Showing papers by "Roberto Car published in 2018"

Deep Potential Molecular Dynamics: A Scalable Model with the Accuracy of Quantum Mechanics

Abstract: We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) 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-principles 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, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

Deep Potential Molecular Dynamics: a Scalable Model with the Accuracy of Quantum Mechanics

Abstract: We introduce a scheme for molecular simulations, the deep potential molecular dynamics (DPMD) 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-principles 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, DPMD gives results that are essentially indistinguishable from the original data, at a cost that scales linearly with system size.

Hydroxide diffuses slower than hydronium in water because its solvated structure inhibits correlated proton transfer.

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 hydroxide diffuses slower than hydronium in water is still not well understood. Herein, we employ state-of-the-art density-functional-theory-based molecular dynamics-with corrections for non-local van der Waals interactions, and self-interaction in the electronic ground state-to model water and hydrated water ions. At this level of theory, we show that structural diffusion of hydronium preserves the previously recognized concerted behaviour. However, by contrast, proton transfer via hydroxide is less temporally correlated, due to a stabilized hypercoordination 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 leads to hydroxide diffusing slower than hydronium.

DeePCG: Constructing coarse-grained models via deep neural networks

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 the 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 find 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.

Ab initio theory and modeling of water

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 Waals interactions that dictates the structure and dynamics of liquid water. Notably, SCAN captures the density difference between water and ice Ih 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.

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

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 and Al-Mg alloys demonstrates that DP-GEN can produce uniformly accurate PES models with a minimal number of reference data.

Why does hydronium diffuse faster than hydroxide in liquid water

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, 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.

From Colossal to Zero: Controlling the Anomalous Hall Effect in Magnetic Heusler Compounds via Berry Curvature Design

Abstract: By engineering the Berry curvature in a Heusler magnet, it is possible to tune the anomalous Hall conductivity without affecting the material's magnetization.

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

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 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.

Reliable and Practical Computational Prediction of Molecular Crystal Polymorphs

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 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.

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

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 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.

Prediction of a magnetic Weyl semimetal without spin-orbit coupling and strong anomalous Hall effect in the Heusler compensated ferrimagnet Ti2MnAl

Abstract: We predict a magnetic Weyl semimetal in the inverse Heusler Ti2MnAl, a compensated ferrimagnet with a vanishing net magnetic moment and a Curie temperature of over 650 K. Despite the vanishing net magnetic moment, we calculate a large intrinsic anomalous Hall effect (AHE) of about 300 S/cm. It derives from the Berry curvature distribution of the Weyl points, which are only 14 meV away from the Fermi level and isolated from trivial bands. Different from antiferromagnets Mn3X (X = Ge, Sn, Ga, Ir, Rh, and Pt), where the AHE originates from the noncollinear magnetic structure, the AHE in Ti2MnAl stems directly from the Weyl points and is topologically protected. The large anomalous Hall conductivity (AHC) together with a low charge carrier concentration should give rise to a large anomalous Hall angle. In contrast to the Co-based ferromagnetic Heusler compounds, the Weyl nodes in Ti2MnAl do not derive from nodal lines due to the lack of mirror symmetries in the inverse Heusler structure. Since the magnetic structure breaks spin-rotation symmetry, the Weyl nodes are stable without SOC. Moreover, because of the large separation between Weyl points of opposite topological charge, the Fermi arcs extent up to 75% of the reciprocal lattice vectors in length. This makes Ti2MnAl an excellent candidate for the comprehensive study of magneticWeyl semimetals. It is the first example of a material withWeyl points, large anomalous Hall effect, and angle despite a vanishing net magnetic moment.

Structure, Polarization, and Sum Frequency Generation Spectrum of Interfacial Water on Anatase TiO2

Abstract: The photocatalytic activity of TiO2 for water splitting has been known for decades, yet the adsorption structure and hydrogen bonding of water at the interface with TiO2 have remained controversial. We investigate the prototypical aqueous interface with anatase TiO2 (101) using ab initio molecular dynamics (AIMD) with the strongly constrained and appropriately normed (SCAN) density functional, recently shown to provide an excellent description of the properties of bulk liquid water. We find that water forms a stable bilayer of intact molecules with ice-like dynamics and enhanced dipole moment and polarizability on the anatase surface. The orientational order and H-bond environment of interfacial water are reflected in the computed sum frequency generation (SFG) spectrum, which agrees well with recent measurements in the OH stretching frequency range (3000–3600 cm–1). Additional AIMD simulations for a model interface with 66% of dissociated water in the contact layer show that surface hydroxyls disrupt the...

Local-order metric for condensed-phase environments

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 tending to one for environments that perfectly match the reference. The site-averaged LOM and its standard deviation define two scalar order parameters, $S$ and $\ensuremath{\delta}S$, that characterize with excellent resolution crystals, liquids, and amorphous materials. We show with molecular dynamics simulations that $S$, $\ensuremath{\delta}S$, 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.

