Efficient DLPNO–CCSD(T)-Based Estimation of Formation Enthalpies for C-, H-, O-, and N-Containing Closed-Shell Compounds Validated Against Critically Evaluated Experimental Data

Toward Accurate Quantum Mechanical Thermochemistry: (1) Extensible Implementation and Comparison of Bond Additivity Corrections and Isodesmic Reactions

Obtaining accurate enthalpies of formation of chemical species, ΔHf, often requires empirical corrections that connect the results of quantum mechanical (QM) calculations with the experimental enthalpies of elements in their standard state. One approach is to use atomization energy corrections followed by bond additivity corrections (BACs), such as those defined by Petersson et al. or Anantharaman and Melius. Another approach is to utilize isodesmic reactions (IDRs) as shown by Buerger et al. We implement both approaches in Arkane, an open-source software that can calculate species thermochemistry using results from various QM software packages. In this work, we collect 421 reference species from the literature to derive ΔHf corrections and fit atomization energy corrections and BACs for 15 commonly used model chemistries. We find that both types of BACs yield similar accuracy, although Anantharaman- and Melius-type BACs appear to generalize better. Furthermore, BACs tend to achieve better accuracy than IDRs for commonly used model chemistries, and IDRs can be less robust because of the sensitivity to the chosen reference species and reactions. Overall, Anantharaman- and Melius-type BACs are our recommended approach for achieving accurate QM corrections for enthalpies.

Dialdehyde starch-enclosed silver nanoparticles substrate with controlled-release "hotspots" for ultrasensitive SERS detection of thiabendazole

Pesticide residues have long been a major concern for food safety. In this study, a dialdehyde starch-encapsulated silver nanoparticles composite with controlled-release "hotspots" was developed as a surface-enhanced Raman scattering (SERS) substrate. At room temperature, most of the Ag NPs were encapsulated in dialdehyde starch, which is beneficial for improving stability, and when heated to the gelatinization point, Ag NPs are completely released and abundant hot spots are formed. We demonstrated sensitive detection of thiabendazole (TBZ) in or on the surface of an apple by means of two ways, i.e., detecting the analyte in solution after pretreatment and in-situ detecting the analyte by using a flexible paper-based substrate. The results showed that the detection limits of TBZ by the two ways were 0.052 ppm and 0.051 ppm respectively, and the recoveries of TBZ range from 96.80 % to 105.46 %. Overall, this SERS substrate shows great potential for pesticide residue detection in food.

Formation Enthalpies of C3 and C4 Brominated Hydrocarbons: Bringing Together Classical Thermodynamics, Modern Mass Spectrometry, and High-Level Ab Initio Calculations

The enthalpies of formation of brominated C3-C4 hydrocarbons were critically evaluated using experimental data sources ranging from classical thermodynamics methods to modern high-precision mass spectrometry and reported in a time span of a century. The experimental data were used in conjunction with the results of modern high-level ab initio calculations. To facilitate quantitative analysis, a recently developed local coupled cluster-based computational protocol was extended to organic compounds containing univalent Br. Several erroneous data sources were identified in a course of the study. Possible reasons for the inconsistency between the ΔfHm° values recommended by the Committee on Data of the International Science Council (CODATA) and Active Thermochemical Tables for HBr in the gas and aqueous solution were discussed. The most up-to-date recommendations based on the comprehensive analysis of collected information are provided for 23 brominated hydrocarbons. For several compounds under consideration, the recommended values were previously lacking, while improved values and uncertainties were obtained for those with existing recommendations.

Gas-Phase Alkali-Metal Cation Affinities of Stabilized Enolates

The chemistry of alkali-metal enolates is dominated by ion pairing. To improve our understanding of the intrinsic interactions between the alkali-metal cations and the enolate anions, we have applied Cooks' kinetic method to determine relative M+ (M=Li, Na, K) affinities of the stabilized enolates derived from acetylacetone, ethyl acetoacetate, diethyl malonate, ethyl cyanoacetate, 2-cyanoacetamide, and methyl malonate monoamide in the gas phase. Quantum chemical calculations support the experimental results and moreover afford insight into the structures of the alkali-metal enolate complexes. The affinities decrease with increasing size of the alkali-metal cations, reflecting weaker electrostatic interactions and lower charge densities of the free M+ ions. For the different enolates, a comparison of their coordinating abilities is complicated by the fact that some of the free anions undergo conformational changes resulting in stabilizing intramolecular interactions. If these complicating effects are disregarded, the M+ affinities correlate with the electron density of the chelating functionalities, that is, the carbonyl and/or the nitrile groups of the enolates. A comparison with the known association constants of the corresponding alkali-metal enolates in solution points to the importance of solvation effects for these systems.

Enthalpy of formation of 6-phenyl-1,5-diazabicyclo[3.1.0]hexane by combustion calorimetry and theoretical approach for efficient prediction of thermochemistry of diaziridines

The combustion energy and standard molar enthalpy of formation of crystalline 6-phenyl-1,5-diazabicyclo[3.1.0]hexane (PDABH) were determined using an isoperibolic calorimeter with a static bomb. PDABH is the first diaziridine for which the experimental value of the enthalpy of formation was obtained. This value was validated by the theoretical values of gas phase enthalpy of formation and enthalpy of sublimation. The gas phase enthalpy of formation was calculated using the DLPNO-CCSD(T1)/CBS method in conjunction with isodesmic-type reactions. This method was chosen in comparison to another high quality evaluative method (G4), which has been shown to provide unreliable results for cyclic nitrogen containing compounds. The descriptors of the molecular electrostatic potential (MEP) were used to estimate the enthalpy of sublimation of PDABH. The proposed MEP model is based on experimental enthalpies of sublimation for 75 compounds structurally similar to PDABH. The high-level ab initio calculations of gas phase enthalpies of formation combined with enthalpies of sublimations estimated using descriptors of MEP allow predicting the enthalpies of formation of diaziridines in the solid phase.

