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The field of machine learning potentials has experienced a rapid surge in progress, thanks to advances in machine learning theory, algorithms, and hardware capabilities. While the underlying methods are continuously evolving, the infrastructure for their deployment has lagged. The community, due to these rapid developments, frequently finds itself split into groups built around different implementations of machine-learned potentials. In this work, we introduce IPSuite, a Python-driven software package designed to connect different methods and algorithms from the comprehensive field of machine-learned potentials into a single platform while also providing a collaborative infrastructure, helping ensure reproducibility. Furthermore, the data management infrastructure of the IPSuitecode enables simple model sharing and deployment in simulations. Currently, IPSuitesupports six state-of-the-art machine learning approaches for the fitting of interatomic potentials as well as a variety of methods for the selection of training data, running of ab initiocalculations, learning-on-the-fly strategies, model evaluation, and simulation deployment.

Organometallic complexes are frequently deposited on solid surfaces, but little is known about how the resulting complex–solid interactions alter their properties. Here, a series of complexes of the type Cu(dppf)(Lx)+(dppf = 1,1′-bis(diphenylphosphino)ferrocene, Lx= mono- and bidentate ligands) were synthesized, physisorbed, ion-exchanged, or covalently immobilized on solid surfaces and investigated by 31P MAS NMR spectroscopy. Complexes adsorbed on silica interacted weakly and were stable, while adsorption on acidic γ-Al2O3resulted in slow complex decomposition. Ion exchange into mesoporous Na-[Al]SBA-15 resulted in magnetic inequivalence of 31P nuclei verified by 31P-31P RFDR and 1H-31P FSLG HETCOR. DFT calculations verified that a MeCN ligand dissociates upon ion exchange. Covalent immobilization via organic linkers as well as ion exchange with bidentate ligands both lead to rigidly bound complexes that cause broad 31P CSA tensors. We thus demonstrate how the interactions between complexes and functional surfaces determine and alter the stability of complexes. The applied Cu(dppf)(Lx)+complex family members are identified as suitable solid-state NMR probes for investigating the influence of support surfaces on deposited inorganic complexes.

In molecular heterogeneous catalysis knowledge about the location and accessibility of the immobilized metal complex inside porous solids is important to assess the catalytic efficiency. Here, we developed a method to quantify accessible Rh complexes in SBA-15 mesopores viasolid state NMR spectroscopy. In order to identify suitable probe molecules several phosphines were screened in solution and their diameters were determined by DFT calculations. The ligation of phosphines at immobilized Rh complexes was then monitored by quantitative 31P MAS NMR spectroscopy. For the first time a polymer too large to enter the mesopores, poly(styrene-co-vinyltriphenylphosphine), PS-co-PVPP, was used to probe selectively Rh complexes immobilized on the external surface, in pore mouths or defects. By combining 31P MAS NMR and ICP-OES the P/Rh ratio was determined revealing that only up to 39% of the immobilized Rh complexes were accessible. Therefore, corrected turnover numbers (TONs) of up to 55 could be calculated for the asymmetric 1,2-addition with immobilized Rh catalysts. With the herein presented methodology the accessibility and spatial distribution of immobilized molecular catalysts can for the first time be evaluated quantitatively.

Understanding confinement effects in molecular heterogeneous catalysis is a challenging task. In a combined experimental and theoretical approach, we studied the influence of the type, polarity, pore size and shape of the mesoporous material as well as of the aryl substituent at the diene, spacer type and lengths on asymmetric Rh diene catalysis under confinement. For this purpose, a library of novel chiral Rh norbornadiene complexes was immobilized on ordered mesoporous silica (OMS), ordered mesoporous carbon (OMC) and non-templated mesoporous SiO2materials with different pore sizes viaazide–alkyne 1,3-dipolar click reaction. Among the different materials, Rh complexes immobilized on OMS performed best in the 1,2-addition of aryl boroxines to N-tosyl imines as a benchmark reaction. High yields were achieved when Rh complexes were connected to pore walls by unbranched linkers of medium lengths (dpore= 5.9 nm). Good enantioselectivities were obtained either by linear alkyl linkers in smaller pores (dpore= 4.9 nm) or branched aminoethanol linkers in larger pores (dpore= 6.8 nm). However, the largest confinement effect was caused by the aryl substituent at the diene moiety, giving up to e.r. 99 : 1 for 1-naphthyl. While complementary X-ray absorption experiments (EXAFS, XANES) could not distinguish between triazole and amide carbonyl coordination at Rh, computational studies supported the triazole coordination.

