Showing 1–50 of 56 results for author: Car, R

fix pimd/langevin: An Efficient Implementation of Path Integral Molecular Dynamics in LAMMPS

Authors: Yifan Li, Axel Gomez, Kehan Cai, Chunyi Zhang, Li Fu, Weile Jia, Yotam M. Y. Feldman, Ofir Blumer, Jacob Higer, Barak Hirshberg, Shenzhen Xu, Axel Kohlmeyer, Roberto Car

Abstract: Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects (NQEs) in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are therefore computationally dema… ▽ More Path integral molecular dynamics (PIMD), which maps a quantum particle onto a fictitious classical system of ring polymers and propagates the "beads" of this extended classical system using molecular dynamics, is widely used to capture nuclear quantum effects (NQEs) in molecular simulations. Accurate PIMD calculations typically require a large number of beads and are therefore computationally demanding. While software packages such as i-PI offer comprehensive PIMD functionality, the high efficiency of simulations driven by machine learning interatomic potentials, such as Deep Potential (DP), calls for more efficient PIMD implementations that fully exploit modern massively parallel supercomputers. Here we present fix pimd/langevin, an efficient PIMD implementation in LAMMPS that supports commonly used features and leverages the Message Passing Interface architecture of LAMMPS to achieve high computational efficiency. We demonstrate the usage and validate the correctness of our code using liquid water as a representative example, and provide a comprehensive overview of the supported features. Then we discuss several important technical aspects of the implementation. Using DP simulations of water as a benchmark, we show that our implementation achieves several-fold acceleration compared to i-PI. Finally, we report strong and weak scaling results that demonstrate the favorable parallel performance of our code. △ Less

Submitted 13 February, 2026; originally announced February 2026.

Comments: 14 pages, 11 figures

Assessment of First-Principles Methods in Modeling the Melting Properties of Water

Authors: Yifan Li, Bingjia Yang, Chunyi Zhang, Axel Gomez, Pinchen Xie, Yixiao Chen, Pablo M. Piaggi, Roberto Car

Abstract: First-principles simulations have played a crucial role in deepening our understanding of the thermodynamic properties of water, and machine learning potentials (MLPs) trained on these first-principles data widen the range of accessible properties. However, the capabilities of different first-principles methods are not yet fully understood due to the lack of systematic benchmarks, the underestimat… ▽ More First-principles simulations have played a crucial role in deepening our understanding of the thermodynamic properties of water, and machine learning potentials (MLPs) trained on these first-principles data widen the range of accessible properties. However, the capabilities of different first-principles methods are not yet fully understood due to the lack of systematic benchmarks, the underestimation of the uncertainties introduced by MLPs, and the neglect of nuclear quantum effects (NQEs). Here, we systematically assess first-principles methods by calculating key melting properties using path integral molecular dynamics (PIMD) driven by Deep Potential (DP) models trained on data from density functional theory (DFT) with SCAN, revPBE0-D3, SCAN0 and revPBE-D3 functionals, as well as from the MB-pol potential. We find that MB-pol is in qualitatively good agreement with the experiment in all properties tested, whereas the four DFT functionals incorrectly predict that NQEs increase the melting temperature. SCAN and SCAN0 slightly underestimate the density change between water and ice upon melting, but revPBE-D3 and revPBE0-D3 severely underestimate it. Moreover, SCAN and SCAN0 correctly predict that the maximum liquid density occurs at a temperature higher than the melting point, while revPBE-D3 and revPBE0-D3 predict the opposite behavior. Our results highlight limitations in widely used first-principles methods and call for a reassessment of their predictive power in aqueous systems. △ Less

Submitted 29 December, 2025; originally announced December 2025.

Ab Initio Melting Properties of Water and Ice from Machine Learning Potentials

Authors: Yifan Li, Bingjia Yang, Chunyi Zhang, Axel Gomez, Pinchen Xie, Yixiao Chen, Pablo M. Piaggi, Roberto Car

Abstract: Liquid water exhibits several important anomalous properties in the vicinity of the melting temperature ($T_{\mathrm{m}}$) of ice Ih, including a higher density than ice and a density maximum at 4~$^{\circ}$C. Experimentally, an isotope effect on $T_{\mathrm{m}}$ is observed: the melting temperature of H$_2$O is approximately 4~K lower than that of D$_2$O. This difference can only be explained by… ▽ More Liquid water exhibits several important anomalous properties in the vicinity of the melting temperature ($T_{\mathrm{m}}$) of ice Ih, including a higher density than ice and a density maximum at 4~$^{\circ}$C. Experimentally, an isotope effect on $T_{\mathrm{m}}$ is observed: the melting temperature of H$_2$O is approximately 4~K lower than that of D$_2$O. This difference can only be explained by nuclear quantum effects (NQEs), which can be accurately captured using path integral molecular dynamics (PIMD). Here we run PIMD simulations driven by Deep Potential (DP) models trained on data from density functional theory (DFT) based on SCAN, revPBE0-D3, SCAN0, and revPBE-D3 and a DP model trained on the MB-pol potential. We calculate the \tm of ice, the density discontinuity at melting, and the temperature of density maximum ($T_{\mathrm{dm}}$) of the liquid. We find that the model based on MB-pol agrees well with experiment. The models based on DFT incorrectly predict that NQEs lower $T_{\mathrm{m}}$. For the density discontinuity, SCAN and SCAN0 predict values close to the experimental result, while revPBE-D3 and revPBE0-D3 significantly underestimate it. Additionally, the models based on SCAN and SCAN0 correctly predict that the $T_{\mathrm{dm}}$ is higher than $T_{\mathrm{m}}$, while those based on revPBE-D3 and revPBE0-D3 predict the opposite. We attribute the deviations of the DFT-based models from experiment to the overestimation of hydrogen bond strength. Our results set the stage for more accurate simulations of aqueous systems grounded on DFT. △ Less

Submitted 29 December, 2025; originally announced December 2025.

Benchmarking Universal Machine Learning Interatomic Potentials for Supported Nanoparticles: Decoupling Energy Accuracy from Structural Exploration

Authors: Jiayan Xu, Abhirup Patra, Amar Deep Pathak, Sharan Shetty, Detlef Hohl, Roberto Car

Abstract: Supported nanoparticle catalysts are widely used in the chemical industry. Computational modeling of supported nanoparticles based on density functional theory (DFT) often involves structural searches of stable local minimum energy configurations and molecular dynamics simulations at finite temperature. These are computationally demanding tasks that are intractable within DFT for large systems. In… ▽ More Supported nanoparticle catalysts are widely used in the chemical industry. Computational modeling of supported nanoparticles based on density functional theory (DFT) often involves structural searches of stable local minimum energy configurations and molecular dynamics simulations at finite temperature. These are computationally demanding tasks that are intractable within DFT for large systems. In the last two decades, machine learning interatomic potentials (MLIPs) have been successfully used to substantially increase the size and time scales accessible to simulations approximating DFT accuracy. However, training reliable MLIPs is non-trivial as it requires many costly DFT calculations. Recently, several universal MLIPs (uMLIPs) have been developed, which are trained on large datasets that cover a wide range of molecules and materials. Here, we benchmark the accuracy and the efficiency of these uMLIPs in describing Cu nanoparticles supported on Al$_2$O$_3$ surfaces against our domain-specific DP-UniAlCu model. We find that the MACE-OMAT can reproduce reasonably well the low-energy structures found in global optimization at an energy accuracy comparable to DP-UniAlCu. Interestingly, the MatterSim-v1.0.0-1M model, which exhibits larger deviations in the binding energies, can find even more stable configurations than the other two models in some supported nanoparticle sizes, showing its capability in structure exploration. For MD simulations, MACE-OMAT and MatterSim-v1.0.0-1M can qualitatively reproduce the mean-squared displacements of Cu atoms (MSD$_\mathrm{Cu}$) predicted by DP-UniAlCu, albeit at roughly two orders of magnitude higher cost. We demonstrate that the uMLIPs can be very useful in simulating supported nanoparticles even without any fine-tuning, though their reduced efficiency remains a limiting factor for large-scale simulations. △ Less

Submitted 25 March, 2026; v1 submitted 4 December, 2025; originally announced December 2025.

