1
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Lambros E, Fetherolf JH, Hammes-Schiffer S, Li X. A Many-Body Perspective of Nuclear Quantum Effects in Aqueous Clusters. J Phys Chem Lett 2024; 15:4070-4075. [PMID: 38587257 DOI: 10.1021/acs.jpclett.4c00439] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/09/2024]
Abstract
Nuclear quantum effects play an important role in the structure and thermodynamics of aqueous systems. By performing a many-body expansion with nuclear-electronic orbital (NEO) theory, we show that proton quantization can give rise to significant energetic contributions for many-body interactions spanning several molecules in single-point energy calculations of water clusters. Although zero-point motion produces a large increase in energy at the one-body level, nuclear quantum effects serve to stabilize higher-order molecular interactions. These results are significant because they demonstrate that nuclear quantum effects play a nontrivial role in many-body interactions of aqueous systems. Our approach also provides a pathway for incorporating nuclear quantum effects into water potential energy surfaces. The NEO approach is advantageous for many-body expansion analyses because it includes nuclear quantum effects directly in the energies.
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Affiliation(s)
- Eleftherios Lambros
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
| | - Jonathan H Fetherolf
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Sharon Hammes-Schiffer
- Department of Chemistry, Princeton University, Princeton, New Jersey 08544, United States
| | - Xiaosong Li
- Department of Chemistry, University of Washington, Seattle, Washington 98195, United States
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2
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Zhai Y, Rashmi R, Palos E, Paesani F. Many-body interactions and deep neural network potentials for water. J Chem Phys 2024; 160:144501. [PMID: 38587225 DOI: 10.1063/5.0203682] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/15/2024] [Accepted: 03/23/2024] [Indexed: 04/09/2024] Open
Abstract
We present a detailed assessment of deep neural network potentials developed within the Deep Potential Molecular Dynamics (DeePMD) framework and trained on the MB-pol data-driven many-body potential energy function. Specific focus is directed at the ability of DeePMD-based potentials to correctly reproduce the accuracy of MB-pol across various water systems. Analyses of bulk and interfacial properties as well as many-body interactions characteristic of water elucidate inherent limitations in the transferability and predictive accuracy of DeePMD-based potentials. These limitations can be traced back to an incomplete implementation of the "nearsightedness of electronic matter" principle, which may be common throughout machine learning potentials that do not include a proper representation of self-consistently determined long-range electric fields. These findings provide further support for the "short-blanket dilemma" faced by DeePMD-based potentials, highlighting the challenges in achieving a balance between computational efficiency and a rigorous, physics-based representation of the properties of water. Finally, we believe that our study contributes to the ongoing discourse on the development and application of machine learning models in simulating water systems, offering insights that could guide future improvements in the field.
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Affiliation(s)
- Yaoguang Zhai
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
- Department of Computer Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
| | - Richa Rashmi
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Etienne Palos
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
- Halicioğlu Data Science Institute, University of California San Diego, La Jolla, California 92093, USA
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, USA
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3
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Savoj R, Agnew H, Zhou R, Paesani F. Molecular Insights into the Influence of Ions on the Water Structure. I. Alkali Metal Ions in Solution. J Phys Chem B 2024; 128:1953-1962. [PMID: 38373140 DOI: 10.1021/acs.jpcb.3c08150] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/21/2024]
Abstract
In this study, we explore the impact of alkali metal ions (Li+, Na+, K+, Rb+, and Cs+) on the hydration structure of water using molecular dynamics simulations carried out with MB-nrg potential energy functions (PEFs). Our analyses include radial distribution functions, coordination numbers, dipole moments, and infrared spectra of water molecules, calculated as a function of solvation shells. The results collectively indicate a highly local influence of all of the alkali metal ions on the hydrogen-bond network established by the surrounding water molecules, with the smallest and most densely charged Li+ ion exerting the most pronounced effect. Remarkably, the MB-nrg PEFs demonstrate excellent agreement with available experimental data for the position and size of the first solvation shells, underscoring their potential as predictive models for realistic simulations of ionic aqueous solutions across various thermodynamic conditions and environments.
