1
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Zaporozhets I, Musil F, Kapil V, Clementi C. Accurate nuclear quantum statistics on machine-learned classical effective potentials. J Chem Phys 2024; 161:134102. [PMID: 39352405 DOI: 10.1063/5.0226764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/03/2024] [Accepted: 09/13/2024] [Indexed: 10/03/2024] Open
Abstract
The contribution of nuclear quantum effects (NQEs) to the properties of various hydrogen-bound systems, including biomolecules, is increasingly recognized. Despite the development of many acceleration techniques, the computational overhead of incorporating NQEs in complex systems is sizable, particularly at low temperatures. In this work, we leverage deep learning and multiscale coarse-graining techniques to mitigate the computational burden of path integral molecular dynamics (PIMD). In particular, we employ a machine-learned potential to accurately represent corrections to classical potentials, thereby significantly reducing the computational cost of simulating NQEs. We validate our approach using four distinct systems: Morse potential, Zundel cation, single water molecule, and bulk water. Our framework allows us to accurately compute position-dependent static properties, as demonstrated by the excellent agreement obtained between the machine-learned potential and computationally intensive PIMD calculations, even in the presence of strong NQEs. This approach opens the way to the development of transferable machine-learned potentials capable of accurately reproducing NQEs in a wide range of molecular systems.
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Affiliation(s)
- Iryna Zaporozhets
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
| | - Félix Musil
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
| | - Venkat Kapil
- Yusuf Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Physics and Astronomy, University College, London WC1E 6BT, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, London WC1E 6BT, United Kingdom
| | - Cecilia Clementi
- Department of Physics, Freie Universität Berlin, Arnimallee 12, 14195 Berlin, Germany
- Department of Chemistry, Rice University, Houston, Texas 77005, USA
- Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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2
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Litman Y, Kapil V, Feldman YMY, Tisi D, Begušić T, Fidanyan K, Fraux G, Higer J, Kellner M, Li TE, Pós ES, Stocco E, Trenins G, Hirshberg B, Rossi M, Ceriotti M. i-PI 3.0: A flexible and efficient framework for advanced atomistic simulations. J Chem Phys 2024; 161:062504. [PMID: 39140447 DOI: 10.1063/5.0215869] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/26/2024] [Accepted: 07/11/2024] [Indexed: 08/15/2024] Open
Abstract
Atomic-scale simulations have progressed tremendously over the past decade, largely thanks to the availability of machine-learning interatomic potentials. These potentials combine the accuracy of electronic structure calculations with the ability to reach extensive length and time scales. The i-PI package facilitates integrating the latest developments in this field with advanced modeling techniques thanks to a modular software architecture based on inter-process communication through a socket interface. The choice of Python for implementation facilitates rapid prototyping but can add computational overhead. In this new release, we carefully benchmarked and optimized i-PI for several common simulation scenarios, making such overhead negligible when i-PI is used to model systems up to tens of thousands of atoms using widely adopted machine learning interatomic potentials, such as Behler-Parinello, DeePMD, and MACE neural networks. We also present the implementation of several new features, including an efficient algorithm to model bosonic and fermionic exchange, a framework for uncertainty quantification to be used in conjunction with machine-learning potentials, a communication infrastructure that allows for deeper integration with electronic-driven simulations, and an approach to simulate coupled photon-nuclear dynamics in optical or plasmonic cavities.
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Affiliation(s)
- Yair Litman
- Y. Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
| | - Venkat Kapil
- Y. Hamied Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, United Kingdom
- Department of Physics and Astronomy, University College London, 17-19 Gordon St, London WC1H 0AH, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, 19 Gordon St, London WC1H 0AH, United Kingdom
| | | | - Davide Tisi
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Tomislav Begušić
- Div. of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena, California 91125, USA
| | - Karen Fidanyan
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Guillaume Fraux
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Jacob Higer
- School of Physics, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Matthias Kellner
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Tao E Li
- Department of Physics and Astronomy, University of Delaware, Newark, Delaware 19716, USA
| | - Eszter S Pós
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Elia Stocco
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - George Trenins
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Barak Hirshberg
- School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
| | - Mariana Rossi
- MPI for the Structure and Dynamics of Matter, Hamburg, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modeling, Institut des Matériaux, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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3
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Tsujimoto M, Kinugawa K. Two liquid states of distinguishable helium-4: The existence of another non-superfluid frozen by heating. J Chem Phys 2024; 161:044501. [PMID: 39052083 DOI: 10.1063/5.0213674] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/12/2024] [Accepted: 07/08/2024] [Indexed: 07/27/2024] Open
Abstract
We show that two liquid states can exist in distinguishable helium-4 (4He) obeying Boltzmann statistics by path integral centroid molecular dynamics (CMD) simulations. This is an indication of quantum liquid polyamorphism induced by the nuclear quantum effect. For 0.08-3.3 K and 1-500 bar, we extensively conducted the isothermal-isobaric CMD simulations to explore not only possible states and state diagram but also the state characteristics. The distinguishable 4He below 25 bar does not freeze down to 0.1 K even though it includes no Bosonic exchange effect and, therefore, no Bose condensation. One liquid state, low quantum-dispersion liquid (LQDL), is nearly identical to normal liquid He-I of real 4He. The other is high quantum-dispersion liquid (HQDL) consisting of atoms with longer quantum wavelength. This is another non-superfluid existing below 0.5 K or the temperatures of LQDL. The HQDL is also a low-entropy and fragile liquid to exhibit, unlike conventional liquids, rather gas-like relaxation of velocity autocorrelation function, while there the atoms diffuse without noticeable contribution from quantum tunneling. The LQDL-HQDL transition is not a thermodynamic phase transition but a continuous crossover accompanied by the change in the expansion factor of quantum wavelength. Freezing of HQDL into the low quantum-dispersion amorphous solid occurs by heating from 0.2 to 0.3 K at 40-50 bar, while this P-T condition coincides with the Kim-Chan normal-supersolid phase boundary of real 4He. The obtained state diagram was compared to that of the confined subnano-scale 4He systems, where Bosonic correlation is considerably suppressed.