Comments: 32 pages, 5 figures, 3 tables; fix table 1, figure 2, and figure 3; add table 3

A Machine Learning Model for the Chemistry of a Solvated Electron

Authors: Ruiqi Gao, Pinchen Xie, Roberto Car

Abstract: In molecular simulations, machine-learning force fields can achieve ab initio accuracy at a lower cost but remain limited in the explicit modeling of electrons. In this work, we develop an electron-aware machine-learning force field, in which an excess electron of interest is modeled quantum mechanically, while the remaining short-range interactions and long-range Coulombic forces are machine-lear… ▽ More In molecular simulations, machine-learning force fields can achieve ab initio accuracy at a lower cost but remain limited in the explicit modeling of electrons. In this work, we develop an electron-aware machine-learning force field, in which an excess electron of interest is modeled quantum mechanically, while the remaining short-range interactions and long-range Coulombic forces are machine-learned to reproduce a density functional theory calculation. We demonstrate the method on the solvated electron in bulk water and its reaction with a hydronium ion. We identify a proton transfer mechanism by which the excess proton recombines with the electron. We determine the forward reaction rates between 350 K and 450 K from first-passage survival functions, which yield an Arrhenius relationship with an activation energy of 3.2 kcal$\cdot$mol$^{-1}$, in good agreement with experiment. From an enhanced sampling simulation, we determine the equilibrium constant, and thus the reaction free energy, which is also consistent with experimental measurements. △ Less

Submitted 27 November, 2025; originally announced November 2025.

Spectral Similarity Masks Structural Diversity at Hydrophobic Water Interfaces

Authors: Yong Wang, Yifan Li, Linhan Du, Chunyi Zhang, Lorenzo Agosta, Marcos Calegari Andrade, Annabella Selloni, Roberto Car

Abstract: The air-water and graphene-water interfaces represent quintessential examples of the liquid-gas and liquid-solid boundaries, respectively. While the sum-frequency generation (SFG) spectra of these interfaces exhibit certain similarities, a consensus on their signals and interpretations has yet to be reached. Leveraging deep learning, we accessed fully first-principles SFG spectra for both systems,… ▽ More The air-water and graphene-water interfaces represent quintessential examples of the liquid-gas and liquid-solid boundaries, respectively. While the sum-frequency generation (SFG) spectra of these interfaces exhibit certain similarities, a consensus on their signals and interpretations has yet to be reached. Leveraging deep learning, we accessed fully first-principles SFG spectra for both systems, addressing recent experimental discrepancies. Despite both interfaces exhibiting microscopically hydrophobic characteristics, our findings reveal that similarities in SFG signals do not translate into comparable interfacial microscopic properties. Instead, graphene-water and air-water interfaces exhibit fundamental differences in SFG-active thicknesses, hydrogen-bonding networks, and dynamic diffusion behavior. These distinctions underscore the stronger confinements imposed by the solid-liquid interface compared with the weaker constraints of the gas-liquid interface. △ Less

Submitted 7 April, 2025; originally announced April 2025.

Dynamic Metal-Support Interaction Dictates Cu Nanoparticle Sintering on Al$_2$O$_3$ Surfaces

Authors: Jiayan Xu, Shreeja Das, Amar Deep Pathak, Abhirup Patra, Sharan Shetty, Detlef Hohl, Roberto Car

Abstract: Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model for Cu nanoparticles on three Al$_2$O$_3$ surfaces ($γ$-Al$_2$O$_3$(100), $γ$-Al$_2$O$_3$(110), and $α$-Al$_2$O$_3$(0001)). Using DP-accelerated simulations, we reveal striking facet-dependent nanoparticle stability and mobility patterns across the three surf… ▽ More Nanoparticle sintering remains a critical challenge in heterogeneous catalysis. In this work, we present a unified deep potential (DP) model for Cu nanoparticles on three Al$_2$O$_3$ surfaces ($γ$-Al$_2$O$_3$(100), $γ$-Al$_2$O$_3$(110), and $α$-Al$_2$O$_3$(0001)). Using DP-accelerated simulations, we reveal striking facet-dependent nanoparticle stability and mobility patterns across the three surfaces. The nanoparticles diffuse several times faster on $α$-Al$_2$O$_3$(0001) than on $γ$-Al$_2$O$_3$(100) at 800 K while expected to be more sluggish based on their larger binding energy at 0 K. Diffusion is facilitated by dynamic metal-support interaction (MSI), where the Al atoms switch out of the surface plane to optimize contact with the nanoparticle and relax back to the plane as the nanoparticle moves away. In contrast, the MSI on $γ$-Al$_2$O$_3$(100) and on $γ$-Al$_2$O$_3$(110) is dominated by more stable and directional Cu-O bonds, consistent with the limited diffusion observed on these surfaces. Our extended long-time MD simulations provide quantitative insights into the sintering processes, showing that the dispersity of nanoparticles (the initial inter-nanoparticle distance) strongly influences coalescence driven by nanoparticle diffusion. We observed that the coalescence of Cu$_{13}$ nanoparticles on $α$-Al$_2$O$_3$(0001) can occur in a short time (10 ns) at 800 K even with an initial inter-nanoparticle distance increased to 30 Å, while the coalescence on $γ$-Al$_2$O$_3$(100) is inhibited significantly by increasing the initial inter-nanoparticle distance from 15 Å to 30 Å. These findings demonstrate that the dynamics of the supporting surface is crucial to understanding the sintering mechanism and offer guidance for designing sinter-resistant catalysts by engineering the support morphology. △ Less

Submitted 28 January, 2025; v1 submitted 21 January, 2025; originally announced January 2025.

Comments: 33 pages, 5 figures; update plot style of fig. 3

Thermal disorder and phonon softening in the ferroelectric phase transition of lead titanate

Authors: Pinchen Xie, Yixiao Chen, Weinan E, Roberto Car

Abstract: We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diff… ▽ More We report a molecular dynamics study of ab initio quality of the ferroelectric phase transition in crystalline PbTiO3. We model anharmonicity accurately in terms of potential energy and polarization surfaces trained on density functional theory data with modern machine learning techniques. Our simulations demonstrate that the transition has a strong order-disorder character, in agreement with diffraction experiments, and provide fresh insight into the approach to equilibrium across the phase transition. We find that the emergence and disappearance of the macroscopic polarization is driven by dipolar switching at the nanometer scale. We also computed the infrared optical absorption spectra in both the ferroelectric and the paraelectric phases, finding good agreement with the experimental Raman frequencies. Often, the almost ideal displacive character of the soft mode detected by Raman scattering in the paraelectric phase has been contrasted with the order-disorder character of the transition suggested by diffraction experiments. We settle this issue by showing that the soft mode coexists with a strong Debye relaxation associated with thermal disordering of the dipoles. The Debye relaxation feature is centered at zero frequency and appears near the transition temperature in both the ferroelectric and the paraelectric phases. △ Less

Submitted 31 March, 2025; v1 submitted 8 October, 2024; originally announced October 2024.

Comments: arXiv admin note: text overlap with arXiv:2205.11839

Journal ref: Phys. Rev. B 111, 094113 (2025)

Deuteration removes quantum dipolar defects from KDP crystals

Authors: Bingjia Yang, Pinchen Xie, Roberto Car

Abstract: The structural, dielectric, and thermodynamic properties of the hydrogen-bonded ferroelectric crystal potassium dihydrogen phosphate ($\mathbf{KH_2PO_4}$), KDP for short, differ significantly from those of DKDP ($\mathbf{KD_2PO_4}$). It is well established that deuteration affects the interplay of hydrogen-bond switches and heavy ion displacements that underlie the emergence of macroscopic polariz… ▽ More The structural, dielectric, and thermodynamic properties of the hydrogen-bonded ferroelectric crystal potassium dihydrogen phosphate ($\mathbf{KH_2PO_4}$), KDP for short, differ significantly from those of DKDP ($\mathbf{KD_2PO_4}$). It is well established that deuteration affects the interplay of hydrogen-bond switches and heavy ion displacements that underlie the emergence of macroscopic polarization, but a detailed microscopic model is missing. Here we show that all-atom path integral molecular dynamics simulations can predict the isotope effects, revealing the microscopic mechanism that differentiates KDP and DKDP. Proton tunneling in the hydrogen bonds generates phosphate configurations that do not contribute to the polarization. These dipolar defects are always present in KDP, but disappear at low temperatures in DKDP, which behaves more classically. Quantum disorder confers residual entropy to ferroelectric KDP, explaining its lower spontaneous polarization and transition entropy relative to DKDP. Tunneling should also contribute to the anomalous heat capacity observed in KDP near absolute zero. The prominent role of quantum fluctuations in KDP is related to the unusual strength of the hydrogen bonds in this system and should be equally important in the other crystals of the KDP family, which exhibit similar isotope effects. △ Less

Submitted 11 April, 2024; originally announced April 2024.

