The Nonlocal Kernel in van der Waals Density Functionals as an Additive Correction: An Extensive Analysis with Special Emphasis on the B97M-V and ωB97M-V Approaches

Modelling ligand exchange in metal complexes with machine learning potentials

Metal ions are irreplaceable in many areas of chemistry, including (bio)catalysis, self-assembly and charge transfer processes. Yet, modelling their structural and dynamic properties in diverse chemical environments remains challenging for both force fields and ab initio methods. Here, we introduce a strategy to train machine learning potentials (MLPs) using MACE, an equivariant message-passing neural network, for metal-ligand complexes in explicit solvents. We explore the structure and ligand exchange dynamics of Mg2+ in water and Pd2+ in acetonitrile as two illustrative model systems. The trained potentials accurately reproduce equilibrium structures of the complexes in solution, including different coordination numbers and geometries. Furthermore, the MLPs can model structural changes between metal ions and ligands in the first coordination shell, and reproduce the free energy barriers for the corresponding ligand exchange. The strategy presented here provides a computationally efficient approach to model metal ions in solution, paving the way for modelling larger and more diverse metal complexes relevant to biomolecules and supramolecular assemblies.

Data-Driven Improvement of Local Hybrid Functionals: Neural-Network-Based Local Mixing Functions and Power-Series Correlation Functionals

Local hybrid functionals (LHs) use a real-space position-dependent admixture of exact exchange (EXX), governed by a local mixing function (LMF). The systematic construction of LMFs has been hampered over the years by a lack of exact physical constraints on their valence behavior. Here, we exploit a data-driven approach and train a new type of "n-LMF" as a relatively shallow neural network. The input features are of meta-GGA character, while the W4-17 atomization-energy and BH76 reaction-barrier test sets have been used for training. Simply replacing the widely used "t-LMF" of the LH20t functional by the n-LMF provides the LH24n-B95 functional. Augmented by DFT-D4 dispersion corrections, LH24n-B95-D4 remarkably improves the WTMAD-2 value for the large GMTKN55 test suite of general main-group thermochemistry, kinetics, and noncovalent interactions (NCIs) from 4.55 to 3.49 kcal/mol. As we found the limited flexibility of the B95c correlation functional to disfavor much further improvement on NCIs, we proceeded to replace it by an optimized B97c-type power-series expansion. This gives the LH24n functional. LH24n-D4 gives a WTMAD-2 value of 3.10 kcal/mol, the so far lowest value of a rung 4 functional in self-consistent calculations. The new functionals perform moderately well for organometallic transition-metal energetics while leaving room for further data-driven improvements in that area. Compared to complete neural-network functionals like DM21, the present more tailored approach to train just the LMF in a flexible but well-defined human-designed LH functional retains the possibility of graphical LMF analyses to gain deeper understanding. We find that both the present n-LMF and the recent x-LMF suppress the so-called gauge problem of local hybrids without adding a calibration function as required for other LMFs. LMF plots show that this can be traced back to large LMF values in the small-density region between the interacting atoms in NCIs for n- and x-LMFs and low values for the t-LMF. We also find that the trained n-LMF has relatively large values in covalent bonds without deteriorating binding energies. The current approach enables fast and efficient routine self-consistent calculations using n-LMFs in Turbomole.

Accurate Enthalpies of Formation for Bioactive Compounds from High-Level Ab Initio Calculations with Detailed Conformational Treatment: A Case of Cannabinoids

Our recently developed approach based on the local coupled-cluster with single, double, and perturbative triple excitation [LCCSD(T)] model gives very efficient means to compute the ideal-gas enthalpies of formation. The expanded uncertainty (95% confidence) of the method is about 3 kJ·mol-1 for medium-sized compounds, comparable to typical experimental measurements. Larger compounds of interest often exhibit many conformations that can significantly differ in intramolecular interactions. Although the present capabilities allow processing even a few hundred distinct conformer structures for a given compound, many systems of interest exhibit numbers well in excess of 1000. In this study, we investigate how to reduce the number of expensive LCCSD(T) calculations for large conformer ensembles while controlling the error of the approximation. The best strategy found was to correct the results of the lower-level, surrogate model (density functional theory, DFT) in a systematic manner. It was also found that the error in the conformational contribution introduced by a surrogate model is mainly driven by a systematic (bias) rather than a random component of the DFT energy deviation from the LCCSD(T) target. This distinction is usually overlooked in DFT benchmarking studies. As a result of this work, the enthalpies of formation for 20 cannabinoid and cannabinoid-related compounds were obtained. Comprehensive uncertainty analysis suggests that the expanded uncertainties of the obtained values are below 4 kJ·mol-1.

Assessment of electron-proton correlation functionals for vibrational spectra of shared-proton systems by constrained nuclear-electronic orbital density functional theory

Proton transfer plays a crucial role in various chemical and biological processes. A major theoretical challenge in simulating proton transfer arises from the quantum nature of the proton. The constrained nuclear-electronic orbital (CNEO) framework was recently developed to efficiently and accurately account for nuclear quantum effects, particularly quantum nuclear delocalization effects, in quantum chemistry calculations and molecular dynamics simulations. In this paper, we systematically investigate challenging proton transfer modes in a series of shared-proton systems using CNEO density functional theory (CNEO-DFT), focusing on evaluating existing electron-proton correlation functionals. Our results show that CNEO-DFT accurately describes proton transfer vibrational modes and significantly outperforms conventional DFT. The inclusion of the epc17-2 electron-proton correlation functional in CNEO-DFT produces similar performance to that without electron-proton correlations, while the epc17-1 functional yields less accurate results, comparable with conventional DFT. These findings hold true for both asymmetrical and symmetrical shared-proton systems. Therefore, until a more accurate electron-proton correlation functional is developed, we currently recommend performing vibrational spectrum calculations using CNEO-DFT without electron-proton correlation functionals.

Analysis of Interaction Features of Cyclo[13]carbon with Small Molecules and Formation Mechanism of Its Dimer

The newly discovered cyclo[13]carbon, the first artificially synthesized odd-numbered carbon ring, is an intriguing carbon isomer that provides a valuable subject for studying low-symmetry carbon materials. In this work, we employed first-principles calculations to explore the geometric structure and electronic properties of cyclo[13]carbon through various techniques such as vibrational mode analysis, bond order analysis, spin density analysis, electron localization analysis, electrostatic potential and van der Waals potential analysis, visualization of weak interactions, and energy decomposition analysis. We investigated the interaction characteristics of cyclo[13]carbon with small molecules and examined its dimer formation mechanism and dynamics features using ab initio molecular dynamics. Our study reveals the unique physicochemical properties of this novel carbon ring system. The antiaromaticity of the low-symmetry cyclo[13]carbon sets it apart from previously synthesized even-numbered carbon rings, with van der Waals interactions playing a crucial role in its binding with small molecules and in the formation of C13 dimers. This research provides theoretical insights that complement experimental observations and theoretical studies, aiding further investigation into the diverse properties of fresh carbon material isomers and promoting the synthesis and application of novel molecular materials in molecular electronics and nanotechnology.

Assessment of the applicability of DFT methods to [Cp*Rh]-catalyzed hydrogen evolution processes

The present computational study provides a benchmark of density functional theory (DFT) methods in describing hydrogen evolution processes catalyzed by [Cp*Rh]-containing organometallic complexes. A test set was composed of 26 elementary reactions featuring chemical transformations and bonding situations essential for the field, including the emerging concept of non-innocent Cp* behavior. Reference values were obtained from a highly accurate 3/4 complete basis set and 6/7 complete PNO space extrapolated DLPNO-CCSD(T) energies. The performance of lower-level extrapolation procedures was also assessed. We considered 84 density functionals (DF) (including 13 generalized gradient approximations (GGA), nine meta-GGAs, 33 hybrids, and 29 double-hybrids) and three composite methods (HF-3c, PBEh-3c, and r2SCAN-3c), combined with different types of dispersion corrections (D3(0), D3BJ, D4, and VV10). The most accurate approach is the PBE0-DH-D3BJ (MAD of 1.36 kcal mol-1) followed by TPSS0-D3BJ (MAD of 1.60 kcal mol-1). Low-cost r2SCAN-3c composite provides a less accurate but much faster alternative (MAD of 2.39 kcal mol-1). The widely used Minnesota-family M06-L, M06, and M06-2X DFs should be avoided (MADs of 3.70, 3.94, and 4.01 kcal mol-1, respectively).