We investigated the field evaporation process of frozen water in atom probe tomography (APT) by density functional simulations. In previous experiments, a strong tailing effect was observed for peaks caused by the molecular structure (H2O)nH+, in contrast to other peaks. In purely field-induced and thermally assisted evaporation simulations, we found that chains of protonated water molecules were pulled out of the dielectric surface by up to 6 Å, which are stable over a wide range of field strengths. Therefore, the resulting water clusters experience only part of the acceleration after evaporation compared to molecules evaporating directly from the surface and, thus, exhibit an energy deficit, which explains the tailing effect. Our simulations provide new insight into the complex evaporation behavior of water in high electrical fields and reveal possibilities for adapting the existing reconstruction algorithms.

A metathesis reaction employing Ag[C(CN)3] and TlBr yielded the expected target compound Tl[C(CN)3] from aqueous solution, but after its structural and Raman-spectroscopic characterization, it became clear rather unexpectedly, that the title compound does not crystallize isotypically to any of the heavy alkali-metal tricyanomethanides. Tl[C(CN)3] adopts the space group R32 with the trigonal cell parameters a= 806.03(6) and c= 709.86(5) pm exhibiting a crystal structure still related to the one of the also trigonally crystallizing compounds A[C(CN)3] (A= Rb and Cs; space group: R3‾c$R\overline{3}c$ ) with doubled c-axes, which display distorted octahedrally coordinated A+cations. In Tl[C(CN)3], the Tl+cations show a trigonal-prismatic coordination sphere with the terminal nitrogen atoms of six tricyanomethanide anions. There is also a long-distance capping of the triangular faces by two tricyanomethanide anions with their central carbon atoms at longer distance (d(Tl–N) = 299 pm; d(Tl⋯C) = 355 pm). Due to these bonding patterns, the tricyanomethanide unit in Tl[C(CN)3] is found to have the smallest volume increment of all [C(CN)3]–anions reported so far. A synopsis of the crystal structures and Raman spectra of all reported tricyanomethanides A[C(CN)3] with monocations (A= Li–Cs, Cu, Ag and Tl) is given. According to quantum-chemical calculations, the central carbon atom within the Y-aromatic π-electron system of the [C(CN)3]–anion and the lone pair at the Tl+cation are assembled to a one-dimensional string along [001] via Kramers-Anderson super-exchange with equidistant atoms (d(Tl⋯C) = 355 pm), which might be addressed as an undistorted Peierls chain.

High-oxidation-state group 6 metal alkylidenes have been dominated by imido and oxo ligands. Here, the first neutral tungsten sulfido alkylidene and cationic tungsten sulfido alkylidene N-heterocyclic carbene (NHC) complexes are presented. A synthesis route that entails the reaction of the corresponding tungsten alkylidyne precursors with H2S in tetrahydrofuran is outlined. Schrock-type complexes bearing chlorides as well as pentafluorophenoxide ligands were synthesized, while variations in the NHC (1,3-dimesityl-1,3-dihydro-2H-imidazol-2-ylidene (IMes), 1,3-dimesityl-4,5-dichloro-1,3-dihydro-2H-imidazol-2-ylidene (IMesCl2), and 1,3-bis(2,6-diisopropylphenyl)-1,3-dihydro-2H-imidazol-2-ylidene (IDipp)) as well as in the anionic ligand (chloride, pentafluorophenoxide, and 2,6-diphenylphenoxide) were carried out for the cationic tungsten sulfido alkylidene NHC complexes. All complexes were tested in benchmark olefin metathesis reactions in which the cationic tungsten sulfido alkylidene NHC complexes showed high productivities. Atomic charges were calculated for several cationic tungsten sulfido alkylidene NHC complexes and compared to those of the analogous tungsten oxo and imido complexes. These calculations revealed charge distribution between the NHC and the metal, yet lower charges at the metal and less polarization of the metal alkylidene bond compared to their tungsten oxo and imido analogs.