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Affiliation(s)
- Roya Savoj
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Henry Agnew
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Ruihan Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- Halicioğlu Data Science Institute, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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4
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Riera M, Knight C, Bull-Vulpe EF, Zhu X, Agnew H, Smith DGA, Simmonett AC, Paesani F. MBX: A many-body energy and force calculator for data-driven many-body simulations. J Chem Phys 2023; 159:054802. [PMID: 37526156 PMCID: PMC10550339 DOI: 10.1063/5.0156036] [Citation(s) in RCA: 4] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/25/2023] [Accepted: 07/11/2023] [Indexed: 08/02/2023] Open
Abstract
Many-Body eXpansion (MBX) is a C++ library that implements many-body potential energy functions (PEFs) within the "many-body energy" (MB-nrg) formalism. MB-nrg PEFs integrate an underlying polarizable model with explicit machine-learned representations of many-body interactions to achieve chemical accuracy from the gas to the condensed phases. MBX can be employed either as a stand-alone package or as an energy/force engine that can be integrated with generic software for molecular dynamics and Monte Carlo simulations. MBX is parallelized internally using Open Multi-Processing and can utilize Message Passing Interface when available in interfaced molecular simulation software. MBX enables classical and quantum molecular simulations with MB-nrg PEFs, as well as hybrid simulations that combine conventional force fields and MB-nrg PEFs, for diverse systems ranging from small gas-phase clusters to aqueous solutions and molecular fluids to biomolecular systems and metal-organic frameworks.
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Affiliation(s)
- Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Christopher Knight
- Argonne National Laboratory, Computational Science Division, Lemont, Illinois 60439, USA
| | - Ethan F. Bull-Vulpe
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Xuanyu Zhu
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Henry Agnew
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | | | - Andrew C. Simmonett
- Laboratory of Computational Biology, National Heart, Lung and Blood Institute, National Institutes of Health, Bethesda, Maryland 20892, USA
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5
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Heindel JP, Herman KM, Xantheas SS. Many-Body Effects in Aqueous Systems: Synergies Between Interaction Analysis Techniques and Force Field Development. Annu Rev Phys Chem 2023; 74:337-360. [PMID: 37093659 DOI: 10.1146/annurev-physchem-062422-023532] [Citation(s) in RCA: 3] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 04/25/2023]
Abstract
Interaction analysis techniques, including the many-body expansion (MBE), symmetry-adapted perturbation theory, and energy decomposition analysis, allow for an intuitive understanding of complex molecular interactions. We review these methods by first providing a historical context for the study of many-body interactions and discussing how nonadditivities emerge from Hamiltonians containing strictly pairwise-additive interactions. We then elaborate on the synergy between these interaction analysis techniques and the development of advanced force fields aimed at accurately reproducing the Born-Oppenheimer potential energy surface. In particular, we focus on ab initio-based force fields that aim to explicitly reproduce many-body terms and are fitted to high-level electronic structure results. These force fields generally incorporate many-body effects through (a) parameterization of distributed multipoles, (b) explicit fitting of the MBE, (c) inclusion of many-atom features in a neural network, and (d) coarse-graining of many-body terms into an effective two-body term. We also discuss the emerging use of the MBE to improve the accuracy and speed of ab initio molecular dynamics.
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Affiliation(s)
- Joseph P Heindel
- Department of Chemistry, University of Washington, Seattle, Washington, USA
| | - Kristina M Herman
- Department of Chemistry, University of Washington, Seattle, Washington, USA
| | - Sotiris S Xantheas
- Department of Chemistry, University of Washington, Seattle, Washington, USA
- Advanced Computing, Mathematics and Data Division, Pacific Northwest National Laboratory, Richland, Washington, USA; ,
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6
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Zhai Y, Caruso A, Bore SL, Luo Z, Paesani F. A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions? J Chem Phys 2023; 158:084111. [PMID: 36859071 DOI: 10.1063/5.0142843] [Citation(s) in RCA: 18] [Impact Index Per Article: 18.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/05/2023] Open
Abstract
Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.