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Affiliation(s)
- Momoko Tsujimoto
- Department of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
| | - Kenichi Kinugawa
- Department of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
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4
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Wang Y, Luo R, Chen J, Zhou X, Wang S, Wu J, Kang F, Yu K, Sun B. Proton Collective Quantum Tunneling Induces Anomalous Thermal Conductivity of Ice under Pressure. PHYSICAL REVIEW LETTERS 2024; 132:264101. [PMID: 38996295 DOI: 10.1103/physrevlett.132.264101] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/14/2023] [Revised: 03/18/2024] [Accepted: 05/20/2024] [Indexed: 07/14/2024]
Abstract
Proton tunneling is believed to be nonlocal in ice, but its range has been shown to be limited to only a few molecules. Here, we measured the thermal conductivity of ice under pressure up to 50 GPa and found it increases with pressure until 20 GPa but decreases at higher pressures. We attribute this nonmonotonic thermal conductivity to the collective tunneling of protons at high pressures, supported by large-scale quantum molecular dynamics simulations. The collective tunneling loops span several picoseconds in time and are as large as nanometers in space, which match the phonon periods and wavelengths, leading to strong phonon scattering at high pressures. Our results show direct evidence of global quantum motion existing in high-pressure ice and provide a new perspective to understanding the coupling between phonon propagation and atomic tunneling.
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Wang C, Zhang L, Liu J, Shao J. Generalized fourth-order decompositions of imaginary time path integral: Implications of the harmonic oscillator. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2205089] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
Abstract
The imaginary time path integral formalism offers a powerful numerical tool for simulating thermodynamic properties of realistic systems. We show that, when second-order and fourth-order decompositions are employed, they share a remarkable unified analytic form for the partition function of the harmonic oscillator. We are then able to obtain the expression of the thermodynamic property and the leading error terms as well. In order to obtain reasonably optimal values of the free parameters in the generalized symmetric fourth-order decomposition scheme, we eliminate the leading error terms to achieve the accuracy of desired order for the thermodynamic property of the harmonic system. Such a strategy leads to an efficient fourth-order decomposition that produces third-order accurate thermodynamic properties for general systems.
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Affiliation(s)
- Cong Wang
- College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China
| | - Lihan Zhang
- Institute of Condensed Matter and Material Physics, School of Physics, Peking University, Beijing 100871, China
| | - Jian Liu
- Beijing National Laboratory for Molecular Sciences, Institute of Theoretical and Computational Chemistry, College of Chemistry and Molecular Engineering, Peking University, Beijing 100871, China
| | - Jiushu Shao
- College of Chemistry and Center for Advanced Quantum Studies, Key Laboratory of Theoretical and Computational Photochemistry, Ministry of Education, Beijing Normal University, Beijing 100875, China
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6
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Louisnard F, Geudtner G, Köster AM, Cuny J. Implementation of the parallel-tempering molecular dynamics method in deMon2k and application to the water hexamer. Theor Chem Acc 2021. [DOI: 10.1007/s00214-021-02765-6] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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7
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Kinugawa K, Takemoto A. Quantum polyamorphism in compressed distinguishable helium-4. J Chem Phys 2021; 154:224503. [PMID: 34241222 DOI: 10.1063/5.0048539] [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
We demonstrate that two amorphous solid states can exist in 4He consisting of distinguishable Boltzmann atoms under compressed conditions. The isothermal compression of normal or supercritical fluid 4He was conducted at 3-25 K using the isobaric-isothermal path integral centroid molecular dynamics simulation. The compression of fluid first produced the low-dispersion amorphous (LDA) state possessing modest extension of atomic necklaces. Further isothermal compression up to the order of 10 kbar to 1 Mbar or an isobaric cooling of LDA induced the transition to the high-dispersion amorphous (HDA) state. The HDA was characterized by long quantum wavelengths of atoms extended over several Angstroms and the promotion of atomic residual diffusion. They were related to the quantum tunneling of atoms bestriding the potential saddle points in this glass. The change in pressure or temperature induced the LDA-HDA transition reversibly with hysteresis, while it resembled the coil-globule transition of classical polymers. The HDA had lower kinetic and higher Gibbs free energies than the LDA at close temperature. The HDA was absent at T ≥ 13 K, while the LDA-HDA transition pressure significantly decreased with lowering temperature. The LDA and HDA correspond to the trapped and tunneling regimes proposed by Markland et al. [J. Chem. Phys. 136, 074511 (2012)], respectively. The same reentrant behavior as they found was observed for the expansion factor of the quantum wavelength as well as for atomic diffusivity.
