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Rashid MAM, Rahman M, Acter T, Uddin N. Identifying the acidic or basic behavior of surface water: a QM/MM-MD study. Phys Chem Chem Phys 2023; 25:31194-31205. [PMID: 37955174 DOI: 10.1039/d3cp02080k] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2023]
Abstract
Controversies on the water surface were theoretically addressed with the help of large scale quantum mechanical molecular dynamics (QMMD) simulations on water surface model systems with and without excess hydroniums and hydroxides. It was revealed that the thermodynamic surface structures of these ions strongly depend on their location and dipole orientation. Fast hydronium diffusion by proton transfer establishes a wider kinetic depth distribution (∼6 Å) than that predicted by its thermodynamic affinity for the water surface, while slow hydroxide is shallowly trapped below the outermost molecular layer (3-4 Å). In addition, the anisotropic orientation of surface water dipole can generate a substantial magnitude of surface potential, which extends to a depth of a few molecular layers. With these distinctively different surface properties of two ions and water molecules, the seemingly contradictory observations of acidic and negatively charged water surfaces may be successfully explained. That is, the negative surface charge of neutral water mostly stems from intrinsic water properties such as water dipole orientation and electron density spillage at the surface, rather than surface OH- ions. The enhanced acidity of the water surface can be attributed in large part to the kinetic depth profile of ion density in addition to static thermodynamic origin. Furthermore, the different depth profiles of the two ions may differently affect the surface-sensitive spectroscopic observations.
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Affiliation(s)
- Md Al Mamunur Rashid
- Clean Energy Research Center, Korea Institute of Science and Technology, Seoul, 02792, South Korea
| | - Mofizur Rahman
- Research and Development Center, Berger Paints Bangladesh Limited, Berger House, Dhaka-1230, Bangladesh
| | - Thamina Acter
- Department of Mathematical and Physical Sciences, East West University, Aftabnagar, Dhaka-1212, Bangladesh
| | - Nizam Uddin
- Department of Nutrition and Food Engineering, Daffodil International University, Birulia, Dhaka-1216, Bangladesh.
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2
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Mouhat F, Peria M, Morresi T, Vuilleumier R, Saitta AM, Casula M. Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer. Nat Commun 2023; 14:6930. [PMID: 37903819 PMCID: PMC10616126 DOI: 10.1038/s41467-023-42366-4] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/12/2022] [Accepted: 09/25/2023] [Indexed: 11/01/2023] Open
Abstract
Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.
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Affiliation(s)
- Félix Mouhat
- Saint Gobain Research Paris, 39, Quai Lucien Lefranc, 93300, Aubervilliers, France
| | - Matteo Peria
- IMPMC, Sorbonne Université, CNRS, MNHN, UMR 7590, 4 Place Jussieu, 75252, Paris, France
| | - Tommaso Morresi
- ECT*-Fondazione Bruno Kessler*, 286 Strada delle Tabarelle, 38123, Trento, Italy
| | - Rodolphe Vuilleumier
- PASTEUR, Département de Chimie, École normale supérieure, PSL Research University, Sorbonne Université, CNRS, 24 Rue Lhomond, 75005, Paris, France
| | - Antonino Marco Saitta
- IMPMC, Sorbonne Université, CNRS, MNHN, UMR 7590, 4 Place Jussieu, 75252, Paris, France
| | - Michele Casula
- IMPMC, Sorbonne Université, CNRS, MNHN, UMR 7590, 4 Place Jussieu, 75252, Paris, France.