The entropic penalty for associative reactions and their physical treatment during routine computations

A systematic study of the entropic penalty for associative reactions is presented. It is shown that computed solution-phase Gibbs free energies typically overestimate entropic contributions. This entropic penalty for associative reactions in solution, i.e., if the number of particles decreases along the reaction coordinate (sum of stoichiometric numbers ), originates from the insufficient treatment of entropic effects by implicit solvent models. We propose an additive correction scheme to Gibbs free energies that is suitable for routine applications by non-expert users. This correction is based on Garza's formalism for the solution-phase entropy [A. J. Garza, J. Chem. Theory Comput., 2019, 15, 3204.] that is physically sound and embedded into an efficient black-box type algorithm. To critically evaluate the entropic penalty and its proposed treatment, we compiled an experimental benchmark set of 31 Δ_rG and 22 in 15 different solvents. Using a representative best-practice computational protocol (at wave function theory (WFT) based DLPNO-CCSD(T) and density functional theory (DFT) based revDSD-PBEP86-D4 level with an implicit solvent model), we determined a sizeable entropic penalty ranging from 2-11 kcal mol^-1. Using the correction scheme presented herein, the entropic penalty is corrected to the chemical accuracy of ≤1 kcal mol^-1 (WFT and DFT). The same applies to at the WFT level. Barriers at the DFT level are overestimated by 2 kcal mol^-1 (classic) and underestimated by 2 kcal mol^-1 (corrected). This effect is attributed to the finding that barriers computed at the DFT level are systematically 2-3 kcal mol^-1 lower than barriers obtained with WFT.

Exploring the Accuracy Limits of PNO-Based Local Coupled-Cluster Calculations for Transition-Metal Complexes

While the domain-based local pair natural orbital coupled-cluster method with singles, doubles, and perturbative triples (DLPNO-CCSD(T)) has proven instrumental for computing energies and properties of large and complex systems accurately, calculations on first-row transition metals with a complex electronic structure remain challenging. In this work, we identify and address the two main error sources that influence the DLPNO-CCSD(T) accuracy in this context, namely, (i) correlation effects from the 3s and 3p semicore orbitals and (ii) dynamic correlation-induced orbital relaxation (DCIOR) effects that are not described by the local MP2 guess. We present a computational strategy that allows us to completely eliminate the DLPNO error associated with semicore correlation effects, while increasing, at the same time, the efficiency of the method. As regards the DCIOR effects, we introduce a diagnostic for estimating the deviation between DLPNO-CCSD(T) and canonical CCSD(T) for systems with significant orbital relaxation.

Thermochemistry of per- and polyfluoroalkyl substances

The determination of gas phase thermochemical properties of per- and polyfluoroalkyl substances (PFAS) is central to understanding the long-range transport behavior of PFAS in the atmosphere. Prior gas-phase studies have reported the properties of perfluorinated sulfonic acid (PFOS) and perfluorinated octanoic acid (PFOA). Here, this study reports the gas phase enthalpies of formation of short- and long-chain PFAS and their precursor molecules determined using density functional theory (DFT) and ab initio approaches. Two density functionals, two ab initio methods and an empirical method were used to compute enthalpies of formation with the total atomization approach and an isogyric reaction. The performance of the computational methods employed in this work were validated against the experimental enthalpies of linear alkanoic acids and perfluoroalkanes. The gas-phase determinations will be useful for future studies of PFAS in the atmosphere, and the methodological choices will be helpful in the study of other PFAS.

Anionic Dimers of Fluorinated Alcohols

Negative-ion mode electrospray ionization of solutions of ethanol (R^F0OH), 2-fluoroethanol (R^F1OH), 2,2-difluoroethanol (R^F2OH), and/or 2,2,2-trifluoroethanol (R^F3OH) produces anionic dimers of the types (R^FnO)₂H^- and (R^FnO)(R^Fn+1O)H^-. The exchange reactions of these anionic dimers with the neutral alcohols are examined in a quadrupole-ion trap to extract kinetic data, from which the reaction Gibbs energies are obtained. In all cases, the formation of anionic dimers containing the more highly fluorinated alcohols is favored. Quantum chemical calculations confirm this trend and, besides affording structural data, also determine the dissociation energies of the anionic dimers. These dissociation energies are much higher than those of the corresponding neutral dimers and increase further for the more highly fluorinated alcohols due to the stronger hydrogen-bond donor ability of the latter. The present results on the interaction of individual alkoxide anions and neutral alcohol molecules contribute to a better understanding of the association of the fluorinated alcohols in solution.

Advancing the Am Extractant Design through the Interplay among Planarity, Preorganization, and Substitution Effects

Advancing the field of chemical separations is important for nearly every area of science and technology. Some of the most challenging separations are associated with the americium ion Am(III) for its extraction in the nuclear fuel cycle, ²⁴¹Am production for industrial usage, and environmental cleanup efforts. Herein, we study a series of extractants, using first-principle calculations, to identify the electronic properties that preferentially influence Am(III) binding in separations. As the most used extractant family and because it affords a high degree of functionalization, the polypyridyl family of extractants is chosen to study the effects of the planarity of the structure, preorganization of coordinating atoms, and substitution of various functional groups. The actinyl ions are used as a structurally simplified surrogate model to quickly screen the most promising candidates that can separate these metal ions. The down-selected extractants are then tested for the Am(III)/Eu(III) system. Our results show that π interactions, especially those between the central terpyridine ring and Am(III), play a crucial role in separation. Adding an electron-donating group onto the terpyridine backbone increases the binding energies to Am(III) and stabilizes Am-terpyridine coordination. Increasing the planarity of the extractant increases the binding strength as well, although this effect is found to be rather weak. Preorganizing the coordinating atoms of an extractant to their binding configuration as in the bound metal complex speeds up the binding process and significantly improves the kinetics of the separation process. This conclusion is validated by the synthesized 1,2-dihydrodipyrido[4,3-b;5,6-b]acridine (13) extractant, a preorganized derivative of the terpyridine extractant, which we experimentally showed was four times more effective than terpyridine at separating Am³⁺ from Eu³⁺ (SF_Am/Eu ∼ 23 ± 1).