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Affiliation(s)
- Kenichi Kinugawa
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
| | - Ayumi Takemoto
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women's University, Nara 630-8506, Japan
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Sutherland BJ, Moore WHD, Manolopoulos DE. Nuclear quantum effects in thermal conductivity from centroid molecular dynamics. J Chem Phys 2021; 154:174104. [PMID: 34241048 DOI: 10.1063/5.0051663] [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
We show that the centroid molecular dynamics (CMD) method provides a realistic way to calculate the thermal diffusivity a = λ/ρcV of a quantum mechanical liquid such as para-hydrogen. Once a has been calculated, the thermal conductivity can be obtained from λ = ρcVa, where ρ is the density of the liquid and cV is the constant-volume heat capacity. The use of this formula requires an accurate quantum mechanical heat capacity cV, which can be obtained from a path integral molecular dynamics simulation. The thermal diffusivity can be calculated either from the decay of the equilibrium density fluctuations in the liquid or by using the Green-Kubo relation to calculate the CMD approximation to λ and then dividing this by the corresponding approximation to ρcV. We show that both approaches give the same results for liquid para-hydrogen and that these results are in good agreement with the experimental measurements of the thermal conductivity over a wide temperature range. In particular, they correctly predict a decrease in the thermal conductivity at low temperatures-an effect that stems from the decrease in the quantum mechanical heat capacity and has eluded previous para-hydrogen simulations. We also show that the method gives equally good agreement with the experimental measurements for the thermal conductivity of normal liquid helium.
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Affiliation(s)
- Benjamin J Sutherland
- Physical and Theoretical Chemistry Laboratory, Department of Chemistry, University of Oxford, South Parks Road, Oxford OX1 3QZ, United Kingdom
| | - William H D Moore
- 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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9
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Yao Y, Kanai Y. Temperature dependence of nuclear quantum effects on liquid water via artificial neural network model based on SCAN meta-GGA functional. J Chem Phys 2020; 153:044114. [DOI: 10.1063/5.0012815] [Citation(s) in RCA: 14] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Yi Yao
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
- Department of Mechanical Engineering and Materials Science, Duke University, Durham, North Carolina 27708, USA
| | - Yosuke Kanai
- Department of Chemistry, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina 27599, USA
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10
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Kapil V, Wieme J, Vandenbrande S, Lamaire A, Van Speybroeck V, Ceriotti M. Modeling the Structural and Thermal Properties of Loaded Metal–Organic Frameworks. An Interplay of Quantum and Anharmonic Fluctuations. J Chem Theory Comput 2019; 15:3237-3249. [DOI: 10.1021/acs.jctc.8b01297] [Citation(s) in RCA: 17] [Impact Index Per Article: 3.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Affiliation(s)
- Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
| | - Jelle Wieme
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Steven Vandenbrande
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Aran Lamaire
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Veronique Van Speybroeck
- Center for Molecular Modeling, Ghent University, Tech Lane Ghent Science Park Campus A, Technologiepark 46, 9052 Zwijnaarde, Belgium
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland
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11
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Thapa MJ, Fang W, Richardson JO. Nonadiabatic quantum transition-state theory in the golden-rule limit. I. Theory and application to model systems. J Chem Phys 2019; 150:104107. [DOI: 10.1063/1.5081108] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Manish J. Thapa
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
| | - Wei Fang
- Laboratory of Physical Chemistry, ETH Zürich, 8093 Zürich, Switzerland
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12
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Takemoto A, Kinugawa K. Quantumness and state boundaries hidden in supercritical helium-4: A path integral centroid molecular dynamics study. J Chem Phys 2018; 149:204504. [DOI: 10.1063/1.5053988] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ayumi Takemoto
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
| | - Kenichi Kinugawa
- Division of Chemistry, Graduate School of Humanities and Sciences, Nara Women’s University, Nara 630-8506, Japan
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13
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Schran C, Brieuc F, Marx D. Converged Colored Noise Path Integral Molecular Dynamics Study of the Zundel Cation Down to Ultralow Temperatures at Coupled Cluster Accuracy. J Chem Theory Comput 2018; 14:5068-5078. [PMID: 30217111 DOI: 10.1021/acs.jctc.8b00705] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022]
Abstract
For a long time, performing converged path integral simulations at ultralow but finite temperatures of a few Kelvin has been a nearly impossible task. However, recent developments in advanced colored noise thermostatting schemes for path integral simulations, namely, the Path Integral Generalized Langevin Equation Thermostat (PIGLET) and the Path Integral Quantum Thermal Bath (PIQTB), have been able to greatly reduce the computational cost of these simulations, thus making the ultralow temperature regime accessible in practice. In this work, we investigate the influence of these two thermostatting schemes on the description of hydrogen-bonded systems at temperatures down to a few Kelvin as encountered, for example, in helium nanodroplet isolation or tagging photodissociation spectroscopy experiments. For this purpose, we analyze the prototypical hydrogen bond in the Zundel cation (H5O2+) as a function of both oxygen-oxygen distance and temperature in order to elucidate how the anisotropic quantum delocalization and, thus, the shape of the shared proton adapts depending on the donor-acceptor distance. The underlying electronic structure of the Zundel cation is described in terms of Behler's Neural Network Potentials of essentially converged Coupled Cluster accuracy, CCSD(T*)-F12a/AVTZ. In addition, the performances of the PIQTB and PIGLET methods for energetic, structural, and quantum delocalization properties are assessed and directly compared. Overall, our results emphasize the validity and practical usefulness of these two modern thermostatting approaches for path integral simulations of hydrogen-bonded systems even at ultralow temperatures.