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3
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Morresi T, Paulatto L, Vuilleumier R, Casula M. Probing anharmonic phonons by quantum correlators: A path integral approach. J Chem Phys 2021; 154:224108. [PMID: 34241203 DOI: 10.1063/5.0050450] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We devise an efficient scheme to determine vibrational properties from Path Integral Molecular Dynamics (PIMD) simulations. The method is based on zero-time Kubo-transformed correlation functions and captures the anharmonicity of the potential due to both temperature and quantum effects. Using analytical derivations and numerical calculations on toy-model potentials, we show that two different estimators built upon PIMD correlation functions fully characterize the phonon spectra and the anharmonicity strength. The first estimator is associated with the force-force quantum correlators and, in the weak anharmonic regime, yields reliable zero-point motion frequencies and thermodynamic properties of the quantum system. The second one is instead connected to displacement-displacement correlators and accurately probes the lowest-energy phonon excitations, regardless of the anharmonicity strength of the system. We also prove that the use of generalized eigenvalue equations, in place of the standard normal mode equations, leads to a significant speed-up in the PIMD phonon calculations, both in terms of faster convergence rate and smaller time step bias. Within this framework, using ab initio PIMD simulations, we compute phonon dispersions of diamond and of the high-pressure I41/amd phase of atomic hydrogen. We find that in the latter case, the anharmonicity is stronger than previously estimated and yields a sizeable red-shift in the vibrational spectrum of atomic hydrogen.
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Affiliation(s)
- T Morresi
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, MNHN, 4 Place Jussieu, 75252 Paris, France
| | - L Paulatto
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, MNHN, 4 Place Jussieu, 75252 Paris, France
| | - R Vuilleumier
- PASTEUR, Département de chimie, École normale supérieure, PSL University, Sorbonne Université, CNRS, 75005 Paris, France
| | - M Casula
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, MNHN, 4 Place Jussieu, 75252 Paris, France
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4
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Tiihonen J, Clay RC, Krogel JT. Toward quantum Monte Carlo forces on heavier ions: Scaling properties. J Chem Phys 2021; 154:204111. [PMID: 34241166 DOI: 10.1063/5.0052266] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
Quantum Monte Carlo (QMC) forces have been studied extensively in recent decades because of their importance with spectroscopic observables and geometry optimization. Here, we benchmark the accuracy and computational cost of QMC forces. The zero-variance zero-bias (ZVZB) force estimator is used in standard variational and diffusion Monte Carlo simulations with mean-field based trial wavefunctions and atomic pseudopotentials. Statistical force uncertainties are obtained with a recently developed regression technique for heavy tailed QMC data [P. Lopez Rios and G. J. Conduit, Phys. Rev. E 99, 063312 (2019)]. By considering selected atoms and dimers with elements ranging from H to Zn (1 ≤ Zeff ≤ 20), we assess the accuracy and the computational cost of ZVZB forces as the effective pseudopotential valence charge, Zeff, increases. We find that the costs of QMC energies and forces approximately follow simple power laws in Zeff. The force uncertainty grows more rapidly, leading to a best case cost scaling relationship of approximately Zeff 6.5(3) for diffusion Monte Carlo. We find that the accessible system size at fixed computational cost scales as Zeff -2, insensitive to model assumptions or the use of the "space warp" variance-reduction technique. Our results predict the practical cost of obtaining forces for a range of materials, such as transition metal oxides where QMC forces have yet to be applied, and underscore the importance of further developing force variance-reduction techniques, particularly for atoms with high Zeff.
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Affiliation(s)
- Juha Tiihonen
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Raymond C Clay
- Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
| | - Jaron T Krogel
- Materials Science and Technology Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
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5
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Kwan V, Consta S. Molecular Characterization of the Surface Excess Charge Layer in Droplets. JOURNAL OF THE AMERICAN SOCIETY FOR MASS SPECTROMETRY 2021; 32:33-45. [PMID: 32597645 DOI: 10.1021/jasms.0c00053] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
The surface excess charge layer (SECL) in droplets has often been associated with distinct chemistry. We examine the effect of the nature of ions in the composition and structure of SECL by using molecular dynamics. We find that in the presence of simple ions the thickness of SECL is invariant not only with respect to droplet size but also with respect to the nature of the ions. In the presence of simple ions, this layer has a thickness of ∼1.5-1.7 nm but in the presence of macroions it may extend to ∼2.0 nm. The proportion of ions contained in SECL depends on the nature of the ions and the droplet size. For the same droplet size, I- and model H3O+ ions show considerably higher concentration than Na+ and Cl- ions. We identify the maximum ion concentration region, which, in nanodrops, may partially overlap with SECL. As the relative shape fluctuations decrease when microdrop size is approached, the overlap between SECL and maximum ion concentration region increases. We suggest the extension of the bilayer droplet structure assumed in the equilibrium partitioning model of Enke to include the maximum ion concentration region that may not coincide with SECL in nanodrops. We compute the ion concentrations in SECL, which are those that should enter the kinetic equation in the ion-evaporation mechanism, instead of the overall drop ion concentration that has been used.