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Affiliation(s)
- Yaoguang Zhai
- Department of Computer Science and Engineering, University of California San Diego, La Jolla, California 92093, USA
| | - Alessandro Caruso
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Sigbjørn Løland Bore
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Zhishang Luo
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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7
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Li XL, Li CM, Zhu JY, Zhou Z, Hao Q, Wang CS. A scheme for rapid evaluation of the intermolecular three-body polarization effect in water clusters. J Comput Chem 2023; 44:677-686. [PMID: 36408852 DOI: 10.1002/jcc.27032] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/06/2022] [Revised: 09/22/2022] [Accepted: 10/24/2022] [Indexed: 11/22/2022]
Abstract
The ability to accurately and rapidly evaluate the intermolecular many-body polarization effect of the water system is very important for computer simulations of biomolecule in aqueous. In this paper, a scheme is proposed based on the polarizable dipole-dipole interaction model and used to rapidly estimate the intermolecular many-body polarization effect in water clusters. We use a bond-dipole-based polarization function to evaluate the polarization energy. We regard two OH bonds of a water molecule as two bond-dipoles and set the permanent OH bond-dipole moment of a water molecule to be 1.51 Debye. We estimate the induced OH bond-dipole moment via a simple formula in which only one correction factor is needed. This scheme is then applied to tens of water clusters to calculate the three- and four-body interaction energies. The three-body interaction energies of 93 water clusters produced by our scheme are compared with those produced by the counterpoise-corrected CCSD(T)/aug-cc-pVDZ, MP2/aug-cc-pVDZ, M06-2X/jul-cc-pVTZ methods, by the AMOEBApro13, iAMOEBA, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The four-body interaction energies of 47 water clusters yielded by our scheme are compared with those yielded by the counterpoise-corrected MP2/aug-cc-pVDZ and M06-2X/ jul-cc-pVTZ methods, by the AMOEBApro13, AMOEBA+, AMOEBA+(CF) methods, and by the MB-pol method. The comparison results show that the scheme proposed in this paper can reproduce the counterpoise-corrected CCSD(T)/aug-cc-pVDZ three-body interaction energies and reproduce the counterpoise-corrected MP2/aug-cc-pVDZ four-body interaction energies both accurately and efficiently. We anticipate the scheme proposed here can be useful for computer simulations of liquid water and aqueous solutions.
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Affiliation(s)
- Xiao-Lei Li
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Chao-Ming Li
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Jia-Yi Zhu
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Zhan Zhou
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Qiang Hao
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
| | - Chang-Sheng Wang
- School of Chemistry and Chemical Engineering, Liaoning Normal University, Dalian, People's Republic of China
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8
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Maginn EJ. Virtual Issue on Carbon Dioxide: Physical Chemistry That Impacts Its Capture, Sequestration, and Conversion. J Phys Chem B 2022; 126:9927-9929. [PMID: 36475713 DOI: 10.1021/acs.jpcb.2c07562] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/13/2022]
Affiliation(s)
- Edward J Maginn
- Department of Chemical and Biomolecular Engineering, University of Notre Dame, Notre Dame, Indiana 46556 United States
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9
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Zhuang D, Riera M, Zhou R, Deary A, Paesani F. Hydration Structure of Na + and K + Ions in Solution Predicted by Data-Driven Many-Body Potentials. J Phys Chem B 2022; 126:9349-9360. [PMID: 36326071 DOI: 10.1021/acs.jpcb.2c05674] [Citation(s) in RCA: 4] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/05/2022]
Abstract
The hydration structure of Na+ and K+ ions in solution is systematically investigated using a hierarchy of molecular models that progressively include more accurate representations of many-body interactions. We found that a conventional empirical pairwise additive force field that is commonly used in biomolecular simulations is unable to reproduce the extended X-ray absorption fine structure (EXAFS) spectra for both ions. In contrast, progressive inclusion of many-body effects rigorously derived from the many-body expansion of the energy allows the MB-nrg potential energy functions (PEFs) to achieve nearly quantitative agreement with the experimental EXAFS spectra, thus enabling the development of a molecular-level picture of the hydration structure of both Na+ and K+ in solution. Since the MB-nrg PEFs have already been shown to accurately describe isomeric equilibria and vibrational spectra of small ion-water clusters in the gas phase, the present study demonstrates that the MB-nrg PEFs effectively represent the long-sought-after models able to correctly predict the properties of ionic aqueous systems from the gas to the liquid phase, which has so far remained elusive.
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Affiliation(s)
- Debbie Zhuang
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Ruihan Zhou
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Alexander Deary
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California92093, United States.,San Diego Supercomputer Center, University of California San Diego, La Jolla, California92093, United States
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10
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Caruso A, Zhu X, Fulton JL, Paesani F. Accurate Modeling of Bromide and Iodide Hydration with Data-Driven Many-Body Potentials. J Phys Chem B 2022; 126:8266-8278. [PMID: 36214512 DOI: 10.1021/acs.jpcb.2c04698] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/05/2023]
Abstract
Ion-water interactions play a central role in determining the properties of aqueous systems in a wide range of environments. However, a quantitative understanding of how the hydration properties of ions evolve from small aqueous clusters to bulk solutions and interfaces remains elusive. Here, we introduce the second generation of data-driven many-body energy (MB-nrg) potential energy functions (PEFs) representing bromide-water and iodide-water interactions. The MB-nrg PEFs use permutationally invariant polynomials to reproduce two-body and three-body energies calculated at the coupled cluster level of theory, and implicitly represent all higher-body energies using classical many-body polarization. A systematic analysis of the hydration structure of small Br-(H2O)n and I-(H2O)n clusters demonstrates that the MB-nrg PEFs predict interaction energies in quantitative agreement with "gold standard" coupled cluster reference values. Importantly, when used in molecular dynamics simulations carried out in the isothermal-isobaric ensemble for single bromide and iodide ions in liquid water, the MB-nrg PEFs predict extended X-ray absorption fine structure (EXAFS) spectra that accurately reproduce the experimental spectra, which thus allows for characterizing the hydration structure of the two ions with a high level of confidence.