Inverse molecular design of alkoxides and phenoxides for aqueous direct air capture of CO2

Aqueous direct air capture (DAC) is a key technology toward a carbon negative infrastructure. Developing sorbent molecules with water and oxygen tolerance and high CO₂ binding capacity is therefore highly desired. We analyze the CO₂ absorption chemistries on amines, alkoxides, and phenoxides with density functional theory calculations, and perform inverse molecular design of the optimal sorbent. The alkoxides and phenoxides are found to be more suitable for aqueous DAC than amines thanks to their water tolerance (lower pK_a prevents protonation by water) and capture stoichiometry of 1:1 (2:1 for amines). All three molecular systems are found to generally obey the same linear scaling relationship (LSR) between [Formula: see text] and [Formula: see text], since both CO₂ and proton are bonded to the nucleophilic (alkoxy or amine) binding site through a majorly [Formula: see text] bonding orbital. Several high-performance alkoxides are proposed from the computational screening. Phenoxides have comparatively poorer correlation between [Formula: see text] and [Formula: see text], showing promise for optimization. We apply a genetic algorithm to search the chemical space of substituted phenoxides for the optimal sorbent. Several promising off-LSR candidates are discovered. The most promising one features bulky ortho substituents forcing the CO₂ adduct into a perpendicular configuration with respect to the aromatic ring. In this configuration, the phenoxide binds CO₂ and a proton using different molecular orbitals, thereby decoupling the [Formula: see text] and [Formula: see text]. The [Formula: see text] trend and off-LSR behaviors are then confirmed by experiments, validating the inverse molecular design framework. This work not only extensively studies the chemistry of the aqueous DAC, but also presents a transferrable computational workflow for understanding and optimization of other functional molecules.

ATOMIC-2 Protocol for Thermochemistry

ATOMIC is a midlevel thermochemistry protocol that uses Pople's concept of bond separation reactions (BSRs) as a theoretical framework to reduce computational demands in the evaluation of atomization energies and enthalpies of formation. Various composite models are available that approximate bond separation energies at the complete-basis-set limit of all-electron CCSD(T), each balancing computational cost with achievable accuracy. Evaluated energies are then combined with very high-level, precomputed atomization energies of all auxiliary molecules appearing in the BSR to obtain the atomization energy of the molecule under study. ATOMIC-2 is a new version of the protocol that retains the overall concept and all previously defined composite models but improves on ATOMIC-1 in various other ways: Geometry optimization and zero-point-energy evaluation are performed at the density functional level (PBE0-D3/6-311G(d)), which shows significant computational savings and better accuracy than the previously employed RI-MP2/cc-pVTZ. The BSR framework is improved, using more accurate complete-basis-set (CBS) extrapolations toward the Full CI limit for the atomization energies of all auxiliary molecules. Finally, and most importantly, an error and uncertainty model termed ATOMIC-2_um is added that estimates average bias and uncertainty for each of the atomization energy contributions that arise from the simplified treatment of some contributions to bond separation energies (CCSD(T)) and the neglect of others (such as higher order, scalar relativistic, or diagonal Born-Oppenheimer corrections) or from residual error in the energies of auxiliary molecules. Large and diverse benchmarks including up to 1179 molecules are used to evaluate necessary reference data and to correlate the observed error for each of the contributions with appropriate proxies that are available without additional quantum-chemical calculations for a particular molecule and represent its size and type. The implementation of ATOMIC-2 considers neutral, closed-shell molecules containing H, C, N, O, and F atoms; compared to ATOMIC-1, the framework has been extended to cover a few challenging but rare bond topologies. In comparison to highly accurate reference data for 184 molecules taken from the ATcT database (V. 1.122r), regular ATOMIC-2 shows noticeable underbinding, but the bias-corrected protocol ATOMIC-2_um is found to be more accurate than either ATOMIC-1 or standard Gaussian-4 theory, and the uncertainty model is consistent with statistics of actually observed errors. Problems arising from ambiguous or challenging Lewis-valence structures defining BSRs are discussed, and computational efficiency is demonstrated. Computer code is made available to perform ATOMIC-2_um analyses.

Open-Shell Variant of the London Dispersion-Corrected Hartree-Fock Method (HFLD) for the Quantification and Analysis of Noncovalent Interaction Energies

The London dispersion (LD)-corrected Hartree–Fock (HF) method (HFLD) is an ab initio approach for the quantification and analysis of noncovalent interactions (NCIs) in large systems that is based on the domain-based local pair natural orbital coupled-cluster (DLPNO-CC) theory. In the original HFLD paper, we discussed the implementation, accuracy, and efficiency of its closed-shell variant. Herein, an extension of this method to open-shell molecular systems is presented. Its accuracy is tested on challenging benchmark sets for NCIs, using CCSD(T) energies at the estimated complete basis set limit as reference. The HFLD scheme was found to be as accurate as the best-performing dispersion-corrected exchange-correlation functionals, while being nonempirical and equally efficient. In addition, it can be combined with the well-established local energy decomposition (LED) for the analysis of NCIs, thus yielding additional physical insights.

