Exploring the Accuracy Limits of Local Pair Natural Orbital Coupled-Cluster Theory

Molecular properties affecting the hydration of acid-base clusters

In the atmosphere, water in all phases is ubiquitous and plays important roles in catalyzing atmospheric chemical reactions, participating in cluster formation and affecting the composition of aerosol particles. Direct measurements of water-containing clusters are limited because water is likely to evaporate before detection, and therefore, theoretical tools are needed to study hydration in the atmosphere. We have studied thermodynamics and population dynamics of the hydration of different atmospherically relevant base monomers as well as sulfuric acid-base pairs. The hydration ability of a base seems to follow in the order of gas-phase base strength whereas hydration ability of acid-base pairs, and thus clusters, is related to the number of hydrogen binding sites. Proton transfer reactions at water-air interfaces are important in many environmental and biological systems, but a deeper understanding of their mechanisms remain elusive. By studying thermodynamics of proton transfer reactions in clusters containing up to 20 water molecules and a base molecule, we found that that the ability of a base to accept a proton in a water cluster is related to the aqueous-phase basicity. We also studied the second deprotonation reaction of a sulfuric acid in hydrated acid-base clusters and found that sulfate formation is most favorable in the presence of dimethylamine. Molecular properties related to the proton transfer ability in water clusters are discussed.

Fragment-Based Local Coupled Cluster Embedding Approach for the Quantification and Analysis of Noncovalent Interactions: Exploring the Many-Body Expansion of the Local Coupled Cluster Energy

Herein, we introduce a fragment-based local coupled cluster embedding approach for the accurate quantification and analysis of noncovalent interactions in molecular aggregates. Our scheme combines two different expansions of the domain-based local pair natural orbital coupled cluster (DLPNO-CCSD(T)) energy: the many-body expansion (MBE) and the local energy decomposition (LED). The low-order terms in the MBE are initially computed in the presence of an environment that is treated at a low level of theory. Then, LED is used to decompose the energy of each term in the embedded MBE into additive fragment and fragment-pairwise contributions. This information is used to quantify the total energy of the system while providing at the same time in-depth insights into the nature and cooperativity of noncovalent interactions. Two different approaches are introduced and tested, in which the environment is treated at different levels of theory: the local coupled cluster in the Hartree-Fock (LCC-in-HF) method, in which the environment is treated at the HF level; and the electrostatically embedded local coupled cluster method (LCC-in-EE), in which the environment is replaced by point charges. Both schemes are designed to preserve as much as possible the accuracy of the parent local coupled cluster method for total energies, while being embarrassingly parallel and less memory intensive. These schemes appear to be particularly promising for the study of large and complex molecular aggregates at the coupled cluster level, such as condensed phase systems and protein-ligand interactions.

Photoredox Catalytic Pentafluorosulfanylative Domino Cyclization of α-Substituted Alkenes to Oxaheterocycles by Using SF6

Virtually inert sulfur hexafluoride becomes a precious pentafluorosulfanylation agent, if properly activated by photoredox catalysis, to access α-fluoro and α-alkoxy SF5 -compounds. This advanced protocol converts SF6 in the presence of alkynols as bifunctional C-C- and C-O-bond forming reagents directly into pentafluorosulfanylated oxygen-containing heterocycles in a single step from α-substituted alkenes. The proposed mechanism is supported by theoretical calculations and gives insights not only in the pentafluorosulfanylation step but also into formation of the carbon-carbon bond and is in full agreement with Baldwin's cyclization rules. The key step is a radical type 5-, 6- respectively 7-exo-dig-cyclization. The synthesized oxaheterocycles cannot be simply prepared by other synthetic methods, show a high level of structural complexity and significantly expand the scope of pentafluorosulfanylated building blocks valuable for medicinal and material chemistry.

Efficient Computation of Geometries for Gold Complexes

Computationally obtaining structural parameters along a reaction coordinate is commonly performed with Kohn‐Sham density functional theory which generally provides a good balance between speed and accuracy. However, CPU times still range from inconvenient to prohibitive, depending on the size of the system under study. Herein, the tight binding GFN2‐xTB method [C. Bannwarth, S. Ehlert, S. Grimme, J. Chem. Theory Comput. 2019, 15, 1652] is investigated as an alternative to produce reasonable geometries along a reaction path, that is, reactant, product and transition state structures for a series of transformations involving gold complexes. A small mean error (1 kcal/mol) was found, with respect to an efficient composite hybrid‐GGA exchange‐correlation functional (PBEh‐3c) paired with a double‐ζ basis set, which is 2–3 orders of magnitude slower. The outlined protocol may serve as a rapid tool to probe the viability of proposed mechanistic pathways in the field of gold catalysis.

Electron Attachment to Cytosine: The Role of Water

We present an EOM-CCSD-based quantum mechanical/molecular mechanical (QM/MM) study on the electron attachment process to solvated cytosine. The electron attachment in the bulk solvated cytosine occurs through a doorway mechanism, where the initial electron is localized on water. The electron is subsequently transferred to cytosine by the mixing of electronic and nuclear degrees of freedom, which occurs on an ultrafast time scale. The bulk water environment stabilizes the cytosine-bound anion by an extensive hydrogen-bond network and drastically enhances the electron transfer rate from that observed in the gas phase. Microhydration studies cannot reproduce the effect of the bulk water environment on the electron attachment process, and one needs to include a large number of water molecules in the calculation to obtain converged results. The predicted adiabatic electron affinity and electron transfer rate obtained from our QM/MM calculations are consistent with the available experimental results.