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Affiliation(s)
- Alessandro Caruso
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - Xuanyu Zhu
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States
| | - John L Fulton
- Physical and Computational Sciences Directorate, Pacific Northwest National Laboratory, Richland, Washington99352, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California92093, United States.,San Diego Supercomputer Center, University of California San Diego, La Jolla, California92093, United States
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11
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Bull-Vulpe EF, Riera M, Bore SL, Paesani F. Data-Driven Many-Body Potential Energy Functions for Generic Molecules: Linear Alkanes as a Proof-of-Concept Application. J Chem Theory Comput 2022. [PMID: 36113028 DOI: 10.1021/acs.jctc.2c00645] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a generalization of the many-body energy (MB-nrg) theoretical/computational framework that enables the development of data-driven potential energy functions (PEFs) for generic covalently bonded molecules, with arbitrary quantum mechanical accuracy. The "nearsightedness of electronic matter" is exploited to define monomers as "natural building blocks" on the basis of their distinct chemical identity. The energy of generic molecules is then expressed as a sum of individual many-body energies of incrementally larger subsystems. The MB-nrg PEFs represent the low-order n-body energies, with n = 1-4, using permutationally invariant polynomials derived from electronic structure data carried out at an arbitrary quantum mechanical level of theory, while all higher-order n-body terms (n > 4) are represented by a classical many-body polarization term. As a proof-of-concept application of the general MB-nrg framework, we present MB-nrg PEFs for linear alkanes. The MB-nrg PEFs are shown to accurately reproduce reference energies, harmonic frequencies, and potential energy scans of alkanes, independently of their length. Since, by construction, the MB-nrg framework introduced here can be applied to generic covalently bonded molecules, we envision future computer simulations of complex molecular systems using data-driven MB-nrg PEFs, with arbitrary quantum mechanical accuracy.
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Affiliation(s)
- Ethan F. Bull-Vulpe
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Sigbjørn L. Bore
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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12
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Liu J, Lan J, He X. Toward High-level Machine Learning Potential for Water Based on Quantum Fragmentation and Neural Networks. J Phys Chem A 2022; 126:3926-3936. [PMID: 35679610 DOI: 10.1021/acs.jpca.2c00601] [Citation(s) in RCA: 8] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
Abstract
Accurate and efficient simulation of liquids, such as water and salt solutions, using high-level wave function theories is still a formidable task for computational chemists owing to the high computational costs. In this study, we develop a deep machine learning potential based on fragment-based second-order Møller-Plesset perturbation theory (DP-MP2) for water through neural networks. We show that the DP-MP2 potential predicts the structural, dynamical, and thermodynamic properties of liquid water in better agreement with the experimental data than previous studies based on density functional theory (DFT). The nuclear quantum effects (NQEs) on the properties of liquid water are also examined, which are noticeable in affecting the structural and dynamical properties of liquid water under ambient conditions. This work provides a general framework for quantitative predictions of the properties of condensed-phase systems with the accuracy of high-level wave function theory while achieving significant computational savings compared to ab initio simulations.