Covalent organic frameworks (COFs) with a pore size beyond 5 nm are still rarely seen in this emerging field. Besides obvious complications such as the elaborated synthesis of large linkers with sufficient solubility, more subtle challenges regarding large-pore COF synthesis, including pore occlusion and collapse, prevail. Here we present two isoreticular series of large-pore imine COFs with pore sizes up to 5.8 nm and correlate the interlayer interactions with the structure and thermal behavior of the COFs. By adjusting interlayer interactions through the incorporation of methoxy groups acting as pore-directing “anchors”, different stacking modes can be accessed, resulting in modified stacking polytypes and, hence, effective pore sizes. A strong correlation between stacking energy toward highly ordered, nearly eclipsed structures, higher structural integrity during thermal stress, and a novel, thermally induced phase transition of stacking modes in COFs was found, which sheds light on viable design strategies for increased structural control and stability in large-pore COFs.

Geometry optimization based on Gaussian process regression (GPR) was extended to internal coordinates. We used delocalized internal coordinates composed of distances and several types of angles and compared two methods of including them. In both cases, the GPR surrogate surface is trained on geometries in internal coordinates. In one case, it predicts the gradient in Cartesian coordinates and in the other, in internal coordinates. We tested both methods on a set of 30 small molecules and one larger Rh complex taken from the study of a catalytic mechanism. The former method is slightly more efficient, while the latter method is somewhat more robust. Both methods reduce the number of required optimization steps compared to GPR in Cartesian coordinates or the standard L-BFGS optimizer. We found it advantageous to use automatically adjusted hyperparameters to optimize them.

Enantioenriched boron chelates show promising synthetic and luminescent properties; however, the challenging synthesis makes these compounds scarce. In our earlier work, we established a chirality transfer from boron O,N-chelates toward enantioenriched C,N-chelates. This methodology proved to be quite robust, in terms of yields and selectivity. However, unexpected steric effects on stereocontrol prompted a deeper investigation of the chirality transfer. In order to gain a holistic understanding of this process, we studied the structure of the O,N- and C,N-chelates as well as the stability of the dative B–N bonds. Furthermore, the proposed ate-complex as a reaction intermediate could be characterized using heteronuclear (2D) NMR spectroscopy. For this ate-complex, a tridentate O,N,N-chelate effect of the borate anion with the Li-cation was observed. Additional experiments indicated that the borate formation governs the stereoselectivity of chirality transfer. For a successful chirality transfer, an unprecedented SN2-type breaking of the dative B–N bond with an organometallic nucleophile was identified by DFT calculations as the most likely reaction path. For other cases, decreased or inverse enantioselectivity was rationalized by a solvent-assisted pathway.