Searching for crystal-ice domains in amorphous ices

Abstract: We employ classical molecular dynamics simulations to investigate the molecular-level structure of water during the isothermal compression of hexagonal ice ($\mathrm{I}h$) 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) [F. Martelli et al., Phys. Rev. B 97, 064105 (2018)] that can discriminate among different crystalline and noncrystalline 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 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 differs 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 $\mathrm{I}h$-to-ice-IV pressure-induced transformation. Both nonequilibrium LDA-to-HDA and $\mathrm{I}h$-to-HDA transformations are two-step processes where a small distortion of the HBN first occurs at low pressures and then, a sudden, extensive rearrangement of hydrogen bonds at the corresponding transformation pressure follows. Interestingly, the $\mathrm{I}h$-to-HDA and LDA-to-HDA transformations occur when LDA and $\mathrm{I}h$ have similar local order, as quantified by the site-averaged LOMs. Since $\mathrm{I}h$ has a perfect tetrahedral HBN while LDA does not, it follows that higher pressures are needed to transform $\mathrm{I}h$ 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 $\mathrm{I}h/\mathrm{LDA}$ samples. Our results shed light on the debated structural properties of amorphous ices and indicate that the kinetics of the $\mathrm{I}h$-to-HDA and LDA-to-HDA transformations require an in-depth inspection of the underlying HBN. Such investigation is currently ongoing.

DeePCG: constructing coarse-grained models via deep neural networks

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 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.

Thermal expansion in dispersion-bound molecular crystals

Abstract: We explore how anharmonicity, nuclear quantum effects (NQE), many-body dispersion interactions, and Pauli repulsion influence thermal properties of dispersion-bound molecular crystals. Accounting for anharmonicity with ab initio molecular dynamics yields cell parameters accurate to within $2%$ of experiment for a set of pyridinelike molecular crystals at finite temperatures and pressures. From the experimental thermal expansion curve, we find that pyridine-I has a Debye temperature just above its melting point, indicating sizable NQE across the entire crystalline range of stability. We find that NQE lead to a substantial volume increase in pyridine-I $(\ensuremath{\approx}40$% more than classical thermal expansion at 153 K) and attribute this to intermolecular Pauli repulsion promoted by intramolecular quantum fluctuations. When predicting delicate properties such as the thermal expansivity, we show that many-body dispersion interactions and more sophisticated density functional approximations improve the accuracy of the theoretical model.

Root-growth of boron nitride nanotubes: experiments and ab initio simulations.

Abstract: We have synthesized boron nitride nanotubes (BNNTs) in an arc in the presence of boron and nitrogen species. We find that BNNTs are often attached to large nanoparticles, suggesting that root-growth is a likely mechanism for their formation. Moreover, the tube-end nanoparticles are composed of boron, without transition metals, indicating that transition metals are not necessary for the arc synthesis of BNNTs. 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.

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

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 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.

Occupation probabilities as variables in electronic structure theory: cooper pairing, OP-NSOFT-Cs,t, and the homogeneous electron liquid

Abstract: The energy functional of a novel electronic structure theory, OP-NSOFT, has as variables the natural spin orbitals (NSO) of the trial function and their joint occupation probabilities in the search for the ground state energy. When occupancy is restricted to the spin-paired NSOs of DOCI, the resulting theory, OP-NSOFT-0, scales as M3, with M the size of the one-electron basis set. Accurate results were obtained for small molecules, particularly near dissociation where single reference theories like DFT are inaccurate. The homogeneous electron liquid (HEL) could serve as a test bed of OP-NSOFT for condensed systems, but OP-NSOFT-0 reduces to the Hartree–Fock approximation for the HEL. Cooper pairing is introduced instead, both singlet pairing, OP-NOFT-Cs, and fully polarized triplet pairing, OP-NSOFT-Ct. The former yields 1/3 of the diffusion-Monte-Carlo correlation energy, the latter 1/2 to 1/3 with decreasing electron density for rs values between 1 and 10. Both yield the discontinuity in the single-particle occupation number required by the Luttinger theorem. Two-state joint occupation probabilities illustrate the importance of electron–electron small-angle scattering in establishing electron correlation in the unpolarized HEL.

Monte Carlo Renormalization Group for Systems with Quenched Disorder

Abstract: We extend to quenched disordered systems the variational scheme for real space renormalization group calculations that we recently introduced for homogeneous spin Hamiltonians. When disorder is present our approach gives access to the flow of the renormalized Hamiltonian distribution, from which one can compute the critical exponents if the correlations of the renormalized couplings retain finite range. Key to the variational approach is the bias potential found by minimizing a convex functional in statistical mechanics. This potential reduces dramatically the Monte Carlo relaxation time in large disordered systems. We demonstrate the method with applications to the two-dimensional dilute Ising model, the random transverse field quantum Ising chain, and the random field Ising in two and three dimensional lattices.

Thermal Expansion in Dispersion-Bound Molecular Crystals

Abstract: We explore how anharmonicity, nuclear quantum effects (NQE), many-body dispersion interactions, and Pauli repulsion influence thermal properties of dispersion-bound molecular crystals. Accounting for anharmonicity with $ab$ $initio$ molecular dynamics yields cell parameters accurate to within 2% of experiment for a set of pyridine-like molecular crystals at finite temperatures and pressures. From the experimental thermal expansion curve, we find that pyridine-I has a Debye temperature just above its melting point, indicating sizable NQE across the entire crystalline range of stability. We find that NQE lead to a substantial volume increase in pyridine-I ($\approx 40$% more than classical thermal expansion at $153$ K) and attribute this to intermolecular Pauli repulsion promoted by intramolecular quantum fluctuations. When predicting delicate properties such as the thermal expansivity, we show that many-body dispersion interactions and sophisticated treatments of Pauli repulsion are needed in dispersion-bound molecular crystals.

Variational Approach to Monte Carlo Renormalization Group

Abstract: We present a Monte Carlo method for computing the renormalized coupling constants and the critical exponents within renormalization theory. The scheme, which derives from a variational principle, overcomes critical slowing down, by means of a bias potential that renders the coarse grained variables uncorrelated. The two-dimensional Ising model is used to illustrate the method.

Searching for crystal-ice domains in amorphous ices

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., 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.