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Affiliation(s)
- Christoph Schran
- Lehrstuhl für Theoretische Chemie , Ruhr-Universität Bochum , 44780 Bochum , Germany
| | - Fabien Brieuc
- Lehrstuhl für Theoretische Chemie , Ruhr-Universität Bochum , 44780 Bochum , Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie , Ruhr-Universität Bochum , 44780 Bochum , Germany
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14
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Jang S, Voth GA. Non-uniqueness of quantum transition state theory and general dividing surfaces in the path integral space. J Chem Phys 2018; 146:174106. [PMID: 28477603 DOI: 10.1063/1.4982053] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Despite the fact that quantum mechanical principles do not allow the establishment of an exact quantum analogue of the classical transition state theory (TST), the development of a quantum TST (QTST) with a proper dynamical justification, while recovering the TST in the classical limit, has been a long standing theoretical challenge in chemical physics. One of the most recent efforts of this kind was put forth by Hele and Althorpe (HA) [J. Chem. Phys. 138, 084108 (2013)], which can be specified for any cyclically invariant dividing surface defined in the space of the imaginary time path integral. The present work revisits the issue of the non-uniqueness of QTST and provides a detailed theoretical analysis of HA-QTST for a general class of such path integral dividing surfaces. While we confirm that HA-QTST reproduces the result based on the ring polymer molecular dynamics (RPMD) rate theory for dividing surfaces containing only a quadratic form of low frequency Fourier modes, we find that it produces different results for those containing higher frequency imaginary time paths which accommodate greater quantum fluctuations. This result confirms the assessment made in our previous work [Jang and Voth, J. Chem. Phys. 144, 084110 (2016)] that HA-QTST does not provide a derivation of RPMD-TST in general and points to a new ambiguity of HA-QTST with respect to its justification for general cyclically invariant dividing surfaces defined in the space of imaginary time path integrals. Our analysis also offers new insights into similar path integral based QTST approaches.
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Affiliation(s)
- Seogjoo Jang
- Department of Chemistry and Biochemistry, Queens College, City University of New York, 65-30 Kissena Boulevard, Queens, New York 11367, USA and Ph.D. Programs in Chemistry and Physics, and Initiative for the Theoretical Sciences, Graduate Center, City University of New York, 365 Fifth Avenue, New York, New York 10016, USA
| | - Gregory A Voth
- Department of Chemistry, James Franck Institute, and Institute for Biophysical Dynamics, The University of Chicago, 5735 S. Ellis Avenue, Chicago, Illinois 60637, USA
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15
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Poltavsky I, DiStasio RA, Tkatchenko A. Perturbed path integrals in imaginary time: Efficiently modeling nuclear quantum effects in molecules and materials. J Chem Phys 2018; 148:102325. [DOI: 10.1063/1.5006596] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/01/2023] Open
Affiliation(s)
- Igor Poltavsky
- Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg L-1511, Luxembourg
| | - Robert A. DiStasio
- Department of Chemistry and Chemical Biology, Cornell University, Ithaca, New York 14853, USA
| | - Alexandre Tkatchenko
- Physics and Materials Science Research Unit, University of Luxembourg, Luxembourg L-1511, Luxembourg
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16
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17
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Lindoy LP, Huang GS, Jordan MJT. Path integrals with higher order actions: Application to realistic chemical systems. J Chem Phys 2018; 148:074106. [PMID: 29471661 DOI: 10.1063/1.5000392] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Quantum thermodynamic parameters can be determined using path integral Monte Carlo (PIMC) simulations. These simulations, however, become computationally demanding as the quantum nature of the system increases, although their efficiency can be improved by using higher order approximations to the thermal density matrix, specifically the action. Here we compare the standard, primitive approximation to the action (PA) and three higher order approximations, the Takahashi-Imada action (TIA), the Suzuki-Chin action (SCA) and the Chin action (CA). The resulting PIMC methods are applied to two realistic potential energy surfaces, for H2O and HCN-HNC, both of which are spectroscopically accurate and contain three-body interactions. We further numerically optimise, for each potential, the SCA parameter and the two free parameters in the CA, obtaining more significant improvements in efficiency than seen previously in the literature. For both H2O and HCN-HNC, accounting for all required potential and force evaluations, the optimised CA formalism is approximately twice as efficient as the TIA formalism and approximately an order of magnitude more efficient than the PA. The optimised SCA formalism shows similar efficiency gains to the CA for HCN-HNC but has similar efficiency to the TIA for H2O at low temperature. In H2O and HCN-HNC systems, the optimal value of the a1 CA parameter is approximately 13, corresponding to an equal weighting of all force terms in the thermal density matrix, and similar to previous studies, the optimal α parameter in the SCA was ∼0.31. Importantly, poor choice of parameter significantly degrades the performance of the SCA and CA methods. In particular, for the CA, setting a1 = 0 is not efficient: the reduction in convergence efficiency is not offset by the lower number of force evaluations. We also find that the harmonic approximation to the CA parameters, whilst providing a fourth order approximation to the action, is not optimal for these realistic potentials: numerical optimisation leads to better approximate cancellation of the fifth order terms, with deviation between the harmonic and numerically optimised parameters more marked in the more quantum H2O system. This suggests that numerically optimising the CA or SCA parameters, which can be done at high temperature, will be important in fully realising the efficiency gains of these formalisms for realistic potentials.