Strong Binding of Noble Gases to [B12X11]-: A Theoretical Study

We systematically explore the stability and properties of [B₁₂X₁₁NG]^- adducts resulting from the binding of noble gas atoms to anionic [B₁₂X₁₁]^- clusters in the gas phase of mass spectrometers. [B₁₂X₁₁]^- can be obtained by stripping one X^- off the icosahedral closo-dodecaborate dianion [B₁₂X₁₂]^2-. We study the binding of the noble gas atoms He, Ne, Ar, Kr, and Xe to [B₁₂X₁₁]^- with substituents X = F, Cl, Br, I, and CN. While He cannot be captured by these clusters and Ne only binds at low temperatures, the complexes with the heavier noble gas atoms Ar, Kr, and Xe show appreciable complexation energies and exceed 1 eV at room temperature in the case of [B₁₂(CN)₁₁Xe]^-. The predicted B-NG equilibrium distance in the complexes with Ar, Kr, and Xe is only 0.10-0.25 Å longer than the sum of the covalent radii of the two corresponding atoms, and a significant charge transfer from the noble gas atom to the icosahedral B₁₂ cage is observed.

DFT study of H2 adsorption at a Cu-SSZ-13 zeolite: a cluster approach

In this work the H2 adsorption at a Cu(i)-SSZ-13 exchanged zeolite was theoretically investigated. A systematic cluster approach was used and different density functionals (B3LYP, B3LYP-D3(BJ), M06L, PBE, PBE-D3(BJ) and ωB97XD) and a def2-SVP basis set were benchmarked. In order to select the best approach to the H2 adsorption over a Cu(i)-SSZ-13 cluster with 78 atoms (16 T-sites), two main tasks were performed: (1) a comparison between theoretical and experimental structures and (2) a comparison between theoretical and experimental adsorption enthalpies. By employing the most suitable functional - the ωB97X-D - the H2 interaction with the zeolite structure was studied by means of NBO, NCI, AIM and DLPNO-CCSD(T)/LED analyses.

Experimental and theoretical assessment of protonated Hoogsteen 9-methylguanine-1-methylcytosine base-pair dissociation: kinetics within a statistical reaction framework

We investigated the collision-induced dissociation (CID) reactions of a protonated Hoogsteen 9-methylguanine-1-methylcytosine base pair (HG-[9MG·1MC + H]+), which aims to address the mystery of the literature reported "anomaly" in product ion distributions and compare the kinetics of a Hoogsteen base pair with its Watson-Crick isomer WC-[9MG·1MC + H]+ (reported recently by Sun et al.; Phys. Chem. Chem. Phys., 2020, 22, 24986). Product ion cross sections and branching ratios were measured as a function of center-of-mass collision energy using guided-ion beam tandem mass spectrometry, from which base-pair dissociation energies were determined. Product structures and energetics were assessed using various theories, of which the composite DLPNO-CCSD(T)/aug-cc-pVTZ//ωB97XD/6-311++G(d,p) was adopted as the best-performing method for constructing a reaction potential energy surface. The statistical Rice-Ramsperger-Kassel-Marcus theory was found to provide a useful framework for rationalizing the dominating abundance of [1MC + H]+ over [9MG + H]+ in the fragment ions of HG-[9MG·1MC + H]+. The kinetics analysis proved the necessity for incorporating into kinetics modeling not only the static properties of reaction minima and transition states but more importantly, the kinetics of individual base-pair conformers that have formed in collisional activation. The analysis also pinpointed the origin of the statistical kinetics of HG-[9MG·1MC + H]+vs. the non-statistical behavior of WC-[9MG·1MC + H]+ in terms of their distinctively different intra-base-pair hydrogen-bonds and consequently the absence of proton transfer between the N1 position of 9MG and the N3' of 1MC in the Hoogsteen base pair. Finally, the Hoogsteen base pair was examined in the presence of a water ligand, i.e., HG-[9MG·1MC + H]+·H2O. Besides the same type of base-pair dissociation as detected in dry HG-[9MG·1MC + H]+, secondary methanol elimination was observed via the SN2 reaction of water with nucleobase methyl groups.

Calculating Reliable Gibbs Free Energies for Formation of Gas-Phase Clusters that Are Critical for Atmospheric Chemistry: (H2SO4)3

The effects of atmospheric aerosols on our climate are one of the biggest uncertainties in global climate models. Calculating the pathway for the formation of pre-nucleation clusters that become aerosols is challenging, requiring a comprehensive analysis of configurational space and highly accurate Gibbs free energy calculations. We identified a large set of minimum energy configurations of (H₂SO₄)₃ using a sampling technique based on a genetic algorithm and a stepwise density functional theory (DFT) approach and computed the thermodynamics of formation of these configurations with more accurate wavefunction-based electronic energies computed on the DFT geometries. The DLPNO-CCSD(T) methods always return more positive energies compared to the DFT energies. Within the DLPNO-CCSD(T) methods, extrapolating to the complete basis set limit gives more positive free energies compared to explicitly correlated single-point energies. The CBS extrapolation was shown to be robust as both the 4-5 inverse polynomial and Riemann zeta function schemes were within chemical accuracy of one another.

CHAL336 Benchmark Set: How Well Do Quantum-Chemical Methods Describe Chalcogen-Bonding Interactions?

