.1038/s41467-023-37667-7] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Accepted: 03/22/2023] [Indexed: 04/09/2023] Open
Abstract
Two-dimensional spectroscopic techniques combining terahertz (THz), infrared (IR), and visible pulses offer a wealth of information about coupling among vibrational modes in molecular liquids, thus providing a promising probe of their local structure. However, the capabilities of these spectroscopies are still largely unexplored due to experimental limitations and inherently weak nonlinear signals. Here, through a combination of equilibrium-nonequilibrium molecular dynamics (MD) and a tailored spectrum decomposition scheme, we identify a relationship between the tetrahedral order of liquid water and its two-dimensional IR-IR-Raman (IIR) spectrum. The structure-spectrum relationship can explain the temperature dependence of the spectral features corresponding to the anharmonic coupling between low-frequency intermolecular and high-frequency intramolecular vibrational modes of water. In light of these results, we propose new experiments and discuss the implications for the study of tetrahedrality of liquid water.
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Affiliation(s)
- Tomislav Begušić
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA.
| | - Geoffrey A Blake
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, CA, 91125, USA.
- Division of Geological and Planetary Sciences, California Institute of Technology, Pasadena, CA, 91125, USA.
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11
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Prada A, Pós ES, Althorpe SC. Comparison of Matsubara dynamics with exact quantum dynamics for an oscillator coupled to a dissipative bath. J Chem Phys 2023; 158:114106. [PMID: 36948794 DOI: 10.1063/5.0138250] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/17/2023] Open
Abstract
We report the first numerical calculations in which converged Matsubara dynamics is compared directly with exact quantum dynamics with no artificial damping of the time-correlation functions (TCFs). The system treated is a Morse oscillator coupled to a harmonic bath. We show that, when the system-bath coupling is sufficiently strong, the Matsubara calculations can be converged by explicitly including up to M = 200 Matsubara modes, with the remaining modes included as a harmonic "tail" correction. The resulting Matsubara TCFs are in near-perfect agreement with the exact quantum TCFs, for non-linear as well as linear operators, at a temperature at which the TCFs are dominated by quantum thermal fluctuations. These results provide compelling evidence that incoherent classical dynamics can arise in the condensed phase at temperatures at which the statistics are dominated by quantum (Boltzmann) effects, as a result of smoothing of imaginary-time Feynman paths. The techniques developed here may also lead to efficient methods for benchmarking system-bath dynamics in the overdamped regime.
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Affiliation(s)
- Adam Prada
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Eszter S Pós
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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12
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Plé T, Mauger N, Adjoua O, Inizan TJ, Lagardère L, Huppert S, Piquemal JP. Routine Molecular Dynamics Simulations Including Nuclear Quantum Effects: From Force Fields to Machine Learning Potentials. J Chem Theory Comput 2023; 19:1432-1445. [PMID: 36856658 DOI: 10.1021/acs.jctc.2c01233] [Citation(s) in RCA: 9] [Impact Index Per Article: 9.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 03/02/2023]
Abstract
We report the implementation of a multi-CPU and multi-GPU massively parallel platform dedicated to the explicit inclusion of nuclear quantum effects (NQEs) in the Tinker-HP molecular dynamics (MD) package. The platform, denoted Quantum-HP, exploits two simulation strategies: the Ring-Polymer Molecular Dynamics (RPMD) that provides exact structural properties at the cost of a MD simulation in an extended space of multiple replicas and the adaptive Quantum Thermal Bath (adQTB) that imposes the quantum distribution of energy on a classical system via a generalized Langevin thermostat and provides computationally affordable and accurate (though approximate) NQEs. We discuss some implementation details, efficient numerical schemes, and parallelization strategies and quickly review the GPU acceleration of our code. Our implementation allows an efficient inclusion of NQEs in MD simulations for very large systems, as demonstrated by scaling tests on water boxes with more than 200,000 atoms (simulated using the AMOEBA polarizable force field). We test the compatibility of the approach with Tinker-HP's recently introduced Deep-HP machine learning potentials module by computing water properties using the DeePMD potential with adQTB thermostatting. Finally, we show that the platform is also compatible with the alchemical free energy estimation capabilities of Tinker-HP and fast enough to perform simulations. Therefore, we study how NQEs affect the hydration free energy of small molecules solvated with the recently developed Q-AMOEBA water force field. Overall, the Quantum-HP platform allows users to perform routine quantum MD simulations of large condensed-phase systems and will help to shed new light on the quantum nature of important interactions in biological matter.