Gas-phase thermochemistry of polycyclic aromatic hydrocarbons: an approach integrating the quantum chemistry composite scheme and reaction generator

We introduce a protocol aimed at predicting the accurate gas-phase enthalpies of formation of polycyclic aromatic hydrocarbons (PAHs). Automatic generation of a dataset of equilibrated chemical reactions preserving the number of carbon atoms in each hybridization state on each side of equations is at the core of our scheme. The performed tests suggest the recommended enthalpy of formation to be derived via a two-step scheme. First, we consider the reactions with a minimal sum of the total number of particles involved, N, and the absolute difference between the total number of products and reactants, |ΔN|. Second, among these reactions, we identify the one with the smallest absolute reaction enthalpy change, . This approach has been applied to predict the gas-phase enthalpies of formation of 113 PAHs via the Feller-Peterson-Dixon approach. Our calculated values provide the mean absolute deviations of 1.7, 1.9, 4.2, 8.1, and 18.5 kJ mol^-1 with respect to the literature group-based error corrected (GBEC) G3MP2B3, ATOMIC (HC), group equivalent M06-2X, GBEC B3LYP, and G4MP2 values. Our predicted values give the mean signed and mean absolute errors of -7.5 and 12.9 kJ mol^-1 with respect to the experimental enthalpies of formation. The combination of our predicted and the experimental values provide the solid-state enthalpies of formation, , which are not available for a few species. Approaching these values as well as , producing large discrepancies from the experimental side, would be indispensable for testing and further tuning of computational chemistry approaches.

A DLPNO-CCSD(T) benchmarking study of intermolecular interactions of ionic liquids

The accuracy of correlation energy recovered by coupled cluster single-, double-, and perturbative triple-excitations, CCSD(T), has led to the method being considered the gold standard of computational chemistry. The application of CCSD(T) has been limited to medium-sized molecular systems due to its steep scaling with molecular size. The recent development of alternative domain-based local pair natural orbital coupled-cluster method, DLPNO-CCSD(T), has significantly broadened the range of chemical systems to which CCSD(T) level calculations can be applied. Condensed systems such as ionic liquids (ILs) have a large contribution from London dispersion forces of up to 150 kJ mol^-1 in large-scale clusters. Ionic liquids show appreciable charge transfer effects that result in the increased valence orbital delocalization over the entire ionic network, raising the question whether the application of methods based on localized orbitals is reliable for these semi-Coulombic materials. Here the performance of DLPNO-CCSD(T) is validated for the prediction of correlation interaction energies of two data sets incorporating single-ion pairs of protic and aprotic ILs. DLPNO-CCSD(T) produced results within chemical accuracy with tight parameter settings and a non-iterative treatment of triple excitations. To achieve spectroscopic accuracy of 1 kJ mol^-1 , especially for hydrogen-bonded ILs and those containing halides, the DLPNO settings had to be increased by two orders of magnitude and include the iterative treatment of triple excitations, resulting in a 2.5-fold increase in computational cost. Two new sets of parameters are put forward to produce the performance of DLPNO-CCSD(T) within chemical and spectroscopic accuracy.

Spiers Memorial Lecture: theory of unimolecular reactions

One hundred years ago, at an earlier Faraday Discussion meeting, Lindemann presented a mechanism that provides the foundation for contemplating the pressure dependence of unimolecular reactions. Since that time, our...

Gas Phase Protolysis of Trisarylzincate Anions

We have applied a combination of tandem-mass spectrometry, quantum-chemical calculations, and statistical rate theory computations to examine the gas phase reactions between the trisarylzincate anions Ar^XZnPh₂^- (Ar^X = p-X-C₆H₄, X = NMe₂, OMe, Me, H, F, and Cl) and 2,2,2-trifluoroethanol at T = 310 ± 20 K. The observed reactions bring about the protonation of one of the aryl anions, which is then released as the corresponding arene, while the formed alkoxide binds to the zinc center. The protonation is faster for the more electron-rich aryl groups and shows a linear Hammett plot if the rate constant for X = NMe₂ is discarded from the analysis. Although the reactions are highly exothermic, they proceed only with relatively low efficiencies (0.1% ≤ φ ≤ 1.3%). According to the quantum-chemical calculations, this behavior can be ascribed to the reactions proceeding through a double-well potential with a tight transition structure located at the central barrier. Based on these potential energy surfaces, the statistical rate theory computations can reproduce the measured rate constants within factors of 2 to 8. A comparison of the protolysis of the trisarylzincates with that of the corresponding free aryl anions demonstrates how the coordination to the metal center not only stabilizes the carbanions energetically but also moderates their reactivity. Thus, our gas phase study contributes to a better understanding of the fundamentals of organometallic reactivity.

Heavy-Atom Kinetic Isotope Effects: Primary Interest or Zero Point?

Chemists have many options for elucidating reaction mechanisms. Global kinetic analysis and classic transition-state probes (e.g., LFERs, Eyring) inevitably form the cornerstone of any strategy, yet their application to increasingly sophisticated synthetic methodologies often leads to a wide range of indistinguishable mechanistic proposals. Computational chemistry provides powerful tools for narrowing the field in such cases, yet wholly simulated mechanisms must be interpreted with great caution. Heavy-atom kinetic isotope effects (KIEs) offer an exquisite but underutilized method for reconciling the two approaches, anchoring the theoretician in the world of calculable observables and providing the experimentalist with atomistic insights. This Perspective provides a personal outlook on this synergy. It surveys the computation of heavy-atom KIEs and their measurement by NMR spectroscopy, discusses recent case studies, highlights the intellectual reward that lies in alignment of experiment and theory, and reflects on the changes required in chemical education in the area.

Addressing the System-Size Dependence of the Local Approximation Error in Coupled-Cluster Calculations

Over the last two decades, the local approximation has been successfully used to extend the range of applicability of the "gold standard" singles and doubles coupled-cluster method with perturbative triples CCSD(T) to systems with hundreds of atoms. The local approximation error grows in absolute value with the increasing system size, i.e., by increasing the number of electron pairs in the system. In this study, we demonstrate that the recently introduced two-point extrapolation scheme for approaching the complete pair natural orbital (PNOs) space limit in domain-based pair natural orbital CCSD(T) calculations drastically reduces the dependence of the error on the system size, thus opening up unprecedented opportunities for the calculation of benchmark quality relative energies for large systems.

Contrasting the Mechanism of H2 Activation by Monomeric and Potassium-Stabilized Dimeric AlI Complexes: Do Potassium Atoms Exert any Cooperative Effect?