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Affiliation(s)
- Lachlan P Lindoy
- School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia
| | - Gavin S Huang
- School of Chemistry, The University of Sydney, Sydney, NSW 2006, Australia
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18
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Karandashev K, Xu ZH, Meuwly M, Vaníček J, Richardson JO. Kinetic isotope effects and how to describe them. STRUCTURAL DYNAMICS (MELVILLE, N.Y.) 2017; 4:061501. [PMID: 29282447 PMCID: PMC5729036 DOI: 10.1063/1.4996339] [Citation(s) in RCA: 27] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 07/16/2017] [Accepted: 08/23/2017] [Indexed: 06/01/2023]
Abstract
We review several methods for computing kinetic isotope effects in chemical reactions including semiclassical and quantum instanton theory. These methods describe both the quantization of vibrational modes as well as tunneling and are applied to the ⋅H + H2 and ⋅H + CH4 reactions. The absolute rate constants computed with the semiclassical instanton method both using on-the-fly electronic structure calculations and fitted potential-energy surfaces are also compared directly with exact quantum dynamics results. The error inherent in the instanton approximation is found to be relatively small and similar in magnitude to that introduced by using fitted surfaces. The kinetic isotope effect computed by the quantum instanton is even more accurate, and although it is computationally more expensive, the efficiency can be improved by path-integral acceleration techniques. We also test a simple approach for designing potential-energy surfaces for the example of proton transfer in malonaldehyde. The tunneling splittings are computed, and although they are found to deviate from experimental results, the ratio of the splitting to that of an isotopically substituted form is in much better agreement. We discuss the strengths and limitations of the potential-energy surface and based on our findings suggest ways in which it can be improved.
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Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Zhen-Hao Xu
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Markus Meuwly
- Department of Chemistry, University of Basel, Klingelbergstrasse 80, CH-4056 Basel, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Jeremy O Richardson
- Laboratory of Physical Chemistry, Department of Chemistry and Applied Biosciences, Eidgenössische Technische Hochschule Zürich (ETHZ), CH-8093 Zürich, Switzerland
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19
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Affiliation(s)
- Ramachandran Subramanian
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York, USA
| | - Andrew J. Schultz
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York, USA
| | - David A. Kofke
- Department of Chemical and Biological Engineering, University at Buffalo, The State University of New York, Buffalo, New York, USA
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20
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Affiliation(s)
- Venkat Kapil
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
| | - Jörg Behler
- Lehrstuhl für Theoretische Chemie, Ruhr-Universität Bochum, Bochum, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, Ecole Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
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21
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Uhl F, Marx D, Ceriotti M. Accelerated path integral methods for atomistic simulations at ultra-low temperatures. J Chem Phys 2016; 145:054101. [DOI: 10.1063/1.4959602] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Felix Uhl
- Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr–Universität Bochum, 44780 Bochum, Germany
| | - Michele Ceriotti
- Laboratory of Computational Science and Modelling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
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22
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Ceriotti M, Fang W, Kusalik PG, McKenzie RH, Michaelides A, Morales MA, Markland TE. Nuclear Quantum Effects in Water and Aqueous Systems: Experiment, Theory, and Current Challenges. Chem Rev 2016; 116:7529-50. [DOI: 10.1021/acs.chemrev.5b00674] [Citation(s) in RCA: 339] [Impact Index Per Article: 42.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022]
Affiliation(s)
- Michele Ceriotti
- Laboratory
of Computational Science and Modeling, Institute of Materials, École Polytechnique Fédérale de Lausanne, 1015 Lausanne, Switzerland
| | - Wei Fang
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Peter G. Kusalik
- Department
of Chemistry, University of Calgary, 2500 University Drive NW, Calgary, Alberta T2N 1N4, Canada
| | - Ross H. McKenzie
- School
of Mathematics and Physics, University of Queensland, Brisbane, 4072 Queensland Australia
| | - Angelos Michaelides
- Thomas
Young Centre, London Centre for Nanotechnology and Department of Physics
and Astronomy, University College London, London WC1E 6BT, United Kingdom
| | - Miguel A. Morales
- Lawrence Livermore National Laboratory, Livermore, California 94550, United States
| | - Thomas E. Markland
- Department
of Chemistry, Stanford University, 333 Campus Drive, Stanford, California 94305, United States
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23
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Karandashev K, Vaníček J. Accelerating quantum instanton calculations of the kinetic isotope effects. J Chem Phys 2015; 143:194104. [DOI: 10.1063/1.4935701] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Konstantin Karandashev
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
| | - Jiří Vaníček
- Laboratory of Theoretical Physical Chemistry, Institut des Sciences et Ingénierie Chimiques, Ecole Polytechnique Fédérale de Lausanne (EPFL), Lausanne CH-1015, Switzerland
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24
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Poltavsky I, Tkatchenko A. Modeling quantum nuclei with perturbed path integral molecular dynamics. Chem Sci 2015; 7:1368-1372. [PMID: 29910893 PMCID: PMC5975916 DOI: 10.1039/c5sc03443d] [Citation(s) in RCA: 29] [Impact Index Per Article: 3.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/12/2015] [Accepted: 10/28/2015] [Indexed: 11/25/2022] Open
Abstract
Here we combine perturbation theory with the Feynman–Kac imaginary-time path integral approach to quantum mechanics for modeling quantum nuclear effects.