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Affiliation(s)
- Thomas Plé
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Nastasia Mauger
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Olivier Adjoua
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | | | - Louis Lagardère
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Simon Huppert
- Institut des Nanosciences de Paris (INSP), CNRS UMR 7588, and Sorbonne Université, F-75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France.,Institut Universitaire de France, 75005 Paris, France.,Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
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13
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Mauger N, Plé T, Lagardère L, Huppert S, Piquemal JP. Improving Condensed-Phase Water Dynamics with Explicit Nuclear Quantum Effects: The Polarizable Q-AMOEBA Force Field. J Phys Chem B 2022; 126:8813-8826. [PMID: 36270033 DOI: 10.1021/acs.jpcb.2c04454] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/11/2023]
Abstract
We introduce a new parametrization of the AMOEBA polarizable force field for water denoted Q-AMOEBA, for use in simulations that explicitly account for nuclear quantum effects (NQEs). This study is made possible thanks to the recently introduced adaptive Quantum Thermal Bath (adQTB) simulation technique which computational cost is comparable to classical molecular dynamics. The flexible Q-AMOEBA model conserves the initial AMOEBA functional form, with an intermolecular potential including an atomic multipole description of electrostatic interactions (up to quadrupole), a polarization contribution based on the Thole interaction model and a buffered 14-7 potential to model van der Waals interactions. It has been obtained by using a ForceBalance fitting strategy including high-level quantum chemistry reference energies and selected condensed-phase properties targets. The final Q-AMOEBA model is shown to accurately reproduce both gas-phase and condensed-phase properties, notably improving the original AMOEBA water model. This development allows the fine study of NQEs on water liquid phase properties such as the average H-O-H angle compared to its gas-phase equilibrium value, isotope effects, and so on. Q-AMOEBA also provides improved infrared spectroscopy prediction capabilities compared to AMOEBA03. Overall, we show that the impact of NQEs depends on the underlying model functional form and on the associated strength of hydrogen bonds. Since adQTB simulations can be performed at near classical computational cost using the Tinker-HP package, Q-AMOEBA can be extended to organic molecules, proteins, and nucleic acids opening the possibility for the large-scale study of the importance of NQEs in biophysics.
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Affiliation(s)
- Nastasia Mauger
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Thomas Plé
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Louis Lagardère
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
| | - Simon Huppert
- Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588 CNRS, 75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, Laboratoire de Chimie Théorique, UMR 7616 CNRS, 75005 Paris, France
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14
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Tan JA, Takahashi K. Vibrational spectrum of a 1D oscillator: The quantum, the Wigner, and the classical ways. J CHIN CHEM SOC-TAIP 2022. [DOI: 10.1002/jccs.202200398] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/07/2022]
Affiliation(s)
- Jake A. Tan
- Institute of Atomic and Molecular Sciences Academia Sinica Taipei Taiwan
| | - Kaito Takahashi
- Institute of Atomic and Molecular Sciences Academia Sinica Taipei Taiwan
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15
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Simulation of Nuclear Quantum Effects in Condensed Matter Systems via Quantum Baths. APPLIED SCIENCES-BASEL 2022. [DOI: 10.3390/app12094756] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/10/2022]
Abstract
This paper reviews methods that aim at simulating nuclear quantum effects (NQEs) using generalized thermal baths. Generalized (or quantum) baths simulate statistical quantum features, and in particular zero-point energy effects, through non-Markovian stochastic dynamics. They make use of generalized Langevin Equations (GLEs), in which the quantum Bose–Einstein energy distribution is enforced by tuning the random and friction forces, while the system degrees of freedom remain classical. Although these baths have been formally justified only for harmonic oscillators, they perform well for several systems, while keeping the cost of the simulations comparable to the classical ones. We review the formal properties and main characteristics of classical and quantum GLEs, in relation with the fluctuation–dissipation theorems. Then, we describe the quantum thermostat and quantum thermal bath, the two generalized baths currently most used, providing several examples of applications for condensed matter systems, including the calculation of vibrational spectra. The most important drawback of these methods, zero-point energy leakage, is discussed in detail with the help of model systems, and a recently proposed scheme to monitor and mitigate or eliminate it—the adaptive quantum thermal bath—is summarised. This approach considerably extends the domain of application of generalized baths, leading, for instance, to the successful simulation of liquid water, where a subtle interplay of NQEs is at play. The paper concludes by overviewing further development opportunities and open challenges of generalized baths.
