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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 865 records · Page 48
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Determining the Effects of Zero-Field Splitting and Magnetic Exchange in Dimeric Europium(II) Complexes

Related BAP [BAP = bis(acyl)phosphide] and Acac (Acac = β-diketonate) molecules perform as robust supports for both lanthanide and actinide metals. Here, a molecular bimetallic Eu 2+ complex was successfully targeted and isolated by employing sodium bis(mesitoyl)phosphide [Na( mes BAP)] in a salt metathesis with EuI 2 , producing [Eu( mes BAP) 2 (et 2 o)] 2 (et 2 o = metal-coordinated diethyl ether). The corresponding Acac-Eu 2+ complex was targeted using mes Acac– (1,3-dimesityl-1,3-propanedione), generating [Eu( mes Acac) 2 (et 2 o)] 2 . Both complexes were characterized by single-crystal X-ray diffraction, UV–vis, IR, and NMR spectroscopies, and variable-temperature magnetic susceptibility. [Eu( mes BAP) 2 (et 2 o)] 2 was persistent under anaerobic, anhydrous conditions, whereas the analogous [Eu( mes Acac) 2 (et 2 o)] 2 showed evidence of decomposition under identical conditions. Finally, variable-temperature magnetic susceptibility and magnetization studies of [Eu( mes BAP) 2 (et 2 o)] 2 and [Eu( mes Acac) 2 (et 2 o)] 2 were performed, resulting in similar magnetic exchange coupling values of J ex = –0.018 and –0.023 cm –1 and axial zero-field-splitting D values of –0.38 and –0.51 cm –1 , respectively.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Comparison of Americium(III) and Neodymium(III) Monothiophosphate Complexes

Mixed-donor ligands, such as those containing a combination of O/N or O/S, have been studied extensively for the selective extraction of trivalent actinides, especially Am 3+ and Cm3+, from lanthanides during the recycling of used nuclear fuel. Oxygen/sulfur donor ligand combinations also result from the hydrolytic and/or radiolytic degradation of dithiophosphates, such as the Cyanex® class of extractants, that are initially converted to monothiophosphates. To understand potential differences between the binding of such degraded ligands to Nd 3+ and Am 3+ , the monothiophosphate complexes [M(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- (M 3+ = Nd 3+ , Am 3+ ) were prepared and characterized by single crystal X-ray diffraction and optical spectroscopy and studied as a function of pressure up ca. 14 GPa using diamond-anvil techniques. Although Nd 3+ and Am 3+ have nearly identical eight-coordinated ionic radii, these structures reveal that while the M-O bond distances in these complexes are nearly equal that the M-S distances are statistically different. Moreover, for [Nd(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the hypersensitive 4 I 9/2 → 4 G 5 / 2 transition shifts as a function of pressure by -11 cm -1 /GPa. Whereas for [Am(OPS(OEt) 2 ) 5 (H 2 O) 2 ] 2- , the 7 F 0 → 7 F 6 transition shows a slightly stronger pressure dependence with a shift of -13 cm -1 /GPa and also exhibits broadening of the 5f →5f transitions at high pressures. This data likely indicates an increased involvement of the 5f orbitals in bonding to Am 3+ relative to that of Nd 3+ in these complexes.

38 RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCLEA↗
DOE OSTI2024

“Mn 3 AlN” is Really Mn 4 N

We investigate the synthesis of antiperovskite “Mn 3 AlN” using the published synthesis procedure, as well as several new reaction pathways. In each case, only a combination of antiperovskite Mn 4 N and Mn 5 Al 8 or precursors is obtained. The identity of the obtained antiperovskite phase is unambiguously determined to be Mn4N via synchrotron powder X-ray diffraction (SPXRD), X-ray absorption spectroscopy (XAS), and magnetometry. The experimental results are further supported by thermochemical calculations informed by density functional theory (DFT), which find Mn 3 AlN to be metastable versus decomposition into Mn and AlN. The DFT-based calculations also predict an antiferromagnetic ground state for Mn3AlN. This directly contradicts the previously reported ferromagnetic behavior of "Mn 3 AlN". Instead, the observed magnetic behavior is consistent with ferrimagnetic Mn 4 N. We examine the data in the original publication and conclude that the compound reported to be Mn 3 AlN is in fact Mn 4 N.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2024