We present the CHAL336 benchmark set-the most comprehensive database for the assessment of chalcogen-bonding (CB) interactions. After careful selection of suitable systems and identification of three high-level reference methods, the set comprises 336 dimers each consisting of up to 49 atoms and covers both σ- and π-hole interactions across four categories: chalcogen-chalcogen, chalcogen-π, chalcogen-halogen, and chalcogen-nitrogen interactions. In a subsequent study of DFT methods, we re-emphasize the need for using proper London dispersion corrections when treating noncovalent interactions. We also point out that the deterioration of results and systematic overestimation of interaction energies for some dispersion-corrected DFT methods does not hint at problems with the chosen dispersion correction but is a consequence of large density-driven errors. We conclude this work by performing the most detailed DFT benchmark study for CB interactions to date. We assess 109 variations of dispersion-corrected and dispersion-uncorrected DFT methods and carry out a detailed analysis of 80 of them. Double-hybrid functionals are the most reliable approaches for CB interactions, and they should be used whenever computationally feasible. The best three double hybrids are SOS0-PBE0-2-D3(BJ), revDSD-PBEP86-D3(BJ), and B2NCPLYP-D3(BJ). The best hybrids in this study are ωB97M-V, PW6B95-D3(0), and PW6B95-D3(BJ). We do not recommend using the popular B3LYP functional nor the MP2 approach, which have both been frequently used to describe CB interactions in the past. We hope to inspire a change in computational protocols surrounding CB interactions that leads away from the commonly used, popular methods to the more robust and accurate ones recommended herein. We would also like to encourage method developers to use our set for the investigation and reduction of density-driven errors in new density functional approximations.

An Unsual Cys-Glu-Lys Catalytic Triad is Responsible for the Catalytic Mechanism of the Nitrilase Superfamily: A QM/MM Study on Nit2

Nitrilase 2 (Nit2) is a representative member of the nitrilase superfamily that catalyzes the hydrolysis of α-ketosuccinamate into oxaloacetate. It has been associated with the metabolism of rapidly dividing cells like cancer cells. The catalytic mechanism of Nit2 employs a catalytic triad formed by Cys191, Glu81 and Lys150. The Cys191 and Glu81 play an active role during the catalytic process while the Lys150 is shown to play only a secondary role. The results demonstrate that the catalytic mechanism of Nit2 involves four steps. The nucleophilic attack of Cys191 to the α-ketosuccinamate, the formation of two tetrahedral enzyme adducts and the hydrolysis of a thioacyl-enzyme intermediate, from which results the formation of oxaloacetate and enzymatic turnover. The rate limiting step of the catalytic process is the formation of the first tetrahedral intermediate with a calculated activation free energy of 18.4 kcal/mol, which agrees very well with the experimental k_cat (17.67 kcal/mol).

Stochastic evaluation of fourth-order many-body perturbation energies

A scalable, stochastic algorithm evaluating the fourth-order many-body perturbation (MP4) correction to energy is proposed. Three hundred Goldstone diagrams representing the MP4 correction are computer generated and then converted into algebraic formulas expressed in terms of Green's functions in real space and imaginary time. They are evaluated by the direct (i.e., non-Markov, non-Metropolis) Monte Carlo (MC) integration accelerated by the redundant-walker and control-variate algorithms. The resulting MC-MP4 method is efficiently parallelized and is shown to display O(n^5.3) size-dependence of cost, which is nearly two ranks lower than the O(n⁷) dependence of the deterministic MP4 algorithm. It evaluates the MP4/aug-cc-pVDZ energy for benzene, naphthalene, phenanthrene, and corannulene with the statistical uncertainty of 10 mE_h (1.1% of the total basis-set correlation energy), 38 mE_h (2.6%), 110 mE_h (5.5%), and 280 mE_h (9.0%), respectively, after about 10⁹ MC steps.

Clusteromics I: Principles, Protocols, and Applications to Sulfuric Acid-Base Cluster Formation

We recently coined the term clusteromics as a holistic approach for obtaining insight into the chemical complexity of atmospheric molecular cluster formation and at the same time providing the foundation for thermochemical databases that can be utilized for developing machine learning models. Here, we present the first paper in the series that applies state-of-the-art computational methods to study multicomponent (SA)0-2(base)0-2 clusters, with SA = sulfuric acid and base = [ammonia (A), methylamine (MA), dimethylamine (DMA), trimethylamine (TMA), and ethylenediamine (EDA)] with all combinations of the five bases. The initial cluster configurations are obtained using the ABCluster program and the number of relevant configurations are reduced based on PM7 and ωB97X-D/6-31++G(d,p) calculations. Thermochemical parameters are calculated based on the ωB97X-D/6-31++G(d,p) cluster structures and vibrational frequencies using the quasi-harmonic approximation. The single-point energies are refined with a high-level DLPNO-CCSD(T0)/aug-cc-pVTZ calculation. Using the calculated thermochemical data, we perform kinetics simulations to evaluate the potential of these small (SA)0-2(base)0-2 clusters to grow into larger cluster sizes. In all cases we find that having more than one type of base molecule present in the cluster will increase the potential for forming larger clusters primarily due to the increased available vapor concentration.

Crystals at a Carrefour on the Way through the Phase Space: A Middle Path

Multiple supramolecular functionalities of cyclic α-alkoxy tellurium-trihalides (including Te---O, Te---X (X = Br, I) and Te---π(C=C) supramolecular synthons) afford rich crystal packing possibilities, which consequently results in polymorphism or Z’ > 1 crystal structures. Example of three crystal forms of cyclohexyl-ethoxy-tellurium-trihalides, one of which combines the packing of two others, affords a unique model to observe the supramolecular synthon evolution at the early stages of crystallization, when crystals on the way find themself at a carrefour between the evolutionally close routes, but fail to choose between two energetically close packing patterns, so taking the “middle path”, which incorporates both of them (and results in two crystallographically independent molecules). In general, this allows a better understanding of the existing structures, and an instrument to search for the new polymorphic forms.