Covalent organic frameworks (COFs) are a class of porous materials whose sorption properties have so far been studied primarily by physisorption. Quantifying the self-diffusion of guest molecules inside their nanometer-sized pores allows for a better understanding of confinement effects or transport limitations and is thus essential for various applications ranging from molecular separation to catalysis. Using a combination of pulsed field gradient nuclear magnetic resonance measurements and molecular dynamics simulations, we have studied the self-diffusion of acetonitrile and chloroform in the 1D pore channels of two imine-linked COFs (PI-3-COF) with different levels of crystallinity and porosity. The higher crystallinity and porosity sample exhibited anisotropic diffusion for MeCN parallel to the pore direction, with a diffusion coefficient of Dpar= 6.1(3) × 10–10m2s–1at 300 K, indicating 1D transport and a 7.4-fold reduction in self-diffusion compared to the bulk liquid. This finding aligns with molecular dynamics simulations predicting 5.4-fold reduction, assuming an offset-stacked COF layer arrangement. In the low-porosity sample, more frequent diffusion barriers result in isotropic, yet significantly reduced diffusivities (DB= 1.4(1) × 10–11m2s–1). Diffusion coefficients for chloroform at 300 K in the pores of the high- (Dpar= 1.1(2) × 10–10m2s–1) and low-porosity (DB= 4.5(1) × 10–12m2s–1) samples reproduce these trends. Our multimodal study thus highlights the significant influence of real structure effects such as stacking faults and grain boundaries on the long-range diffusivity of molecular guest species while suggesting efficient intracrystalline transport at short diffusion times.

The hydrogen abstraction reaction between H and H2S, yielding HS and H2as products, has been studied within the framework of interstellar surface chemistry. High-temperature rate constants below 2000 K are calculated in the gas phase and are in agreement with previously reported values. Subsequently, low-temperature rate constants down to 55 K are presented for the first time that are of interest to astrochemistry, i.e., covering both bimolecular and unimolecular reaction mechanisms. For this, a so-called implicit surface model is used. In strict terms, this is a structural gas-phase model in which the restriction of the rotation in the solid state is taken into account. The calculated kinetic isotope effects are explained in terms of the difference in activation and delocalization. All rate constants are calculated at the UCCSD(T)-F12/cc-VTZ-F12 level of theory. Finally, we show that the energetics of the reaction is affected to an only small extent by the presence of H2O or H2S molecular clusters that simulate an ice surface, calculated at the MPWB1K/def2-TZVP level of theory.

Molybdenum alkylidyne N-heterocyclic carbene (NHC) complexes of the type [Mo(C-p-C6H4Y)(OC(R)(CF3)2)2(L)(NHC)][B(ArF)4] (Y = OMe, NO2; R = CH3, CF3; L = none, pivalonitrile, tetrahydrofuran; NHC = 1,3-dimesitylimidazol-2-ylidene (IMes), 1,3-dimesityl-3,4-dihydroimidazol-2-ylidene (IMesH2), 1,3-dimesityl-3,4-dichloroimidazol-2-ylidene (IMesCl2), 1,3-diisopropylimidazol-2-ylidene (IiPr); B(ArF)4–= tetrakis(3,5-bis(trifluoromethyl)phen-1-yl)borate) were used in the ring expansion metathesis polymerization (REMP) of cyclic olefins. With cis-cyclooctene (cCOE) cyclic, low molecular weight oligomers were obtained at low monomer concentrations and the cyclic nature of the polymer was confirmed by MALDI-TOF measurements. High-molecular weight cyclic poly(cCOE) became available at high monomer concentrations. Also, post-REMP allowed for converting low-molecular-weight cyclic poly(cCOE) into high-molecular-weight cyclic poly(cCOE). Tailored catalysts together with suitable additives offered access to the stereoselective REMP of functional norbornenes providing functional cis-isotactic (cis-it), cis-syndiotactic (cis-st) and trans-itpoly(norbornene)s with up to 99% stereoselectivity. Mechanistic details supported by density functional theory (DFT) calculations are outlined.