Rhenium-Sulfido and -Dithiolato Corroles: Reflections on Chalcophilicity

The high-temperature (~180 °C) reaction between free-base meso-triarylcorroles and Re 2 (CO) 10 , followed by exposure to PCl 3 and thiols (or elemental sulfur), affords rhenium-sulfido (ReS) corroles in 67-76% yields. The use of shorter reaction times, lower temperatures (~130 °C), and a dithiol (e.g., ethane-1,2-dithiol) also allows the isolation of rhenium-dithiolato corroles, presumptive intermediates on the path to ReS corroles. The ReS corroles exhibit high thermal stability and two reversible oxidations and reductions in their cyclic voltammograms, with redox potentials nearly identical to those observed for analogous ReO corroles. The electrochemical HOMO-LUMO gaps of the complexes, at 2.2 eV, are consistent with ligand-centered oxidation and reduction. The UV-vis spectra of ReS corroles, on the other hand, differ significantly from those of their ReO counterparts. Scalar-relativistic DFT calculations suggest that this difference reflects low-energy LUMO+2 and LUMO+3 levels, consisting of Re-S π-antibonding interactions; the ReO corroles, in contrast, exhibit a larger LUMO+1/LUMO+2 gap, as expected for a relatively classical Gouterman-type metalloporphyrin analogue. The high stability of ReS corroles is consistent with geochemists' view of rhenium as a moderately chalcophilic element (i.e., one that partitions into sulfide melts) as well as with a recent quantitative analysis of thiophilicity, which indicates that rhenium's oxophilicity and thiophilicity are essentially evenly balanced.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

Small-Molecule Models of Hydrogen-Evolving MX 2 (M = Mo, W; X = S, Se) Bulk Solids: Composition–Activity Relationships

Triangular metal chalcogenide clusters of the form [M 3 Q 7 L 3 ]An (M = Mo or W; Q = S or Se; L = i Bu 2 NCS 2 – , (CF 3 CH 2 ) 2 NCS 2 – , i Bu 2 NCSe 2 – , or i Bu 2 PS 2 – ; An = Cl – or I – ) have been investigated as molecular analogues of layered metal dichalcogenide (MX 2 ) H 2 -evolution catalysts. These clusters have been evaluated for their relative H 2 -evolving ability under a common photolysis protocol implementing [Ru(bpy) 3 ] 2+ as chromophore and Et 3 N as sacrificial electron donor. With M constant as Mo and with constant supporting ligand, clusters with an all-sulfide core enable greater H 2 -TON than clusters with an all-selenide core. A more active catalyst is produced by [Mo 3 S 7 (S 2 CN i Bu 2 ) 3 ] + I – than its W 3 analogue with the same core sulfide composition and supporting dithiocarbamate ligands. Dichalcogenocarbamate ligands provide more active catalysts than dialkyldithiophosphate ligated clusters, and within the dichalcogenocarbamate set, greater H 2 -turnovers correlate with more-electron-donating ligands (i.e., i Bu 2 NCS 2 – > (CF 3 CH 2 ) 2 NCS 2 – > i Bu 2 NCSe 2 – ). Cluster cations with Cl – as counteranion are very similar in activity H 2 -evolving levels to identical clusters with I – , ruling out any significant interfering effect by I – upon the electron transfer relay between Et 3 N and catalyst. In the aggregate, observations are consistent with a mechanism for H 2 evolution that involves reductive extrusion of H 2 from a metal hydride intermediate.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

X-ray Spectroscopy Characterization of Electronic Structure and Metal–Metal Bonding in Dicobalt Complexes