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16
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Li TE, Nitzan A, Hammes-Schiffer S, Subotnik JE. Quantum Simulations of Vibrational Strong Coupling via Path Integrals. J Phys Chem Lett 2022; 13:3890-3895. [PMID: 35471100 DOI: 10.1021/acs.jpclett.2c00613] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/14/2023]
Abstract
A quantum simulation of vibrational strong coupling (VSC) in the collective regime via thermostated ring-polymer molecular dynamics (TRPMD) is reported. For a collection of liquid-phase water molecules resonantly coupled to a single lossless cavity mode, the simulation shows that as compared with a fully classical calculation, the inclusion of nuclear and photonic quantum effects does not lead to a change in the Rabi splitting but does broaden polaritonic line widths roughly by a factor of 2. Moreover, under thermal equilibrium, both quantum and classical simulations predict that the static dielectric constant of liquid water is largely unchanged inside vs outside the cavity. This result disagrees with a recent experiment demonstrating that the static dielectric constant of liquid water can be resonantly enhanced under VSC, suggesting either limitations of our approach or perhaps other experimental factors that have not yet been explored.
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Affiliation(s)
- Tao E Li
- Department of Chemistry, Yale University, New Haven, Connecticut 06520, United States
| | - Abraham Nitzan
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
- School of Chemistry, Tel Aviv University, Tel Aviv 69978, Israel
| | | | - Joseph E Subotnik
- Department of Chemistry, University of Pennsylvania, Philadelphia, Pennsylvania 19104, United States
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17
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Depondt P, Huppert S, Finocchi F. The quantum taste of hydrogen. EPJ WEB OF CONFERENCES 2022. [DOI: 10.1051/epjconf/202226301014] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Electronic properties of materials are dominated by quantum effects, but nuclei, being much heavier, are usually treated as classical particles. This approximation, although tremendously convenient, is not always valid, even in close to ambient pressure and temperature conditions, especially when light nuclei such as hydrogen are involved. Zero point energy and proton tunneling can be relevant. Isotopic effects, obtained by replacing hydrogen with deuterium, are observed experimentally and are a clear indication of Nuclear Quantum Effects (NQE) since mean values obtained through classical statistical physics do not depend on mass. Introducing NQEs into simulations at an acceptable computational cost raises fundamental questions and yields subtle and unexpected results.