Enhanced Deep Potential Model for Fast and Accurate Molecular Dynamics; Application to the Hydrated Electron

Authors: Ruiqi Gao, Yifan Li, Roberto Car

Abstract: In molecular simulations, neural network force fields aim at achieving \emph{ab initio} accuracy with reduced computational cost. This work introduces enhancements to the Deep Potential network architecture, integrating a message-passing framework and a new lightweight implementation with various improvements. Our model achieves accuracy on par with leading machine learning force fields and offers… ▽ More In molecular simulations, neural network force fields aim at achieving \emph{ab initio} accuracy with reduced computational cost. This work introduces enhancements to the Deep Potential network architecture, integrating a message-passing framework and a new lightweight implementation with various improvements. Our model achieves accuracy on par with leading machine learning force fields and offers significant speed advantages, making it well-suited for large-scale, accuracy-sensitive systems. We also introduce a new iterative model for Wannier center prediction, allowing us to keep track of electron positions in simulations of general insulating systems. We apply our model to study the solvated electron in bulk water, an ostensibly simple system that is actually quite challenging to represent with neural networks. Our trained model is not only accurate, but can also transfer to larger systems. Our simulation confirms the cavity model, where the electron's localized state is observed to be stable. Through an extensive run, we accurately determine various structural and dynamical properties of the solvated electron. △ Less

Submitted 5 April, 2024; originally announced April 2024.

Electrical double layer and capacitance of TiO2 electrolyte interfaces from first principles simulations

Authors: Chunyi Zhang, Marcos Calegari Andrade, Zachary K. Goldsmith, Abhinav S. Raman, Yifan Li, Pablo Piaggi, Xifan Wu, Roberto Car, Annabella Selloni

Abstract: The electrical double layer (EDL) at aqueous solution-metal oxide interfaces critically affects many fundamental processes in electrochemistry, geology and biology, yet understanding its microscopic structure is challenging for both theory and experiments. Here we employ ab initio-based machine learning potentials including long-range electrostatics in large-scale atomistic simulations of the EDL… ▽ More The electrical double layer (EDL) at aqueous solution-metal oxide interfaces critically affects many fundamental processes in electrochemistry, geology and biology, yet understanding its microscopic structure is challenging for both theory and experiments. Here we employ ab initio-based machine learning potentials including long-range electrostatics in large-scale atomistic simulations of the EDL at the TiO2-electrolyte interface. Our simulations provide a molecular-scale picture of the EDL that demonstrates the limitations of standard mean-field models. We further develop a method to accurately calculate the electrostatic potential drop at the interface. The computed capacitance originating from the adsorbed charges and the potential drop agrees with experiments, supporting the reliability of our description of the EDL. The larger interfacial capacitance of basic relative to acidic solutions originates from the higher affinity of the cations for the oxide surface and gives rise to distinct charging mechanisms on negative and positive surfaces. △ Less

Submitted 29 March, 2024; originally announced April 2024.

DeePMD-kit v2: A software package for Deep Potential models

Authors: Jinzhe Zeng, Duo Zhang, Denghui Lu, Pinghui Mo, Zeyu Li, Yixiao Chen, Marián Rynik, Li'ang Huang, Ziyao Li, Shaochen Shi, Yingze Wang, Haotian Ye, Ping Tuo, Jiabin Yang, Ye Ding, Yifan Li, Davide Tisi, Qiyu Zeng, Han Bao, Yu Xia, Jiameng Huang, Koki Muraoka, Yibo Wang, Junhan Chang, Fengbo Yuan , et al. (22 additional authors not shown)

Abstract: DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced… ▽ More DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials (MLP) known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, Deep Potential - Range Correction (DPRc), Deep Potential Long Range (DPLR), GPU support for customized operators, model compression, non-von Neumann molecular dynamics (NVNMD), and improved usability, including documentation, compiled binary packages, graphical user interfaces (GUI), and application programming interfaces (API). This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, the article benchmarks the accuracy and efficiency of different models and discusses ongoing developments. △ Less

Submitted 18 April, 2023; originally announced April 2023.

Comments: 51 pages, 2 figures

ACM Class: J.2

Journal ref: J. Chem. Phys. 159, 054801 (2023)

Melting curves of ice polymorphs in the vicinity of the liquid-liquid critical point

Authors: Pablo M. Piaggi, Thomas E. Gartner III, Roberto Car, Pablo G. Debenedetti

Abstract: The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate in part due to the challenges associated with providing definitive experimental evidence. Pioneering work by Mishima and Stanley [Nature 392, 164 (1998) and Phys. Rev. Lett. 85, 334 (2000)] sought to shed light on this problem by studying the melting curves of different ice polymorphs… ▽ More The possible existence of a liquid-liquid critical point in deeply supercooled water has been a subject of debate in part due to the challenges associated with providing definitive experimental evidence. Pioneering work by Mishima and Stanley [Nature 392, 164 (1998) and Phys. Rev. Lett. 85, 334 (2000)] sought to shed light on this problem by studying the melting curves of different ice polymorphs and their metastable continuation in the vicinity of the expected location of the liquid-liquid transition and its associated critical point. Based on the continuous or discontinuous changes in slope of the melting curves, Mishima suggested that the liquid-liquid critical point lies between the melting curves of ice III and ice V. Here, we explore this conjecture using molecular dynamics simulations with a purely-predictive machine learning model based on ab initio quantum-mechanical calculations. We study the melting curves of ices III, IV, V, VI, and XIII using this model and find that the melting lines of all the studied ice polymorphs are supercritical and do not intersect the liquid-liquid transition locus. We also find a pronounced, yet continuous, change in slope of the melting lines upon crossing of the locus of maximum compressibility of the liquid. Finally, we analyze critically the literature in light of our findings, and conclude that the scenario in which melting curves are supercritical is favored by the most recent computational and experimental evidence. Thus, although the preponderance of experimental and computational evidence is consistent with the existence of a second critical point in water, the behavior of the melting lines of ice polymorphs does not provide strong evidence in support of this viewpoint, according to our calculations. △ Less

Submitted 16 February, 2023; originally announced February 2023.

Comments: 21 pages, 4 figures, supplementary information

Journal ref: J. Chem. Phys. 159, 054502 (2023)

Hybrid Auxiliary Field Quantum Monte Carlo for Molecular Systems

Authors: Yixiao Chen, Linfeng Zhang, Weinan E, Roberto Car

Abstract: We propose a quantum Monte Carlo approach to solve the ground state many-body Schrodinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations d… ▽ More We propose a quantum Monte Carlo approach to solve the ground state many-body Schrodinger equation for the electronic ground state. The method combines optimization from variational Monte Carlo and propagation from auxiliary field quantum Monte Carlo, in a way that significantly alleviates the sign problem. In application to molecular systems, we obtain highly accurate results for configurations dominated by either dynamic or static electronic correlation. △ Less

Submitted 20 April, 2023; v1 submitted 19 November, 2022; originally announced November 2022.

Ab Initio Generalized Langevin Equation

Authors: Pinchen Xie, Roberto Car, Weinan E

Abstract: We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig form… ▽ More We introduce a machine learning-based approach called ab initio generalized Langevin equation (AIGLE) to model the dynamics of slow collective variables in materials and molecules. In this scheme, the parameters are learned from atomistic simulations based on ab initio quantum mechanical models. Force field, memory kernel, and noise generator are constructed in the context of the Mori-Zwanzig formalism, under the constraint of the fluctuation-dissipation theorem. Combined with deep potential molecular dynamics and electronic density functional theory, this approach opens the way to multi-scale modeling in a variety of situations. Here, we demonstrate this capability with a study of two mesoscale processes in crystalline lead titanate, namely the field-driven dynamics of a planar ferroelectric domain wall, and the dynamics of an extensive lattice of coarse-grained electric dipoles. In the first case, AIGLE extends the reach of ab initio simulations to a regime of noise-driven motions not accessible to molecular dynamics. In the second case, AIGLE deals with an extensive set of collective variables by adopting a local approximation for the memory kernel and retaining only short-range noise correlations. The scheme is computationally more efficient than molecular dynamics by several orders of magnitude, and mimics the microscopic dynamics at low frequencies where it reproduces accurately the dominant far-infrared absorption frequency. △ Less

Submitted 15 February, 2024; v1 submitted 11 November, 2022; originally announced November 2022.