The quantum nature of nuclear motions plays a vital role in the structure, stability, and thermodynamics of molecules and materials. The standard approach to model nuclear quantum fluctuations in chemical and biological systems is to use path-integral molecular dynamics. Unfortunately, conventional path-integral simulations can have an exceedingly large computational cost due to the need to employ an excessive number of coupled classical subsystems (beads) for quantitative accuracy. Here, we combine perturbation theory with the Feynman–Kac imaginary-time path integral approach to quantum mechanics and derive an improved non-empirical partition function and estimators to calculate converged quantum observables. Our perturbed path-integral (PPI) method requires the same ingredients as the conventional approach, but increases the accuracy and efficiency of path integral simulations by an order of magnitude. Results are presented for the thermodynamics of fundamental model systems, an empirical water model containing 256 water molecules within periodic boundary conditions, and ab initio simulations of nitrogen and benzene molecules. For all of these examples, PPI simulations with 4 to 8 classical beads recover the nuclear quantum contribution to the total energy and heat capacity at room temperature within a 3% accuracy, paving the way toward seamless modeling of nuclear quantum effects in realistic molecules and materials.
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Affiliation(s)
- Igor Poltavsky
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , 14195 Berlin , Germany .
| | - Alexandre Tkatchenko
- Fritz-Haber-Institut der Max-Planck-Gesellschaft , Faradayweg 4-6 , 14195 Berlin , Germany .
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25
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Engel H, Eitan R, Azuri A, Major DT. Nuclear quantum effects in chemical reactions via higher-order path-integral calculations. Chem Phys 2015. [DOI: 10.1016/j.chemphys.2015.01.001] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/25/2022]
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26
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Mielke SL, Truhlar DG. Improved methods for Feynman path integral calculations and their application to calculate converged vibrational–rotational partition functions, free energies, enthalpies, entropies, and heat capacities for methane. J Chem Phys 2015; 142:044105. [PMID: 25637967 DOI: 10.1063/1.4905526] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Steven L. Mielke
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431, USA
| | - Donald G. Truhlar
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant St. S.E., Minneapolis, Minnesota 55455-0431, USA
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27
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Cheng B, Ceriotti M. Direct path integral estimators for isotope fractionation ratios. J Chem Phys 2014; 141:244112. [DOI: 10.1063/1.4904293] [Citation(s) in RCA: 25] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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28
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Nagashima H, Tsuda S, Tsuboi N, Koshi M, Hayashi KA, Tokumasu T. An analysis of quantum effects on the thermodynamic properties of cryogenic hydrogen using the path integral method. J Chem Phys 2014; 140:134506. [DOI: 10.1063/1.4870036] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
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29
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Marsalek O, Chen PY, Dupuis R, Benoit M, Méheut M, Bačić Z, Tuckerman ME. Efficient Calculation of Free Energy Differences Associated with Isotopic Substitution Using Path-Integral Molecular Dynamics. J Chem Theory Comput 2014; 10:1440-53. [DOI: 10.1021/ct400911m] [Citation(s) in RCA: 31] [Impact Index Per Article: 3.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Ondrej Marsalek
- Department
of Chemistry, New York University, New York, New York 10003, United States
| | - Pei-Yang Chen
- Department
of Chemistry, New York University, New York, New York 10003, United States
| | - Romain Dupuis
- Géosciences
Environnement Toulouse, OMP−Université Paul Sabatier, 14 avenue
Edouard Belin, 31400 Toulouse, France
| | - Magali Benoit
- CEMES−CNRS−UPR
8011, 29 rue Jeanne Marvig, 31055 Toulouse, France
| | - Merlin Méheut
- Géosciences
Environnement Toulouse, OMP−Université Paul Sabatier, 14 avenue
Edouard Belin, 31400 Toulouse, France
| | - Zlatko Bačić
- Department
of Chemistry, New York University, New York, New York 10003, United States
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
| | - Mark E. Tuckerman
- Department
of Chemistry and Courant Institute of Mathematical Sciences, New York University, New York, New York 10003, United States
- Institute for Pure and Applied Mathematics, 460 Portola Plaza, Los Angeles, California 90095, United States
- NYU-ECNU Center for Computational Chemistry at NYU Shanghai, Shanghai 200062, China
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30
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Buchowiecki M, Vaníček J. Monte Carlo evaluation of the equilibrium isotope effects using the Takahashi–Imada factorization of the Feynman path integral. Chem Phys Lett 2013. [DOI: 10.1016/j.cplett.2013.09.070] [Citation(s) in RCA: 17] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
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31
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BANDRAUK ANDRÉD, LU HUIZHONG. EXPONENTIAL PROPAGATORS (INTEGRATORS) FOR THE TIME-DEPENDENT SCHRÖDINGER EQUATION. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2013. [DOI: 10.1142/s0219633613400014] [Citation(s) in RCA: 56] [Impact Index Per Article: 5.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
The time-dependent Schrödinger Equation (TDSE) is a parabolic partial differential equation (PDE) comparable to a diffusion equation but with imaginary time. Due to its first order time derivative, exponential integrators or propagators are natural methods to describe evolution in time of the TDSE, both for time-independent and time-dependent potentials. Two splitting methods based on Fer and/or Magnus expansions allow for developing unitary factorizations of exponentials with different accuracies in the time step △t. The unitary factorization of exponentials to high order accuracy depends on commutators of kinetic energy operators with potentials. Fourth-order accuracy propagators can involve negative or complex time steps, or real time steps only but with gradients of potentials, i.e. forces. Extending the propagators of TDSE's to imaginary time allows to also apply these methods to classical many-body dynamics, and quantum statistical mechanics of molecular systems.