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Affiliation(s)
- Victor Kwan
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7
| | - Styliani Consta
- Department of Chemistry, The University of Western Ontario, London, Ontario, Canada N6A 5B7
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6
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Prebiotic chemistry and origins of life research with atomistic computer simulations. Phys Life Rev 2020; 34-35:105-135. [DOI: 10.1016/j.plrev.2018.09.004] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/30/2018] [Accepted: 09/10/2018] [Indexed: 02/02/2023]
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7
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Cassone G. Nuclear Quantum Effects Largely Influence Molecular Dissociation and Proton Transfer in Liquid Water under an Electric Field. J Phys Chem Lett 2020; 11:8983-8988. [PMID: 33035059 DOI: 10.1021/acs.jpclett.0c02581] [Citation(s) in RCA: 48] [Impact Index Per Article: 12.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Proton transfer in liquid water controls acid-base chemistry, crucial enzyme reactions, and the functioning of fuel cells. Externally applied static electric fields in water are capable of dissociating molecules and transferring protons across the H-bond network. However, the impact of nuclear quantum effects (NQEs) on these fundamental field-induced phenomena has not yet been reported. By comparing state-of-the-art ab initio molecular dynamics (AIMD) and path integral AIMD simulations of water under electric fields, I show that quantum delocalization of the proton lowers the molecular ionization threshold to approximately one-third. Moreover, also the water behavior as a protonic semiconductor is considerably modified by the inclusion of NQEs. In fact, when the quantum nature of the nuclei is taken into account, the proton conductivity is ∼50% larger. This work proves that NQEs sizably affect the protolysis phenomenon and proton transfer in room-temperature liquid water.
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Affiliation(s)
- Giuseppe Cassone
- Institute for Chemical-Physical Processes, National Research Council, Viale F. Stagno d'Alcontres 37, 98158 Messina, Italy
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8
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Nakano K, Attaccalite C, Barborini M, Capriotti L, Casula M, Coccia E, Dagrada M, Genovese C, Luo Y, Mazzola G, Zen A, Sorella S. TurboRVB: A many-body toolkit for ab initio electronic simulations by quantum Monte Carlo. J Chem Phys 2020; 152:204121. [DOI: 10.1063/5.0005037] [Citation(s) in RCA: 21] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/18/2022] Open
Affiliation(s)
- Kousuke Nakano
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
- Japan Advanced Institute of Science and Technology (JAIST), Asahidai 1-1, Nomi, Ishikawa 923-1292, Japan
| | - Claudio Attaccalite
- Aix-Marseille Université, CNRS, CINaM UMR 7325, Campus de Luminy, 13288 Marseille, France
| | | | - Luca Capriotti
- New York University, Tandon School of Engineering, 6 MetroTech Center, Brooklyn, New York 11201, USA
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Michele Casula
- Institut de Minéralogie, de Physique des Matériaux et de Cosmochimie (IMPMC), Sorbonne Université, CNRS UMR 7590, IRD UMR 206, MNHN, 4 Place Jussieu, 75252 Paris, France
| | - Emanuele Coccia
- Department of Chemical and Pharmaceutical Sciences, University of Trieste, Via L. Giorgieri 1, 34127 Trieste, Italy
| | - Mario Dagrada
- Forescout Technologies, John F. Kennedylaan 2, 5612AB Eindhoven, The Netherlands
| | - Claudio Genovese
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
| | - Ye Luo
- Computational Science Division, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
- Argonne Leadership Computing Facility, Argonne National Laboratory, 9700 S. Cass Avenue, Lemont, Illinois 60439, USA
| | | | - Andrea Zen
- Department of Earth Sciences, University College London, Gower Street, London WC1E 6BT, United Kingdom
- Thomas Young Centre and London Centre for Nanotechnology, 17-19 Gordon Street, London WC1H 0AH, United Kingdom
| | - Sandro Sorella
- International School for Advanced Studies (SISSA), Via Bonomea 265, 34136 Trieste, Italy
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9