A comprehensive guide for accurate conformational energies of microsolvated Li+ clusters with organic carbonates

Organic carbonates and their mixtures are frequently used in electrolyte solutions in lithium-ion batteries. Rationalization and tuning of the related Li+ solvation processes are rooted in the proper identification of the representative low-energy spatial structures of the microsolvated Li+(S)n clusters. In this study, we introduce an automatically generated database of conformational energies (CEs), LICARBCONF806, comprising 806 diverse conformers of Li+ clusters with 7 common organic carbonates. A number of standard and composite density functional theory (DFT) approaches and fast semi-empirical methods are examined to reproduce the reference CEs obtained at the RI-SCS-MP2/CBS level of theory. A hybrid PBE0-D4 functional paired with the def2-QZVP basis set is the most robust in reproducing the reference values while composite B97-3c demonstrates the best cost-benefit ratio. Contemporary tight-binding semi-empirical methods GFNn-xTB can be used for the filtering of high-energy structures, but their performance worsens significantly when the limited number of low-energy (CE < 3 kcal mol-1) conformers are to be sorted. Thermal corrections used to convert electronic energies to respective Gibbs free energies and especially corrections imposed by a continuum solvation model can significantly influence both the conformer ranking and the width of the CE distribution. These should be appropriately taken into account to identify lowest energy conformers in solution and at non-zero temperatures. The almost black-box conformation generation workflow used in this work successfully predicts representitative low-energy four-coordinated conformers of Li+ clusters with cyclic carbonates and unravels the complex conformational nature of the clusters with flexible linear carbonates.

Assessment of Charge Transfer Energies of Noncovalently Bounded Ar-TCNE Complexes Using Range-Separated Density Functionals and Double-hybrid Density Functionals

Charge Transfer (CT) molecular complexes have recently received much attention in a broad variety of fields. The time-dependent density functional theory (TDDFT), which is essential for studying CT complexes, is a well-established tool to study the excited states of relatively large molecular systems. However, when dealing with donor-acceptor molecules with CT characteristics, TDDFT calculations based on standard functionals can severely underestimate the excitation energies. The TDDFT methodology, combined with range-separated DFT and range-separated double-hybrid DFT functionals, had previously been used by different research groups to reliably predict the excitation energies of different charge transfer molecular complexes. We follow the same path to calculate the excited state charge transfer energy of some selected molecular complexes, such as, Ar-TCNE (TCNE=tetracyanoethylene; Ar= benzene, naphthalene, anthracene, etc.). The interactions between the donor-acceptor moieties of these molecular complexes are also studied and the relationship between the interaction and the charge transfer energies are shown here.

Stability of [10-12]cycloparaphenylene complexes with pristine fullerenes C76,78,84 and endohedral metallofullerenes M3N@C78,80

[n]Cycloparaphenylenes ([n]CPPs) are strained macrocycles, comprising only sp2-hybridized carbon atoms. In recent years, [n]CPPs have become of great research interest in the field of supramolecular chemistry since their special structure enables the formation of novel host-guest complexes. In this work, we investigate the gas-phase chemistry of noncovalent complexes of [10-12]CPP with the pristine fullerenes C76/78/84 and the endohedral metallofullerenes (EMFs) Sc3N@D3h-C78, Sc3N@D5h-C80 and M3N@Ih-C80 (M = Sc, Y, Lu, Gd). The [1 : 1] complexes with [10-12]CPP are detected as radical cations. The stability and charge distributions of these complexes are studied using energy-resolved collision-induced dissociation (ER-CID). Our results assess the size complementarity, the influence of fullerene symmetry and size as well as the role of the metal size inside the EMF on the binding affinity and complex stability. Two main trends in complex stability have been found: First, [10-12]CPP form more stable complexes with EMFs than with pristine fullerenes and second, all complexes of EMFs with the C80 skeleton show similar stability despite the different metal clusters encapsulated. Another major finding is the fact that [11]CPP is generally the most suitable host for fullerenes with a C76/78/80/84 skeleton. Considering the charge distributions, we observe the existence of two different fragmentation channels for complexes with EMFs where the radical cation is either located at the CPP or at the EMF: (1) [n]CPP+˙ + EMF and (2) [n]CPP + EMF+˙. This behavior allows a clear distinction of the cage isomers ([11]CPP⊃Sc3N@Ih-C80)+˙ and ([11]CPP⊃Sc3N@D5h-C80)+˙ in the MS2 experiment. The experimental results are accompanied by density functional theory (DFT) calculations of ionization potentials (IPs) and fragmentation energies. The computational results fully confirm the measured order of complex stabilities and explain the prevalence of EMF or CPP signals in the spectra by the trend in ionization potentials.

Constructing Accurate and Efficient General-Purpose Atomistic Machine Learning Model with Transferable Accuracy for Quantum Chemistry

Density functional theory (DFT) has been a cornerstone in computational science, providing powerful insights into structure-property relationships for molecules and materials through first-principles quantum-mechanical (QM) calculations. However, the advent of atomistic machine learning (ML) is reshaping the landscape by enabling large-scale dynamics simulations and high-throughput screening at DFT-equivalent accuracy with drastically reduced computational cost. Yet, the development of general-purpose atomistic ML models as surrogates for QM calculations faces several challenges, particularly in terms of model capacity, data efficiency, and transferability across chemically diverse systems. This work introduces a novel extension of the polarizable atom interaction neural network (namely, XPaiNN) to address these challenges. Two distinct training strategies have been employed, one direct-learning and the other Δ-ML on top of a semiempirical QM method. These methodologies have been implemented within the same framework, allowing for a detailed comparison of their results. The XPaiNN models, in particular the one using Δ-ML, not only demonstrate competitive performance on standard benchmarks, but also demonstrate the effectiveness against other ML models and QM methods on comprehensive downstream tasks, including noncovalent interactions, reaction energetics, barrier heights, geometry optimization and reaction thermodynamics, etc. This work represents a significant step forward in the pursuit of accurate and efficient atomistic ML models of general-purpose, capable of handling complex chemical systems with transferable accuracy.

Unravelling the complex speciation of halozincate ionic liquids using X-ray spectroscopies and calculations

Using a combination of liquid-phase X-ray spectroscopy experiments and small-scale calculations we have gained new insights into the speciation of halozincate anions in ionic liquids (ILs). Both core and valence X-ray photoelectron spectroscopy (XPS) experiments were performed directly on the liquid-phase ILs, supplemented by Zn 1s X-ray absorption near edge structure (XANES) spectroscopy. Density functional theory (DFT) calculations were carried out on both 1- and 2- halozincate anions, in both a generalised solvation model SMD (Solvation Model based on Density) and the gas phase, to give XP spectra and total energy differences; time-dependent DFT was used to calculate XANES spectra. Speciation judgements were made using a combination of the shape and width of the experimental spectra, and visual matches to the calculated spectra. For 2- halozincate anions, excellent matches were found between the experimental and calculated XP spectra, clearly showing that only 2- halozincate anions were present at all zinc halide mole fractions, x, studied. At specific values of x (0.33, 0.50, 0.60) only one halozincate anion was present; equilibria of different halozincate anions at those values of x were not observed. All findings show that chlorozincate anion and bromozincate anion speciation matched at the same x. Based on the results, predictions are made of the halozincate anion speciation for all values of x up to 0.67. Caution is advised when using differences in calculated total energies obtained from DFT to judge halozincate anion speciation, even when the SMD was employed, as predictions based on total energy differences did not always match the findings from the experimental and calculated spectra. Our findings clearly establish that the combination of high-quality experimental data from multiple spectroscopies and a wide range of calculated structures are essential to have high confidence in halozincate anion speciation identification.