Atom probe tomography allows us to measure the three-dimensional composition of materials with up to atomic resolution by evaporating the material using high electric fields. Initially developed for metals, it is increasingly used for covalently bound structures. To aid the interpretation of the obtained fragmentation pattern, we modeled the fragmentation and desorption of self-assembled monolayers of thiolate molecules on a gold surface in strong electrostatic fields using density functional theory. We used a cluster model and a periodic model of amino-undecanethiolate, NH2(CH2)11S, and fluoro-decanethiolate, CF3(CF2)7(CH2)2S. In the former molecule, the fragment CH2NH2+was found to evaporate at fields of 5.4–7.7 V/nm. It was followed by different hydrocarbon fragments. Fluoro-decanethiolate evaporates CF3+at fields of 5.7–6.7 V/nm in the cluster model and at 15.4–23.1 V/nm in the periodic model, followed by CF2+and C2F42+. Detailed analysis of the electronic structure during the evaporation process revealed a stepwise accumulation of the charge in the head groups exposed to the strongest fields, followed by dissociation of covalent bonds. These observations will facilitate the analysis of atom probe experiments of covalently bound structures.

DFT calculations were carried out to explore all relevant pathways for the ring-closing metathesis (RCM) reaction of a cationic molybdenum imido alkylidene N-heterocyclic carbene (NHC) catalyst with α,ω-dienes. Besides the catalytic cycle, which produces the desired cycloalkene in two consecutive metathesis steps, the initiation, a nonproductive cycle, and a degenerative catalytic path were also investigated. On the basis of the approaching face of the diene, two further possibilities were considered for all pathways: syn-and anti-addition. Steric repulsion on the metallacyclobutane ring of the trigonal-bipyramidal (TBP) intermediate appears to be one of the important influencing factors. We found the nonproductive cycle to compete with the catalytic conversion of the substrate. The TBP intermediate formed during the catalytic cycle is energetically lower than the corresponding TBP intermediate of the nonproductive cycle. However, the barriers for the nonproductive cycle are slightly lower than the barrier for the catalytic cycle. Thus, the nonproductive cycle can be expected to be used during catalysis, but it will only have a weak detrimental effect on the turnover rate because it is faster than the catalytic cycle. Of the four different initiation paths, the α-anti-addition path was found to be the energetically most favorable one. Notably, the catalyst was found to be fairly stable against degradation via β-hydride (β-H) transfer to the metal. High activation barriers for the conversion of the TBP intermediate to a square-pyramidal (SP)-based intermediate and a higher energy of a later intermediate suggest a stability of catalyst against degradation. A very high barrier for β-H transfer also disfavors the degradation reaction. The 1H NMR spectrum of the reaction between [Mo(N-2,6-Me2-C6H3)(CHCMe2Ph)(IMes)(OCH(CF3)2)+B(ArF)4–] and 1,7-octadiene confirms the absence of any β-H transfer.

The influence of nuclearity and charge of chiral Rh diene complexes on the activity and enantioselectivity in catalytic asymmetric 1,2-additions of organoboron reagents to N-tosylimines and 1,4-additions to enones was investigated. For this purpose, cationic dimeric Rh(I) complex [(Rh(1))2Cl]SbF6and cationic monomeric Rh(I) complex [RhOH2(2)]SbF6were synthesized from oxazolidinone-substituted 3-phenylnorbornadiene ligands 1and 2, which differ in the substitution pattern at oxazolidinone C-5′ (CMe2vs CH2) and compared with the corresponding neutral dimeric and monomeric Rh(I) complexes [RhCl(1)]2and [RhCl(2)]. Structural, electronic, and mechanistic insights were gained by X-ray crystallography, cyclic voltammetry (CV), X-ray absorption spectroscopy (XAS), and DFT calculations. CV revealed an increased stability of cationic vs neutral Rh complexes toward oxidation. Comparison of solid-state and solution XAS (extended X-ray absorption fine structure (EXAFS), X-ray absorption near edge structure (XANES)) data showed that the monomeric Rh complex [RhCl(2)] maintained its electronic state and coordination sphere in solution, whereas the dimeric Rh complex [RhCl(1)]2exchanges bridging chloro ligands by dioxane molecules in solution. In both 1,2- and 1,4-addition reactions, monomeric Rh complexes [RhCl(2)] and [RhOH2(2)]SbF6gave better yields as compared to dimeric complexes [RhCl(1)]2and [(Rh(1))2Cl]SbF6. Regarding enantioselectivities, dimeric Rh species [RhCl(1)]2and [(Rh(1))2Cl]SbF6performed better than monomeric Rh species in the 1,2-addition, while the opposite was true for the 1,4-addition. Neutral Rh complexes performed better than cationic complexes. Microemulsions improved the yields of 1,2-additions due to a most probable enrichment of Rh complexes in the amphiphilic film and provided a strong influence of the complex nuclearity and charge on the stereocontrol. A strong nonlinear-like effect (NLLE) was observed in 1,2-additions, when diastereomeric mixtures of ligands 1and epi-1were employed. The pronounced substrate dependency of the 1,4-addition could be rationalized by DFT calculations.