Aluminyl anions are low-valent, anionic, and carbenoid aluminum species commonly found stabilized with potassium cations from the reaction of Al-halogen precursors and alkali compounds. These systems are very reactive toward the activation of σ-bonds and in reactions with electrophiles. Various research groups have detected that the potassium atoms play a stabilization role via electrostatic and cation ⋯ π interactions with nearby (aromatic)-carbocyclic rings from both the ligand and from the reaction with unsaturated substrates. Since stabilizing K⋯H bonds are witnessed in the activation of this class of molecules, we aim to unveil the role of these metals in the activation of the smaller and less polarizable H₂ molecule, together with a comprehensive characterization of the reaction mechanism. In this work, the activation of H₂ utilizing a NON-xanthene-Al dimer, [K{Al(NON)}]₂ (D) and monomeric, [Al(NON)]^- (M) complexes are studied using density functional theory and high-level coupled-cluster theory to reveal the potential role of K⁺ atoms during the activation of this gas. Furthermore, we aim to reveal whether D is more reactive than M (or vice versa), or if complicity between the two monomer units exits within the D complex toward the activation of H₂ . The results suggest that activation energies using the dimeric and monomeric complexes were found to be very close (around 33 kcal mol^-1 ). However, a partition of activation energies unveiled that the nature of the energy barriers for the monomeric and dimeric complexes are inherently different. The former is dominated by a more substantial distortion of the reactants (and increased interaction energies between them). Interestingly, during the oxidative addition, the distortion of the Al complex is minimal, while H₂ distorts the most, usually over 0.77 Δ E d i s t ≠ . Overall, it is found here that electrostatic and induction energies between the complexes and H₂ are the main stabilizing components up to the respective transition states. The results suggest that the K⁺ atoms act as stabilizers of the dimeric structure, and their cooperative role on the reaction mechanism may be negligible, acting as mere spectators in the activation of H₂ . Cooperation between the two monomers in D is lacking, and therefore the subsequent activation of H₂ is wholly disengaged.

Efficient Ab Initio Estimation of Formation Enthalpies for Organic Compounds: Extension to Sulfur and Critical Evaluation of Experimental Data

The efficient protocol for the estimation of gas-phase enthalpies of formation developed previously for C, H, O, N, and F elements was extended to sulfur. The protocol is based on a local coupled cluster with single, double, and perturbative triple excitation [CCSD(T)] approximation and allows rapid evaluation of compounds with sizes computationally prohibitive to canonical CCSD(T) using quadruple zeta basis sets. As a part of model development, a comprehensive review and critical evaluation of experimental data were performed for 87 sulfur-containing organic and inorganic compounds. A compact model with only three empirical parameters for sulfur introduced to address the effects beyond frozen core CCSD(T) was developed. The model exhibits approximately 2 kJ·mol^-1 standard deviation over a set of experimental values for a diverse collection of sulfur-containing compounds. The complete basis set version of the model demonstrates a similar performance and requires only one empirical parameter. Multiple problems with the existing experimental data were identified and discussed. In addition, a lack of reliable data for certain important classes of sulfur compounds was found to impede the model generalization and confident performance assessment.

Electrochemical characterization and thermodynamic analysis of TEMPO derivatives in ionic liquids

In this study we investigate the reversibility of the reduction process of three TEMPO derivatives - TEMPOL, 4-cyano-TEMPO, and 4-oxo-TEMPO. The [C2mim][BF4] and [C4mpyr][OTf] ionic liquids (ILs) were used to perform cyclic voltammetry (CV) to analyse the redox potentials of the TEMPO derivatives. The former was previously shown to quench the aminoxy anion of TEMPO through a proton transfer reaction with the cation, whereas the latter supported the irreversibility of the TEMPO reduction process. In CV results on TEMPO derivatives, it was shown that [C4mpyr][OTf] could allow for a high degree of reversibility in the reduction of 4-cyano-TEMPO and a moderate degree of reversibility in the reduction of TEMPOL. In comparison, reduction of 4-cyano-TEMPO was predominantly irreversible in [C2mim][BF4], whilst TEMPOL showed complete irreversibility. 4-Oxo-TEMPO did not show any notable reduction reversibility in either IL tested. Reduction potentials showed little variation between the derivatives and 0.2 V variation between the ILs, with the most negative reduction potential being observed at -1.43 V vs. Fc/Fc+ for TEMPOL in [C4mpyr][OTf]. To explain the varying degrees of reversibility of the reduction process, four types of side reactions involving proton transfer to the aminoxy anion were studied using highly correlated quantum chemical methods. Proton transfer from the IL cation was shown to have the ability to quench all three aminoxy anions depending on the IL used. On average, TEMPOL was shown to be the most susceptible to proton transfer from the IL cation, having an average Gibbs free energy (GFE) of 10.5 kJ mol-1 more negative than that of 4-cyano-TEMPO, which was shown to have the highest GFE of proton transfer. Side reactions between water and aminoxy anions were also seen to have the potential to contribute to degradation of the aminoxy anions tested, with 4-oxo-TEMPO being shown to be the most reactive to degradation with water with a GFE of -12.6 kJ mol-1. 4-Oxo-TEMPO was found to be highly susceptible to self-quenching by its aminoxy anion and radical form with highly negative proton transfer GFEs of -47.9 kJ mol-1 and -57.7 kJ mol-1, respectively. Overall, 4-cyano-TEMPO is recommended as being the most stable of the aminoxy anions tested with TEMPOL, thus providing a viable alternative to improve solubility should the IL be tuned to maximize its stability.