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18
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Begušić T, Tao X, Blake GA, Miller TF. Equilibrium-nonequilibrium ring-polymer molecular dynamics for nonlinear spectroscopy. J Chem Phys 2022; 156:131102. [PMID: 35395895 DOI: 10.1063/5.0087156] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022] Open
Abstract
Two-dimensional Raman and hybrid terahertz-Raman spectroscopic techniques provide invaluable insight into molecular structures and dynamics of condensed-phase systems. However, corroborating experimental results with theory is difficult due to the high computational cost of incorporating quantum-mechanical effects in the simulations. Here, we present the equilibrium-nonequilibrium ring-polymer molecular dynamics (RPMD), a practical computational method that can account for nuclear quantum effects on the two-time response function of nonlinear optical spectroscopy. Unlike a recently developed approach based on the double Kubo transformed (DKT) correlation function, our method is exact in the classical limit, where it reduces to the established equilibrium-nonequilibrium classical molecular dynamics method. Using benchmark model calculations, we demonstrate the advantages of the equilibrium-nonequilibrium RPMD over classical and DKT-based approaches. Importantly, its derivation, which is based on the nonequilibrium RPMD, obviates the need for identifying an appropriate Kubo transformed correlation function and paves the way for applying real-time path-integral techniques to multidimensional spectroscopy.
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Affiliation(s)
- Tomislav Begušić
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Xuecheng Tao
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Geoffrey A Blake
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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19
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Fletcher T, Zhu A, Lawrence JE, Manolopoulos DE. Fast quasi-centroid molecular dynamics. J Chem Phys 2021; 155:231101. [PMID: 34937347 DOI: 10.1063/5.0076704] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We describe a fast implementation of the quasi-centroid molecular dynamics (QCMD) method in which the quasi-centroid potential of mean force is approximated as a separable correction to the classical interaction potential. This correction is obtained by first calculating quasi-centroid radial and angular distribution functions in a short path integral molecular dynamics simulation and then using iterative Boltzmann inversion to obtain an effective classical potential that reproduces these distribution functions in a classical NVT simulation. We illustrate this approach with example applications to the vibrational spectra of gas phase molecules, obtaining excellent agreement with QCMD reference calculations for water and ammonia and good agreement with the quantum mechanical vibrational spectrum of methane.
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Affiliation(s)
- Theo Fletcher
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Andrew Zhu
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - Joseph E Lawrence
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - David E Manolopoulos
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
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20
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Haggard C, Sadhasivam VG, Trenins G, Althorpe SC. Testing the quasicentroid molecular dynamics method on gas-phase ammonia. J Chem Phys 2021; 155:174120. [PMID: 34742190 DOI: 10.1063/5.0068250] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quasicentroid molecular dynamics (QCMD) is a path-integral method for approximating nuclear quantum effects in dynamics simulations, which has given promising results for gas- and condensed-phase water. In this work, by simulating the infrared spectrum of gas-phase ammonia, we test the feasibility of extending QCMD beyond water. Overall, QCMD works as well for ammonia as for water, reducing or eliminating blue shifts from the classical spectrum without introducing the artificial red shifts or broadening associated with other imaginary-time path-integral methods. However, QCMD gives only a modest improvement over the classical spectrum for the position of the symmetric bend mode, which is highly anharmonic (since it correlates with the inversion pathway). We expect QCMD to have similar problems with large-amplitude degrees of freedom in other molecules but otherwise to work as well as for water.
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Affiliation(s)
- Christopher Haggard
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Vijay Ganesh Sadhasivam
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - George Trenins
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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21
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Benson RL, Althorpe SC. On the "Matsubara heating" of overtone intensities and Fermi splittings. J Chem Phys 2021; 155:104107. [PMID: 34525826 DOI: 10.1063/5.0056829] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
Classical molecular dynamics (MD) and imaginary-time path-integral dynamics methods underestimate the infrared absorption intensities of overtone and combination bands by typically an order of magnitude. Plé et al. [J. Chem. Phys. 155, 2863 (2021)] have shown that this is because such methods fail to describe the coupling of the centroid to the Matsubara dynamics of the fluctuation modes; classical first-order perturbation theory (PT) applied to the Matsubara dynamics is sufficient to recover most of the lost intensity in simple models and gives identical results to quantum (Rayleigh-Schrödinger) PT. Here, we show numerically that the results of this analysis can be used as post-processing correction factors, which can be applied to realistic (classical MD or path-integral dynamics) simulations of infrared spectra. We find that the correction factors recover most of the lost intensity in the overtone and combination bands of gas-phase water and ammonia and much of it for liquid water. We then re-derive and confirm the earlier PT analysis by applying canonical PT to Matsubara dynamics, which has the advantage of avoiding secular terms and gives a simple picture of the perturbed Matsubara dynamics in terms of action-angle variables. Collectively, these variables "Matsubara heat" the amplitudes of the overtone and combination vibrations of the centroid to what they would be in a classical system with the oscillators (of frequency Ωi) held at their quantum effective temperatures [of ℏΩi coth(βℏΩi/2)/2kB]. Numerical calculations show that a similar neglect of "Matsubara heating" causes path-integral methods to underestimate Fermi resonance splittings.