1.3 Å Crystal Structure of E. coli Peptidyl-Prolyl Isomerase B with Uniform Substitution of Valine by (2S,3S)-4-Fluorovaline Reveals Structure Conservation and Multiple Staggered Rotamers of CH2F Groups

(2S,3S)-4-Fluorovaline (FVal) is an analogue of valine, where a single CH3 group is substituted by a CH2F group. In the absence of valine, E. coli valyl-tRNA synthetase uses FVal as a substitute, enabling the production of proteins uniformly labeled with FVal. Here, we describe the production and analysis of E. coli peptidyl-prolyl isomerase B where all 16 valine residues have been replaced by FVal synthesized with a 13C-labeled CH2F group. Although the melting temperature is lower by about 11 °C relative to the wild-type protein, the three-dimensional protein structure is almost completely conserved, as shown by X-ray crystallography. The CH2F groups invariably populate staggered rotamers. Most CH2F groups populate two different rotamers. The increased space requirement of fluorine versus hydrogen does not prohibit rotamers that position fluorine next to a backbone carbonyl carbon. 19F NMR spectra show a signal dispersion over 25 ppm. The most high-field shifted 19F resonances correlate with large 3JHF coupling constants, confirming the impact of the γ-gauche effect on the signal dispersion. The present work is the second experimental verification of the effect and extends its validity to fluorovaline. The abundance of valine in proteins and structural conservation with FVal renders this valine analogue attractive for probing proteins by 19F NMR spectroscopy.

Exploring ortho-dianthrylbenzenes for molecular solar thermal energy storage

Molecular solar thermal systems, which absorb light, store it, and release it as heat, have been extensively researched, yet many potential candidates remain unexplored. To expand this range, five specifically designed ortho-dianthrylbenzenes were investigated. Anthracene dimers have been underexplored due to issues like photooxidation and varying photodimerization efficiency. The presented systems address these challenges by aryl-linking two anthracene moieties, achieving photodimerization quantum yields ranging from 11.5% to 16% in mesitylene. The impact of donor or acceptor groups on energy storage time (9-37 years), energy storage density (0.14-0.2 MJ kg-1), and solar energy storage efficiency (0.38-0.66%) was evaluated. The experimental results, supported by density functional theory-based modeling, highlight the potential of anthracene-based photoswitches for molecular solar thermal applications and encourage further exploration of similar systems.

Massive Assessment of the Geometries of Atmospheric Molecular Clusters

Atmospheric molecular clusters are important for the formation of new aerosol particles in the air. However, current experimental techniques are not able to yield direct insight into the cluster geometries. This implies that to date there is limited information about how accurately the applied computational methods depict the cluster structures. Here we massively benchmark the molecular geometries of atmospheric molecular clusters. We initially assessed how well different DF-MP2 approaches reproduce the geometries of 45 dimer clusters obtained at a high DF-CCSD(T)-F12b/cc-pVDZ-F12 level of theory. Based on the results, we find that the DF-MP2/aug-cc-pVQZ level of theory best resembles the DF-CCSD(T)-F12b/cc-pVDZ-F12 reference level. We subsequently optimized 1283 acid-base cluster structures (up to tetramers) at the DF-MP2/aug-cc-pVQZ level of theory and assessed how more approximate methods reproduce the geometries. Out of the tested semiempirical methods, we find that the newly parametrized atmospheric molecular cluster extended tight binding method (AMC-xTB) is most reliable for locating the correct lowest energy configuration and yields the lowest root mean square deviation (RMSD) compared to the reference level. In addition, we find that the DFT-3c methods show similar performance as the usually employed ωB97X-D/6-31++G(d,p) level of theory at a potentially reduced computational cost. This suggests that these methods could prove to be valuable for large-scale screening of cluster structures in the future.

Nutmeg and SPICE: Models and Data for Biomolecular Machine Learning

We describe version 2 of the SPICE data set, a collection of quantum chemistry calculations for training machine learning potentials. It expands on the original data set by adding much more sampling of chemical space and more data on noncovalent interactions. We train a set of potential energy functions called Nutmeg on it. They are based on the TensorNet architecture. They use a novel mechanism to improve performance on charged and polar molecules, injecting precomputed partial charges into the model to provide a reference for the large-scale charge distribution. Evaluation of the new models shows that they do an excellent job of reproducing energy differences between conformations even on highly charged molecules or ones that are significantly larger than the molecules in the training set. They also produce stable molecular dynamics trajectories and are fast enough to be useful for routine simulation of small molecules.

Exploring non-covalent interactions in excited states: beyond aromatic excimer models

Time-dependent density functional theory (TD-DFT) offers a relatively accurate and inexpensive approach for excited state calculations. However, conventional TD-DFT may suffer from the same poor description of non-covalent interactions (NCIs) which is known from ground-state DFT. In this work we present a comprehensive benchmark study of TD-DFT for excited-state NCIs. This is achieved by calculating dissociation curves for excited complexes ('exciplexes'), whose binding strength depends on excited-state NCIs including electrostatics, Pauli repulsion, charge-transfer, and London dispersion. Reference dissociation curves are calculated with the reasonably accurate wave function method SCS-CC2/CBS(3,4) which is used to benchmark a range of TD-DFT methods. Additionally, we test the effect of ground-state dispersion corrections, DFT-D3(BJ) and VV10, for exciplex binding. Overall, we find that TD-DFT methods generally under-bind exciplexes which can be explained by the missing dispersion forces. Underbinding errors reduce going up the rungs of Jacob's ladder. Further, the D3(BJ) dispersion correction is essential for good accuracy in most cases. Likewise, the VV10-type non-local kernel yields relatively low errors and has comparable performance in either its fully self-consistent implementation or as a post-SCF additive correction, but its impact is solely on ground-state energies and not on excitation energies. From our analysis, the most robust TD-DFT methods for exciplexes with localised excitations in their equilibrium and non-equilibrium geometries are the double hybrids B2GP-PLYP-D3(BJ) and B2PLYP-D3(BJ). Their range-separated versions ωB2(GP-)PLYP-D3(BJ) or the spin-opposite scaled, range-separated double hybrid SOS-ωB88PP86 can be recommended when charge transfer plays a role in the excitations. We also identify the need for a state-specific dispersion correction as the next step for improved TD-DFT performance.

Toward Reliable Conformational Energies of Amino Acids and Dipeptides─The DipCONFS Benchmark and DipCONL Datasets

Simulating peptides and proteins is becoming increasingly important, leading to a growing need for efficient computational methods. These are typically semiempirical quantum mechanical (SQM) methods, force fields (FFs), or machine-learned interatomic potentials (MLIPs), all of which require a large amount of accurate data for robust training and evaluation. To assess potential reference methods and complement the available data, we introduce two sets, DipCONFL and DipCONFS, which cover large parts of the conformational space of 17 amino acids and their 289 possible dipeptides in aqueous solution. The conformers were selected from the exhaustive PeptideCS dataset by Andris et al. [ J. Phys. Chem. B 2022, 126, 5949-5958]. The structures, originally generated with GFN2-xTB, were reoptimized using the accurate r2SCAN-3c density functional theory (DFT) composite method including the implicit CPCM water solvation model. The DipCONFS benchmark set contains 918 conformers and is one of the largest sets with highly accurate coupled cluster conformational energies so far. It is employed to evaluate various DFT and wave function theory (WFT) methods, especially regarding whether they are accurate enough to be used as reliable reference methods for larger datasets intended for training and testing more approximated SQM, FF, and MLIP methods. The results reveal that the originally provided BP86-D3(BJ)/DGauss-DZVP conformational energies are not sufficiently accurate. Among the DFT methods tested as an alternative reference level, the revDSD-PBEP86-D4 double hybrid performs best with a mean absolute error (MAD) of 0.2 kcal mol-1 compared with the PNO-LCCSD(T)-F12b reference. The very efficient r2SCAN-3c composite method also shows excellent results, with an MAD of 0.3 kcal mol-1, similar to the best-tested hybrid ωB97M-D4. With these findings, we compiled the large DipCONFL set, which includes over 29,000 realistic conformers in solution with reasonably accurate r2SCAN-3c reference conformational energies, gradients, and further properties potentially relevant for training MLIP methods. This set, also in comparison to DipCONFS, is used to assess the performance of various SQM, FF, and MLIP methods robustly and can complement training sets for those.