Liquid-liquid transition in water from first principles

Authors: Thomas E. Gartner III, Pablo M. Piaggi, Roberto Car, Athanassios Z. Panagiotopoulos, Pablo G. Debenedetti

Abstract: A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange cor… ▽ More A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles. △ Less

Submitted 2 November, 2022; v1 submitted 29 August, 2022; originally announced August 2022.

Comments: 14 pages, 3 figures. Supplemental material contains 11 pages, 8 figures

Homogeneous ice nucleation in an ab initio machine learning model of water

Authors: Pablo M. Piaggi, Jack Weis, Athanassios Z. Panagiotopoulos, Pablo G. Debenedetti, Roberto Car

Abstract: Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine learning model trained on density-funct… ▽ More Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine learning model trained on density-functional theory (DFT) energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation) which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates. △ Less

Submitted 24 August, 2022; v1 submitted 2 March, 2022; originally announced March 2022.

Comments: 20 pages, 5 figures

Journal ref: Proc. Natl. Acad. Sci. 2021, 119 (33) e2207294119

Many-Body Effects in the X-ray Absorption Spectra of Liquid Water

Authors: Fujie Tang, Zhenglu Li, Chunyi Zhang, Steven G. Louie, Roberto Car, Diana Y. Qiu, Xifan Wu

Abstract: X-ray absorption spectroscopy (XAS) is a powerful experimental technique to probe the local order in materials with core electron excitations. Experimental interpretation requires supporting theoretical calculations. For water, these calculations are very demanding and, to date, could only be done with major approximations that limited the accuracy of the calculated spectra. This prompted an inten… ▽ More X-ray absorption spectroscopy (XAS) is a powerful experimental technique to probe the local order in materials with core electron excitations. Experimental interpretation requires supporting theoretical calculations. For water, these calculations are very demanding and, to date, could only be done with major approximations that limited the accuracy of the calculated spectra. This prompted an intense debate on whether a substantial revision of the standard picture of tetrahedrally bonded water was necessary to improve the agreement of theory and experiment. Here, we report a new first-principles calculation of the XAS of water that avoids the approximations of prior work thanks to recent advances in electron excitation theory. The calculated XAS spectra, and their variation with changes of temperature and/or with isotope substitution, are in excellent quantitative agreement with experiments. The approach requires accurate quasi-particle wavefunctions beyond density functional theory approximations, accounts for the dynamics of quasi-particles and includes dynamic screening as well as renormalization effects due to the continuum of valence-level excitations. The three features observed in the experimental spectra are unambiguously attributed to excitonic effects. The pre-edge feature is associated to a bound intramolecular exciton, the main-edge feature is associated to an exciton localized within the coordination shell of the excited molecule, while the post-edge one is delocalized over more distant neighbors, as expected for a resonant state. The three features probe the local order at short, intermediate, and longer range relative to the excited molecule. The calculated spectra are fully consistent with a standard tetrahedral picture of water. △ Less

Submitted 24 January, 2022; originally announced January 2022.

Comments: 11 pages, 3 figures

Journal ref: Proc. Natl. Acad. Sci. U.S.A., 2022, 119, e2201258119

A deep potential model with long-range electrostatic interactions

Authors: Linfeng Zhang, Han Wang, Maria Carolina Muniz, Athanassios Z. Panagiotopoulos, Roberto Car, Weinan E

Abstract: Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that d… ▽ More Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make possible molecular simulations with the accuracy of quantum mechanical density functional theory, at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei+core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the deep potential long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples, the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal. △ Less

Submitted 16 February, 2022; v1 submitted 26 December, 2021; originally announced December 2021.

Heat transport in liquid water from first-principles and deep-neural-network simulations

Authors: Davide Tisi, Linfeng Zhang, Riccardo Bertossa, Han Wang, Roberto Car, Stefano Baroni

Abstract: We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represe… ▽ More We compute the thermal conductivity of water within linear response theory from equilibrium molecular dynamics simulations, by adopting two different approaches. In one, the potential energy surface (PES) is derived on the fly from the electronic ground state of density functional theory (DFT) and the corresponding analytical expression is used for the energy flux. In the other, the PES is represented by a deep neural network (DNN) trained on DFT data, whereby the PES has an explicit local decomposition and the energy flux takes a particularly simple expression. By virtue of a gauge invariance principle, established by Marcolongo, Umari, and Baroni, the two approaches should be equivalent if the PES were reproduced accurately by the DNN model. We test this hypothesis by calculating the thermal conductivity, at the GGA (PBE) level of theory, using the direct formulation and its DNN proxy, finding that both approaches yield the same conductivity, in excess of the experimental value by approximately 60%. Besides being numerically much more efficient than its direct DFT counterpart, the DNN scheme has the advantage of being easily applicable to more sophisticated DFT approximations, such as meta-GGA and hybrid functionals, for which it would be hard to derive analytically the expression of the energy flux. We find in this way, that a DNN model, trained on meta-GGA (SCAN) data, reduce the deviation from experiment of the predicted thermal conductivity by about 50%, leaving the question open as to whether the residual error is due to deficiencies of the functional, to a neglect of nuclear quantum effects in the atomic dynamics, or, likely, to a combination of the two. △ Less

Submitted 23 December, 2021; v1 submitted 24 August, 2021; originally announced August 2021.

Journal ref: Phys. Rev. B 104 (2021), 224202

Quantum ESPRESSO toward the exascale

Authors: Paolo Giannozzi, Oscar Baseggio, Pietro Bonfà, Davide Brunato, Roberto Car, Ivan Carnimeo, Carlo Cavazzoni, Stefano de Gironcoli, Pietro Delugas, Fabrizio Ferrari Ruffino, Andrea Ferretti, Nicola Marzari, Iurii Timrov, Andrea Urru, Stefano Baroni

Abstract: Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper we present a motivation and brief re… ▽ More Quantum ESPRESSO is an open-source distribution of computer codes for quantum-mechanical materials modeling, based on density-functional theory, pseudopotentials, and plane waves, and renowned for its performance on a wide range of hardware architectures, from laptops to massively parallel computers, as well as for the breadth of its applications. In this paper we present a motivation and brief review of the ongoing effort to port Quantum ESPRESSO onto heterogeneous architectures based on hardware accelerators, which will overcome the energy constraints that are currently hindering the way towards exascale computing. △ Less

Submitted 22 April, 2021; v1 submitted 21 April, 2021; originally announced April 2021.

Journal ref: J. Chem. Phys. 152, 154105 (2020)

The Phase Diagram of a Deep Potential Water Model

Authors: Linfeng Zhang, Han Wang, Roberto Car, Weinan E

Abstract: Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Sati… ▽ More Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII$''$ and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments. △ Less

Submitted 11 February, 2021; v1 submitted 9 February, 2021; originally announced February 2021.

Journal ref: Phys. Rev. Lett. 126, 236001 (2021)

Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional

Authors: Pablo M. Piaggi, Athanassios Z. Panagiotopoulos, Pablo G. Debenedetti, Roberto Car

Abstract: Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye towards studying ice nucleation. The machine learning model is based on deep neura… ▽ More Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye towards studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ice Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic. △ Less

Submitted 12 January, 2021; originally announced January 2021.

Comments: 20 pages, 9 figures

Journal ref: J. Chem. Theory Comput. 2021, 17, 5, 3065-3077

Critical Need for a National Initiative in Low Temperature Plasma Research

Authors: Philip Efthimion, Igor Kaganovich, Yevgeny Raitses, M. Keidar, Hyo-Chang Lee, Mikhail Shneider, R. Car

Abstract: In the white paper we describe a national program in Low Temperature Plasma (LTP). The program should take advantage of the research opportunities of 3 rapidly growing areas (nanomaterial plasma synthesis, plasma medicine, microelectronics). The main theme is to achieve a fundamental understanding of Low Temperature Plasmas as they are applied to these different applications. This understanding wi… ▽ More In the white paper we describe a national program in Low Temperature Plasma (LTP). The program should take advantage of the research opportunities of 3 rapidly growing areas (nanomaterial plasma synthesis, plasma medicine, microelectronics). The main theme is to achieve a fundamental understanding of Low Temperature Plasmas as they are applied to these different applications. This understanding will allow U.S. industry to meet the challenges of international competition. △ Less

Submitted 17 July, 2020; originally announced July 2020.