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Schran C, Behler J, Marx D. Automated Fitting of Neural Network Potentials at Coupled Cluster Accuracy: Protonated Water Clusters as Testing Ground. J Chem Theory Comput 2019; 16:88-99. [DOI: 10.1021/acs.jctc.9b00805] [Citation(s) in RCA: 56] [Impact Index Per Article: 11.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/20/2022]
Affiliation(s)
- Christoph Schran
- Lehrstuhl für Theoretische Chemie, Ruhr−Universität Bochum, 44780 Bochum, Germany
| | - Jörg Behler
- Universität Göttingen, Institut für Physikalische Chemie, Theoretische Chemie, Tammannstrasse 6, 37077 Göttingen, Germany
| | - Dominik Marx
- Lehrstuhl für Theoretische Chemie, Ruhr−Universität Bochum, 44780 Bochum, Germany
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10
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Bertaina G, Di Liberto G, Ceotto M. Reduced rovibrational coupling Cartesian dynamics for semiclassical calculations: Application to the spectrum of the Zundel cation. J Chem Phys 2019; 151:114307. [PMID: 31542046 DOI: 10.1063/1.5114616] [Citation(s) in RCA: 19] [Impact Index Per Article: 3.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
We study the vibrational spectrum of the protonated water dimer, by means of a divide-and-conquer semiclassical initial value representation of the quantum propagator, as a first step in the study of larger protonated water clusters. We use the potential energy surface from the work of Huang et al. [J. Chem. Phys. 122, 044308 (2005)]. To tackle such an anharmonic and floppy molecule, we employ fully Cartesian dynamics and carefully reduce the coupling to global rotations in the definition of normal modes. We apply the time-averaging filter and obtain clean power spectra relative to suitable reference states that highlight the spectral peaks corresponding to the fundamental excitations of the system. Our trajectory-based approach allows for the physical interpretation of the very challenging proton transfer modes. We find that it is important, for such a floppy molecule, to selectively avoid initially exciting lower energy modes, in order to obtain cleaner spectra. The estimated vibrational energies display a mean absolute error (MAE) of ∼29 cm-1 with respect to available multiconfiguration time-dependent Hartree calculations and MAE ∼ 14 cm-1 when compared to the optically active experimental excitations of the Ne-tagged Zundel cation. The reasonable scaling in the number of trajectories for Monte Carlo convergence is promising for applications to higher dimensional protonated cluster systems.
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Affiliation(s)
- G Bertaina
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
| | - G Di Liberto
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
| | - M Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
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11
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Plé T, Huppert S, Finocchi F, Depondt P, Bonella S. Sampling the thermal Wigner density via a generalized Langevin dynamics. J Chem Phys 2019; 151:114114. [PMID: 31542021 DOI: 10.1063/1.5099246] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Abstract
The Wigner thermal density is a function of considerable interest in the area of approximate (linearized or semiclassical) quantum dynamics where it is employed to generate initial conditions for the propagation of appropriate sets of classical trajectories. In this paper, we propose an original approach to compute the Wigner density based on a generalized Langevin equation. The stochastic dynamics is nontrivial in that it contains a coordinate-dependent friction coefficient and a generalized force that couples momenta and coordinates. These quantities are, in general, not known analytically and have to be estimated via auxiliary calculations. The performance of the new sampling scheme is tested on standard model systems with highly nonclassical features such as relevant zero point energy effects, correlation between momenta and coordinates, and negative parts of the Wigner density. In its current brute force implementation, the algorithm, whose convergence can be systematically checked, is accurate and has only limited overhead compared to schemes with similar characteristics. We briefly discuss potential ways to further improve its numerical efficiency.
