MolSym: A Python package for handling symmetry in molecular quantum chemistry.

A consideration of the point group symmetry of molecules is often advantageous from a computational efficiency standpoint and sometimes necessary for the correct treatment of chemical physics problems. Many modern electronic structure software packages include a treatment of symmetry, but these are sometimes incomplete or unusable outside of that program's environment. Therefore, we have developed the MolSym package for handling molecular symmetry and its associated functionalities to provide a platform for including symmetry in the implementation and development of other methods. Features include point group detection, molecule symmetrization, arbitrary generation of symmetry element sets and character tables, and symmetry adapted linear combinations of real spherical harmonic basis functions, Cartesian displacement coordinates, and internal coordinates. We present some of the advantages of using molecular symmetry as achieved by MolSym, particularly with respect to Hartree-Fock theory, and the reduction of finite difference displacements in gradient/Hessian computations. This package is designed to be easily integrated into other software development efforts and may be extended to further symmetry applications.

Binuclear Lantern Complexes of All First-Row 3d Metals Scandium to Zinc: Metal-Metal Bond Lengths and Bond Orders, with Measures of Intrinsic Metal-Metal Bond Strength.

The B3LYP and M06-L functionals with the cc-pVTZ basis set are used to study lantern-type binuclear complexes of all the first-row (3d block) metals scandium to zinc in various low-energy spin states, out of which the ground states are predicted. These complexes are studied as models using mostly the unsubstituted formamidinate ligand. For each metal, metal-metal (MM) bond lengths are related to the formal MM bond orders (zero to five), derived by MO analysis and by electron counting. The predicted ground-state spin multiplicities and MM bond lengths of the model complexes generally agree fairly well with available experimental results on substituted analogues. Finally, values of the formal shortness ratio and Wiberg index for the MM bonds in all of these complexes in all spin states studied are categorized into ranges according to the MM bond orders 0 to 5 in steps of 0.5. The trends shown validate their use in estimating intrinsic metal-metal bond strength regardless of the metal.

A Stable Aluminum Tris(dithiolene) Triradical.

A stable aluminum tris(dithiolene) triradical (3) was experimentally realized through a low-temperature reaction of the sterically demanding lithium dithiolene radical (2) with aluminum iodide. Compound 3 was characterized by single-crystal X-ray diffraction, UV-vis and EPR spectroscopy, SQUID magnetometry, and theoretical computations. The quartet ground state of triradical 3 has been unambiguously confirmed by variable-temperature continuous wave EPR experiments and SQUID magnetometry. Both SQUID magnetometry and broken-symmetry DFT computations reveal a small doublet-quartet energy gap [ΔEDQ = 0.18 kcal mol-1 (SQUID); ΔEDQ = 0.14 kcal mol-1 (DFT)]. The pulsed EPR experiment (electron spin echo envelop modulation) provides further evidence for the interaction of these dithiolene-based radicals with the central aluminum nucleus of 3.

Biomimetic Frustrated Lewis Pair Catalysts for Hydrogenation of CO to Methanol at Low Temperatures.

The industrial production of methanol through CO hydrogenation using the Cu/ZnO/Al2O3 catalyst requires harsh conditions, and the development of new catalysts with low operating temperatures is highly desirable. In this study, organic biomimetic FLP catalysts with good tolerance to CO poison are theoretically designed. The base-free catalytic reaction contains the 1,1-addition of CO into a formic acid intermediate and the hydrogenation of the formic acid intermediate into methanol. Low-energy spans (25.6, 22.1, and 20.6 kcal/mol) are achieved, indicating that CO can be hydrogenated into methanol at low temperatures. The new extended aromatization-dearomatization effect involving multiple rings is proposed to effectively facilitate the rate-determining CO 1,1-addition step, and a new CO activation model is proposed for organic catalysts.

A wealth of structures for the Ge2H2+ radical cation: comparison of theory and experiment.