Energetics of Formation of Cyclacenes from 2,3-Didehydroacenes and Implications for Astrochemistry

The carriers of the diffuse interstellar bands (DIBs) are still largely unknown although polycyclic aromatic hydrocarbons, carbon chains, and fullerenes are likely candidates. A recent analysis of the properties of n-acenes of general formula C4n+2 H2n+4 suggested that these could be potential carriers of some DIBs. Dehydrogenation reactions of n-acenes after absorption of an interstellar UV photon may result in dehydroacenes. Here the reaction energies and barriers for formation of n-cyclacenes from 2,3-didehydroacenes (n-DDA) by intramolecular Diels-Alder reaction to dihydro-etheno-cyclacenes (n-DEC) followed by ejection of ethyne by retro-Diels-Alder reactions are analyzed using thermally assisted occupation density functional theory (TAO-DFT) for n=10-20. It is found that the barriers for each of the steps depend on the ring strain of the underlying n-cyclacene, and that the ring strain of n-DEC is about 75 % of that of the corresponding n-cyclacene. In each case, ethyne extrusion is the step with the highest energy barrier, but these barriers are smaller than CH bond dissociation energies, suggesting that formation of cyclacenes is an energetically conceivable fate of n-acenes after multiple absorption of UV photons.

Selective Oxidation of 5-Hydroxymethylfurfural to 2,5-Diformylfuran by Visible Light-Driven Photocatalysis over In Situ Substrate-Sensitized Titania

Solar energy-driven processes for biomass valorization are priority for the growing industrialized society. To address this challenge, efficient visible light-active photocatalyst for the selective oxidation of biomass-derived platform chemical is highly desirable. Herein, selective oxidation of 5-hydroxymethylfurfural (HMF) to 2,5-diformylfuran (DFF) was achieved by visible light-driven photocatalysis over titania. Pristine titania is photocatalytically inactive under visible light, so an unconventional approach was employed for the visible light (λ=515 nm) sensitization of titania via a formation of a visible light-absorbing complex of HMF (substrate) on the titania surface. Surface-complexation of HMF on titania mediated ligand-to-metal charge transfer (LMCT) under visible light, which efficiently catalyzed the oxidation of HMF to DFF. A high DFF selectivity of 87 % was achieved with 59 % HMF conversion after 4 h of illumination. The apparent quantum yield obtained for DFF production was calculated to be 6.3 %. It was proposed that the dissociative interaction of hydroxyl groups of HMF and the titania surface is responsible for the surface-complex formation. When the hydroxyl groups of titania were modified via surface-fluorination or calcination the oxidation of HMF was inhibited under visible light, signifying that hydroxyl groups are decisive for photocatalytic activity.

Accuracy of DLPNO-CCSD(T): Effect of Basis Set and System Size

The DLPNO-CCSD(T) method is designed to study large molecular systems at significantly reduced cost relative to its canonical counterpart. However, the error in this approach is also size-extensive and relies on cancellation of errors for the calculation of relative energies. This work provides a direct comparison of canonical CCSD(T) and TightPNO DLPNO-CCSD(T) calculations of reaction energies and barriers of a broad range of chemical reactions. The dataset includes acidities, anion binding affinities, enolization, Diels-Alder, nucleophilic substitution, and atom transfer reactions and complements existing theoretical datasets in terms of system size as well as new reaction types (e.g., anion binding affinities and chlorine atom transfer reactions). The performance of DLPNO-CCSD(T) was further examined with respect to systematic variation of basis set and system size and amounts of nonbonded interaction present in the system. The errors in the DLPNO-CCSD(T) were found to be relatively insensitive to the choice of basis set for small systems but increase monotonically with system size. Additionally, calculations of barriers appear to be more challenging than reaction energies with errors exceeding 5 kJ mol^-1 for many Diels-Alder reactions. Further tests on three realistic organic reactions reveal the impact of the DLPNO approximation in calculating absolute and relative barriers that are important for predictions such as stereoselectivity.

Replacing thymine with a strongly pairing fifth Base: A combined quantum mechanics and molecular dynamics study

The non-natural ethynylmethylpyridone C-nucleoside (W), a thymidine (T) analogue that can be incorporated in oligonucleotides by automated synthesis, has recently been reported to form a high fidelity base pair with adenosine (A) and to be well accommodated in B-DNA duplexes. The enhanced binding affinity for A of W, as compared to T, makes it an ideal modification for biotechnological applications, such as efficient probe hybridization for the parallel detection of multiple DNA strands. In order to complement the experimental study and rationalize the impact of the non-natural W nucleoside on the structure, stability and dynamics of DNA structures, we performed quantum mechanics (QM) calculations along with molecular dynamics (MD) simulations. Consistently with the experimental study, our QM calculations show that the A:W base pair has an increased stability as compared to the natural A:T pair, due to an additional CH-π interaction. Furthermore, we show that mispairing between W and guanine (G) causes a distortion in the planarity of the base pair, thus explaining the destabilization of DNA duplexes featuring a G:W pair. MD simulations show that incorporation of single or multiple consecutive A:W pairs in DNA duplexes causes minor changes to the intra- and inter-base geometrical parameters, while a moderate widening/shrinking of the major/minor groove of the duplexes is observed. QM calculations applied to selected stacks from the MD simulations also show an increased stacking energy for W, over T, with the neighboring bases.