Comments: 9 pages, submitted for the Community Planning Process for fusion energy (https://sites.google.com/pppl.gov/dpp-cpp/),

Pushing the limit of molecular dynamics with ab initio accuracy to 100 million atoms with machine learning

Authors: Weile Jia, Han Wang, Mohan Chen, Denghui Lu, Lin Lin, Roberto Car, Weinan E, Linfeng Zhang

Abstract: For 35 years, {\it ab initio} molecular dynamics (AIMD) has been the method of choice for modeling complex atomistic phenomena from first principles. However, most AIMD applications are limited by computational cost to systems with thousands of atoms at most. We report that a machine learning-based simulation protocol (Deep Potential Molecular Dynamics), while retaining {\it ab initio} accuracy, c… ▽ More For 35 years, {\it ab initio} molecular dynamics (AIMD) has been the method of choice for modeling complex atomistic phenomena from first principles. However, most AIMD applications are limited by computational cost to systems with thousands of atoms at most. We report that a machine learning-based simulation protocol (Deep Potential Molecular Dynamics), while retaining {\it ab initio} accuracy, can simulate more than 1 nanosecond-long trajectory of over 100 million atoms per day, using a highly optimized code (GPU DeePMD-kit) on the Summit supercomputer. Our code can efficiently scale up to the entire Summit supercomputer, attaining $91$ PFLOPS in double precision ($45.5\%$ of the peak) and {$162$/$275$ PFLOPS in mixed-single/half precision}. The great accomplishment of this work is that it opens the door to simulating unprecedented size and time scales with {\it ab initio} accuracy. It also poses new challenges to the next-generation supercomputer for a better integration of machine learning and physical modeling. △ Less

Submitted 14 September, 2020; v1 submitted 1 May, 2020; originally announced May 2020.

86 PFLOPS Deep Potential Molecular Dynamics simulation of 100 million atoms with ab initio accuracy

Authors: Denghui Lu, Han Wang, Mohan Chen, Jiduan Liu, Lin Lin, Roberto Car, Weinan E, Weile Jia, Linfeng Zhang

Abstract: We present the GPU version of DeePMD-kit, which, upon training a deep neural network model using ab initio data, can drive extremely large-scale molecular dynamics (MD) simulation with ab initio accuracy. Our tests show that the GPU version is 7 times faster than the CPU version with the same power consumption. The code can scale up to the entire Summit supercomputer. For a copper system of 113, 2… ▽ More We present the GPU version of DeePMD-kit, which, upon training a deep neural network model using ab initio data, can drive extremely large-scale molecular dynamics (MD) simulation with ab initio accuracy. Our tests show that the GPU version is 7 times faster than the CPU version with the same power consumption. The code can scale up to the entire Summit supercomputer. For a copper system of 113, 246, 208 atoms, the code can perform one nanosecond MD simulation per day, reaching a peak performance of 86 PFLOPS (43% of the peak). Such unprecedented ability to perform MD simulation with ab initio accuracy opens up the possibility of studying many important issues in materials and molecules, such as heterogeneous catalysis, electrochemical cells, irradiation damage, crack propagation, and biochemical reactions. △ Less

Submitted 7 September, 2020; v1 submitted 24 April, 2020; originally announced April 2020.

Comments: 29 pages, 11 figures

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations

Authors: Pablo M. Piaggi, Roberto Car

Abstract: We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of a… ▽ More We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. We analyze the effect of the system size on the ice Ih-liquid free energy differences and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih. △ Less

Submitted 11 May, 2020; v1 submitted 17 April, 2020; originally announced April 2020.

Comments: 9 pages, 6 figures

Raman Spectrum and Polarizability of Liquid Water from Deep Neural Networks

Authors: Grace M. Sommers, Marcos F. Calegari Andrade, Linfeng Zhang, Han Wang, Roberto Car

Abstract: We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio… ▽ More We introduce a scheme based on machine learning and deep neural networks to model the environmental dependence of the electronic polarizability in insulating materials. Application to liquid water shows that training the network with a relatively small number of molecular configurations is sufficient to predict the polarizability of arbitrary liquid configurations in close agreement with ab initio density functional theory calculations. In combination with a neural network representation of the interatomic potential energy surface,the scheme allows us to calculate the Raman spectra along 2-nanosecond classical trajectories at different temperatures for H2O and D2O. The vast gains in efficiency provided by the machine learning approach enable longer trajectories and larger system sizes relative to ab initio methods, reducing the statistical error and improving the resolution of the low-frequency Raman spectra. Decomposing the spectra into intramolecular and intermolecular contributions elucidates the mechanisms behind the temperature dependence of the low-frequency and stretch modes. △ Less

Submitted 15 April, 2020; originally announced April 2020.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based $Ab$ $Initio$ Molecular Dynamics I: Theory, Algorithm, and Performance

Authors: Hsin-Yu Ko, Junteng Jia, Biswajit Santra, Xifan Wu, Roberto Car, Robert A. DiStasio Jr

Abstract: By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX… ▽ More By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semi-local density functional theory (DFT), and thereby furnish a more accurate and reliable description of the electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we have devised a linear-scaling yet formally exact approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions, MLWFs) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems at the hybrid DFT level. We provide a comprehensive description of the exx algorithm, which is currently implemented in the Quantum ESPRESSO program and employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize high-performance computing (HPC) resources. This is followed by a critical assessment of the accuracy and parallel performance of this approach when performing AIMD simulations of liquid water in the canonical ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT based AIMD simulations of condensed-phase systems containing 500-1000 atoms with a walltime cost that is comparable to semi-local DFT. In doing so, exx takes us closer to routinely performing AIMD simulations of large-scale condensed-phase systems for sufficiently long timescales at the hybrid DFT level of theory. △ Less

Submitted 6 May, 2021; v1 submitted 24 November, 2019; originally announced November 2019.

Comments: 34 pages and 10 figures

Deep neural network for the dielectric response of insulators

Authors: Linfeng Zhang, Mohan Chen, Xifan Wu, Han Wang, Weinan E, Roberto Car

Abstract: We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab-initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the Deep Potential model of the atomic potential energy surface, the scheme pred… ▽ More We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab-initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the Deep Potential model of the atomic potential energy surface, the scheme predicts the dielectric response of insulators for trajectories inaccessible to direct ab-initio simulation. The scheme is non-perturbative and can capture the response of a mutating chemical environment. We demonstrate the approach by calculating the infrared spectra of liquid water at standard conditions, and of ice under extreme pressure, when it transforms from a molecular to an ionic crystal. △ Less

Submitted 9 June, 2020; v1 submitted 27 June, 2019; originally announced June 2019.

Journal ref: Phys. Rev. B 102, 041121 (2020)

Isotope Effects in Liquid Water via Deep Potential Molecular Dynamics

Authors: Hsin-Yu Ko, Linfeng Zhang, Biswajit Santra, Han Wang, Weinan E, Robert A. DiStasio Jr., Roberto Car

Abstract: A comprehensive microscopic understanding of ambient liquid water is a major challenge for $ab$ $initio$ simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes… ▽ More A comprehensive microscopic understanding of ambient liquid water is a major challenge for $ab$ $initio$ simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g., H or D), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g., isotope effects), and therefore provide yet another challenge for $ab$ $initio$ approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretized path-integral (PI) approach, and machine learning (ML) constitutes a versatile $ab$ $initio$ based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model---a neural-network representation of the $ab$ $initio$ PES---in conjunction with a PI approach based on the generalized Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid H$_2$O and D$_2$O. Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects. △ Less

Submitted 3 June, 2019; v1 submitted 9 April, 2019; originally announced April 2019.

Comments: 19 pages, 5 figures, and 1 table

Active Learning of Uniformly Accurate Inter-atomic Potentials for Materials Simulation

Authors: Linfeng Zhang, De-Ye Lin, Han Wang, Roberto Car, Weinan E

Abstract: An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg… ▽ More An active learning procedure called Deep Potential Generator (DP-GEN) is proposed for the construction of accurate and transferable machine learning-based models of the potential energy surface (PES) for the molecular modeling of materials. This procedure consists of three main components: exploration, generation of accurate reference data, and training. Application to the sample systems of Al, Mg and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data. △ Less

Submitted 6 February, 2019; v1 submitted 28 October, 2018; originally announced October 2018.