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Affiliation(s)
- ANDRÉ D. BANDRAUK
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, QC, Canada, J1K 2R1, Canada
| | - HUIZHONG LU
- Laboratoire de Chimie Théorique, Faculté des Sciences, Université de Sherbrooke, QC, Canada, J1K 2R1, Canada
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32
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Ceriotti M, Markland TE. Efficient methods and practical guidelines for simulating isotope effects. J Chem Phys 2013; 138:014112. [DOI: 10.1063/1.4772676] [Citation(s) in RCA: 67] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023] Open
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33
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Mielke SL, Dinpajooh M, Siepmann JI, Truhlar DG. Efficient methods for including quantum effects in Monte Carlo calculations of large systems: Extension of the displaced points path integral method and other effective potential methods to calculate properties and distributions. J Chem Phys 2013; 138:014110. [PMID: 23298031 DOI: 10.1063/1.4772667] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Steven L Mielke
- Department of Chemistry, Chemical Theory Center, and Supercomputing Institute, University of Minnesota, 207 Pleasant Street SE, Minneapolis, Minnesota 55455-0431, USA.
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34
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Shiga M, Fujisaki H. A quantum generalization of intrinsic reaction coordinate using path integral centroid coordinates. J Chem Phys 2012; 136:184103. [DOI: 10.1063/1.4709723] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/29/2022] Open
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35
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PREDESCU CRISTIAN. SPATIALLY-DISCRETIZED HIGH-TEMPERATURE APPROXIMATIONS AND THEIR O(N) IMPLEMENTATION ON A GRID. JOURNAL OF THEORETICAL & COMPUTATIONAL CHEMISTRY 2011. [DOI: 10.1142/s0219633606002246] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/18/2022]
Abstract
We consider the problem of performing imaginary-time propagation of wavefunctions on a grid. We demonstrate that spatially-continuous high-temperature approximations can be discretized in such a way that their convergence order is preserved. Requirements of minimal computational work and reutilization of data then uniquely determine the optimal grid, quadrature technique, and propagation method. It is shown that the optimal propagation technique is O(N), with respect to the grid size. The grid technique is utilized to compare the Monte Carlo efficiency of the Trotter–Suzuki approximation against a recently introduced fourth-order high-temperature approximation, while circumventing the issue of statistical noise, which usually prevents such comparisons from being carried out. We document the appearance of a systematic bias in the Monte Carlo estimators that involve temperature differentiation of the density matrix, bias that is due to the dependence of the eigenvalues on the inverse temperature. This bias is negotiated more successfully by the short-time approximations having higher convergence order, which leads to non-trivial computational savings.
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Affiliation(s)
- CRISTIAN PREDESCU
- Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720, USA
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36
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Ceriotti M, Brain GAR, Riordan O, Manolopoulos DE. The inefficiency of re-weighted sampling and the curse of system size in high-order path integration. Proc Math Phys Eng Sci 2011. [DOI: 10.1098/rspa.2011.0413] [Citation(s) in RCA: 33] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Computing averages over a target probability density by statistical re-weighting of a set of samples with a different distribution is a strategy which is commonly adopted in fields as diverse as atomistic simulation and finance. Here we present a very general analysis of the accuracy and efficiency of this approach, highlighting some of its weaknesses. We then give an example of how our results can be used, specifically to assess the feasibility of high-order path integral methods. We demonstrate that the most promising of these techniques—which is based on re-weighted sampling—is bound to fail as the size of the system is increased, because of the exponential growth of the statistical uncertainty in the re-weighted average.
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Affiliation(s)
- Michele Ceriotti
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK
| | - Guy A. R. Brain
- Physical and Theoretical Chemistry Laboratory, South Parks Road, Oxford OX1 3QZ, UK
| | - Oliver Riordan
- Mathematical Institute, 24-29 Saint Giles', Oxford OX1 3LB, UK
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37
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Pérez A, Tuckerman ME. Improving the convergence of closed and open path integral molecular dynamics via higher order Trotter factorization schemes. J Chem Phys 2011; 135:064104. [PMID: 21842923 DOI: 10.1063/1.3609120] [Citation(s) in RCA: 51] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Alejandro Pérez
- Department of Chemistry, New York University, New York, New York 10003, USA.