Critical benchmarking of popular composite thermochemistry models and density functional approximations on a probabilistically pruned benchmark dataset of formation enthalpies

First-principles calculation of the standard formation enthalpy, ΔH_f° (298 K), in such a large scale as required by chemical space explorations, is amenable only with density functional approximations (DFAs) and certain composite wave function theories (cWFTs). Unfortunately, the accuracies of popular range-separated hybrid, "rung-4" DFAs, and cWFTs that offer the best accuracy-vs-cost trade-off have until now been established only for datasets predominantly comprising small molecules; their transferability to larger systems remains vague. In this study, we present an extended benchmark dataset of ΔH_f° for structurally and electronically diverse molecules. We apply quartile-ranking based on boundary-corrected kernel density estimation to filter outliers and arrive at probabilistically pruned enthalpies of 1694 compounds (PPE1694). For this dataset, we rank the prediction accuracies of G4, G4(MP2), ccCA, CBS-QB3, and 23 popular DFAs using conventional and probabilistic error metrics. We discuss systematic prediction errors and highlight the role an empirical higher-level correction plays in the G4(MP2) model. Furthermore, we comment on uncertainties associated with the reference empirical data for atoms and the systematic errors stemming from these that grow with the molecular size. We believe that these findings will aid in identifying meaningful application domains for quantum thermochemical methods.

Learning to fly: thermochemistry of energetic materials by modified thermogravimetric analysis and highly accurate quantum chemical calculations

The standard state enthalpy of formation and the enthalpy of sublimation are essential thermochemical parameters determining the performance and application prospects of energetic materials (EM). Direct experimental measurements of these properties are complicated by low volatility and high heat release in bomb calorimetry experiments. As a result, the uncertainties in the reported enthalpies of formation for a number of even well-known CHNO-containing compounds might amount up to tens kJ mol-1, while for some novel high-nitrogen molecules they reach even hundreds of kJ mol-1. The present study reports a facile approach to determining the solid-state formation enthalpies comprised of complementary high-level quantum chemical calculations of the gas-phase thermochemistry and advanced thermal analysis techniques yielding sublimation enthalpies. The thermogravimetric procedure for the measurement of sublimation enthalpy was modified by using low external pressures (down to 0.2 Pa). This allows for observing sublimation/vaporization instead of thermal decomposition of the compounds studied. Extensive benchmarking on nonenergetic and energetic compounds reveals the average and maximal absolute errors of the sublimation enthalpies of 3.3 and 11.0 kJ mol-1, respectively. The comparison of the results with those obtained from the widely used Trouton-Williams empirical equation shows that the latter underestimates the sublimation enthalpy up to 140 kJ mol-1. Therefore, we performed a reparametrization of the latter equation with simple chemical descriptors that reduces the mean error down to 30 kJ mol-1. Highly accurate multi-level procedures W2-F12 and/or W1-F12 in conjunction with the atomization energy approach were used to calculate theoretically the gas-phase formation enthalpies. In several cases, the DLPNO-CCSD(T) enthalpies of isodesmic reactions were also employed to obtain the gas-phase thermochemistry for medium-sized important EMs. Combining the obtained thermochemical properties, we determined the solid-state enthalpies of formation for nearly 60 species containing various important explosophoric groups, from common nitroaromatics, nitroethers, and nitramines to novel nitrogen-rich heterocyclic species (e.g., the derivatives of pyrazole, tetrazole, furoxan, etc.). The large-scale benchmarking against the available experimental solid-state enthalpies of formation yielded the maximal inaccuracy of the proposed method of 25 kJ mol-1.

New insights on the ESIPT process based on solid-state data and state-of-the-art computational methods

Benzothiazole derivatives were used as models to study the excited-state intramolecular proton transfer (ESIPT) from an experimental and theoretical point of view. The experimental electronic and vibrational results were compared with a comprehensive selection of state-of-the-art computational methods in a workflow approach. The latter were performed based on modern techniques, such as DLPNO-CCSD(T), which gives the reference energies and current methodologies for ESIPT analysis, such as molecular dynamics and charge density difference testing. The theoretical vibrational results were focused on the stretch vibrational-mode of the hydroxyl group, which indicated a large increase in the intramolecular hydrogen bond strength, which facilitates the ESIPT process. Theoretically, the optimization of a large number of molecules shows that π-stacking plays a fundamental role in benzothiazole stabilization, with a remarkably strong intramolecular hydrogen bond. The potential energy surface of the ESIPT reactive benzothiazole (4HBS) has a clear transition state where ESIPT is easily observed with a large difference in energy between the enol and keto tautomer. Additionally, molecular dynamics showed that the ESIPT process occurs very fast. The tautomer appears around 8.7 fs and the enolic form is regenerated in just 24 fs, closing the Förster cycle. The calculated Stokes shift could be related to the ESIPT process and the experimental solid-state emission spectrum matched almost perfectly with the theoretical one. In contrast, for the non-ESIPT benzothiazole (4HBSN), the agreement between theory and experiment was limited, probably due to intermolecular interaction effects that are not considered in these calculations.

Strong bases behave as weak bases in nanoscale chemical environments: implication in humidity-swing CO2 air capture

Hydration of ions/molecules in nanometer-sized clusters or nanoscopic pores is ubiquitous and plays a key role in many chemical and physical systems. In this work, guanidine-H2O reactions with n = 1-8 water molecules were systematically studied by ab initio methods. The result suggests that the reduced availability of water molecules greatly inhibits the strong base guanidine from producing OH-. That is, guanidine exhibits the behavior of a weak bases in low-humidity nanoscale environments. Intriguingly, this effect is not limited to guanidine but could be applied to other strong bases. Furthermore, we demonstrate that the direction of guanidine-CO2 reactions can be controlled by changing the number of water molecules present, which in turn responds to the humidity change in air. These findings not only shed some light on unconventional chemical reactions of strong bases in atmospheric clusters and on solid porous surfaces, but also provide insights into the development of guanidine-based CO2 air-capture sorbents.

Atomic Partial Charges as Descriptors for Barrier Heights

Atomic partial charges are found to be valuable descriptors for barrier heights of unimolecular reactions due to the considerable information about the electronic structure embedded in them. If the chemical changes of the reactions are somewhat centralized at a single atom, the respective partial charge is a potentially meaningful descriptor and might outperform bond dissociation energies as descriptors. We propose that atomic partial charges should be considered as barrier height descriptors in future research.