Five structures of Ge2H2 and Ge2H2+ are investigated in this study. Optimized geometries at the CCSD(T)/cc-pwCVQZ-PP level of theory were obtained. Focal point analyses were performed on these optimized geometries to determine relative energies using the CCSD(T) method with polarized basis sets up to quintuple-zeta. Energy corrections include full T and pertubative (Q) coupled-cluster effects plus anharmonic corrections to the zero-point vibrational energy. Relative ordering in energy from lowest to highest of the five Ge2H2+ structures is butterfly, germylidene, monobridged, trans, then linear. In neutral Ge2H2, the monobridged structure lies lower in energy than the germylidene structure. Fundamental vibrational frequencies and IR intensities were computed for the minima at the CCSD(T)/cc-pwCVTZ-PP level of theory to compare with experimental research. Partial atomic charges and natural bonding orbital analyses indicated that the positive charge of Ge2H2+ is contained in the region of the Ge-Ge bond.

Convergent ab initio analysis of the multi-channel HOBr + H reaction.

High-level potential energy surfaces for three reactions of hypobromous acid with atomic hydrogen were computed at the CCSDTQ/CBS//CCSDT(Q)/complete basis set level of theory. Focal point analysis was utilized to extrapolate energies and gradients for energetics and optimizations, respectively. The H attack at Br and subsequent Br-O cleavage were found to proceed barrierlessly. The slightly submerged transition state lies -0.2 kcal mol-1 lower in energy than the reactants and produces OH and HBr. The two other studied reaction paths are the radical substitution to produce H2O and Br with a 4.0 kcal mol-1 barrier and the abstraction at hydrogen to produce BrO and H2 with an 11.2 kcal mol-1 barrier. The final product energies lie -37.2, -67.9, and -7.3 kcal mol-1 lower in energy than reactants, HOBr + H, for the sets of products OH + HBr, H2O + Br, and H2 + BrO, respectively. Additive corrections computed for the final energetics, particularly the zero-point vibrational energies and spin-orbit corrections, significantly impacted the final stationary point energies, with corrections up to 6.2 kcal mol-1.

Correction: Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance.

Correction for 'Pericyclic reaction benchmarks: hierarchical computations targeting CCSDT(Q)/CBS and analysis of DFT performance' by Pascal Vermeeren et al., Phys. Chem. Chem. Phys., 2022, 24, 18028-18042, https://doi.org/10.1039/D2CP02234F.

Unusual nucleophilic reactivity of a dithiolene-based N-heterocyclic silane.

While the dithiolene-based N-heterocyclic silane (4) reacts with two equivalents of BX3 (X = Br, I) to give zwitterionic Lewis adducts 5 and 8, respectively, the parallel reaction of 4 with BCl3 results in 10, a dithiolene-substituted N-heterocyclic silane, via the Si-S bond cleavage. Unlike 5, the labile 8 may be readily converted to 9via BI3-mediated cleavage of the Si-N bond. The formation of 5 and 8 confirms that 4 uniquely possesses dual nucleophilic sites: (a) the terminal sulphur atom of the dithiolene moiety; and (b) the backbone carbon of the N-heterocyclic silane unit.

Exploring the Tl 2 H 2 potential energy surface: A comparative analysis with group 13 systems and experiment.

Thallium chemistry is experiencing unprecedented importance. Therefore, it is valuable to characterize some of the simplest thallium compounds. Stationary points along the singlet and triplet Tl 2 H 2 potential energy surface have been characterized. Stationary point geometries were optimized with the CCSD(T)/aug-cc-pwCVQZ-PP method. Harmonic vibrational frequencies were computed at the same level of theory while anharmonic vibrational frequencies were computed at the CCSD(T)/aug-cc-pwCVTZ-PP level of theory. Final energetics were obtained with the CCSDT(Q) method. Basis sets up to augmented quintuple-zeta cardinality (aug-cc-pwCV5Z-PP) were employed to obtain energetics in order to extrapolate to the complete basis set limits using the focal point approach. Zero-point vibrational energy corrections were appended to the extrapolated energies in order to determine relative energies at 0 K. It was found that the planar dibridged isomer lies lowest in energy while the linear structure lies highest in energy. The results were compared to other group 13 M 2 H 2 (M = B, Al, Ga, In, and Tl) theoretical studies and some interesting variations are found. With respect to experiment, incompatibilities exist.