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38
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Azuri A, Engel H, Doron D, Major DT. Path-Integral Calculations of Nuclear Quantum Effects in Model Systems, Small Molecules, and Enzymes via Gradient-Based Forward Corrector Algorithms. J Chem Theory Comput 2011; 7:1273-86. [DOI: 10.1021/ct100716c] [Citation(s) in RCA: 29] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Affiliation(s)
- Asaf Azuri
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Hamutal Engel
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Dvir Doron
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
| | - Dan Thomas Major
- Department of Chemistry and the Lise Meitner-Minerva Center of Computational Quantum Chemistry, Bar-Ilan University, Ramat-Gan 52900, Israel
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39
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Ceriotti M, Manolopoulos DE, Parrinello M. Accelerating the convergence of path integral dynamics with a generalized Langevin equation. J Chem Phys 2011; 134:084104. [PMID: 21361524 DOI: 10.1063/1.3556661] [Citation(s) in RCA: 126] [Impact Index Per Article: 9.7] [Reference Citation Analysis] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Michele Ceriotti
- Computational Science, Department of Chemistry and Applied Biosciences, ETH Zürich, Lugano, Switzerland.
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40
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Sakkos K, Casulleras J, Boronat J. High order Chin actions in path integral Monte Carlo. J Chem Phys 2009; 130:204109. [DOI: 10.1063/1.3143522] [Citation(s) in RCA: 60] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
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41
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Anderson KE, Mielke SL, Siepmann JI, Truhlar DG. Bond Angle Distributions of Carbon Dioxide in the Gas, Supercritical, and Solid Phases. J Phys Chem A 2009; 113:2053-9. [DOI: 10.1021/jp808711y] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/30/2022]
Affiliation(s)
- Kelly E. Anderson
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455-0431
| | - Steven L. Mielke
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455-0431
| | - J. Ilja Siepmann
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455-0431
| | - Donald G. Truhlar
- Department of Chemistry and Minnesota Supercomputing Institute, University of Minnesota, 207 Pleasant St. SE, Minneapolis, Minnesota 55455-0431
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42
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Paesani F, Zhang W, Case DA, Cheatham TE, Voth GA. An accurate and simple quantum model for liquid water. J Chem Phys 2007; 125:184507. [PMID: 17115765 DOI: 10.1063/1.2386157] [Citation(s) in RCA: 167] [Impact Index Per Article: 9.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/26/2022] Open
Abstract
The path-integral molecular dynamics and centroid molecular dynamics methods have been applied to investigate the behavior of liquid water at ambient conditions starting from a recently developed simple point charge/flexible (SPC/Fw) model. Several quantum structural, thermodynamic, and dynamical properties have been computed and compared to the corresponding classical values, as well as to the available experimental data. The path-integral molecular dynamics simulations show that the inclusion of quantum effects results in a less structured liquid with a reduced amount of hydrogen bonding in comparison to its classical analog. The nuclear quantization also leads to a smaller dielectric constant and a larger diffusion coefficient relative to the corresponding classical values. Collective and single molecule time correlation functions show a faster decay than their classical counterparts. Good agreement with the experimental measurements in the low-frequency region is obtained for the quantum infrared spectrum, which also shows a higher intensity and a redshift relative to its classical analog. A modification of the original parametrization of the SPC/Fw model is suggested and tested in order to construct an accurate quantum model, called q-SPC/Fw, for liquid water. The quantum results for several thermodynamic and dynamical properties computed with the new model are shown to be in a significantly better agreement with the experimental data. Finally, a force-matching approach was applied to the q-SPC/Fw model to derive an effective quantum force field for liquid water in which the effects due to the nuclear quantization are explicitly distinguished from those due to the underlying molecular interactions. Thermodynamic and dynamical properties computed using standard classical simulations with this effective quantum potential are found in excellent agreement with those obtained from significantly more computationally demanding full centroid molecular dynamics simulations. The present results suggest that the inclusion of nuclear quantum effects into an empirical model for water enhances the ability of such model to faithfully represent experimental data, presumably through an increased ability of the model itself to capture realistic physical effects.
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Affiliation(s)
- Francesco Paesani
- Center for Biophysical Modeling and Simulation, University of Utah, Salt Lake City, Utah 84112, USA
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43
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Yang S, Yamamoto T, Miller WH. Path-integral virial estimator for reaction-rate calculation based on the quantum instanton approximation. J Chem Phys 2006; 124:084102. [PMID: 16512703 DOI: 10.1063/1.2171693] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/18/2023] Open
Abstract
The quantum instanton approximation is a type of quantum transition-state theory that calculates the chemical reaction rate using the reactive flux correlation function and its low-order derivatives at time zero. Here we present several path-integral estimators for the latter quantities, which characterize the initial decay profile of the flux correlation function. As with the internal energy or heat-capacity calculation, different estimators yield different variances (and therefore different convergence properties) in a Monte Carlo calculation. Here we obtain a virial (-type) estimator by using a coordinate scaling procedure rather than integration by parts, which allows more computational benefits. We also consider two different methods for treating the flux operator, i.e., local-path and global-path approaches, in which the latter achieves a smaller variance at the cost of using second-order potential derivatives. Numerical tests are performed for a one-dimensional Eckart barrier and a model proton transfer reaction in a polar solvent, which illustrates the reduced variance of the virial estimator over the corresponding thermodynamic estimator.
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Affiliation(s)
- Sandy Yang
- Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, University of California, Berkeley, California 94720-1460, USA
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44
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Predescu C. Comment on “Path-integral virial estimator based on the scaling of fluctuation coordinates: Application to quantum clusters with fourth-order propagators” [J. Chem. Phys. 123, 104101 (2005)]. J Chem Phys 2005; 123:217102. [PMID: 16356074 DOI: 10.1063/1.2132281] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Cristian Predescu
- Department of Chemistry, University of California, Berkeley, California 94720, USA.
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