Gas-Phase Thermochemistry of MX3 and M2X6 (M = Sc, Y; X = F, Cl, Br, I) from a Composite Reaction-Based Approach: Homolytic versus Heterolytic Cleavage

A domain-based local-pair natural-orbital coupled-cluster approach with single, double, and improved linear-scaling perturbative triple correction via an iterative algorithm, DLPNO-CCSD(T₁), was applied within the framework of the Feller-Peterson-Dixon approach to derive gas-phase heats of formation of scandium and yttrium trihalides and their dimers via a set of homolytic and heterolytic dissociation reactions. All predicted heats of formation moderately depend on the reaction type with the most and least negative values obtained for homolytic and heterolytic dissociation, respectively. The basis set size dependence, as well as the influence of static correlation effects not covered by the standard (DLPNO-)CCSD(T) approach, suggests that exploitation of the heterolytic dissociation reactions with the formation of M³⁺ and X^- ions leads to the most robust heats of formation. The gas-phase formation enthalpies ΔH_f°(0 K)/ΔH_f°(298.15 K) and absolute entropies S°(298.15 K) were obtained for the first time for the Sc₂F₆, Sc₂Br₆, and Sc₂I₆ species. For ScBr₃, ScI₃, Sc₂Cl₆, and Y₂Cl₆, we suggest a reexamination of the experimental heats of formation available in the literature. For other compounds, the predicted values were found to be in good agreement with the experimental estimates. Extracted MX₃ (M = Sc, Y; X = F, Cl, Br, and I) 0 K atomization enthalpies indicate weaker bonding when moving from fluorine to iodine and from yttrium to scandium. Likewise, the stability of yttrium trihalide dimers degrades when going from fluorine to iodine. Respective scandium trihalide dimers are less stable, with 0 K dimer dissociation energy decreasing in the row fluorine - chlorine - bromine ≈ iodine. Correlation of the (n - 1)s²p⁶ electrons on bromine and iodine, inclusion of zero-point energy, relativistic effects, and the effective-core-potential correction as well as amelioration of the DLPNO localization inaccuracy are shown to be of similar magnitude, which is critical if accurate heats of formation are a goal.

DFT, DLPNO-CCSD(T), and NEVPT2 benchmark study of the reaction between ferrocenium and trimethylphosphine

The reaction between ferrocenium and trimethylphosphine was studied using density functional theory (DFT), domain-based local pair natural orbital coupled cluster theory with single-, double-, and perturbative triple excitations (DLPNO-CCSD(T)), and N-electron valence state perturbation theory (NEVPT2). The accuracy of the DFT functionals decreases compared to the DLPNO-CCSD(T) level in the following order: M06-L > TPSS > M06, BLYP > PBE, PBE0, B3LYP > > PWPB95 > > DSD-BLYP. The roles of thermochemical, continuum solvation (SMD), and counterpoise corrections were evaluated. Grimme's D3 empirical dispersion correction is essential for all functionals studied except M06 and M06-L. The reliability of the frequency calculations performed directly within the SMD was confirmed. The systems showed no significant multireference character according to T₁ and T₂ diagnostics and the fractional occupation number (FOD) weighted electron density analysis. The multireference NEVPT2 calculations gave qualitatively valid conclusions about the reaction mechanism. However, a multireference approach is generally not recommended because it requires arbitrary chosen active spaces.

Accurate prediction of norbornadiene cycle enthalpies by DLPNO-CCSD(T1 )/CBS method

The DLPNO-CCSD(T₁ )/CBS method combined with simple reactions containing small reference species leads to an improvement in the accuracy of theoretically evaluated enthalpies of formation of medium-sized polyalicyclic hydrocarbons when compared with the widely used composite approach. The efficiency of the DLPNO-CCSD(T₁ )/CBS method is most vividly demonstrated by comparing with the results of G4 calculations for adamantane. The most important factor in choosing appropriate working reaction is the same number of species on both sides of the equation. Among these reactions, the reactions with small enthalpy change usually provide a better cancellation of errors. The DLPNO-CCSD(T₁ )/CBS method was used to calculate the enthalpies of formation of compounds belonging to the norbornadiene cycle (norbornadiene, quadricyclane, norbornene, nortricyclane, and norbornane). The most reliable experimental enthalpies of formation are recommended for these compounds by comparing calculated values with conflicting experimental data.

Extrapolation to the Limit of a Complete Pair Natural Orbital Space in Local Coupled-Cluster Calculations

The domain-based local pair natural orbital (PNO) coupled-cluster DLPNO-CCSD(T) method allows one to perform single point energy calculations for systems with hundreds of atoms while retaining essentially the accuracy of its canonical counterpart, with errors that are typically smaller than 1 kcal/mol for relative energies. Crucial to the accuracy and efficiency of the method is a proper definition of the virtual space in which the coupled-cluster equations are solved, which is spanned by a highly compact set of pair natural orbitals (PNOs) that are specific for each electron pair. The dimension of the PNO space is controlled by the T_CutPNO threshold: only PNOs with an occupation number greater than T_CutPNO are included in the correlation space of a given electron pair, whilst the remaining PNOs are discarded. To keep the error of the method small, a conservative T_CutPNO value is used in standard DLPNO-CCSD(T) calculations. This often leads to unnecessarily large PNO spaces, which limits the efficiency of the method. Herein, we introduce a new computational strategy to approach the complete PNO space limit (for a given basis set) that consists in extrapolating the results obtained with different T_CutPNO values. The method is validated on the GMTKN55 set using canonical CCSD(T) data as the reference. Our results demonstrate that a simple two-point extrapolation scheme can be used to significantly increase the efficiency and accuracy of DLPNO-CCSD(T) calculations, thus extending the range of applicability of the technique.