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Affiliation(s)
- Jinfeng Liu
- Department of Basic Medicine and Clinical Pharmacy, China Pharmaceutical University, Nanjing 210009, China.,Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China
| | - Jinggang Lan
- Chaire de Simulation à l'Echelle Atomique (CSEA), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland
| | - Xiao He
- Shanghai Engineering Research Center of Molecular Therapeutics and New Drug Development, Shanghai Frontiers Science Center of Molecule Intelligent Syntheses, School of Chemistry and Molecular Engineering, East China Normal University, Shanghai 200062, China.,New York University-East China Normal University Center for Computational Chemistry, NYU Shanghai, Shanghai 200062, China
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13
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Robinson VN, Ghosh R, Egan CK, Riera M, Knight C, Paesani F, Hassanali A. The behavior of methane-water mixtures under elevated pressures from simulations using many-body potentials. J Chem Phys 2022; 156:194504. [PMID: 35597630 DOI: 10.1063/5.0089773] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Abstract
Non-polarizable empirical potentials have been proven to be incapable of capturing the mixing of methane-water mixtures at elevated pressures. Although density functional theory-based ab initio simulations may circumvent this discrepancy, they are limited in terms of the relevant time and length scales associated with mixing phenomena. Here, we show that the many-body MB-nrg potential, designed to reproduce methane-water interactions with coupled cluster accuracy, successfully captures this phenomenon up to 3 GPa and 500 K with varying methane concentrations. Two-phase simulations and long time scales that are required to fully capture the mixing, affordable due to the speed and accuracy of the MBX software, are assessed. Constructing the methane-water equation of state across the phase diagram shows that the stable mixtures are denser than the sum of their parts at a given pressure and temperature. We find that many-body polarization plays a central role, enhancing the induced dipole moments of methane by 0.20 D during mixing under pressure. Overall, the mixed system adopts a denser state, which involves a significant enthalpic driving force as elucidated by a systematic many-body energy decomposition analysis.
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Affiliation(s)
- Victor Naden Robinson
- The 'Abdus Salam' International Centre for Theoretical Physics, I-34151 Trieste, Italy
| | - Raja Ghosh
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA
| | - Colin K Egan
- The 'Abdus Salam' International Centre for Theoretical Physics, I-34151 Trieste, Italy
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA
| | - Christopher Knight
- Computational Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Lemont, Illinois 60439, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, California 92093, USA
| | - Ali Hassanali
- The 'Abdus Salam' International Centre for Theoretical Physics, I-34151 Trieste, Italy
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14
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Palos E, Lambros E, Swee S, Hu J, Dasgupta S, Paesani F. Assessing the Interplay between Functional-Driven and Density-Driven Errors in DFT Models of Water. J Chem Theory Comput 2022; 18:3410-3426. [PMID: 35506889 DOI: 10.1021/acs.jctc.2c00050] [Citation(s) in RCA: 9] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We investigate the interplay between functional-driven and density-driven errors in different density functional approximations within density functional theory (DFT) and the implications of these errors for simulations of water with DFT-based data-driven potentials. Specifically, we quantify density-driven errors in two widely used dispersion-corrected functionals derived within the generalized gradient approximation (GGA), namely BLYP-D3 and revPBE-D3, and two modern meta-GGA functionals, namely strongly constrained and appropriately normed (SCAN) and B97M-rV. The effects of functional-driven and density-driven errors on the interaction energies are first assessed for the water clusters of the BEGDB dataset. Further insights into the nature of functional-driven errors are gained from applying the absolutely localized molecular orbital energy decomposition analysis (ALMO-EDA) to the interaction energies, which demonstrates that functional-driven errors are strongly correlated with the nature of the interactions. We discuss cases where density-corrected DFT (DC-DFT) models display higher accuracy than the original DFT models and cases where reducing the density-driven errors leads to larger deviations from the reference energies due to the presence of large functional-driven errors. Finally, molecular dynamics simulations are performed with data-driven many-body potentials derived from DFT and DC-DFT data to determine the effect that minimizing density-driven errors has on the description of liquid water. Besides rationalizing the performance of widely used DFT models of water, we believe that our findings unveil fundamental relations between the shortcomings of some common DFT approximations and the requirements for accurate descriptions of molecular interactions, which will aid the development of a consistent, DFT-based framework for the development of data-driven and machine-learned potentials for simulations of condensed-phase systems.
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Affiliation(s)
- Etienne Palos
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Steven Swee
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Jie Hu
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Saswata Dasgupta
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States.,San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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15
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Uptake of N 2O 5 by aqueous aerosol unveiled using chemically accurate many-body potentials. Nat Commun 2022; 13:1266. [PMID: 35273144 PMCID: PMC8913772 DOI: 10.1038/s41467-022-28697-8] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/20/2021] [Accepted: 01/28/2022] [Indexed: 11/24/2022] Open
Abstract
The reactive uptake of N2O5 to aqueous aerosol is a major loss channel for nitrogen oxides in the troposphere. Despite its importance, a quantitative picture of the uptake mechanism is missing. Here we use molecular dynamics simulations with a data-driven many-body model of coupled-cluster accuracy to quantify thermodynamics and kinetics of solvation and adsorption of N2O5 in water. The free energy profile highlights that N2O5 is selectively adsorbed to the liquid–vapor interface and weakly solvated. Accommodation into bulk water occurs slowly, competing with evaporation upon adsorption from gas phase. Leveraging the quantitative accuracy of the model, we parameterize and solve a reaction–diffusion equation to determine hydrolysis rates consistent with experimental observations. We find a short reaction–diffusion length, indicating that the uptake is dominated by interfacial features. The parameters deduced here, including solubility, accommodation coefficient, and hydrolysis rate, afford a foundation for which to consider the reactive loss of N2O5 in more complex solutions. The reactive uptake of N2O5 to aqueous aerosol is a major loss channel for nitrogen oxides in the troposphere. Here authors report a theoretical investigation on the N2O5 uptake into aqueous aerosol and determine the hydrolysis rates by numerically solving a molecularly detailed reaction–diffusion equation.