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Affiliation(s)
- Raz L Benson
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Stuart C Althorpe
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
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22
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Plé T, Huppert S, Finocchi F, Depondt P, Bonella S. Anharmonic spectral features via trajectory-based quantum dynamics: A perturbative analysis of the interplay between dynamics and sampling. J Chem Phys 2021; 155:104108. [PMID: 34525824 DOI: 10.1063/5.0056824] [Citation(s) in RCA: 15] [Impact Index Per Article: 5.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The performance of different approximate algorithms for computing anharmonic features in vibrational spectra is analyzed and compared on model and more realistic systems that present relevant nuclear quantum effects. The methods considered combine approximate sampling of the quantum thermal distribution with classical time propagation and include Matsubara dynamics, path integral dynamics approaches, linearized initial value representation, and the recently introduced adaptive quantum thermal bath. A perturbative analysis of these different methods enables us to account for the observed numerical performance on prototypes for overtones and combination bands and to draw qualitatively correct trends for the numerical results obtained for Fermi resonances. Our results prove that the unequal performances of these approaches often derive from the method employed to sample initial conditions and not, as usually assumed, from the lack of coherence in the time propagation. Furthermore, as confirmed by the analysis reported in Benson and Althorpe, J. Chem. Phys. 130, 194510 (2021), we demonstrate, both via the perturbative approach and numerically, that path integral dynamics methods fail to reproduce the intensities of these anharmonic features and follow purely classical trends with respect to their temperature behavior. Finally, the remarkably accurate performance of the adaptive quantum thermal bath approach is documented and motivated.
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Affiliation(s)
- Thomas Plé
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Simon Huppert
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Fabio Finocchi
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Philippe Depondt
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Sara Bonella
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland
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23
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Mauger N, Plé T, Lagardère L, Bonella S, Mangaud É, Piquemal JP, Huppert S. Nuclear Quantum Effects in Liquid Water at Near Classical Computational Cost Using the Adaptive Quantum Thermal Bath. J Phys Chem Lett 2021; 12:8285-8291. [PMID: 34427440 DOI: 10.1021/acs.jpclett.1c01722] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/13/2023]
Abstract
We demonstrate the accuracy and efficiency of a recently introduced approach to account for nuclear quantum effects (NQEs) in molecular simulations: the adaptive quantum thermal bath (adQTB). In this method, zero-point energy is introduced through a generalized Langevin thermostat designed to precisely enforce the quantum fluctuation-dissipation theorem. We propose a refined adQTB algorithm with improved accuracy and report adQTB simulations of liquid water. Through extensive comparison with reference path integral calculations, we demonstrate that it provides excellent accuracy for a broad range of structural and thermodynamic observables as well as infrared vibrational spectra. The adQTB has a computational cost comparable to that of classical molecular dynamics, enabling simulations of up to millions of degrees of freedom.