Journal ref: Phys. Rev. Materials 3, 023804 (2019)

End-to-end Symmetry Preserving Inter-atomic Potential Energy Model for Finite and Extended Systems

Authors: Linfeng Zhang, Jiequn Han, Han Wang, Wissam A. Saidi, Roberto Car, Weinan E

Abstract: Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES for a w… ▽ More Machine learning models are changing the paradigm of molecular modeling, which is a fundamental tool for material science, chemistry, and computational biology. Of particular interest is the inter-atomic potential energy surface (PES). Here we develop Deep Potential - Smooth Edition (DeepPot-SE), an end-to-end machine learning-based PES model, which is able to efficiently represent the PES for a wide variety of systems with the accuracy of ab initio quantum mechanics models. By construction, DeepPot-SE is extensive and continuously differentiable, scales linearly with system size, and preserves all the natural symmetries of the system. Further, we show that DeepPot-SE describes finite and extended systems including organic molecules, metals, semiconductors, and insulators with high fidelity. △ Less

Submitted 20 December, 2018; v1 submitted 23 May, 2018; originally announced May 2018.

Journal ref: Conference on Neural Information Processing Systems (NeurIPS), 2018

Searching for crystal-ice domains in amorphous ices

Authors: Fausto Martelli, Nicolas Giovambattista, Salvatore Torquato, Roberto Car

Abstract: We employ classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice (I$h$) and low-density amorphous (LDA) ice at low temperatures. In both cases, the system transforms to high-density amorphous ice (HDA) via a first-order-like phase transition. We employ a sensitive local order metric (LOM) [Martelli et. al.,… ▽ More We employ classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice (I$h$) and low-density amorphous (LDA) ice at low temperatures. In both cases, the system transforms to high-density amorphous ice (HDA) via a first-order-like phase transition. We employ a sensitive local order metric (LOM) [Martelli et. al., Phys. Rev. B, 97, 064105 (2018)], that can discriminate among different crystalline and non crystalline ice structures and is based on the positions of the oxygen atoms in the first and/or second hydration shell. Our results confirm that LDA and HDA are indeed amorphous, i.e., they lack of polydispersed ice domains. Interestingly, HDA contains a small number of domains that are reminiscent of the unit cell of ice IV, although the hydrogen-bond network (HBN) of these domains differ from the HBN of ice IV. The presence of ice IV-like domains provides some support to the hypothesis that HDA could be the result of a detour on the HBN rearrangement along the I$h$-to-ice IV pressure induced transformation. Both nonequilibrium LDA-to-HDA and I$h$-to-HDA transformations are two-steps processes where a small distortion of the HBN first occurs at low pressures and then, a sudden, extensive re-arrangement of hydrogen bonds at the corresponding transformation pressure follows. Interestingly, the I$h$-to-HDA and LDA-to-HDA transformations occur when LDA and I$h$ have similar local order, as quantified by the site-averaged LOMs. Since I$h$ has a perfect tetrahedral HBN, while LDA does not, it follows that higher pressures are needed to transform I$h$ into HDA than that for the conversion of LDA to HDA. In correspondence with both first-order-like phase transitions, the samples are composed of a large HDA cluster that percolates within the I$h$/LDA samples. △ Less

Submitted 7 May, 2018; originally announced May 2018.

Journal ref: Phys. Rev. Materials 2, 075601 (2018)

Root-Growth of Boron Nitride Nanotubes: Experiments and \textit{Ab Initio} Simulations

Authors: Biswajit Santra, Hsin-Yu Ko, Yao-Wen Yeh, Fausto Martelli, Igor Kaganovich, Yevgeny Raitses, Roberto Car

Abstract: We have synthesized boron nitride nanotubes (BNNTs) in an arc in presence of boron and nitrogen species only, without transition metals. We find that BNNTs are often attached to pure boron nanoparticles, suggesting that root-growth is a likely mechanism for their formation. To gain further insight into this process we have studied key mechanisms for root growth of BNNTs on the surface of a liquid… ▽ More We have synthesized boron nitride nanotubes (BNNTs) in an arc in presence of boron and nitrogen species only, without transition metals. We find that BNNTs are often attached to pure boron nanoparticles, suggesting that root-growth is a likely mechanism for their formation. To gain further insight into this process we have studied key mechanisms for root growth of BNNTs on the surface of a liquid boron droplet by ab initio molecular dynamics simulations. We find that nitrogen atoms reside predominantly on the droplet surface where they organize to form boron nitride islands below 2400 K. To minimize contact with the liquid particle underneath, the islands assume non-planar configurations that are likely precursors for the thermal nucleation of cap structures. Once formed, the caps are stable and can easily incorporate nitrogen and boron atoms at their base, resulting in further growth. Our simulations support the root-growth mechanism of BNNTs and provide comprehensive evidence of the active role played by liquid boron. △ Less

Submitted 6 September, 2018; v1 submitted 30 March, 2018; originally announced March 2018.

Comments: supporting inofrmation inlcuded

Reliable and Practical Computational Prediction of Molecular Crystal Polymorphs

Authors: Johannes Hoja, Hsin-Yu Ko, Marcus A. Neumann, Roberto Car, Robert A. DiStasio Jr., Alexandre Tkatchenko

Abstract: The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications in the design and formulation of pharmaceuticals. In this case, detailed knowledge of the polymorphic energy landscape for an active pharmaceutical ingredient… ▽ More The ability to reliably predict the structures and stabilities of a molecular crystal and its polymorphs without any prior experimental information would be an invaluable tool for a number of fields, with specific and immediate applications in the design and formulation of pharmaceuticals. In this case, detailed knowledge of the polymorphic energy landscape for an active pharmaceutical ingredient yields profound insight regarding the existence and likelihood of late-appearing polymorphs. However, the computational prediction of the structures and stabilities of molecular crystal polymorphs is particularly challenging due to the high dimensionality of conformational and crystallographic space accompanied by the need for relative (free) energies to within $\approx$ 1 kJ/mol per molecule. In this work, we combine the most successful crystal structure sampling strategy with the most accurate energy ranking strategy of the latest blind test of organic crystal structure prediction (CSP), organized by the Cambridge Crystallographic Data Centre (CCDC). Our final energy ranking is based on first-principles density functional theory (DFT) calculations that include three key physical contributions: (i) a sophisticated treatment of Pauli exchange-repulsion and electron correlation effects with hybrid functionals, (ii) inclusion of many-body van der Waals dispersion interactions, and (iii) account of vibrational free energies. In doing so, this combined approach has an optimal success rate in producing the crystal structures corresponding to the five blind-test molecules. With this practical approach, we demonstrate the feasibility of obtaining reliable structures and stabilities for molecular crystals of pharmaceutical importance, paving the way towards an enhanced fundamental understanding of polymorphic energy landscapes and routine industrial application of molecular CSP methods. △ Less

Submitted 20 March, 2018; originally announced March 2018.

Journal ref: Sci. Adv. 5, eaau3338 (2019)

DeePCG: constructing coarse-grained models via deep neural networks

Authors: Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, Weinan E

Abstract: We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- and/or three-body contributions. The scheme, called Deep Coarse-Grained Potential (abbreviated DeePCG), exploits a carefully crafted neural network to construct a many-body coarse-grained potential. The network is trained with full atomistic data in… ▽ More We introduce a general framework for constructing coarse-grained potential models without ad hoc approximations such as limiting the potential to two- and/or three-body contributions. The scheme, called Deep Coarse-Grained Potential (abbreviated DeePCG), exploits a carefully crafted neural network to construct a many-body coarse-grained potential. The network is trained with full atomistic data in a way that preserves the natural symmetries of the system. The resulting model is very accurate and can be used to sample the configurations of the coarse-grained variables in a much faster way than with the original atomistic model. As an application we consider liquid water and use the oxygen coordinates as the coarse-grained variables, starting from a full atomistic simulation of this system at the ab-initio molecular dynamics level. We found that the two-body, three-body and higher order oxygen correlation functions produced by the coarse-grained and full atomistic models agree very well with each other, illustrating the effectiveness of the DeePCG model on a rather challenging task. △ Less

Submitted 8 June, 2018; v1 submitted 23 February, 2018; originally announced February 2018.

Why does hydronium diffuse faster than hydroxide in liquid water?