Toward the identification of cyano-astroCOMs via vibrational features: benzonitrile as a test case

The James Webb Space Telescope (JWST) opened a new era for the identification of molecular systems in the interstellar medium (ISM) by vibrational features. One group of molecules of increasing interest is cyano-derivatives of aromatic organic molecules, which have already been identified in the ISM on the basis of the analysis of rotational signatures, and so, are plausible candidates for the detection by the JWST. Benzonitrile considered in this work represents a suitable example for the validation of a computational strategy, which can be further applied for different, larger, and not-yet observed molecules. For this purpose, anharmonic simulations of infrared (IR) spectra have been compared with recent FTIR experimental studies. The anharmonic computations using the generalized second-order vibrational perturbation theory (GVPT2) in conjunction with a hybrid force field combining the harmonic part of revDSD-PBEP86-D3/jun-cc-pVTZ with anharmonic corrections from B3LYP-D3/SNSD show very good agreement with those in the experiment, with a mean error of 11 c m - 1 for all fundamental transitions overall and only 2 c m - 1 for the C ≡ N stretching fundamental at 4.49 μ m . The inclusion of overtones up to three-quanta transitions also allowed the prediction of spectra in the near-infrared region, which shows distinct features due to C ≡ N overtones at the 2.26 μ m and 1.52 μ m . The remarkable accuracy of the GVPT2 results opens a pathway for the reliable prediction of spectra for a broader range of cyano-astroCOMs.

Combined Multireference-Multiscale Approach to the Description of Photosynthetic Reaction Centers

A first-principles description of the primary photochemical processes that drive photosynthesis and sustain life on our planet remains one of the grand challenges of modern science. Recent research established that explicit incorporation of protein electrostatics in excited-state calculations of photosynthetic pigments, achieved for example with quantum-mechanics/molecular-mechanics (QM/MM) approaches, is essential for a meaningful description of the properties and function of pigment-protein complexes. Although time-dependent density functional theory has been used productively so far in QM/MM approaches for the study of such systems, this methodology has limitations. Here we pursue for the first time a QM/MM description of the reaction center in the principal enzyme of oxygenic photosynthesis, Photosystem II, using multireference wave function theory for the high-level QM region. We identify best practices and establish guidelines regarding the rational choice of active space and appropriate state-averaging for the efficient and reliable use of complete active space self-consistent field (CASSCF) and the N-electron valence state perturbation theory (NEVPT2) in the prediction of low-lying excited states of chlorophyll and pheophytin pigments. Given that the Gouterman orbitals are inadequate as a minimal active space, we define specific minimal and extended active spaces for the NEVPT2 description of electronic states that fall within the Q and B bands. Subsequently, we apply our multireference-QM/MM protocol to the description of all pigments in the reaction center of Photosystem II. The calculations reproduce the electrochromic shifts induced by the protein matrix and the ordering of site energies consistent with the identity of the primary donor (ChlD1) and the experimentally known asymmetric and directional electron transfer. The optimized protocol sets the stage for future multireference treatments of multiple pigments, and hence for multireference studies of charge separation, while it is transferable to the study of any photoactive embedded tetrapyrrole system.

Harmonic and anharmonic vibrational computations for biomolecular building blocks: Benchmarking DFT and basis sets by theoretical and experimental IR spectrum of glycine conformers

Advanced vibrational spectroscopic experiments have reached a level of sophistication that can only be matched by numerical simulations in order to provide an unequivocal analysis, a crucial step to understand the structure-function relationship of biomolecules. While density functional theory (DFT) has become the standard method when targeting medium-size or larger systems, the problem of its reliability and accuracy are well-known and have been abundantly documented. To establish a reliable computational protocol, especially when accuracy is critical, a tailored benchmark is usually required. This is generally done over a short list of known candidates, with the basis set often fixed a priori. In this work, we present a systematic study of the performance of DFT-based hybrid and double-hybrid functionals in the prediction of vibrational energies and infrared intensities at the harmonic level and beyond, considering anharmonic effects through vibrational perturbation theory at the second order. The study is performed for the six-lowest energy glycine conformers, utilizing available "state-of-the-art" accurate theoretical and experimental data as reference. Focusing on the most intense fundamental vibrations in the mid-infrared range of glycine conformers, the role of the basis sets is also investigated considering the balance between computational cost and accuracy. Targeting larger systems, a broad range of hybrid schemes with different computational costs is also tested.

Iodine Clusters in the Atmosphere I: Computational Benchmark and Dimer Formation of Oxyacids and Oxides

The contribution of iodine-containing compounds to atmospheric new particle formation is still not fully understood, but iodic acid and iodous acid are thought to be significant contributors. While several quantum chemical studies have been carried out on clusters containing iodine, there is no comprehensive benchmark study quantifying the accuracy of the applied methods. Here, we present the first study in a series that investigate the role of iodine species in atmospheric cluster formation. In this work, we have studied the iodic acid, iodous acid, iodine tetroxide, and iodine pentoxide monomers and their dimers formed with common atmospheric precursors. We have tested the accuracy of commonly applied methods for calculating the geometry of the monomers, thermal corrections of monomers and dimers, the contribution of spin-orbit coupling to monomers and dimers, and finally, the accuracy of the electronic energy correction calculated at different levels of theory. We find that optimizing the structures either at the ωB97X-D3BJ/aug-cc-pVTZ-PP or the M06-2X/aug-cc-pVTZ-PP level achieves the best thermal contribution to the binding free energy. The electronic energy correction can then be calculated at the ZORA-DLPNO-CCSD(T0) level with the SARC-ZORA-TZVPP basis for iodine and ma-ZORA-def2-TZVPP for non-iodine atoms. We applied this methodology to calculate the binding free energies of iodine-containing dimer clusters, where we confirm the qualitative trends observed in previous studies. However, we identify that previous studies overestimate the stability of the clusters by several kcal/mol due to the neglect of relativistic effects. This means that their contributions to the currently studied nucleation pathways of new particle formation are likely overestimated.

Redox-Responsive Halogen Bonding as a Highly Selective Interaction for Electrochemical Separations

Leveraging specific noncovalent interactions can broaden the mechanims for selective electrochemical separations beyond solely electrostatic interactions. Here, we explore redox-responsive halogen bonding (XB) for selective electrosorption in nonaqueous media, by taking advantage of directional interactions of XB alongisde a cooperative and synergistic ferrocene redox-center. We designed and evaluated a new redox-active XB donor polymer, poly(5-iodo-4-ferrocenyl-1-(4-vinylbenzyl)-1H-1,2,3-triazole) (P(FcTS-I)), for the electrochemically switchable binding and release of target organic and inorganic ions at a heterogeneous interface. Under applied potential, the oxidized ferrocene amplifies the halogen binding site, leading to significantly enhanced uptake and selectivity towards key inorganic and organic species, including chloride, bisulfate, and benzenesulfonate, compared to the open-circuit potential or the hydrogen bonding donor analog. Density functional theory calculations, as well as spectroscopic analysis, offer mechanistic insight into the degree of amplification of σ-holes at a molecular level, with selectivity modulated by charge transfer and dispersion interactions. Our work highlights the potential of XB in selective electrosorption by uniquely leveraging noncovalent interactions for redox-mediated electrochemical separations.

Modelling chemical processes in explicit solvents with machine learning potentials

Solvent effects influence all stages of the chemical processes, modulating the stability of intermediates and transition states, as well as altering reaction rates and product ratios. However, accurately modelling these effects remains challenging. Here, we present a general strategy for generating reactive machine learning potentials to model chemical processes in solution. Our approach combines active learning with descriptor-based selectors and automation, enabling the construction of data-efficient training sets that span the relevant chemical and conformational space. We apply this strategy to investigate a Diels-Alder reaction in water and methanol. The generated machine learning potentials enable us to obtain reaction rates that are in agreement with experimental data and analyse the influence of these solvents on the reaction mechanism. Our strategy offers an efficient approach to the routine modelling of chemical reactions in solution, opening up avenues for studying complex chemical processes in an efficient manner.