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Affiliation(s)
- Nastasia Mauger
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Thomas Plé
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
| | - Louis Lagardère
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
| | - Sara Bonella
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland
| | - Étienne Mangaud
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
| | - Jean-Philip Piquemal
- Sorbonne Université, LCT, UMR 7616 CNRS, F-75005 Paris, France
- Institut Universitaire de France, 75005 Paris, France
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, United States
| | - Simon Huppert
- CNRS, Sorbonne Université, Institut des NanoSciences de Paris, UMR 7588, 4 Place Jussieu, F-75005 Paris, France
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24
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Inakollu VSS, Yu H. Comparative studies of IR spectra of deprotonated serine with classical and thermostated ring polymer molecular dynamics simulations. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2021; 8:054101. [PMID: 34549074 PMCID: PMC8443303 DOI: 10.1063/4.0000124] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 06/17/2021] [Accepted: 08/30/2021] [Indexed: 06/13/2023]
Abstract
Here we report the vibrational spectra of deprotonated serine calculated from the classical molecular dynamics (MD) simulations and thermostated ring-polymer molecular dynamics (TRPMD) simulation with third-order density-functional tight-binding. In our earlier study [Inakollu and Yu, "A systematic benchmarking of computational vibrational spectroscopy with DFTB3: Normal mode analysis and fast Fourier transform dipole autocorrelation function," J. Comput. Chem. 39, 2067 (2018)] of deprotonated serine, we observed a significant difference in the vibrational spectra with the classical MD simulations compared to the infrared multiple photon dissociation spectra. It was postulated that this is due to neglecting the nuclear quantum effects (NQEs). In this work, NQEs are considered in spectral calculation using the TRPMD simulations. With the help of potential of mean force calculations, the conformational space of deprotonated serine is analyzed and used to understand the difference in the spectra of classical MD and TRPMD simulations at 298.15 and 100 K. The high-frequency vibrational bands in the spectra are characterized using Fourier transform localized vibrational mode (FT-νN AC) and interatomic distance histograms. At room temperature, the quantum effects are less significant, and the free energy profiles in the classical MD and the TRPMD simulations are very similar. However, the hydrogen bond between the hydroxyl-carboxyl bond is slightly stronger in TRPMD simulations. At 100 K, the quantum effects are more prominent, especially in the 2600-3600 cm-1, and the free energy profile slightly differs between the classical MD and TRPMD simulations. Using the FT-νN AC and the interatomic distance histograms, the high-frequency vibrational bands are discussed in detail.
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Affiliation(s)
| | - Haibo Yu
- Author to whom correspondence should be addressed:
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25
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Drużbicki K, Gaboardi M, Fernandez-Alonso F. Dynamics & Spectroscopy with Neutrons-Recent Developments & Emerging Opportunities. Polymers (Basel) 2021; 13:1440. [PMID: 33947108 PMCID: PMC8125526 DOI: 10.3390/polym13091440] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2021] [Accepted: 04/27/2021] [Indexed: 12/19/2022] Open
Abstract
This work provides an up-to-date overview of recent developments in neutron spectroscopic techniques and associated computational tools to interrogate the structural properties and dynamical behavior of complex and disordered materials, with a focus on those of a soft and polymeric nature. These have and continue to pave the way for new scientific opportunities simply thought unthinkable not so long ago, and have particularly benefited from advances in high-resolution, broadband techniques spanning energy transfers from the meV to the eV. Topical areas include the identification and robust assignment of low-energy modes underpinning functionality in soft solids and supramolecular frameworks, or the quantification in the laboratory of hitherto unexplored nuclear quantum effects dictating thermodynamic properties. In addition to novel classes of materials, we also discuss recent discoveries around water and its phase diagram, which continue to surprise us. All throughout, emphasis is placed on linking these ongoing and exciting experimental and computational developments to specific scientific questions in the context of the discovery of new materials for sustainable technologies.