Developing multimetallic complexes with tunable metal–metal interactions has long been a target of synthetic inorganic chemistry efforts due to the unique properties that such compounds can exhibit. However, understanding relationships between metal–metal bonding and chemical properties is challenging due to system-dependent factors that influence metal–metal and metal–ligand interactions, including ligand identity, coordination geometry, and metal–metal distance. In this work, we apply X-ray absorption and emission spectroscopy and quantum chemical calculations to describe electronic structure and bonding in a series of dicobalt complexes. The compounds with silane ligands and pseudo-octahedral coordination geometry exhibit Co–Co σ and multicentered bonding character, which we characterize from both the occupied and vacant perspectives via their contributions to the Co X-ray emission and absorption spectra, respectively. In contrast, the dicobalt complexes with a pseudotetrahedral coordination environment do not exhibit Co–Co bonding due to symmetry constraints on orbital overlap. We extend these insights to the theoretical evaluation of related dicobalt complexes to explain how ligand coordination and symmetry dictate the presence or absence of a Co–Co bond. In conclusion, this work highlights how fundamental insights into electronic structure and bonding through X-ray spectroscopy uncover important factors governing metal–metal interactions and guide the rational design of multimetallic complexes with tunable metal–metal bonds.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2025

A Note to Reviewers Suggesting Post-reaction Catalyst Characterization: Know What You’re Asking For

Here, we highlight examples of post-reaction characterization in thermo- and electrocatalysis to present the challenges in obtaining reliable data to answer specific questions about the true identity of the active site and/or catalyst deactivation/degradation. We use this editorial to suggest to reviewers that, when formulating comments to authors that involve materials characterization after reaction testing, they should consider what specific, meaningful information can be attained or what targeted question can be answered that adds value to the individual paper and to the field in general, and how to reasonably obtain that data. In contrast, reviewers should avoid vague, open-ended comments that suggest unguided post-reaction characterization that would not add significant value to the report and, similarly, avoid comments that are substantial enough that they could form the basis of an entirely separate report.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Triel-Defined Helicity in One-Dimensional III–VI–VII van der Waals Crystals

Inorganic extended lattice solids that bear complex helical motifs manifest unusual physical and quantum states that arise due to their noncentrosymmetric or chiral nature. However, the systematic understanding of how elemental composition influences the structure and physical properties in helical inorganic crystals has been precluded by the rarity of these materials and the lack of modular phases that display such motifs. Here, we report the synthesis of AlSeI single crystals, the first aluminum-containing helical crystal in the III-VI-VII 1D van der Waals class. AlSeI completes the experimentally accessible triel series in the helical selene iodides alongside InSeI and GaSeI. Using the Al, Ga, and In triel series in this selene iodide class, we experimentally demonstrate the evolution of the local quasi-tetrahedral building unit geometry, chain packing, helical parameters, and band gaps based primarily on the identity of the triel atom. Our results underscore the chemical modularity of these phases, the broad range of helical parameters, and the spectrum of electronic states from the visible to the ultraviolet range in this emergent class of 1D, exfoliable, and helical extended lattice solids.

Chemical structure↗
DOE OSTI2025

Solving the “Coloring Problem” in InPd 3– x Ag x ( x = 0–0.7) by Phase Diagrams Modeling and Diffraction Experiments

Here, a series of InPd 3–x Ag x (x = 0–1) compositions were synthesized by conventional high-temperature synthesis, and as-synthesized samples were characterized by powder X-ray diffraction experiments. Up to x = 0.7, InPd 3–x Ag x adopts the ternary substitutional variant of the InPd 3 structure (TiAl 3 -type), when x > 0.7, elemental Ag starts to segregate along with the main phase. Accurate structural characterization in InPd 3–x Ag x faces a critical challenge due to the narrow X-ray scattering contrast among constituents In, Pd, and Ag and nearly identical neutron scattering lengths of Pd and Ag. To overcome this “coloring problem”, a combination of calculation of phase diagrams modeling (CALPHAD) and diffraction techniques (X-ray and neutron) was employed. In the compositional range 0 ≤ x ≤ 0.7, InPd 3–x Ag x presents a ternary variant of the TiAl 3 -type structure, where Ag atoms selectively substitute one (the 2b Wyckoff site) of the two Pd sites in InPd 3 . Notably, in contrast to the isologous InPd 3–x Cu x (x = 0–1) system, Ag substitution does not form an ordered VRh 2 Sn-type structure at the limiting composition. The distinct site preference in InPd 3–x Ag x is elucidated by charge population analysis, electronic structure calculations, and orbital-resolved chemical bonding investigations, and the extent of substitution is supported by formation free energy calculations.