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Affiliation(s)
- Thomas Plé
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Simon Huppert
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Fabio Finocchi
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Philippe Depondt
- Sorbonne Université, CNRS, Institut des NanoSciences de Paris, INSP, 4 Place Jussieu, F-75005 Paris, France
| | - Sara Bonella
- CECAM Centre Européen de Calcul Atomique et Moléculaire, École Polytechnique Fédérale de Lausanne, Batochimie, Avenue Forel 2, 1015 Lausanne, Switzerland
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12
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Affiliation(s)
- Wei Fang
- School of Physics and Collaborative Innovation Centre of Quantum Matter, Peking University, Beijing, People's Republic of China
- Thomas Young Centre, London Centre for Nanotechnology, and Department of Physics and Astronomy, University College London, London, UK
- Laboratory of Physical Chemistry, ETH Zurich, Zurich, Switzerland
| | - Ji Chen
- Department of Electronic Structure Theory, Max Plank Institute for Solid State Research, Stuttgart, Germany
| | - Yexin Feng
- School of Physics and Electronics, Hunan University, Changsha, People's Republic of China
| | - Xin-Zheng Li
- School of Physics and Collaborative Innovation Centre of Quantum Matter, Peking University, Beijing, People's Republic of China
- State Key Laboratory for Artificial Microstructure and Mesoscopic Physics, Peking University, Beijing, People's Republic of China
| | - Angelos Michaelides
- Thomas Young Centre, London Centre for Nanotechnology, and Department of Physics and Astronomy, University College London, London, UK
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13
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Luo Y, Esler KP, Kent PRC, Shulenburger L. An efficient hybrid orbital representation for quantum Monte Carlo calculations. J Chem Phys 2018; 149:084107. [DOI: 10.1063/1.5037094] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/14/2022] Open
Affiliation(s)
- Ye Luo
- Argonne Leadership Computing Facility, Argonne National Laboratory, Argonne, Illinois 60439, USA
| | - Kenneth P. Esler
- Stone Ridge Technology, 2015 Emmorton Rd. Suite 204, Bel Air, Maryland 21015, USA
| | - Paul R. C. Kent
- Center for Nanophase Materials Sciences and Computational Sciences and Engineering Division, Oak Ridge National Laboratory, Oak Ridge, Tennessee 37831, USA
| | - Luke Shulenburger
- HEDP Theory Department, Sandia National Laboratories, Albuquerque, New Mexico 87185, USA
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14
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Micciarelli M, Conte R, Suarez J, Ceotto M. Anharmonic vibrational eigenfunctions and infrared spectra from semiclassical molecular dynamics. J Chem Phys 2018; 149:064115. [DOI: 10.1063/1.5041911] [Citation(s) in RCA: 27] [Impact Index Per Article: 4.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/15/2022] Open
Affiliation(s)
- Marco Micciarelli
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
| | - Riccardo Conte
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
| | - Jaime Suarez
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
| | - Michele Ceotto
- Dipartimento di Chimica, Università degli Studi di Milano, via C. Golgi 19, 20133 Milano, Italy
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15
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16
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Saraei N, Hietsoi O, Mullins CS, Gupta AJ, Frye BC, Mashuta MS, Buchanan RM, Grapperhaus CA. Streams, cascades, and pools: various water cluster motifs in structurally similar Ni( ii) complexes. CrystEngComm 2018. [DOI: 10.1039/c8ce01153b] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/24/2022]
Abstract
Hydrogen bonding (HB) interactions are well known to impact the properties of water in the bulk and within hydrated materials.
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Affiliation(s)
- Nina Saraei
- Department of Chemistry
- University of Louisville
- Louisville
- USA
| | | | | | | | - Brian C. Frye
- Department of Chemistry
- University of Louisville
- Louisville
- USA
| | - Mark S. Mashuta
- Department of Chemistry
- University of Louisville
- Louisville
- USA
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