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Affiliation(s)
- Kacper Drużbicki
- Materials Physics Center, CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastian, Spain;
- Polish Academy of Sciences, Center of Molecular and Macromolecular Studies, Sienkiewicza 112, 90-363 Lodz, Poland
| | - Mattia Gaboardi
- Elettra—Sincrotrone Trieste S.C.p.A., S.S. 14 km 163.5 in Area Science Park, 34149 Trieste, Italy;
| | - Felix Fernandez-Alonso
- Materials Physics Center, CSIC-UPV/EHU, Paseo Manuel de Lardizabal 5, 20018 Donostia-San Sebastian, Spain;
- Donostia International Physics Center (DIPC), Paseo Manuel de Lardizabal 4, 20018 Donostia-San Sebastian, Spain
- Department of Physics and Astronomy, University College London, Gower Street, London WC1E 6BT, UK
- IKERBASQUE, Basque Foundation for Science, Plaza Euskadi 5, 48009 Bilbao, Spain
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26
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Talotta F, Agostini F, Ciccotti G. Quantum Trajectories for the Dynamics in the Exact Factorization Framework: A Proof-of-Principle Test. J Phys Chem A 2020; 124:6764-6777. [PMID: 32786992 DOI: 10.1021/acs.jpca.0c03969] [Citation(s) in RCA: 10] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
In the framework of the exact factorization of the time-dependent electron-nuclear wave function, we investigate the possibility of solving the nuclear time-dependent Schrödinger equation based on trajectories. The nuclear equation is separated in a Hamilton-Jacobi equation for the phase of the wave function, and a continuity equation for its (squared) modulus. For illustrative adiabatic and nonadiabatic one-dimensional models, we implement a procedure to follow the evolution of the nuclear density along the characteristics of the Hamilton-Jacobi equation. Those characteristics are referred to as quantum trajectories, since they are generated via ordinary differential equations similar to Hamilton's equations, but including the so-called quantum potential, and they can be used to reconstruct exactly the quantum-mechanical nuclear wave function, provided infinite initial conditions are propagated in time.
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Affiliation(s)
- Francesco Talotta
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Federica Agostini
- Université Paris-Saclay, CNRS, Institut de Chimie Physique UMR8000, 91405, Orsay, France.,Université Paris-Saclay, CNRS, Institut des Sciences Moléculaires d'Orsay, 91405, Orsay, France
| | - Giovanni Ciccotti
- CNR, Institute for Applied Computing "Mauro Picone" (IAC), Via dei Taurini 19, 00185 Rome, Italy.,School of Physics, University College of Dublin UCD - Belfield, Dublin 4, Ireland.,Dipartimento di Fisica, Università di Roma La Sapienza, P. le A. Moro 5, 00185 Roma, Italy
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27
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Brieuc F, Schran C, Uhl F, Forbert H, Marx D. Converged quantum simulations of reactive solutes in superfluid helium: The Bochum perspective. J Chem Phys 2020; 152:210901. [DOI: 10.1063/5.0008309] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Affiliation(s)
- Fabien Brieuc
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Christoph Schran
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Felix Uhl
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Harald Forbert
- Center for Solvation Science ZEMOS, Ruhr-Universität Bochum, 44780 Bochum, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, 44780 Bochum, Germany
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28
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Bafile U, Neumann M, Colognesi D, Guarini E. Time dependence of quantum correlation functions. Phys Rev E 2020; 101:052110. [PMID: 32575332 DOI: 10.1103/physreve.101.052110] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2020] [Accepted: 04/21/2020] [Indexed: 01/02/2023]
Abstract
In the past few years, the exponential expansion analysis of time autocorrelation functions has provided profound insight into the leading microscopic processes driving the atomic-scale dynamics and has made it possible to highlight the presence and the role of various relaxation channels through which the fundamental correlation functions decay with time. Here we apply this method to the determination of the full time dependence of a correlation function c(t) in a quantum system at nonzero temperature, by making explicit its relationship with its Kubo transform c_{K}(t), which in some cases can be approximately computed with the presently available quantum simulation techniques. We obtain an exact expression for c(t) in terms of the exponential modes that describe the time behavior of c_{K}(t). The relative importance of the various modes in determining the overall shape of c(t) can then be studied in detail. This work extends to the full time domain the results of a previous paper [Guarini et al., Phys. Rev. Lett. 123, 135301 (2019)PRLTAO0031-900710.1103/PhysRevLett.123.135301], in which we employed the same method to calculate the zero time value of the velocity autocorrelation function, to obtain a microscopic description of the quantum mean kinetic energy in a fluid. In particular, we show that the decay constants and the frequencies of the dominant microscopic modes of c(t) are the same as those of c_{K}(t), but the dynamics of the quantum system also contains an additional term decaying on a time scale determined solely by temperature of the system.