Computational methods for investigating organic radical species

Computational analysis of organic radical species presents significant challenges. This study compares the efficacy of various DFT and wavefunction methods in predicting radical stabilisation energies, bond dissociation energies, and redox potentials for organic radicals. The hybrid meta-GGA M062X-D3(0), and the range-separated hybrids ωB97M-V and ωB97M-D3(BJ) emerged as the most reliable functionals, consistently providing accurate predictions across different basis sets including 6-311G**, cc-pVTZ, and def2-TZVP.

How do spin-scaled double hybrids designed for excitation energies perform for noncovalent excited-state interactions? An investigation on aromatic excimer models

Time-dependent double hybrids with spin-component or spin-opposite scaling to their second-order perturbative correlation correction have demonstrated competitive robustness in the computation of electronic excitation energies. Some of the most robust are those recently published by our group (M. Casanova-Páez, L. Goerigk, J. Chem. Theory Comput. 2021, 20, 5165). So far, the implementation of these functionals has not allowed correctly calculating their ground-state total energies. Herein, we define their correct spin-scaled ground-state energy expressions which enables us to test our methods on the noncovalent excited-state interaction energies of four aromatic excimers. A range of 22 double hybrids with and without spin scaling are compared to the reasonably accurate wavefunction reference from our previous work (A. C. Hancock, L. Goerigk, RSC Adv. 2023, 13, 35964). The impact of spin scaling is highly dependent on the underlying functional expression, however, the smallest overall errors belong to spin-scaled functionals with range separation: SCS- and SOS- ω PBEPP86, and SCS-RSX-QIDH. We additionally determine parameters for DFT-D3(BJ)/D4 ground-state dispersion corrections of these functionals, which reduce errors in most cases. We highlight the necessity of dispersion corrections for even the most robust TD-DFT methods but also point out that ground-state based corrections are insufficient to completely capture dispersion effects for excited-state interaction energies.

In-depth exploration of catalytic sites on amorphous solid water: I. The astrosynthesis of aminomethanol

Chemical processes taking place on ice-grain mantles are pivotal to the complex chemistry of interstellar environments. In this study, we conducted a comprehensive analysis of the catalytic effects of an amorphous solid water (ASW) surface on the reaction between ammonia (NH3) and formaldehyde (H2CO) to form aminomethanol (NH2CH2OH) using density functional theory. We identified potential catalytic sites based on the binding energy distribution of NH3 and H2CO reactants, on a set-of-clusters surface model composed of 22 water molecules and found a total of 14 reaction paths. Our results indicate that the catalytic sites can be categorized into four groups, depending on the interactions of the carbonyl oxygen and the amino group with the ice surface in the reactant complex. A detailed analysis of the reaction mechanism using Intrinsic Reaction Coordinate and reaction force analysis, revealed three distinct chemical events for this reaction: formation of the C-N bond, breaking of the N-H bond, and formation of the O-H hydroxyl bond. Depending on the type of catalytic site, these events can occur within a single, concerted, albeit asynchronous, step, or can be isolated in a step-wise mechanism, with the lowest overall transition state energy observed at 1.3 kcal mol-1. A key requirement for the low-energy mechanism is the presence of a pair of dangling OH bonds on the surface, found at 5% of the potential catalytic sites on an ASW porous surface.

Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach

Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.

Photochemical Generation of Allenylidenes from Cyclopropanated Phenanthrenes: An Experimental and Computational Study

To address the scarcity of generally applicable photochemical routes to allenylidenes in solution, phenanthrene-based sources have been investigated. Specifically, the syntheses of 1-vinylidene-1a,9b-dihydro-1H-cyclopropa[l]phenanthrene, 1-(2-phenylvinylidene)-1a,9b-dihydro-1H-cyclopropa[l]phenanthrene, and 1-(2-methylvinylidene)-1a,9b-dihydro-1H-cyclopropa[l]phenanthrene, photochemical precursors to propadienylidene, 3-phenylpropadienylidene, and 3-methylpropadienylidene have been carried out. Photolysis of these new precursors in olefin traps and benzene afforded the expected cyclopropane adducts of the corresponding allenylidenes. Quantum chemical calculations show that the ground state of all three carbenes is a singlet with a singlet-triplet gap of ∼29, 30, and 33 kcal/mol for propadienylidene, 3-phenylpropadienylidene, and 3-methylpropadienylidene, respectively.

Facilitating Electron Transfer by Resizing Cyclocarbon Acceptor from C18 to C16

Recent advances in synthetic methods, combined with tip-induced on-surface chemistry, have enabled the formation of numerous cyclocarbon molecules. Here, we investigate computationally the experimentally studied C16 and C18 molecules as well as their van der Waals (vdW) complexes with several typical donor and acceptor molecules. Our results demonstrate a remarkable electron-withdrawing ability of cyclocarbon molecules. The vdW complexes of C16 and C18 exhibit a thermodynamically favorable photoinduced electron transfer (ET) from the donor partner to the cyclocarbons that occurs on a picosecond time scale. The lower reorganization energy of C16 compared to C18 leads to a significant acceleration of the ET reactions.

Chemiluminescence and electrochemiluminescence of water-soluble iridium(III) complexes containing a tetraethylene-glycol functionalised triazolylpyridine ligand

BACKGROUND

Iridium(III) complexes, exhibiting high luminescence quantum yields and a wide range of emission colours, are promising alternatives to tris(2,2'-bipyridine)ruthenium(II) for chemiluminescence (CL) and electrochemiluminescence (ECL) detection. This emerging class of reagent, however, is limited by the poor solubility of many iridium(III) complexes in aqueous solution, and lack of understanding of their remarkably variable selectivities towards different analytes.

RESULTS

Seven [Ir(C^N)2(pt-TEG)]+ complexes, exhibiting a wide range of reduction potentials and emission energies, were examined with six model analytes. For CL, cerium(IV) was used as the oxidant. The alkylamine analytes generally produced greater CL and ECL with the more readily oxidised Ir(III) complexes (C^N = piq, bt, ppy), predominantly through the 'direct' pathway requiring oxidation of both metal complex and analyte. Aniline derivatives that did not also contain secondary or tertiary alkylamines elicited CL from the less readily oxidised complexes (C^N = df-ppy-CF3, df-ppy) via energy transfer. The most difficult to oxidise complexes (C^N = df(CF3)-ppy-Me, df(CN)-ppy) gave poor responses due to the limited potential window of the solvent and inefficiency of energy transfer to their high energy excited states. Greater CL and/or ECL intensities were generally obtained for each analyte with at least one Ir(III) complex than with [Ru(bpy)3]2+; superior limits of detection for two analytes were demonstrated.

SIGNIFICANCE

This exploration of CL/ECL in which the properties of luminophore, analyte and oxidant are all varied provides a new understanding of the influence of the metal-complex potentials and excited state energy on the light-producing and quenching pathways, and consequently, their distinct selectivity towards different analytes. These findings will guide the development of water-soluble Ir(III) complexes as CL and ECL reagents.

A reactive neural network framework for water-loaded acidic zeolites

Under operating conditions, the dynamics of water and ions confined within protonic aluminosilicate zeolite micropores are responsible for many of their properties, including hydrothermal stability, acidity and catalytic activity. However, due to high computational cost, operando studies of acidic zeolites are currently rare and limited to specific cases and simplified models. In this work, we have developed a reactive neural network potential (NNP) attempting to cover the entire class of acidic zeolites, including the full range of experimentally relevant water concentrations and Si/Al ratios. This NNP has the potential to dramatically improve sampling, retaining the (meta)GGA DFT level accuracy, with the capacity for discovery of new chemistry, such as collective defect formation mechanisms at the zeolite surface. Furthermore, we exemplify how the NNP can be used as a basis for further extensions/improvements which include data-efficient adoption of higher-level (hybrid) references via Δ-learning and the acceleration of rare event sampling via automatic construction of collective variables. These developments represent a significant step towards accurate simulations of realistic catalysts under operando conditions.