Bootstrap Embedding For Large Molecular Systems

Recent developments in quantum embedding theories have provided attractive approaches to correlated calculations for large systems. In this work, we extend our previous work [J. Chem. Theory Comput. 2019, 15, 4497-4506; J. Phys. Chem. Lett. 2019, 10, 6368-6374] on bootstrap embedding (BE) to enable correlated ab initio calculations at the coupled cluster with singles and doubles (CCSD) level for large molecules. We introduce several new algorithmic developments that significantly reduce the computational cost of BE, while maintaining its accuracy. The resulting implementation scales as O(N³) for the integral transform and O(N) for the CCSD calculation. Numerical results on a series of conjugated molecules suggest that BE with reasonably sized fragments can recover more than 99.5% of the total correlation energy of a full CCSD calculation, while the required computational resources (time and storage) compare favorably to one popular local correlation scheme: domain localized pair natural orbital (DLPNO). The largest BE calculation in this work involves ∼2900 basis functions and can be performed on a single node with 16 CPU cores and 64 GB of memory in a few days. We anticipate that these developments represent an important step toward the application of BE to solve practical problems.

Canonical and DLPNO-Based G4(MP2)XK-Inspired Composite Wave Function Methods Parametrized against Large and Chemically Diverse Training Sets: Are They More Accurate and/or Robust than Double-Hybrid DFT?

The large and chemically diverse GMTKN55 benchmark was used as a training set for parametrizing composite wave function thermochemistry protocols akin to G4(MP2)XK theory (Chan, B.; Karton, A.; Raghavachari, K. J. Chem. Theory Comput. 2019, 15, 4478–4484). On account of their availability for elements H through Rn, Karlsruhe def2 basis sets were employed. Even after reparametrization, the GMTKN55 WTMAD2 (weighted mean absolute deviation, type 2) for G4(MP2)-XK is actually inferior to that of the best rung-4 DFT functional, ωB97M-V. By increasing the basis set for the MP2 part to def2-QZVPPD, we were able to substantially improve performance at modest cost (if an RI-MP2 approximation is made), with WTMAD2 for this G4(MP2)-XK-D method now comparable to the better rung-5 functionals (albeit at greater cost). A three-tier approach with a scaled MP3/def2-TZVPP intermediate step, however, leads to a G4(MP3)-D method that is markedly superior to even the best double hybrids ωB97M(2) and revDSD-PBEP86-D4. Evaluating the CCSD(T) component with a triple-ζ, rather than split-valence, basis set yields only a modest further improvement that is incommensurate with the drastic increase in computational cost. G4(MP3)-D and G4(MP2)-XK-D have about 40% better WTMAD2, at similar or lower computational cost, than their counterparts G4 and G4(MP2), respectively: detailed comparison reveals that the difference lies in larger molecules due to basis set incompleteness error. An E2/{T,Q} extrapolation and a CCSD(T)/def2-TZVP step provided the G4-T method of high accuracy and with just three fitted parameters. Using KS orbitals in MP2 leads to the G4(MP3|KS)-D method, which entirely eliminates the CCSD(T) step and has no steps costlier than scaled MP3; this shows a path forward to further improvements in double-hybrid density functional methods. None of our final selections require an empirical HLC correction; this cuts the number of empirical parameters in half and avoids discontinuities on potential energy surfaces. G4-T-DLPNO, a variant in which post-MP2 corrections are evaluated at the DLPNO-CCSD(T) level, achieves nearly the accuracy of G4-T but is applicable to much larger systems.

The ANI-1ccx and ANI-1x data sets, coupled-cluster and density functional theory properties for molecules

Maximum diversification of data is a central theme in building generalized and accurate machine learning (ML) models. In chemistry, ML has been used to develop models for predicting molecular properties, for example quantum mechanics (QM) calculated potential energy surfaces and atomic charge models. The ANI-1x and ANI-1ccx ML-based general-purpose potentials for organic molecules were developed through active learning; an automated data diversification process. Here, we describe the ANI-1x and ANI-1ccx data sets. To demonstrate data diversity, we visualize it with a dimensionality reduction scheme, and contrast against existing data sets. The ANI-1x data set contains multiple QM properties from 5 M density functional theory calculations, while the ANI-1ccx data set contains 500 k data points obtained with an accurate CCSD(T)/CBS extrapolation. Approximately 14 million CPU core-hours were expended to generate this data. Multiple QM calculated properties for the chemical elements C, H, N, and O are provided: energies, atomic forces, multipole moments, atomic charges, etc. We provide this data to the community to aid research and development of ML models for chemistry.

Detailed Pair Natural Orbital-Based Coupled Cluster Studies of Spin Crossover Energetics

In this work, a detailed study of spin-state splittings in three spin crossover model compounds with DLPNO-CCSD(T) is presented. The performance in comparison to canonical CCSD(T) is assessed in detail. It was found that spin-state splittings with chemical accuracy, compared to the canonical results, are achieved when the full iterative triples (T1) scheme and TightPNO settings are applied and relativistic effects are taken into account. Having established the level of accuracy that can be reached relative to the canonical results, we have undertaken a detailed basis set study in the second part of the study. The slow convergence of the results of correlated calculations with respect to basis set extension is particularly acute for spin-state splittings for reasons discussed in detail in this Article. In fact, for some of the studied systems, 5Z basis sets are necessary in order to come close to the basis set limit that is estimated here by basis set extrapolation. Finally, the results of the present work are compared to available literature. In general, acceptable agreement with previous CCSD(T) results is found, although notable deviations stemming from differences in methodology and basis sets are noted. It is noted that the published CASPT2 numbers are far away from the extrapolated CCSD(T) numbers. In addition, dynamic quantum Monte Carlo results differ by several tens of kcal/mol from the CCSD(T) numbers. A comparison to DFT results produced with a range of popular density functionals shows the expected scattering of results and showcases the difficulty of applying DFT to spin-state energies.