Random-Phase Approximation in Many-Body Noncovalent Systems: Methane in a Dodecahedral Water Cage

The many-body expansion (MBE) of energies of molecular clusters or solids offers a way to detect and analyze errors of theoretical methods that could go unnoticed if only the total energy of the system was considered. In this regard, the interaction between the methane molecule and its enclosing dodecahedral water cage, CH₄···(H₂O)₂₀, is a stringent test for approximate methods, including density functional theory (DFT) approximations. Hybrid and semilocal DFT approximations behave erratically for this system, with three- and four-body nonadditive terms having neither the correct sign nor magnitude. Here, we analyze to what extent these qualitative errors in different MBE contributions are conveyed to post-Kohn-Sham random-phase approximation (RPA), which uses approximate Kohn-Sham orbitals as its input. The results reveal a correlation between the quality of the DFT input states and the RPA results. Moreover, the renormalized singles energy (RSE) corrections play a crucial role in all orders of the many-body expansion. For dimers, RSE corrects the RPA underbinding for every tested Kohn-Sham model: generalized-gradient approximation (GGA), meta-GGA, (meta-)GGA hybrids, as well as the optimized effective potential at the correlated level. Remarkably, the inclusion of singles in RPA can also correct the wrong signs of three- and four-body nonadditive energies as well as mitigate the excessive higher-order contributions to the many-body expansion. The RPA errors are dominated by the contributions of compact clusters. As a workable method for large systems, we propose to replace those compact contributions with CCSD(T) energies and to sum up the remaining many-body contributions up to infinity with supermolecular or periodic RPA. As a demonstration of this approach, we show that for RPA(PBE0)+RSE it suffices to apply CCSD(T) to dimers and 30 compact, hydrogen-bonded trimers to get the methane-water cage interaction energy to within 1.6% of the reference value.

Cluster-in-Molecule Local Correlation Method with an Accurate Distant Pair Correction for Large Systems

The cluster-in-molecule (CIM) local correlation approach with an accurate distant pair correlation energy correction is presented. For large systems, the inclusion of distant pair correlation energies is essential for the accurate prediction of absolute correlation energies and relative energies. Here, we propose a simple and efficient scheme for evaluating the distant pair correlation energy correction for the CIM approaches. The corrections can be readily extracted from electron correlation calculations of clusters with almost no additional effort. Benchmark calculations show that the improved CIM approach can recover more than 99.94% of the correlation energy calculated by the parent method. By combining the CIM approach with the domain-based local pair natural orbital (DLPNO) local correlation approach, we have provided accurate binding energies at the CIM-DLPNO-CCSD(T) level for a test set consisting of eight weakly bound complexes ranging in size from 200 to 1027 atoms. With these results as the reference data, the accuracy and applicability of other electron correlation methods and a few density functional methods for large systems have been assessed.

Thermochemistry of Tungsten-3p Elements for Density Functional Theory, Caveat Lector!

There are two primary foci in this research on WE (E = Si, P, and S) bonds: prediction of their bond dissociation enthalpies (BDEs), including σ- and π-bond energy components, and assessing the uncertainty of these BDE predictions for levels of theory commonly used in the literature. The internal standards for computational accuracy include metal-element bond lengths (mean absolute error = 1.8 ± 1.2%), main group homolog BDEs versus higher levels of ab initio theory (W1U and G4 BDEs, R² = 0.98), and DLPNO-CCSD(T)/def2-QZVPP calculations for metal-ligand BDEs (R² = 0.88). The W═Si first π-bond is underreported for density functional theory (DFT)/MP2 methods versus DLPNO-CCSD(T), while the latter shows negligible strength for the W;Si second π-bond, consistent with the literature. This research highlights clear issues with the underlying assumptions required for the use of perturbation theory methods for the fragments derived from W-P homolysis. The difficulties associated with modeling the metal thermochemistry with DFT (and MP2) levels of theory are manifest in the broad standard deviations observed. However, the average BDEs found using 48 popular DFT and MP2 levels of theory are reliable, 10.8 ± 6.8% mean absolute error (with W-P removed) versus DLPNO-CCSD(T), with the caveat that the individual basis set/pseudopotential/valence basis set combination can vary wildly. Analysis of the absolute error percentages with respect to the level of theory indicates little benefit to going higher on Jacob's Ladder, as simpler methods have lower error versus high-level ab initio techniques such as G4 and DLPNO-CCSD(T).