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16
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Yue S, Riera M, Ghosh R, Panagiotopoulos AZ, Paesani F. Transferability of data-driven, many-body models for CO2 simulations in the vapor and liquid phases. J Chem Phys 2022; 156:104503. [DOI: 10.1063/5.0080061] [Citation(s) in RCA: 3] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Shuwen Yue
- Princeton University, United States of America
| | - Marc Riera
- Chemistry and Biochemistry, University of California San Diego Department of Chemistry and Biochemistry, United States of America
| | - Raja Ghosh
- University of California San Diego, United States of America
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17
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He X, Walker B, Man VH, Ren P, Wang J. Recent progress in general force fields of small molecules. Curr Opin Struct Biol 2022; 72:187-193. [PMID: 34942567 PMCID: PMC8860847 DOI: 10.1016/j.sbi.2021.11.011] [Citation(s) in RCA: 7] [Impact Index Per Article: 3.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/12/2021] [Revised: 09/10/2021] [Accepted: 11/16/2021] [Indexed: 02/03/2023]
Abstract
Recent advances in computational hardware and free energy algorithms enable a broader application of molecular simulation of binding interactions between receptors and small-molecule ligands. The underlying molecular mechanics force fields (FFs) for small molecules have also achieved advancements in accuracy, user-friendliness, and speed during the past several years (2018-2020). Besides the expansion of chemical space coverage of ligand-like molecules among major popular classical additive FFs and polarizable FFs, new charge models have been proposed for better accuracy and transferability, new chemical perception of avoiding predefined atom types have been applied, and new automated parameterization toolkits, including machine learning approaches, have been developed for users' convenience.
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Affiliation(s)
- Xibing He
- Department of Pharmaceutical Sciences and Computational Chemical Genomics Screening Center, School of Pharmacy, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Brandon Walker
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA
| | - Viet H. Man
- Department of Pharmaceutical Sciences and Computational Chemical Genomics Screening Center, School of Pharmacy, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA
| | - Pengyu Ren
- Department of Biomedical Engineering, The University of Texas at Austin, Austin, Texas 78712, USA,Corresponding authors: Pengyu Ren (), Junmei Wang ()
| | - Junmei Wang
- Department of Pharmaceutical Sciences and Computational Chemical Genomics Screening Center, School of Pharmacy, University of Pittsburgh, Pittsburgh, Pennsylvania 15261, USA,Corresponding authors: Pengyu Ren (), Junmei Wang ()
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18
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Pruteanu CG, Robinson VN, Hassanali AA, Scandolo S, Loveday J, Ackland G. How to determine solubility in binary mixtures from Neutron Scattering data: the case of methane and water. J Chem Phys 2022; 156:054502. [DOI: 10.1063/5.0077912] [Citation(s) in RCA: 2] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ciprian Gabriel Pruteanu
- Physics and Astronomy, The University of Edinburgh School of Physics and Astronomy, United Kingdom
| | - Victor Naden Robinson
- Abdus Salam International Centre for Theoretical Physics Condensed Matter and Statistical Physics Section, Italy
| | | | | | - John Loveday
- School of Physics and Astronomy, University of Edinburgh, United Kingdom
| | - Graeme Ackland
- Department of Physics and Astronomy, The University of Edinburgh, United Kingdom
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19
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Theoretical Description of Water from Single-Molecule to Condensed Phase: a Review of Recent Progress on Potential Energy Surfaces and Molecular Dynamics. CHINESE J CHEM PHYS 2022. [DOI: 10.1063/1674-0068/cjcp2201005] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022]
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20
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Dasgupta S, Lambros E, Perdew JP, Paesani F. Elevating density functional theory to chemical accuracy for water simulations through a density-corrected many-body formalism. Nat Commun 2021; 12:6359. [PMID: 34737311 PMCID: PMC8569147 DOI: 10.1038/s41467-021-26618-9] [Citation(s) in RCA: 34] [Impact Index Per Article: 11.3] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2021] [Accepted: 10/08/2021] [Indexed: 11/09/2022] Open
Abstract
Density functional theory (DFT) has been extensively used to model the properties of water. Albeit maintaining a good balance between accuracy and efficiency, no density functional has so far achieved the degree of accuracy necessary to correctly predict the properties of water across the entire phase diagram. Here, we present density-corrected SCAN (DC-SCAN) calculations for water which, minimizing density-driven errors, elevate the accuracy of the SCAN functional to that of "gold standard" coupled-cluster theory. Building upon the accuracy of DC-SCAN within a many-body formalism, we introduce a data-driven many-body potential energy function, MB-SCAN(DC), that quantitatively reproduces coupled cluster reference values for interaction, binding, and individual many-body energies of water clusters. Importantly, molecular dynamics simulations carried out with MB-SCAN(DC) also reproduce the properties of liquid water, which thus demonstrates that MB-SCAN(DC) is effectively the first DFT-based model that correctly describes water from the gas to the liquid phase.