Authors: Mohan Chen, Lixin Zheng, Biswajit Santra, Hsin-Yu Ko, Robert A. DiStasio Jr., Michael L. Klein, Roberto Car, Xifan Wu

Abstract: Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid-base chemistry, certain enzyme reactions, and even infection by the flu. Despite two-centuries of investigation, the mechanism underlying why hydronium diffuses faster than hydroxide in water is still not well understood. Herein, we employ state of the art Density Functional Theory based molecular dynamics,… ▽ More Proton transfer via hydronium and hydroxide ions in water is ubiquitous. It underlies acid-base chemistry, certain enzyme reactions, and even infection by the flu. Despite two-centuries of investigation, the mechanism underlying why hydronium diffuses faster than hydroxide in water is still not well understood. Herein, we employ state of the art Density Functional Theory based molecular dynamics, with corrections for nonlocal van der Waals interactions, and self-interaction in the electronic ground state, to model water and the hydrated water ions. At this level of theory, structural diffusion of hydronium preserves the previously recognized concerted behavior. However, by contrast, proton transfer via hydroxide is dominated by stepwise events, arising from a stabilized hyper-coordination solvation structure that discourages proton transfer. Specifically, the latter exhibits non-planar geometry, which agrees with neutron scattering results. Asymmetry in the temporal correlation of proton transfer enables hydronium to diffuse faster than hydroxide. △ Less

Submitted 23 January, 2018; originally announced January 2018.

Comments: accepted by Nature Chemistry, more information will be updated once published

Journal ref: Nature Chemistry 10, 413-419 (2018)

Ab initio theory and modeling of water

Authors: Mohan Chen, Hsin-Yu Ko, Richard C. Remsing, Marcos F. Calegari Andrade, Biswajit Santra, Zhaoru Sun, Annabella Selloni, Roberto Car, Michael L. Klein, John P. Perdew, Xifan Wu

Abstract: Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der… ▽ More Water is of the utmost importance for life and technology. However, a genuinely predictive ab initio model of water has eluded scientists. We demonstrate that a fully ab initio approach, relying on the strongly constrained and appropriately normed (SCAN) density functional, provides such a description of water. SCAN accurately describes the balance among covalent bonds, hydrogen bonds, and van der Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice I{\it h} at ambient conditions, as well as many important structural, electronic, and dynamic properties of liquid water. These successful predictions of the versatile SCAN functional open the gates to study complex processes in aqueous phase chemistry and the interactions of water with other materials in an efficient, accurate, and predictive, ab initio manner. △ Less

Submitted 29 September, 2017; originally announced September 2017.

Journal ref: Proc. Natl. Acad. Sci., 114, 10846 (2017)

Deep Potential Molecular Dynamics: a scalable model with the accuracy of quantum mechanics

Authors: Linfeng Zhang, Jiequn Han, Han Wang, Roberto Car, Weinan E

Abstract: We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components asi… ▽ More We introduce a scheme for molecular simulations, the Deep Potential Molecular Dynamics (DeePMD) method, based on a many-body potential and interatomic forces generated by a carefully crafted deep neural network trained with ab initio data. The neural network model preserves all the natural symmetries in the problem. It is "first principle-based" in the sense that there are no ad hoc components aside from the network model. We show that the proposed scheme provides an efficient and accurate protocol in a variety of systems, including bulk materials and molecules. In all these cases, DeePMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size. △ Less

Submitted 11 December, 2017; v1 submitted 29 July, 2017; originally announced July 2017.

Journal ref: Phys. Rev. Lett. 120, 143001 (2018)

Deep Potential: a general representation of a many-body potential energy surface

Authors: Jiequn Han, Linfeng Zhang, Roberto Car, Weinan E

Abstract: We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems.… ▽ More We present a simple, yet general, end-to-end deep neural network representation of the potential energy surface for atomic and molecular systems. This methodology, which we call Deep Potential, is "first-principle" based, in the sense that no ad hoc approximations or empirical fitting functions are required. The neural network structure naturally respects the underlying symmetries of the systems. When tested on a wide variety of examples, Deep Potential is able to reproduce the original model, whether empirical or quantum mechanics based, within chemical accuracy. The computational cost of this new model is not substantially larger than that of empirical force fields. In addition, the method has promising scalability properties. This brings us one step closer to being able to carry out molecular simulations with accuracy comparable to that of quantum mechanics models and computational cost comparable to that of empirical potentials. △ Less

Submitted 29 July, 2017; v1 submitted 5 July, 2017; originally announced July 2017.

Journal ref: Commun. Comput. Phys., 23 (2018), pp. 629-639

Migration of a Carbon Adatom on a Charged Single-Walled Carbon Nanotube

Authors: Longtao Han, Predrag Krstic, Igor Kaganovich, Roberto Car

Abstract: We find that negative charges on an armchair single-walled carbon nanotube (SWCNT) can significantly enhance the migration of a carbon adatom on the external surfaces of SWCNTs, along the direction of the tube axis. Nanotube charging results in stronger binding of adatoms to SWCNTs and consequent longer lifetimes of adatoms before desorption, which in turn increases their migration distance severa… ▽ More We find that negative charges on an armchair single-walled carbon nanotube (SWCNT) can significantly enhance the migration of a carbon adatom on the external surfaces of SWCNTs, along the direction of the tube axis. Nanotube charging results in stronger binding of adatoms to SWCNTs and consequent longer lifetimes of adatoms before desorption, which in turn increases their migration distance several orders of magnitude. These results support the hypothesis of diffusion enhanced SWCNT growth in the volume of arc plasma. This process could enhance effective carbon flux to the metal catalyst. △ Less

Submitted 13 March, 2017; originally announced March 2017.

Journal ref: Carbon,116 (2017) 174-180

In situ Characterization of Nanoparticles Using Rayleigh Scattering

Authors: Biswajit Santra, Mikhail N. Shneider, Roberto Car

Abstract: We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the… ▽ More We report a theoretical analysis showing that Rayleigh scattering could be used to monitor the growth of nanoparticles under arc discharge conditions. We compute the Rayleigh scattering cross sections of the nanoparticles by combining light scattering theory for gas-particle mixtures with calculations of the dynamic electronic polarizability of the nanoparticles. We find that the resolution of the Rayleigh scattering probe is adequate to detect nanoparticles as small as C60 at the expected concentrations of synthesis conditions in the arc periphery. Larger asymmetric nanoparticles would yield brighter signals, making possible to follow the evolution of the growing nanoparticle population from the evolution of the scattered intensity. Observable spectral features include characteristic resonant behaviour, shape-dependent depolarization ratio, and mass-dependent line shape. Direct observation of nanoparticles in the early stages of growth with unobtrusive laser probes should give insight on the particle formation mechanisms and may lead to better-controlled synthesis protocols. △ Less

Submitted 27 February, 2017; originally announced February 2017.

Journal ref: Scientific Reports 7, 40230 (2017)

A well-scaling natural orbital theory

Authors: Ralph Gebauer, Morrel H. Cohen, Roberto Car

Abstract: We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latt… ▽ More We introduce an energy functional for ground-state electronic structure calculations. Its variables are the natural spin-orbitals of singlet many-body wave functions and their joint occupation probabilities deriving from controlled approximations to the two-particle density matrix that yield algebraic scaling in general, and Hartree-Fock scaling in its seniority-zero version. Results from the latter version for small molecular systems are compared with those of highly accurate quantum-chemical computations. The energies lie above full configuration interaction calculations, close to doubly occupied configuration interaction calculations. Their accuracy is considerably greater than that obtained from current density-functional theory approximations and from current functionals of the one-particle density matrix. △ Less

Submitted 26 November, 2016; originally announced November 2016.

Comments: http://www.pnas.org/cgi/doi/10.1073/pnas.1615729113. arXiv admin note: text overlap with arXiv:1309.3929

Journal ref: Proceedings of the National Academy of Sciences of the United States of America, vol. 113, no. 46, pp. 12913-12918 (2016)

A local order metric for condensed phase environments

Authors: Fausto Martelli, Hsin-Yu Ko, Erdal C. Oguz, Roberto Car

Abstract: We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and t… ▽ More We introduce a local order metric (LOM) that measures the degree of order in the neighborhood of an atomic or molecular site in a condensed medium. The LOM maximizes the overlap between the spatial distribution of sites belonging to that neighborhood and the corresponding distribution in a suitable reference system. The LOM takes a value tending to zero for completely disordered environments and tending to one for environments that match perfectly the reference. The site averaged LOM and its standard deviation define two scalar order parameters, $S$ and $δS$, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that $S$, $δS$ and the LOM provide very insightful information in the study of structural transformations, such as those occurring when ice spontaneously nucleates from supercooled water or when a supercooled water sample becomes amorphous upon progressive cooling. △ Less

Submitted 11 September, 2016; originally announced September 2016.