36 MATERIALS SCIENCE↗
DOE OSTI2026

Effects of He-Ion Radiation on Solid-State Uranyl Nitrate Compounds under Dry and Hydrated Atmospheric Conditions

Radioactive decay of uranium (U) and its related daughter/fission products emit ionizing radiation, including γ (γ) rays and α (α) particles, that result in the formation of radical species and induce chemical reactivity in materials. While radioactivity is inherent to the chemistry of U there are limited studies that detail changes at an atomistic level. Here, this work describes the He-ion radiolysis of four solid-state U(VI) species: [UO 2 (NO 3 ) 2 ]·3(H 2 O) and M[UO 2 (NO 3 ) 3 ] (M = K + , Rb + , Cs + ). These materials were irradiated under different conditions (i.e. closed, open – Ar gas, or open – H 2 O-saturated Ar gas) to further evaluate the impact of water radiolysis on the chemical modification of these materials. Pre- and post-irradiation analyses were conducted using EPR, Raman, and ATR-IR spectroscopy on materials irradiated to 0, 5, 10, and 25 MGy. The results indicated the presence of nitrate radical (NO 3 • ) formation in all solid-state materials with similarities to those observed in γ-radiation studies. Irradiation of [UO 2 (NO 3 ) 2 ]·3(H 2 O) did not show evidence of reactive oxygen species bound to the U(VI) cation under inert conditions; however, surface reactivity was observed for samples irradiated in the H 2 O-saturated environment. Similar chemical changes were observed in the uranyl trinitrato compounds irradiated in the presence of H 2 O vapor and there were observed differences in the reactivity depending on the identity of the alkali cation.

38 - RADIATION CHEMISTRY, RADIOCHEMISTRY, AND NUCL↗
DOE OSTI2026

From Serendipity to Exploration: Synthesis and Properties of PtSiSb

PtSiSb is a compound with covalent Si–Sb bonds, which are relatively rare instances in solid-state materials. The original report on PtSiSb indicates synthetic challenges for the isolation of single-phase samples, as well as potential discrepancies in the predicted electronic structure and experimental transport properties. In this work, we considered PtSiSb as a case study with the objective of demonstrating the importance of synthesis as a bridge between theoretical predictions and experimental properties. Using guidance from in situ powder X-ray diffraction, the synthesis of single-phase polycrystalline samples was developed, allowing further experimental characterization of transport and catalytic properties. Thermal conductivity and heat capacity demonstrated anomalous behavior, indicating an unconventional phonon scattering mechanism in PtSiSb. Charge transport measurements indicated semimetallic behavior. Hydrogen evolution reaction (HER) tests in acidic electrolyte revealed that the PtSiSb cathode needs an overpotential η 10 = 120 mV to achieve a current density j = −10 mA/cm 2 . This is lower activity than elemental Pt but comparable to known and active transition-metal phosphide HER catalysts, such as CoP, with η 10 = 93 mV when measured at identical conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Tetrel Bond-Mediated Photophysical Modulation and Fluoride Recognition in Carbazole-Organosilanes

Silicon-centered orbitals are typically regarded as electronically inert in donor–acceptor systems. Here, we show that silole-based carbazole–silane architectures can render these orbitals electronically relevant, enabling modulation of excited-state behavior and anion-responsive photophysics. Two carbazole–Dipp–silanes exhibit identical carbazole-localized LE singlet emission in solution yet diverge markedly in the solid state: one compound displays a broad long-wavelength emission band in the prompt spectrum and enhanced long-lived emission consistent with a triplet-derived excited state, likely arising from a combination of intramolecular structural locking and solid-state packing effects, whereas the more flexible analogue remains predominantly LE-emissive. Fluoride coordination further differentiates the two systems, producing ratiometric red-shifted emission in one case and fluorescence quenching in the other through a fully reversible coordination process. These results identify σ*(Si–Ar) orbitals as tunable contributors to excited-state landscapes in organosilane luminophores and suggest a broader design strategy for controlling excited-state behavior in tetrel-based photofunctional systems.