Scalable Electron Correlation Methods. 8. Explicitly Correlated Open-Shell Coupled-Cluster with Pair Natural Orbitals PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12

We present explicitly correlated open-shell pair natural orbital local coupled-cluster methods, PNO-RCCSD(T)-F12 and PNO-UCCSD(T)-F12. The methods are extensions of our previously reported PNO-R/UCCSD methods (J. Chem. Theory Comput., 2020, 16, 3135-3151, https://pubs.acs.org/doi/10.1021/acs.jctc.0c00192) with additions of explicit correlation and perturbative triples corrections. The explicit correlation treatment follows the spin-orbital CCSD-F12b theory using Ansatz 3*A, which is found to yield comparable or better basis set convergence than the more rigorous Ansatz 3C in computed ionization potentials and reaction energies using double- to quaduple-ζ basis sets. The perturbative triples correction is adapted from the spin-orbital (T) theory to use triples natural orbitals (TNOs). To address the coupling due to off-diagonal Fock matrix elements, the local triples amplitudes are iteratively solved using small domains of TNOs, and a semicanonical (T0) domain correction with larger domains is applied to reduce the domain errors. The performance of the methods is demonstrated through benchmark calculations on ionization potentials, radical stabilization energies, reaction energies of fragmentations and rearrangements in radical cations, and spin-state energy differences of iron complexes. For a few test sets where canonical calculations are feasible, PNO-RCCSD(T)-F12 results agree with the canonical ones to within 0.4 kcal mol^-1, and this maximum error is reduced to below 0.2 kcal mol^-1 when large local domains are used. For larger systems, results using different thresholds for the local approximations are compared to demonstrate that 1 kcal mol^-1 level of accuracy can be achieved using our default settings. For a couple of difficult cases, it is demonstrated that the errors from individual approximations are only a fraction of 1 kcal mol^-1, and the overall accuracy of the method does not rely on error compensations. In contrast to canonical calculations, the use of spin-orbitals does not lead to a significant increase of computational time and memory usage in the most expensive steps of PNO-R/UCCSD(T)-F12 calculations. The only exception is the iterative solution of the (T) amplitudes, which can be avoided without significant errors by using a perturbative treatment of the off-diagonal coupling, known as (T1) approximation. For most systems, even the semicanonical approximation (T0) leads only to small errors in relative energies. Our program is well parallelized and capable of computing accurate correlation energies for molecules with 100-200 atoms using augmented triple-ζ basis sets in less than a day of elapsed time on a small computer cluster.

When are two hydrogen bonds better than one? Accurate first-principles models explain the balance of hydrogen bond donors and acceptors found in proteins

Hydrogen bonds (HBs) play an essential role in the structure and catalytic action of enzymes, but a complete understanding of HBs in proteins challenges the resolution of modern structural (i.e., X-ray diffraction) techniques and mandates computationally demanding electronic structure methods from correlated wavefunction theory for predictive accuracy. Numerous amino acid sidechains contain functional groups (e.g., hydroxyls in Ser/Thr or Tyr and amides in Asn/Gln) that can act as either HB acceptors or donors (HBA/HBD) and even form simultaneous, ambifunctional HB interactions. To understand the relative energetic benefit of each interaction, we characterize the potential energy surfaces of representative model systems with accurate coupled cluster theory calculations. To reveal the relationship of these energetics to the balance of these interactions in proteins, we curate a set of 4000 HBs, of which >500 are ambifunctional HBs, in high-resolution protein structures. We show that our model systems accurately predict the favored HB structural properties. Differences are apparent in HBA/HBD preference for aromatic Tyr versus aliphatic Ser/Thr hydroxyls because Tyr forms significantly stronger O–H⋯O HBs than N–H⋯O HBs in contrast to comparable strengths of the two for Ser/Thr. Despite this residue-specific distinction, all models of residue pairs indicate an energetic benefit for simultaneous HBA and HBD interactions in an ambifunctional HB. Although the stabilization is less than the additive maximum due both to geometric constraints and many-body electronic effects, a wide range of ambifunctional HB geometries are more favorable than any single HB interaction.

Correlated wavefunction theory predicts and high-resolution crystal structure analysis confirms the important, stabilizing effect of simultaneous hydrogen bond donor and acceptor interactions in proteins.

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.

B12X11(H2)−: exploring the limits of isotopologue selectivity of hydrogen adsorption

We study the isotopologue-selective binding of dihydrogen at the undercoordinated boron site of B₁₂X₁₁⁻ (X = H, F, Cl, Br, I, CN) using ab initio quantum chemistry. With a Gibbs free energy of H₂ attachment reaching up to 80 kJ mol⁻¹ (ΔG at 300 K for X = CN), these sites are even more attractive than most undercoordinated metal centers studied so far. We thus believe that they can serve as an edge case close to the upper limit of isotopologue-selective H₂ adsorption sites. Differences of the zero-point energy of attachment average 5.0 kJ mol⁻¹ between D₂ and H₂ and 2.7 kJ mol⁻¹ between HD and H₂, resulting in hypothetical isotopologue selectivities as high as 2.0 and 1.5, respectively, even at 300 K. Interestingly, even though attachment energies vary substantially according to the chemical nature of X, isotopologue selectivities remain very similar. We find that the H–H activation is so strong that it likely results in the instantaneous heterolytic dissociation of H₂ in all cases (except, possibly, for X = H), highlighting the extremely electrophilic nature of B₁₂X₁₁⁻ despite its negative charge. Unfortunately, this high reactivity also makes B₁₂X₁₁⁻ unsuitable for practical application in the field of dihydrogen isotopologue separation. Thus, this example stresses the two-edged nature of strong H₂ affinity, yielding a higher isotopologue selectivity on the one hand but risking dissociation on the other, and helps define a window of adsorption energies into which a material for selective adsorption near room temperature should ideally fall.

The extreme H₂ affinity of B₁₂X₁₁⁻ gives a glimpse of how higher selectivities in adsorptive isotopologue separation may be achieved.