Journal ref: Phys. Rev. B 97, 064105 (2018)

Performance of a Nonempirical Density Functional on Molecules and Hydrogen-Bonded Complexes

Authors: Yuxiang Mo, Guocai Tian, Roberto Car, Viktor N. Staroverov, Gustavo E. Scuseria, Jianmin Tao

Abstract: Recently, Tao and Mo (TM) derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinitie… ▽ More Recently, Tao and Mo (TM) derived a meta-generalized gradient approximation functional based on a model exchange-correlation hole. In this work, the performance of this functional is assessed on standard test sets, using the 6-311++G(3df,3pd) basis set. These test sets include 223 G3/99 enthalpies of formation, 99 atomization energies, 76 barrier heights, 58 electron affinities, 8 proton affinities, 96 bond lengths, 82 harmonic vibrational frequencies, 10 hydrogen-bonded molecular complexes, and 22 atomic excitation energies. Our calculations show that the TM functional can achieve high accuracy for most properties considered, relative to the LSDA, PBE, and TPSS functionals. In particular, it yields the best accuracy for proton affinities, harmonic vibrational frequencies, hydrogen-bonded dissociation energies and bond lengths, and atomic excitation energies. △ Less

Submitted 15 December, 2016; v1 submitted 18 July, 2016; originally announced July 2016.

Analytical nuclear gradients for the range-separated many-body dispersion model of noncovalent interactions

Authors: Martin A. Blood-Forsythe, Thomas Markovich, Robert A. DiStasio Jr., Roberto Car, Alán Aspuru-Guzik

Abstract: Accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrossetti et al., J. Che… ▽ More Accurate treatment of the long-range electron correlation energy, including van der Waals (vdW) or dispersion interactions, is essential for describing the structure, dynamics, and function of a wide variety of systems. Among the most accurate models for including dispersion into density functional theory (DFT) is the range-separated many-body dispersion (MBD) method [A. Ambrossetti et al., J. Chem. Phys. 140, 18A508 (2014)], in which the correlation energy is modeled at short-range by a semi-local density functional and at long-range by a model system of coupled quantum harmonic oscillators. In this work, we develop analytical gradients of the MBD energy with respect to nuclear coordinates, including all implicit coordinate dependencies arising from the partitioning of the charge density into Hirshfeld effective volumes. To demonstrate the efficiency and accuracy of these MBD gradients for geometry optimizations of systems with intermolecular and intramolecular interactions, we optimized conformers of the benzene dimer and isolated small peptides with aromatic side-chains. We find excellent agreement with the wavefunction theory reference geometries of these systems (at a fraction of the computational cost) and find that MBD consistently outperforms the popular TS and D3(BJ) dispersion corrections. To demonstrate the performance of the MBD model on a larger system with supramolecular interactions, we optimized the C$_{60}$@C$_{60}$H$_{28}$ buckyball catcher host-guest complex. Finally, we find that neglecting the implicit nuclear coordinate dependence arising from the charge density partitioning, as has been done in prior numerical treatments, leads to an unacceptable error in the MBD forces, with relative errors of ~20% (on average) that can extend well beyond 100%. △ Less

Submitted 1 September, 2015; originally announced September 2015.

Comments: 18 pages including 5 figures; plus 9 pages supplementary information including 5 additional figures

Journal ref: Chem. Sci., 7, (2016) 1712-1728

Local Structure Analysis in $Ab$ $Initio$ Liquid Water

Authors: Biswajit Santra, Robert A. DiStasio Jr., Fausto Martelli, Roberto Car

Abstract: Within the framework of density functional theory, the inclusion of exact exchange and non-local van der Waals/dispersion (vdW) interactions is crucial for predicting a microscopic structure of ambient liquid water that quantitatively agrees with experiment. In this work, we have used the local structure index (LSI) order parameter to analyze the local structure in such highly accurate $ab$… ▽ More Within the framework of density functional theory, the inclusion of exact exchange and non-local van der Waals/dispersion (vdW) interactions is crucial for predicting a microscopic structure of ambient liquid water that quantitatively agrees with experiment. In this work, we have used the local structure index (LSI) order parameter to analyze the local structure in such highly accurate $ab$ $initio$ liquid water. At ambient conditions, the LSI probability distribution, P($I$), was unimodal with most water molecules characterized by more disordered high-density-like local environments. With thermal excitations removed, the resultant bimodal P($I$) in the inherent potential energy surface (IPES) exhibited a 3:1 ratio between high- and low-density-like molecules, with the latter forming small connected clusters amid the predominant population. By considering the spatial correlations and hydrogen bond network topologies $among$ water molecules with the same LSI identities, we demonstrate that the signatures of the experimentally observed low- (LDA) and high-density (HDA) amorphous phases of ice are present in the IPES of ambient liquid water. Analysis of the LSI autocorrelation function uncovered a persistence time of $\sim$ 4 ps---a finding consistent with the fact that natural thermal fluctuations are responsible for transitions between these distinct yet transient local aqueous environments in ambient liquid water. △ Less

Submitted 27 February, 2015; originally announced March 2015.

Comments: 12 pages, 6 figures

Journal ref: Molecular Physics 113, 829 (2015)

The Individual and Collective Effects of Exact Exchange and Dispersion Interactions on the Ab Initio Structure of Liquid Water

Authors: Robert A. DiStasio Jr., Biswajit Santra, Zhaofeng Li, Xifan Wu, Roberto Car

Abstract: In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local vdW/dispersion interactions, via a fully self-consistent den… ▽ More In this work, we report the results of a series of density functional theory (DFT) based ab initio molecular dynamics (AIMD) simulations of ambient liquid water using a hierarchy of exchange-correlation (XC) functionals to investigate the individual and collective effects of exact exchange (Exx), via the PBE0 hybrid functional, non-local vdW/dispersion interactions, via a fully self-consistent density-dependent dispersion correction, and approximate nuclear quantum effects (aNQE), via a 30 K increase in the simulation temperature, on the microscopic structure of liquid water. Based on these AIMD simulations, we found that the collective inclusion of Exx, vdW, and aNQE as resulting from a large-scale AIMD simulation of (H$_2$O)$_{128}$ at the PBE0+vdW level of theory, significantly softens the structure of ambient liquid water and yields an oxygen-oxygen structure factor, $S_{\rm OO}(Q)$, and corresponding oxygen-oxygen radial distribution function, $g_{\rm OO}(r)$, that are now in quantitative agreement with the best available experimental data. This level of agreement between simulation and experiment as demonstrated herein originates from an increase in the relative population of water molecules in the interstitial region between the first and second coordination shells, a collective reorganization in the liquid phase which is facilitated by a weakening of the hydrogen bond strength by the use of the PBE0 hybrid XC functional, coupled with a relative stabilization of the resultant disordered liquid water configurations by the inclusion of non-local vdW/dispersion interactions. △ Less

Submitted 20 May, 2014; originally announced May 2014.

Journal ref: J. Chem. Phys. 141, 084502 (2014)

A favorably-scaling natural-orbital functional theory based on higher-order occupation probabilities

Authors: Ralph Gebauer, Morrel H. Cohen, Roberto Car

Abstract: We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The functional derives from a sequence of controlled approximations to the two-particle density matrix. Algebraic scaling of computational cost with electron number… ▽ More We introduce a novel energy functional for ground-state electronic-structure calculations. Its fundamental variables are the natural spin-orbitals of the implied singlet many-body wave function and their joint occupation probabilities. The functional derives from a sequence of controlled approximations to the two-particle density matrix. Algebraic scaling of computational cost with electron number is obtainable in general, and Hartree-Fock scaling in the seniority-zero version of the theory. Results obtained with the latter version for saturated small molecular systems are compared with those of highly-accurate quantum-chemical computations. The numerical results are variational, capturing most of the correlation energy from equilibrium to dissociation. Their accuracy is considerably greater than that obtainable with current density-functional theory approximations and with current functionals of the one-particle density matrix only. △ Less

Submitted 20 June, 2015; v1 submitted 16 September, 2013; originally announced September 2013.