Haque, Md Hasanul↗
DOE OSTI2026

Synthesis and Reactivity of Heteroleptic U 4+ Alkyl, Benzyl, and Hydride Imidophosphorane Complexes

A series of heteroleptic U 4+ benzyl, neopentyl, and methyl complexes supported by the imidophosphorane ligand, [N = P(N,N′-ditert-butylethylenediamide)(diethylamide)] 1− (NP*), were synthesized from the monoiodide precursor, [UI(NP*) 3 ]. These heteroleptic complexes were synthesized through the selective formation of [UI(NP*) 3 ] under transmetalation conditions in the reaction between [UI 4 (1,4-dioxane) 2 ] and K[NP*]. Formation of the homoleptic complex [U(NP*) 4 ] was not observed even in the presence of excess K[NP*]. The oxidation and hydrogenolysis reactivity of the neopentyl complex, [U(Npt)- (NP*) 3 ] (Npt = neopentyl) was explored. While cyclic voltammetry indicates a potentially isolable U5+ alkyl cation, chemical oxidation of the neopentyl complex results in the isolation of a cationic U 4+ complex with a bound diethyl ether in the primary coordination sphere, [U4+(NP*)) 3 (Et 2 O)][(BArF 24 )] (BArF 24 = tetrakis(3,5-bis(trifluoromethyl)phenyl)borate). Notably, hydrogenolysis of [U(Npt)(NP*) 3 ] with H2 gas at −20 °C results in the formation of a terminal hydride intermediate confirmed by in situ NMR spectroscopy and deuterium labeling with D 2 . The connectivity and structural parameters of this hydride intermediate, [UH(NP*) 3 ], which rapidly thermally decomposes to the homoleptic complex, [U(NP*) 4 ], can be confirmed by single-crystal X-ray diffraction studies of a crystal grown by chilling the reaction mixture. The identity of [U(NP*) 4 ] was confirmed by its direct, bulk synthesis from [U(Me)(NP*) 3 ] and HNP* in a protonolysis reaction.

Alkyls↗
DOE OSTI2021

Self-Consistent Field Methods for Excited States in Strong Magnetic Fields: A Comparison Between Energy - and Variance-based Approaches

An efficient implementation of geometrical derivatives at the Hartree–Fock (HF) and current-density functional theory (CDFT) levels is presented for the study of molecular structure in strong magnetic fields. The required integral derivatives are constructed using a hybrid McMurchie–Davidson and Rys quadrature approach, which combines the amenability of the former to the evaluation of derivative integrals with the efficiency of the latter for basis sets with high angular momentum. In addition to its application to evaluating derivatives of four-center integrals, this approach is also applied to gradients using the resolution-of-the-identity approximation, enabling efficient optimization of molecular structure for many-electron systems under a strong magnetic field. The CDFT contributions have been implemented for a wide range of density functionals up to and including the meta-GGA level with current-density dependent contributions and (range-separated) hybrids for the first time. Illustrative applications are presented to the OH and benzene molecules, revealing the rich and complex chemistry induced by the presence of an external magnetic field. Challenges for geometry optimization in strong fields are highlighted, along with the requirement for careful analysis of the resulting electronic structure at each stationary point. The importance of correlation effects is examined by comparison of results at the HF and CDFT levels. The present implementation of molecular gradients at the CDFT level provides a cost-effective approach to the study of molecular structure under strong magnetic fields, opening up many new possibilities for the study of chemistry in this regime.