Predicting valence tautomerism in diverse cobalt-dioxolene complexes: elucidation of the role of ligands and solvent

The ability of molecular switches to reversibly interconvert between different forms promises potential applications at the scale of single molecules up to bulk materials. One type of molecular switch comprises cobalt-dioxolene compounds that exhibit thermally-induced valence tautomerism (VT) interconversions between low spin Co(iii)-catecholate (LS-CoIII-cat) and high spin Co(ii)-semiquinonate (HS-CoII-sq) forms. Two families of these compounds have been investigated for decades but have generally been considered separately: neutral [Co(diox)(sq)(N2L)] and cationic [Co(diox)(N4L)]+ complexes (diox = generic dioxolene, N2L/N4L = bidentate/tetradentate N-donor ancillary ligand). Computational identification of promising new candidate compounds prior to experimental exploration is beneficial for environmental and cost considerations but requires a thorough understanding of the underlying thermochemical parameters that influence the switching. Herein, we report a robust approach for the analysis of both cobalt-dioxolene families, which involved a quantitative density functional theory-based study benchmarked with reliable quasi-experimental references. The best-performing M06L-D4/def2-TZVPP level of theory has subsequently been verified by the synthesis and experimental investigation of three new complexes, two of which exhibit thermally-induced VT, while the third remains in the LS-CoIII-cat form across all temperatures, in agreement with prediction. Valence tautomerism in solution is markedly solvent-dependent, but the origin of this has not been definitively established. We have extended our computational approach to elucidate the correlation of VT transition temperature with solvent stabilisation energy and change in dipole moment. This new understanding may inform the development of VT compounds for applications in soft materials including films, gels, and polymers.

Multilevel Framework for Analysis of Protein Folding Involving Disulfide Bond Formation

In this study, a three-layered multicenter ONIOM approach is implemented to characterize the naive folding pathway of bovine pancreatic trypsin inhibitor (BPTI). Each layer represents a distinct level of theory, where the initial layer, encompassing the entire protein, is modeled by a general all-atom force-field GFN-FF. An intermediate electronic structure layer consisting of three multicenter fragments is introduced with the state-of-the-art semiempirical tight-binding method GFN2-xTB. Higher accuracy, specifically addressing the breaking and formation of the three disulfide bonds, is achieved at the innermost layer using the composite DFT method r2SCAN-3c. Our analysis sheds light on the structural stability of BPTI, particularly the significance of interlinking disulfide bonds. The accuracy and efficiency of the multicenter QM/SQM/MM approach are benchmarked using the oxidative formation of cystine. For the folding pathway of BPTI, relative stabilities are investigated through the calculation of free energy contributions for selected intermediates, focusing on the impact of the disulfide bond. Our results highlight the intricate trade-off between accuracy and computational cost, demonstrating that the multicenter ONIOM approach provides a well-balanced and comprehensive solution to describe electronic structure effects in biomolecular systems. We conclude that multiscale energy landscape exploration provides a robust methodology for the study of intriguing biological targets.

Conformational energies of biomolecules in solution: Extending the MPCONF196 benchmark with explicit water molecules

A prerequisite for the computational prediction of molecular properties like conformational energies of biomolecules is a reliable, robust, and computationally affordable method usually selected according to its performance for relevant benchmark sets. However, most of these sets comprise molecules in the gas phase and do not cover interactions with a solvent, even though biomolecules typically occur in aqueous solution. To address this issue, we introduce a with explicit water molecules solvated version of a gas-phase benchmark set containing 196 conformers of 13 peptides and other relevant macrocycles, namely MPCONF196 [J. Řezáč et al., JCTC 2018, 14, 1254-1266], and provide very accurate PNO-LCCSD(T)-F12b/AVQZ' reference values. The novel solvMPCONF196 benchmark set features two additional challenges beyond the description of conformers in the gas phase: conformer-water and water-water interactions. The overall best performing method for this set is the double hybrid revDSDPBEP86-D4/def2-QZVPP yielding conformational energies of almost coupled cluster quality. Furthermore, some (meta-)GGAs and hybrid functionals like B97M-V and ω B97M-D with a large basis set reproduce the coupled cluster reference with an MAD below 1 kcal mol- 1  . If more efficient methods are required, the composite DFT-method r2 SCAN-3c (MAD of 1.2 kcal mol- 1 ) is a good alternative, and when conformational energies of polypeptides or macrocycles with more than 500-1000 atoms are in the focus, the semi-empirical GFN2-xTB or the MMFF94 force field (for very large systems) are recommended.

Incorporating Neural Networks into the AMOEBA Polarizable Force Field

Neural network potentials (NNPs) offer significant promise to bridge the gap between the accuracy of quantum mechanics and the efficiency of molecular mechanics in molecular simulation. Most NNPs rely on the locality assumption that ensures the model's transferability and scalability and thus lack the treatment of long-range interactions, which are essential for molecular systems in the condensed phase. Here we present an integrated hybrid model, AMOEBA+NN, which combines the AMOEBA potential for the short- and long-range noncovalent atomic interactions and an NNP to capture the remaining local covalent contributions. The AMOEBA+NN model was trained on the conformational energy of the ANI-1x data set and tested on several external data sets ranging from small molecules to tetrapeptides. The hybrid model demonstrated substantial improvements over the baseline models in term of accuracy as the molecule size increased, suggesting its potential as a next-generation approach for chemically accurate molecular simulations.

Quantum chemical modeling of hydrogen binding in metal-organic frameworks: validation, insight, predictions and challenges

A detailed chemical understanding of H2 interactions with binding sites in the nanoporous crystalline structure of metal-organic frameworks (MOFs) can lay a sound basis for the design of new sorbent materials. Computational quantum chemical calculations can aid in this quest. To set the stage, we review general thermodynamic considerations that control the usable storage capacity of a sorbent. We then discuss cluster modeling of H2 ligation at MOF binding sites using state-of-the-art density functional theory (DFT) calculations, and how the binding can be understood using energy decomposition analysis (EDA). Employing these tools, we illustrate the connections between the character of the MOF binding site and the associated adsorption thermodynamics using four experimentally characterized MOFs, highlighting the role of open metal sites (OMSs) in accessing binding strengths relevant to room temperature storage. The sorbents are MOF-5, with no open metal sites, Ni2(m-dobdc), containing Lewis acidic Ni(II) sites, Cu(I)-MFU-4l, containing π basic Cu(I) sites and V2Cl2.8(btdd), also containing π-basic V(II) sites. We next explore the potential for binding multiple H2 molecules at a single metal site, with thermodynamics useful for storage at ambient temperature; a materials design goal which has not yet been experimentally demonstrated. Computations on Ca2+ or Mg2+ bound to catecholate or Ca2+ bound to porphyrin show the potential for binding up to 4 H2; there is precedent for the inclusion of both catecholate and porphyrin motifs in MOFs. Turning to transition metals, we discuss the prediction that two H2 molecules can bind at V(II)-MFU-4l, a material that has been synthesized with solvent coordinated to the V(II) site. Additional calculations demonstrate binding three equivalents of hydrogen per OMS in Sc(I) or Ti(I)-exchanged MFU-4l. Overall, the results suggest promising prospects for experimentally realizing higher capacity hydrogen storage MOFs, if nontrivial synthetic and desolvation challenges can be overcome. Coupled with the unbounded chemical diversity of MOFs, there is ample scope for additional exploration and discovery.