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Affiliation(s)
- Saswata Dasgupta
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, 92093, USA
| | - Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, 92093, USA
| | - John P Perdew
- Department of Physics, Temple University, Philadelphia, PA, 19122, USA
- Department of Chemistry, Temple University, Philadelphia, PA, 19122, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California, San Diego, La Jolla, CA, 92093, USA.
- Materials Science and Engineering, University of California, San Diego, La Jolla, CA, 92093, USA.
- San Diego Supercomputer Center, University of California, San Diego, La Jolla, CA, 92093, USA.
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21
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Bull-Vulpe EF, Riera M, Götz AW, Paesani F. MB-Fit: Software infrastructure for data-driven many-body potential energy functions. J Chem Phys 2021; 155:124801. [PMID: 34598567 DOI: 10.1063/5.0063198] [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
Many-body potential energy functions (MB-PEFs), which integrate data-driven representations of many-body short-range quantum mechanical interactions with physics-based representations of many-body polarization and long-range interactions, have recently been shown to provide high accuracy in the description of molecular interactions from the gas to the condensed phase. Here, we present MB-Fit, a software infrastructure for the automated development of MB-PEFs for generic molecules within the TTM-nrg (Thole-type model energy) and MB-nrg (many-body energy) theoretical frameworks. Besides providing all the necessary computational tools for generating TTM-nrg and MB-nrg PEFs, MB-Fit provides a seamless interface with the MBX software, a many-body energy and force calculator for computer simulations. Given the demonstrated accuracy of the MB-PEFs, particularly within the MB-nrg framework, we believe that MB-Fit will enable routine predictive computer simulations of generic (small) molecules in the gas, liquid, and solid phases, including, but not limited to, the modeling of quantum isomeric equilibria in molecular clusters, solvation processes, molecular crystals, and phase diagrams.
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Affiliation(s)
- Ethan F Bull-Vulpe
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Andreas W Götz
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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22
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Lambros E, Dasgupta S, Palos E, Swee S, Hu J, Paesani F. General Many-Body Framework for Data-Driven Potentials with Arbitrary Quantum Mechanical Accuracy: Water as a Case Study. J Chem Theory Comput 2021; 17:5635-5650. [PMID: 34370954 DOI: 10.1021/acs.jctc.1c00541] [Citation(s) in RCA: 22] [Impact Index Per Article: 7.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022]
Abstract
We present a general framework for the development of data-driven many-body (MB) potential energy functions (MB-QM PEFs) that represent the interactions between small molecules at an arbitrary quantum-mechanical (QM) level of theory. As a demonstration, a family of MB-QM PEFs for water is rigorously derived from density functionals belonging to different rungs across Jacob's ladder of approximations within density functional theory (MB-DFT) and from Møller-Plesset perturbation theory (MB-MP2). Through a systematic analysis of individual MB contributions to the interaction energies of water clusters, we demonstrate that all MB-QM PEFs preserve the same accuracy as the corresponding ab initio calculations, with the exception of those derived from density functionals within the generalized gradient approximation (GGA). The differences between the DFT and MB-DFT results are traced back to density-driven errors that prevent GGA functionals from accurately representing the underlying molecular interactions for different cluster sizes and hydrogen-bonding arrangements. We show that this shortcoming may be overcome, within the MB formalism, by using density-corrected functionals (DC-DFT) that provide a more consistent representation of each individual MB contribution. This is demonstrated through the development of a MB-DFT PEF derived from DC-PBE-D3 data, which more accurately reproduce the corresponding ab initio results.