Comparison↗
DOE OSTI2021

Electronic Structure Theory Calculations Using Modern Architectures: KNL vs Haswell

The time to solution and parallel efficiency of several commonly used electronic structure methods (Hartree–Fock, density functional theory, second order perturbation theory, resolution of the identity second order perturbation theory, coupled cluster) are evaluated on both the Intel Xeon Haswell and the Intel Xeon Phi Knights Landing (KNL) architectures. The Haswell completes the benchmark calculations with a faster time to solution than the KNL for all molecules and methods tested. While the Haswell exhibits an average speedup of at least 3.5 relative to the KNL for all nonthreaded computations, the KNL has a better parallel efficiency than the Haswell with increasing core counts. The architectures are further tested using a more computationally costly coupled cluster method on a transition state reaction. The Haswell appears to be the best choice to minimize the time to solution, though for very large systems and high levels of theory that require memory intensive processes the superior memory hierarchy and larger on node memory of the KNL can make it a better choice. These results are used to showcase aspects of novel architectures that will increase efficiency for quantum chemistry applications.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Molecular Dynamics Driven by the Many-Body Expansion (MBE-MD)

Here, we present a protocol for classical and nuclear quantum dynamics, in which the energies and forces are generated by the many-body expansion (MBE), and apply it to water clusters using the TTM2.1-F and MB-Pol interaction potentials at various temperatures. We carry out MBE-MD classical and nuclear quantum dynamical simulations in which the energies and forces of the full system are approximated by the 2-, 3-, and 4-body terms of the MBE expansion and compare the average potential and the vibrational density of states (VDOS) with the full simulation, i.e., the one for which no MBE is used. Our results indicate that the thermally averaged potential energy from the MBE up to the 4-body term converges with near identical behavior to the one from the full simulation. The 3-body makes a substantial contribution (~20%) to the energy, whereas the 4- body is necessary for obtaining quantitatively accurate energetics and forces, albeit making a small contribution to each (~2%). We further show that the harmonic frequencies are reproduced to within a few wavenumbers (cm -1 ) at the 4-body level, and that the slowest modes to converge with the MBE rank are those involving the strongest hydrogen bonds. Anharmonicity exacerbates this effect, so that a 4-body description of the energies and forces is needed to achieve accurate anharmonic vibrational frequencies in the hydrogen-bonded OH-stretching region. We also discuss the asymptotic scaling of the MBE-MD protocol with respect to the cost of the underlying potential energy evaluation, suggesting that electronic structure methods that scale at least as N 4 ,N being the size of the system, are needed to result in savings over the traditional full MD simulation. We anticipate that MBE-MD protocol can evolve into a powerful and practical method, which will allow for highly accurate ab initio MD simulations on a much broader range of molecular systems than can be currently handled.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Stochastic Real-Time Second-Order Green’s Function Theory for Neutral Excitations in Molecules and Nanostructures

We present a real-time second-order Green’s function (GF) method for computing excited states in molecules and nanostructures, with a computational scaling of O(N e 3 ), where N e is the number of electrons. The cubic scaling is achieved by adopting the stochastic resolution of the identity to decouple the 4-index electron repulsion integrals. To improve the time propagation and the spectral resolution, we adopt the dynamic mode decomposition technique and assess the accuracy and efficiency of the combined approach for a chain of hydrogen dimer molecules of different lengths. We find that the stochastic implementation accurately reproduces the deterministic results for the electronic dynamics and excitation energies. Furthermore, we provide a detailed analysis of the statistical errors, bias, and long-time extrapolation. Overall, the approach offers an efficient route to investigate excited states in extended systems with open or closed boundary conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables

The typically rugged nature of molecular free energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for data-driven discovery of CVs parameterizing the important large scale motions of the system. A challenge to CV discovery is learning CVs invariant to symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multi-molecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate Permutation Invariant Vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation, and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand sampling of configurational phase space and obtain converged CVs and free energy landscapes. Here, we demonstrate the Permutationally Invariant Network for Enhanced Sampling (PINES) approach in applications to the self-assembly of a 13-atom Argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C 45 H 92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