Exploring CPS-Extrapolated DLPNO-CCSD(T1) Reference Values for Benchmarking DFT Methods on Enzymatically Catalyzed Reactions

Domain-based local pair natural orbital coupled-cluster singles doubles with perturbative triples [DLPNO-CCSD(T)] is regularly used to calculate reliable benchmark reference values at a computational cost significantly lower than that of canonical CCSD(T). Recent work has shown that even greater accuracy can be obtained at only a small additional cost through extrapolation to the complete PNO space (CPS) limit. Herein, we test two levels of CPS extrapolation, CPS(5,6), which approximates the accuracy of standard TightPNO, and CPS(6,7), which surpasses it, as benchmark values to test density functional approximations (DFAs) on a small set of organic and transition-metal-dependent enzyme active site models. Between the different reference levels of theory, there are changes in the magnitudes of the absolute deviations for all functionals, but these are small and there is minimal impact on the relative rankings of the tested DFAs. The differences are more significant for the metalloenzymes than the organic enzymes, so we repeat the tests on our entire ENZYMES22 set of organic enzyme active site models [Wappett, D. A.; Goerigk, L. J. Phys. Chem. A 2019, 123, 7057-7074] to confirm that using the CPS extrapolations for the reference values has negligible impact on the benchmarking outcomes. This means that we can particularly recommend CPS(5,6) as an alternative to standard TightPNO settings for calculating reference values, increasing the applicability of DLPNO-CCSD(T) in benchmarking reaction energies and barrier heights of larger models of organic enzymes. DLPNO-CCSD(T1)/CPS(6,7) energies for ENZYMES22 are finally presented as updated reference values for the set, reflecting the recent improvements in the method.

OpenMM 8: Molecular Dynamics Simulation with Machine Learning Potentials

Machine learning plays an important and growing role in molecular simulation. The newest version of the OpenMM molecular dynamics toolkit introduces new features to support the use of machine learning potentials. Arbitrary PyTorch models can be added to a simulation and used to compute forces and energy. A higher-level interface allows users to easily model their molecules of interest with general purpose, pretrained potential functions. A collection of optimized CUDA kernels and custom PyTorch operations greatly improves the speed of simulations. We demonstrate these features in simulations of cyclin-dependent kinase 8 (CDK8) and the green fluorescent protein chromophore in water. Taken together, these features make it practical to use machine learning to improve the accuracy of simulations with only a modest increase in cost.

Balance between Physical Interpretability and Energetic Predictability in Widely Used Dispersion-Corrected Density Functionals

We assess the performance of different dispersion models for several popular density functionals across a diverse set of noncovalent systems, ranging from the benzene dimer to molecular crystals. By analyzing the interaction energies and their individual components, we demonstrate that there exists variability across different systems for empirical dispersion models, which are calibrated for reproducing the interaction energies of specific systems. Thus, parameter fitting may undermine the underlying physics, as dispersion models rely on error compensation among the different components of the interaction energy. Energy decomposition analyses reveal that, the accuracy of revPBE-D3 for some aqueous systems originates from significant compensation between dispersion and charge transfer energies. However, revPBE-D3 is less accurate in describing systems where error compensation is incomplete, such as the benzene dimer. Such cases highlight the propensity for unpredictable behavior in various dispersion-corrected density functionals across a wide range of molecular systems, akin to the behavior of force fields. On the other hand, we find that SCAN-rVV10, a targeted-dispersion approach, affords significant reductions in errors associated with the lattice energies of molecular crystals, while it has limited accuracy in reproducing structural properties. Given the ubiquitous nature of noncovalent interactions and the key role of density functional theory in computational sciences, the future development of dispersion models should prioritize the faithful description of the dispersion energy, a shift that promises greater accuracy in capturing the underlying physics across diverse molecular and extended systems.

Prediction of 19F NMR chemical shifts for organic compounds with ORCA

Accurate assignment of 19F NMR has long been a challenge, and quantum chemical methods are possible solutions. Herein we reported a scaling method for the prediction of 19F NMR chemical shift with freely available ORCA program package. Performance of 31 DFT functionals coupled with 11 basis sets were evaluated and influence of geometry optimization was also studied with five functionals coupled with three basis sets. The significance of geometry was further examined through the execution of relaxed surface scans of seven flexible compounds, and averaged shieldings of obtained conformers yielded notable improvement of the correlation between calculated isotropic shielidings and experimental chemical shifts. Utilization of the best scaling factor obtained successfully assigned of fluorine atoms in multifluorinated molecules with different conformations. The method reported here was computationally inexpensive, easily available with acceptable accuracy.

Noncovalently bound excited-state dimers: a perspective on current time-dependent density functional theory approaches applied to aromatic excimer models

Excimers are supramolecular systems whose binding strength is influenced by many factors that are ongoing challenges for computational methods, such as charge transfer, exciton coupling, and London dispersion interactions. Treating the various intricacies of excimer binding at an adequate level is expected to be particularly challenging for time-dependent Density Functional Theory (TD-DFT) methods. In addition to well-known limitations for some TD-DFT methods in the description of charge transfer or exciton coupling, the inherent London dispersion problem from ground-state DFT translates to TD-DFT. While techniques to appropriately treat dispersion in DFT are well-developed for electronic ground states, these dispersion corrections remain largely untested for excited states. Herein, we aim to shed light on current TD-DFT methods, including some of the newest developments. The binding of four model excimers is studied across nine density functionals with and without the application of additive dispersion corrections against a wave function reference of SCS-CC2/CBS(3,4) quality, which approximates select CCSDR(3)/CBS data adequately. To our knowledge, this is the first study that presents single-reference wave function dissociation curves at the complete basis set level for the assessed model systems. It is also the first time range-separated double-hybrid density functionals are applied to excimers. In fact, those functionals turn out to be the most promising for the description of excimer binding followed by global double hybrids. Range-separated and global hybrids-particularly with large fractions of Fock exchange-are outperformed by double hybrids and yield worse dissociation energies and inter-molecular equilibrium distances. The deviation between each assessed functional and reference increases with system size, most likely due to missing dispersion interactions. Additive dispersion corrections of the DFT-D3(BJ) and DFT-D4 types reduce the average errors for TD-DFT methods but do so inconsistently and therefore do not offer a black-box solution in their ground-state parametrised form. The lack of appropriate description of dispersion effects for TD-DFT methods is likely hindering the practical application of the herein identified more efficient methods. Dispersion corrections parametrised for excited states appear to be an important next step to improve the applicability of TD-DFT methods and we hope that our work assists with the future development of such corrections.

Benchmarking Density Functional Theory Methods for Metalloenzyme Reactions: The Introduction of the MME55 Set

We present a new benchmark set of metalloenzyme model reaction energies and barrier heights that we call MME55. The set contains 10 different enzymes, representing eight transition metals, both open and closed shell systems, and system sizes of up to 116 atoms. We use four DLPNO-CCSD(T)-based approaches to calculate reference values against which we then benchmark the performance of a range of density functional approximations with and without dispersion corrections. Dispersion corrections improve the results across the board, and triple-ζ basis sets provide the best balance of efficiency and accuracy. Jacob's ladder is reproduced for the whole set based on averaged mean absolute (percent) deviations, with the double hybrids SOS0-PBE0-2-D3(BJ) and revDOD-PBEP86-D4 standing out as the most accurate methods for the MME55 set. The range-separated hybrids ωB97M-V and ωB97X-V also perform well here and can be recommended as a reliable compromise between accuracy and efficiency; they have already been shown to be robust across many other types of chemical problems, as well. Despite the popularity of B3LYP in computational enzymology, it is not a strong performer on our benchmark set, and we discourage its use for enzyme energetics.

Range-Separated Local Hybrid Functionals with Small Fractional-Charge and Fractional-Spin Errors: Escaping the Zero-Sum Game of DFT Functionals

Extending recent developments on strong-correlation (sc) corrections to local hybrid functionals to the recent accurate ωLH22t range-separated local hybrid, a series of highly flexible strong-correlation-corrected range-separated local hybrids (scRSLHs) has been constructed and evaluated. This has required the position-dependent reduction of both short- and long-range exact-exchange admixtures in regions of space characterized by strong static correlations. Using damping procedures provides scRSLHs that retain largely the excellent performance of ωLH22t for weakly correlated situations and, in particular, for accurate quasiparticle energies of a wide variety of systems while reducing dramatically static-correlation errors, e.g., in stretched-bond situations. An additional correction to the local mixing function to reduce delocalization errors in abnormal open-shell situations provides further improvements in thermochemical and kinetic parameters, making scRSLH functionals such as ωLH23tdE or ωLH23tdP promising tools for complex molecular or condensed-phase systems, where low fractional-charge and fractional-spin errors are simultaneously important. The proposed rung 4 functionals thereby largely escape the usual zero-sum game between these two quantities and are expected to open new areas of accurate computations by Kohn-Sham DFT. At the same time, they require essentially no extra computational effort over the underlying ωLH22t functional, which means that their use is only moderately more demanding than that of global, local, or range-separated hybrid functionals.