We show how Gaussian process regression can be used to update Hessian matrices using gradient-based information in the course of an optimization procedure. This is done by building a Gaussian process with at least one initial Hessian and some further energies and gradients from electronic structure calculations and evaluating the desired second derivative of the resulting Gaussian process. To a certain extent, we can overcome the significant scaling problems that occur when training a Gaussian process with Hessian information. We demonstrate in benchmark runs using the partitioned rational function optimization (P-RFO) that this new update method can outperform classical Hessian update methods for small systems.

New tungsten and molybdenum alkylidyne complexes bearing mono-, bi-, and tridentate N-heterocyclic carbenes (NHCs) have been synthesized. Formation of unprecedented structures in complexes bearing N-tert-butyl substituents on the imidazol(in)-2-ylidene was observed, leading to molybdenum complexes containing an abnormal carbene (Mo-4) and a bridging O,C,C-pincer ligand (Mo-10) and to a tungsten complex containing a cationic imidazolinium-tagged alkoxide forming an inner salt with an anionic tungsten center (W-5). Both the abnormal carbene binding in Mo-4and the O,C,C-pincer-type structure of Mo-10were confirmed by single-crystal X-ray analysis, and the proposed structure of W-5is supported by the single-crystal X-ray structure of a minor byproduct (W-8) formed during the synthesis of W-4, displaying the aforementioned inner-salt-like structure. The novel alkylidyne complexes were also investigated for their capability to form a previously postulated quasi-cationic species with a weakly coordinating anion (WCA) during the alkyne homometathesis of 1-phenyl-1-propyne. Overall, incorporation of bidentate and strongly σ donating NHCs as well as introduction of better leaving groups did not lead to the expected increase in catalytic activity. Despite identical ligand spheres, changing from molybdenum to tungsten led to complete loss of activity in the bidentate systems.

We implemented a gradient-based algorithm for finding minimum energy paths (MEPs) using Gaussian process regression (GPR). A subsequent search for transition states can be performed very fast. We describe the algorithm in detail and compare its performance to the nudged elastic band (NEB) method in 27 test systems. Additionally, three different possibilities for an initial guess of the path are evaluated. We found the new optimizer to considerably decrease the number of required energy and gradient evaluations.

We calculated reaction rate constants including atom tunneling for the hydrogen abstraction reaction CH3OH + H → CH2OH + H2with the instanton method. The potential energy was fitted by a neural network that was trained to UCCSD(T)-F12/VTZ-F12 data. Bimolecular gas-phase rate constants were calculated using microcanonic instanton theory. All H/D isotope patterns on the CH3group and the incoming H atom are studied. Unimolecular reaction rate constants, representing the reaction on a surface, down to 30 K, are presented for all isotope patterns. At 30 K, they range from 4100 for the replacement of the abstracted H by D to ∼8 for the replacement of the abstracting H to ∼2 to 6 for secondary KIEs. The 12C/13C kinetic isotope effect is 1.08 at 30 K, while the 16O/18O kinetic isotope effect is extremely small. A simple kinetic surface model using these data predicts high abundances of the deuterated forms of methanol.