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Affiliation(s)
- Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Saswata Dasgupta
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Etienne Palos
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Steven Swee
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Jie Hu
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States.,San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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23
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Caruso A, Paesani F. Data-driven many-body models enable a quantitative description of chloride hydration from clusters to bulk. J Chem Phys 2021; 155:064502. [PMID: 34391363 DOI: 10.1063/5.0059445] [Citation(s) in RCA: 17] [Impact Index Per Article: 5.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/19/2022] Open
Abstract
We present a new data-driven potential energy function (PEF) describing chloride-water interactions, which is developed within the many-body-energy (MB-nrg) theoretical framework. Besides quantitatively reproducing low-order many-body energy contributions, the new MB-nrg PEF is able to correctly predict the interaction energies of small chloride-water clusters calculated at the coupled cluster level of theory. Importantly, classical and quantum molecular dynamics simulations of a single chloride ion in water demonstrate that the new MB-nrg PEF predicts x-ray spectra in close agreement with the experimental results. Comparisons with an popular empirical model and a polarizable PEF emphasize the importance of an accurate representation of short-range many-body effect while demonstrating that pairwise additive representations of chloride-water and water-water interactions are inadequate for correctly representing the hydration structure of chloride in both gas-phase clusters and solution. We believe that the analyses presented in this study provide additional evidence for the accuracy and predictive ability of the MB-nrg PEFs, which can then enable more realistic simulations of ionic aqueous systems in different environments.
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Affiliation(s)
- Alessandro Caruso
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, USA
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24
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Lambros E, Hu J, Paesani F. Assessing the Accuracy of the SCAN Functional for Water through a Many-Body Analysis of the Adiabatic Connection Formula. J Chem Theory Comput 2021; 17:3739-3749. [DOI: 10.1021/acs.jctc.1c00141] [Citation(s) in RCA: 7] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Affiliation(s)
- Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Jie Hu
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
- Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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25
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Cruzeiro VWD, Lambros E, Riera M, Roy R, Paesani F, Götz AW. Highly Accurate Many-Body Potentials for Simulations of N 2O 5 in Water: Benchmarks, Development, and Validation. J Chem Theory Comput 2021; 17:3931-3945. [PMID: 34029079 DOI: 10.1021/acs.jctc.1c00069] [Citation(s) in RCA: 9] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/14/2022]
Abstract
Dinitrogen pentoxide (N2O5) is an important intermediate in the atmospheric chemistry of nitrogen oxides. Although there has been much research, the processes that govern the physical interactions between N2O5 and water are still not fully understood at a molecular level. Gaining a quantitative insight from computer simulations requires going beyond the accuracy of classical force fields while accessing length scales and time scales that are out of reach for high-level quantum-chemical approaches. To this end, we present the development of MB-nrg many-body potential energy functions for nonreactive simulations of N2O5 in water. This MB-nrg model is based on electronic structure calculations at the coupled cluster level of theory and is compatible with the successful MB-pol model for water. It provides a physically correct description of long-range many-body interactions in combination with an explicit representation of up to three-body short-range interactions in terms of multidimensional permutationally invariant polynomials. In order to further investigate the importance of the underlying interactions in the model, a TTM-nrg model was also devised. TTM-nrg is a more simplistic representation that contains only two-body short-range interactions represented through Born-Mayer functions. In this work, an active learning approach was employed to efficiently build representative training sets of monomer, dimer, and trimer structures, and benchmarks are presented to determine the accuracy of our new models in comparison to a range of density functional theory methods. By assessing the binding curves, distortion energies of N2O5, and interaction energies in clusters of N2O5 and water, we evaluate the importance of two-body and three-body short-range potentials. The results demonstrate that our MB-nrg model has high accuracy with respect to the coupled cluster reference, outperforms current density functional theory models, and thus enables highly accurate simulations of N2O5 in aqueous environments.
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Affiliation(s)
- Vinícius Wilian D Cruzeiro
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States.,Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Eleftherios Lambros
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Marc Riera
- Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States
| | - Ronak Roy
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
| | - Francesco Paesani
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States.,Department of Chemistry and Biochemistry, University of California San Diego, La Jolla, California 92093, United States.,Materials Science and Engineering, University of California San Diego, La Jolla, California 92093, United States
| | - Andreas W Götz
- San Diego Supercomputer Center, University of California San Diego, La Jolla, California 92093, United States
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