Nitro-, Cyano-, and Methylfuroxans, and Their Bis-Derivatives: From Green Primary to Melt-Cast Explosives

In the present work, we studied in detail the thermochemistry, thermal stability, mechanical sensitivity, and detonation performance for 20 nitro-, cyano-, and methyl derivatives of 1,2,5-oxadiazole-2-oxide (furoxan), along with their bis-derivatives. For all species studied, we also determined the reliable values of the gas-phase formation enthalpies using highly accurate multilevel procedures W2-F12 and/or W1-F12 in conjunction with the atomization energy approach and isodesmic reactions with the domain-based local pair natural orbital (DLPNO) modifications of the coupled-cluster techniques. Apart from this, we proposed reliable benchmark values of the formation enthalpies of furoxan and a number of its (azo)bis-derivatives. Additionally, we reported the previously unknown crystal structure of 3-cyano-4-nitrofuroxan. Among the monocyclic compounds, 3-nitro-4-cyclopropyl and dicyano derivatives of furoxan outperformed trinitrotoluene, a benchmark melt-cast explosive, exhibited decent thermal stability (decomposition temperature >200 °C) and insensitivity to mechanical stimuli while having notable volatility and low melting points. In turn, 4,4′-azobis-dicarbamoyl furoxan is proposed as a substitute of pentaerythritol tetranitrate, a benchmark brisant high explosive. Finally, the application prospects of 3,3′-azobis-dinitro furoxan, one of the most powerful energetic materials synthesized up to date, are limited due to the tremendously high mechanical sensitivity of this compound. Overall, the investigated derivatives of furoxan comprise multipurpose green energetic materials, including primary, secondary, melt-cast, low-sensitive explosives, and an energetic liquid.

Canonical and DLPNO-Based Composite Wavefunction Methods Parametrized against Large and Chemically Diverse Training Sets. 2: Correlation-Consistent Basis Sets, Core-Valence Correlation, and F12 Alternatives

A hierarchy of wavefunction composite methods (cWFT), based on G4-type cWFT methods available for elements H through Rn, was recently reported by the present authors [J. Chem. Theor. Comput.2020, 16, 4238]. We extend this hierarchy by considering the inner-shell correlation energy in the second-order Møller–Plesset correction and replacing the Weigend–Ahlrichs def2-mZVPP(D) basis sets used with complete basis set extrapolation from augmented correlation-consistent core–valence triple-ζ, aug-cc-pwCVTZ(-PP), and quadruple-ζ, aug-cc-pwCVQZ(-PP), basis sets, thus creating cc-G4-type methods. For the large and chemically diverse GMTKN55 benchmark suite, they represent a substantial further improvement and bring WTMAD2 (weighted mean absolute deviation) down below 1 kcal/mol. Intriguingly, the lion’s share of the improvement comes from better capture of valence correlation; the inclusion of core–valence correlation is almost an order of magnitude less important. These robust correlation-consistent cWFT methods approach the CCSD(T) complete basis limit with just one or a few fitted parameters. Particularly, the DLPNO variants such as cc-G4-T-DLPNO are applicable to fairly large molecules at a modest computational cost, as is (for a reduced range of elements) a different variant using MP2-F12/cc-pVTZ-F12 for the MP2 component.

Transition-metal-mediated reduction and reversible double-cyclization of cyanuric triazide to an asymmetric bitetrazolate involving cleavage of the six-membered aromatic ring

Cyanuric triazide reacts with several transition metal precursors, extruding one equivalent of N₂ and reducing the putative diazidotriazeneylnitrene species by two electrons, which rearranges to N-(1'H-[1,5'-bitetrazol]-5-yl)methanediiminate (biTzI^2-) dianionic ligand, which ligates the metal and dimerizes, and is isolated from pyridine as [M(biTzI)]₂Py₆ (M = Mn, Fe, Zn, Cu, Ni). Reagent scope, product analysis, and quantum chemical calculations were combined to elucidate the mechanism of formation as a two-electron reduction preceding ligand rearrangement.

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.

Heterocyclopentanediyls vs Heterocyclopentadienes: A Question of Silyl Group Migration

The reaction of the singlet biradical [P(μ-NHyp)]₂ (Hyp = hypersilyl, (Me₃Si)₃Si) with different isonitriles afforded a series of five-membered N₂P₂C heterocycles. Depending on the steric bulk of the substituent at the isonitrile, migration of a Hyp group was observed, resulting in two structurally similar but electronically very different isomers. As evidenced by comprehensive spectroscopic and theoretical studies, the heterocyclopentadiene isomer may be regarded as a rather unreactive closed-shell singlet species with one localized N═P and one C═P double bond, whereas the heterocyclopentanediyl isomer represents an open-shell singlet biradical with interesting photochemical properties, such as photoisomerization under irradiation with red light to a [2.1.0]-housane-type species.

Halogen bonding in crystals of free 1,2-diiodo-ethene (C2H2I2) and its π-complex [CpMn(CO)2](π-C2H2I2)

1,2-trans-diiodo-ethene (C2H2I2) – is an overlooked halogen bond donor, which demonstrate the distinct similarity of the geometry and directionality of I···I halogen bonds around the iodine atoms in its native and CpMn(CO)2(C2H2I2) π-complex crystals. Distortion of the planar geometry of C2H2I2 upon the π-coordination result the distortion of the native planar layered geometry of C2H2I2, so that [CpMn(CO)2](π-C2H2I2) features more complex I···I XB assisted 3D network. Unusual structural parallels between the native C2H2I2 crystals and solid iodine are discussed.