Structures and Energetics of E2H3+ (E = As, Sb, and Bi) Cations.

E2H2 (E = As, Sb, Bi) structures involving multiple bonds have attracted much attention recently. The E2H3+ cations (protonated E2H2) are predicted to be viable with substantial proton affinities (>180 kcal/mol). Herein, the bonding characters and energetics of a number of E2H3+ isomers are explored through CCSD(T) and DFT methods. For the As2H3+ system, the CCSD(T)/cc-pVQZ-PP method predicts that the vinylidene-like structure lies lowest in energy, with the trans and cis isomers higher by 6.7 and 9.3 kcal/mol, respectively. However, for Sb2H3+ and Bi2H3+ systems, the trans isomer is the global minimum, while the energies of the cis and vinylidene-like structures are higher, respectively, by 2.0 and 2.4 kcal/mol for Sb2H3+ and 1.6 and 15.0 kcal/mol for Bi2H3+. Thus, the vinyledene-like structure is the lowest energy for the arsenic system but only a transition state of the bismuth system. With permanent dipole moments, all minima may be observable in microwave experiments. Besides, we have also obtained transition states and planar-cis structures with higher energies. The current results should provide new insights into the various isomers and provide a number of predictions for future experiments.

From Carbene-Dithiolene Zwitterion Mediated B-H Bond Activation to BH3·SMe2-Assisted Boron-Boron Bond Formation.

The 1:1 reaction of the carbene-stabilized dithiolene zwitterion 1 with BH3·SMe2 gave the dithiolene-based hydroborane 2 and the doubly hydrogen-capped CAAC species 3 via hydride-coupled reverse electron transfer processes. The mechanism of this transformation was probed computationally using density functional theory. The subsequent 2:1 reaction of 2 with 1 resulted in 4 and 3, suggesting that 1 can mediate the B-H bond activation not only for BH3 but also for monohydroboranes. In the presence of BH3·SMe2, 2 was unexpectedly converted to the corresponding diborane(4) complex 5 through a dehydrocoupling reaction at an elevated temperature.

Competition between Solvent···Solvent and Solvent···Solute Interactions in the Microhydration of the Tetrafluoroborate Anion, BF4-(H2O)n=1,2,3,4.

This study systematically examines the interactions of the tetrafluoroborate anion (BF4-) with up to four water molecules (BF4-(H2O)n=1,2,3,4). Full geometry optimizations and subsequent harmonic vibrational frequency computations are performed using a variety of density functional theory (DFT) methods (B3LYP, B3LYP-D3BJ, and M06-2X) and the MP2 ab initio method with a triple-ζ correlation consistent basis set augmented with diffuse functions on all non-hydrogen atoms (cc-pVTZ for H and aug-cc-pVTZ for B, O, and F; denoted as haTZ). Optimized structures and harmonic vibrational frequencies were also obtained with the CCSD(T) ab initio method and the haTZ basis set for the mono- and dihydrate (n = 1, 2) structures. The 2-body:Many-body (2b:Mb) technique, in which CCSD(T) computations capture the 1- and 2-body contributions to the interactions and MP2 computations recover all higher-order contributions, was used to extend these demanding computations to the tri- and tetrahydrate (n = 3, 4) systems. Four, five, and eight new stationary points have been identified for the di-, tri-, and tetrahydrate systems, respectively. The global minimum of the monohydrate adopts a symmetric double ionic hydrogen bond motif with C2v symmetry and an electronic dissociation energy of 13.17 kcal mol-1 at the CCSD(T)/haTZ level of theory. This strong solvent···solute interaction, however, competes with solute···solute interactions in the lowest-energy BF4-(H2O)n=2,3,4 minima that are not seen in the other di-, tri-, or tetrahydrate minima. The latter interactions help increase the 2b:Mb dissociation energies to more than 26, 41, and 51 kcal mol-1 for n = 2, 3, and 4, respectively. Structures that form hydrogen bonds between the solvating water molecules also exhibit the largest shifts in the harmonic OH stretching frequencies for the waters of hydration. These shifts can exceed -280 cm-1 relative to an isolated H2O molecule at the 2b:Mb/haTZ level of theory.