High-Dimensional Neural Network Potentials for Accurate Prediction of Equation of State: A Case Study of Methane

Machine learning-based interatomic potentials, such as those provided by neural networks, are increasingly important in molecular dynamics simulations. In the present work, we consider the applicability and robustness of machine learning molecular dynamics to predict the equation of state properties of methane by using high-dimensional neural network potentials (HDNNPs). We investigate two different strategies for generating training data: one strategy based upon bulk representations using periodic cells and another strategy based upon clusters of molecules. We assess the accuracy of the trained potentials by predicting the equilibrium mass density for a wide range of thermodynamic conditions to characterize the liquid phase, supercritical fluid, and gas phase, as well as the liquid-vapor coexistence curve. Our results show an excellent agreement with reference phase diagrams, with an average error below ∼2% for all studied phases. Moreover, we confirm the applicability of models trained on cluster data sets for producing accurate and reliable results.

Liberation of carbon monoxide from formic acid mediated by molybdenum oxyanions

Multistage mass spectrometry experiments, isotope labelling and DFT calculations were used to explore whether selective decarbonylation of formic acid could be mediated by molybdate anions [(MoO3)x(OH)]- (x = 1 and 2) via a formal catalytic cycle involving two steps. In step 1, both molybdate anions undergo gas-phase ion-molecule reactions (IMR) with formic acid to produce the coordinated formates [(MoO3)x(O2CH)]- and H2O. In step 2, both coordinated formates [(MoO3)x(O2CH)]- undergo decarbonylation under collision-induced dissociation (CID) conditions to reform the molybdate anions [(MoO3)x(OH)]- (x = 1 and 2), thus closing a formal catalytic cycle. In the case of [MoO3(O2CH)]- an additional decarboxylation channel also occurs to yield [MoO3(H)]-, which is unreactive towards formic acid. The reaction between [Mo18O3(18OH)]- and formic acid gives rise to [Mo18O3(O2CH)]- highlighting that ligand substitution occurs without 18O/16O exchange between the coordinated 18OH ligand and HC16O2H. The reaction between [(MoO3)x(OD)]- (x = 1 and 2) and DCO2H initially produces [(MoO3)x(OH)]- (x = 1 and 2), indicating that D/H exchange occurs. DFT calculations were carried out to investigate the reaction mechanisms and energetics associated with both steps of the formal catalytic cycle and to better understand the competition between decarbonylation and decarboxylation, which is crucial in developing a selective catalyst. The CO and CO2 loss channels from the monomolybdate anion [MoO3(O2CH)]- have similar barrier heights which is in agreement with experimental results where both fragmentation channels are observed. In contrast, the dimolybdate anion is more selective, since the decarbonylation pathway of [(MoO3)2(O2CH)]- is both kinetically and thermodynamically favoured, which agrees with experimental observations where the CO loss channel is solely observed.

A transferable quantum mechanical energy model for intermolecular interactions using a single empirical parameter

The calculation of intermolecular interactions in molecular crystals using model energies provides a unified route to understanding the complex interplay of driving forces in crystallization, elastic properties and more. Presented here is a new single-parameter interaction energy model (CE-1p), extending the previous CrystalExplorer energy model and calibrated using density functional theory (DFT) calculations at the ωB97M-V/def2-QZVP level over 1157 intermolecular interactions from 147 crystal structures. The new model incorporates an improved treatment of dispersion interactions and polarizabilities using the exchange-hole dipole model (XDM), along with the use of effective core potentials (ECPs), facilitating application to molecules containing elements across the periodic table (from H to Rn). This new model is validated against high-level reference data with outstanding performance, comparable to state-of-the-art DFT methods for molecular crystal lattice energies over the X23 set (mean absolute deviation 3.6 kJ mol-1) and for intermolecular interactions in the S66x8 benchmark set (root mean-square deviation 3.3 kJ mol-1). The performance of this model is further examined compared to the GFN2-xTB tight-binding model, providing recommendations for the evaluation of intermolecular interactions in molecular crystal systems.

Regime Switch in the Dual-Catalyzed Coupling of Alkyl Silicates with Aryl Bromides

Metallaphotoredox catalyzed cross-coupling of an arylbromide (Ar-Br) with an alkyl bis(catecholato)silicate (R-Si⊖ ) has been analyzed in depth using a continuum of analytical techniques (EPR, fluorine NMR, electrochemistry, photophysics) and modeling (micro-kinetics and DFT calculations). These studies converged on the impact of four control parameters consisting in the initial concentrations of the iridium photocatalyst ([Ir]0 ), nickel precatalyst ([Ni]0 ) and silicate ([R-Si⊖ ]0 ) as well as light intensity I0 for an efficient reaction between Ar-Br and R-Si⊖ . More precisely, two regimes were found to be possibly at play. The first one relies on an equimolar consumption of Ar-Br with R-Si⊖ smoothly leading to Ar-R, with no side-product from R-Si⊖ and a second one in which R-Si⊖ is simultaneously coupled to Ar-Br and degraded to R-H. This integrative approach could serve as a case study for the investigation of other metallaphotoredox catalysis manifolds of synthetic significance.

Adamantylidenecarbene: Photochemical Generation, Trapping, and Theoretical Studies

Photolysis of 1-(2-adamantylidene)-1a,9b-dihydro-1H-cyclopropa[l]phenanthrene in benzene (or benzene-d6) at ambient temperature produces adamantylidenecarbene. The carbene undergoes dimerization to a cumulene and may also be trapped in a stereospecific fashion by cis- and trans-4-methyl-2-pentene. No products attributable to 4-homoadamantyne, resulting from ring expansion of the carbene, could be detected. Coupled cluster/density functional theory calculations place the singlet carbene ∼49 kcal/mol below the triplet and show that the former must overcome a barrier of ∼13.5 kcal/mol to rearrange into 4-homoadamantyne.

Donor Radii in Rare-Earth Complexes

We present a set of donor radii for the rare-earth cations obtained from the analysis of structural data available in the Cambridge Structural Database (CSD). Theoretical calculations using density functional theory (DFT) and wave function approaches (NEVPT2) demonstrate that the Ln-donor distances can be broken down into contributions of the cation and the donor atom, with the minimum in electron density (ρ) that defines the position of (3,-1) critical points corresponding well with Shannon's crystal radii (CR). Subsequent linear fits of the experimental bond distances for all rare earth cations (except Pm3+) afforded donor radii (rD) that allow for the prediction of Ln-donor distances regardless of the nature of the rare-earth cation and its oxidation state. This set of donor radii can be used to rationalize structural data and identify particularly weak or strong interactions, which has important implications in the understanding of the stability and reactivity of complexes of these metal ions. A few cases of incorrect atom assignments in X-ray structures were also identified using the derived rD values.

Investigating the accuracy of density functional methods for molecules in electric fields

The use of oriented external electric fields (OEEFs) as a potential tool for catalyzing chemical reactions has gained traction in recent years. Electronic structure calculations using OEEFs are commonly done using methods based on density functional theory (DFT), but until now, the performance of DFT methods for calculating molecules in OEEFs had not been assessed in a more general scope. Looking at the accuracy of molecular geometries, electronic energies, and electric dipole moments compared to accurate coupled-cluster with perturbative triples data, we have investigated a wide variety of density functionals using different basis sets to determine how well the individual functionals perform on various types of chemical bonds. We found that most functionals accurately calculate geometries in OEEFs and that small basis sets are sufficient in many cases. Calculations of electronic energies show a significant error introduced by the OEEF, which the use of a larger basis set helps mitigate. Our findings show that DFT methods can be used for accurate calculations in OEEFs, allowing researchers to make full use of the advantages that they bring.