The proton affinity (PA) of a range of structurally different N-heterocycles with an exocyclic double bond (= N-heterocyclic olefins, NHOs) has been determined using DFT calculations on the BLYP/def2-TZVPP level. It was found that NHOs belong to the upper end of the superbasicity scale, covering PA values from 262 to 296 kcal/mol. Different types of NHOs are compared with each other and with frequently employed organocatalysts. To boost PA, (a) the ability to delocalize the positive charge and (b) steric pressure/ring strain which can be relieved after protonation were identified as key tuning parameters. Importantly, by analyzing PA alongside partial charges and molecular electrostatic potentials, it is shown that an increase of double bond polarization is not a necessary prerequisite for high PA. In contrast, the more basic, more sterically congested NHOs minimize unfavorable interactions by partly pyramidalyzing the nitrogen atoms, rendering the olefinic bond less electron rich and less polarized. These findings are in excellent agreement with experimental evidence on NHO catalysis, not only providing guidelines for a more rational design regarding PA/basicity but also suggesting that NHOs could be specifically tailored toward either nucleophilic or base-type reaction pathways.

Canonical instanton theory is a widespread approach to describe the dynamics of chemical reactions in low temperature environments when tunneling effects become dominant. It is a semiclassical theory which requires locating classical periodic orbits on the upside-down potential energy surface, so-called instantons, and the computation of second order quantum corrections. The calculation of these corrections usually involves a matrix diagonalization. In this paper we present an alternative approach, which requires to solve only linear systems of equations involving sparse matrices. Furthermore, the proposed method provides a reliable and numerically stable way to obtain stability parameters in multidimensional systems, which are of particular interest in the context of microcanonical instanton theory.

We implemented a gradient-based algorithm for transition state search which uses Gaussian process regression. Besides a description of the algorithm, we provide a method to find the starting point for the optimization if only the reactant and product minima are known. We perform benchmarks on 27 test systems against the dimer method and partitioned rational function optimization as implemented in the DL-FIND library. We found the new optimizer to significantly decrease the number of required energy and gradient evaluations.

Instanton theory is an established method to calculate rate constants of chemical reactions including atom tunneling. Technical and methodological improvements increased its applicability. Still, a large number of energy and gradient calculations is necessary to optimize the instanton tunneling path, and second derivatives of the potential energy along the tunneling path have to be evaluated, restricting the range of suitable electronic structure methods. To enhance the applicability of instanton theory, we present a dual-level approach in which instanton optimizations and Hessian calculations are performed using an efficient but approximate electronic structure method, and the potential energy along the tunneling path is recalculated using a more accurate method. This procedure extends the applicability of instanton theory to high-level electronic structure methods for which analytic gradients may not be available, like local linear-scaling approaches. We demonstrate for the analytical Eckart barrier and three molecular systems how the dual-level instanton approach corrects for the largest part of the error caused by the inaccuracy of the efficient electronic structure method. This reduces the error of the calculated rate constants significantly.

Room temperature sodium-sulfur (RT Na-S) batteries are considered potential candidates for stationary power storage applications due to their low cost, broad active material availability and low toxicity. Challenges, such as high volume expansion of the S-cathode upon discharge, low electronic conductivity of S as active material and herewith limited rate capability as well as the shuttling of polysulfides (PSs) as intermediates often impede the cycle stability and practical application of Na-S batteries. Sulfurized poly(acrylonitrile) (SPAN) inherently inhibits the shuttling of PSs and shows compatibility with carbonate-based electrolytes, however, its exact redox mechanism remained unclear to date. Herein, we implement a commercially available and simple electrolyte into the Na-SPAN cell chemistry and demonstrate its high rate and cycle stability. Through the application of in situ techniques utilizing electronic impedance spectroscopy (EIS) and X-ray absorption spectroscopy (XAS) at different depths of charge and discharge, an insight into SPAN’s redox chemistry is obtained.