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Affiliation(s)
- Ubaldo Bafile
- Consiglio Nazionale delle Ricerche, Istituto di Fisica Applicata "Nello Carrara", via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Martin Neumann
- Fakultät für Physik der Universität Wien, Strudlhofgasse 4, A-1090 Wien, Austria
| | - Daniele Colognesi
- Consiglio Nazionale delle Ricerche, Istituto di Fisica Applicata "Nello Carrara", via Madonna del Piano 10, I-50019 Sesto Fiorentino, Italy
| | - Eleonora Guarini
- Dipartimento di Fisica e Astronomia, Università degli Studi di Firenze, via G. Sansone 1, I-50019 Sesto Fiorentino, Italy
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29
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Sommers GM, Calegari Andrade MF, Zhang L, Wang H, Car R. Raman spectrum and polarizability of liquid water from deep neural networks. Phys Chem Chem Phys 2020; 22:10592-10602. [DOI: 10.1039/d0cp01893g] [Citation(s) in RCA: 49] [Impact Index Per Article: 12.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Using deep neural networks to model the polarizability and potential energy surfaces, we compute the Raman spectrum of liquid water at several temperatures with ab initio molecular dynamics accuracy.
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Affiliation(s)
| | | | - Linfeng Zhang
- Program in Applied and Computational Mathematics
- Princeton University
- Princeton
- USA
| | - Han Wang
- Laboratory of Computational Physics
- Institute of Applied Physics and Computational Mathematics
- Beijing 100088
- P. R. China
| | - Roberto Car
- Department of Physics
- Princeton University
- Princeton
- USA
- Department of Chemistry
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30
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Korol R, Bou-Rabee N, Miller TF. Cayley modification for strongly stable path-integral and ring-polymer molecular dynamics. J Chem Phys 2019; 151:124103. [PMID: 31575166 DOI: 10.1063/1.5120282] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Path-integral-based molecular dynamics (MD) simulations are widely used for the calculation of numerically exact quantum Boltzmann properties and approximate dynamical quantities. A nearly universal feature of MD numerical integration schemes for equations of motion based on imaginary-time path integrals is the use of harmonic normal modes for the exact evolution of the free ring-polymer positions and momenta. In this work, we demonstrate that this standard practice creates numerical artifacts. In the context of conservative (i.e., microcanonical) equations of motion, it leads to numerical instability. In the context of thermostated (i.e., canonical) equations of motion, it leads to nonergodicity of the sampling. These pathologies are generally proven to arise at integration time steps that depend only on the system temperature and the number of ring-polymer beads, and they are numerically demonstrated for the cases of conventional ring-polymer MD (RPMD) and thermostated RPMD (TRPMD). Furthermore, it is demonstrated that these numerical artifacts are removed via replacement of the exact free ring-polymer evolution with a second-order approximation based on the Cayley transform. The Cayley modification introduced here can immediately be employed with almost every existing integration scheme for path-integral-based MD-including path-integral MD (PIMD), RPMD, TRPMD, and centroid MD-providing strong symplectic stability and ergodicity to the numerical integration, at no penalty in terms of computational cost, algorithmic complexity, or accuracy of the overall MD time step. Furthermore, it is shown that the improved numerical stability of the Cayley modification allows for the use of larger MD time steps. We suspect that the Cayley modification will therefore find useful application in many future path-integral-based MD simulations.
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Affiliation(s)
- Roman Korol
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Nawaf Bou-Rabee
- Department of Mathematical Sciences Rutgers University Camden, Camden, New Jersey 08102, USA
| | - Thomas F Miller
- Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
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