Reversible switching between housane and cyclopentanediyl isomers: an isonitrile-catalysed thermal reverse reaction

The photo-isomerization of an isolable five-membered singlet biradical based on C, N, and P ([TerNP]2CNDmp, 2a) selectively afforded a closed-shell housane-type isomer (3a) by forming a transannular P-P bond. In the dark, the housane-type species re-isomerized to the biradical, resulting in a fully reversible overall process. In the present study, the influence of tBuNC on the thermal reverse reaction was investigated: the isonitrile acted as a catalyst, thus allowing control over the thermal reaction rate. Moreover, tBuNC also reacted with the biradical to form an adduct species ([TerNP]2CNDmp·CNtBu, 4a), which can be regarded as the resting state of the system. The reactive species 2a and 3a could be re-generated in situ by irradiation with red light. The results of this study extend our understanding of this new class of molecular switches.

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.

Formulation of a Dressed Coupled-Cluster Method with Implicit Triple Excitations and Benchmark Application to Hydrogen-Bonded Systems

In this paper, we present a coupled-cluster theory based on a double-exponential wave operator ansatz, which is capable of mimicking the effects of connected triple excitations in an iterative manner. The triply excited manifold is spanned via the action of a set of scattering operators on doubly excited determinants, whereas their action annihilates the Hartree-Fock reference determinant. The effect of triple excitations is included at a computational scaling slightly higher than that of conventional coupled-cluster singles and doubles. Furthermore, we demonstrate two approximate schemes, which arise naturally, and argue that both these schemes come equipped with certain renormalization terms capable of handling nonbonding interactions due to robust inclusion of the screened Coulomb interaction. We justify our claims from both a theoretical perspective and a number of numerical applications to prototypical water clusters, in a number of basis functions. Our methods show overall comparable performance to the canonical coupled-cluster theory with singles, doubles, and perturbative triples (CCSD(T)) and allied methods, however, at a lower computational scaling.

Isomerism and Biradical Character of Tetrapnictide Dianions: A Computational Study

We present a computational study on tetrapnictide dianions Pn₄^2– (Pn = P, As, Sb, Bi), using density functional theory (DFT), coupled‐cluster [DLPNO‐CCSD(T)] and complete active space self‐consistent field (CASSCF) methods. Environmental effects such as solvation and coordination of counterions are included. The calculations reveal that out of three isomers (square‐planar, butterfly and capped‐triangle), the square planar isomers are generally the most stable. The counterion (Li⁺ and Mg²⁺) used in the calculations have a substantial effect on the relative stabilities. The square planar isomers show considerable biradical character. Calculated reactions toward alkenes indicate that this unusual electronic structure has significant implications on the reactivity of the Pn₄^2– dianions.

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.

Occurrence and stability of lone pair-π and OH-π interactions between water and nucleobases in functional RNAs

We identified over 1000 instances of water-nucleobase stacking contacts in a variety of RNA molecules from a non-redundant set of crystal structures with resolution ≤3.0 Å. Such contacts may be of either the lone pair-π (lp-π) or the OH-π type, in nature. The distribution of the distances of the water oxygen from the nucleobase plane peaks at 3.5 Å for A, G and C, and approximately at 3.1-3.2 Å for U. Quantum mechanics (QM) calculations confirm, as expected, that the optimal energy is reached at a shorter distance for the lp-π interaction as compared to the OH-π one (3.0 versus 3.5 Å). The preference of each nucleobase for either type of interaction closely correlates with its electrostatic potential map. Furthermore, QM calculations show that for all the nucleobases a favorable interaction, of either the lp-π or the OH-π type, can be established at virtually any position of the water molecule above the nucleobase skeleton, which is consistent with the uniform projection of the OW atoms over the nucleobases ring we observed in the experimental occurrences. Finally, molecular dynamics simulations of a model system for the characterization of water-nucleobase stacking contacts confirm the stability of these interactions also under dynamic conditions.

Ab initio kinetics predictions for the role of pre-reaction complexes in hydrogen abstraction from 2-butanone by OH radicals

The existence of pre- and post-reaction complexes has been proposed to influence hydrogen abstraction reaction kinetics, but the significance still remains controversial. A theoretical study is presented to discuss the effects of complexes on hydrogen abstraction from 2-butanone by OH radicals based on the detailed PESs at the DLPNO-CCSD(T)/aug-cc-pVTZ//M06-2x-D3/may-cc-pVTZ level with five pre-reaction complexes at the entrance of the channels and four post-reaction complexes at the exit. The hydrogen bond interactions, steric effects, and contributions to the bonding orbital of the OH radical species and 2-butanone species in the complex structures were visualized and investigated by wavefunction analyses. Three kinds of mechanisms-the general bimolecular reaction, the reaction with the complexes considered, and the well-skipping reaction-were compared based on high-pressure-limit rate constants, predicted branching ratios, and fractional populations of reactants and products in the temperature range of 250-2000 K. The existence of complexes was proved to be crucial in the kinetics and mechanisms of the hydrogen abstraction from 2-butanone molecules by OH radicals.

Origin of the Diastereoselectivity of the Heterogeneous Hydrogenation of a Substituted Indolizine

In this work, the stereoselective heterogeneous hydrogenation of a tetrasubstituted indolizine was studied. Partial hydrogenation products were obtained in three steps from a substituted pyridine-2-carboxaldehyde prepared from commercial pyridoxine hydrochloride. The hydrogenation of the indolizine ring was shown to be diastereoselective, forming trans-6b and cis-9. Theoretical calculations (ab initio and DFT) were used to rationalize the unusual trans stereoselectivity for 6b, and a keto–enol tautomerism under kinetic control has been proposed as the source of diastereoselectivity.