Germanium(II) Dithiolene Complexes.

The 1 : 2 reaction of the imidazole-based dithiolate (2) with GeCl2 • dioxane in THF/TMEDA gives 3, a TMEDA-complexed dithiolene-based germylene. Compound 3 is converted to monothiolate-complexed (5) and N-heterocyclic carbene-complexed (7) germanium(II) dithiolene complexes via Lewis base ligand exchange. A bis-dithiolene-based germylene (8), involving a 3c-4e S-Ge-S bond, has also been synthesized through controlled hydrolysis of 7. The bonding nature of 3, 5, and 8 was investigated by both experimental and theoretical methods.

Comparison of multifidelity machine learning models for potential energy surfaces.

Multifidelity modeling is a technique for fusing the information from two or more datasets into one model. It is particularly advantageous when one dataset contains few accurate results and the other contains many less accurate results. Within the context of modeling potential energy surfaces, the low-fidelity dataset can be made up of a large number of inexpensive energy computations that provide adequate coverage of the N-dimensional space spanned by the molecular internal coordinates. The high-fidelity dataset can provide fewer but more accurate electronic energies for the molecule in question. Here, we compare the performance of several neural network-based approaches to multifidelity modeling. We show that the four methods (dual, Δ-learning, weight transfer, and Meng-Karniadakis neural networks) outperform a traditional implementation of a neural network, given the same amount of training data. We also show that the Δ-learning approach is the most practical and tends to provide the most accurate model.

The multichannel i-propyl + O2 reaction system: A model of secondary alkyl radical oxidation.

The i-propyl + O2 reaction mechanism has been investigated by definitive quantum chemical methods to establish this system as a benchmark for the combustion of secondary alkyl radicals. Focal point analyses extrapolating to the ab initio limit were performed based on explicit computations with electron correlation treatments through coupled cluster single, double, triple, and quadruple excitations and basis sets up to cc-pV5Z. The rigorous coupled cluster single, double, and triple excitations/cc-pVTZ level of theory was used to fully optimize all reaction species and transition states, thus, removing some substantial flaws in reference geometries existing in the literature. The vital i-propylperoxy radical (MIN1) and its concerted elimination transition state (TS1) were found 34.8 and 4.4 kcal mol-1 below the reactants, respectively. Two ß-hydrogen transfer transition states (TS2, TS2') lie above the reactants by (1.4, 2.5) kcal mol-1 and display large Born-Oppenheimer diagonal corrections indicative of nearby surface crossings. An α-hydrogen transfer transition state (TS5) is discovered 5.7 kcal mol-1 above the reactants that bifurcates into equivalent α-peroxy radical hanging wells (MIN3) prior to a highly exothermic dissociation into acetone + OH. The reverse TS5 → MIN1 intrinsic reaction path also displays fascinating features, including another bifurcation and a conical intersection of potential energy surfaces. An exhaustive conformational search of two hydroperoxypropyl (QOOH) intermediates (MIN2 and MIN3) of the i-propyl + O2 system located nine rotamers within 0.9 kcal mol-1 of the corresponding lowest-energy minima.

Simulation of the VUV Absorption Spectra of Oxygenates and Hydrocarbons: A Joint Theoretical-Experimental Study.

Vacuum UV absorption spectroscopy is regularly used to provide unambiguous identification of a target species, insight into the electronic structure of molecules, and quantitative species concentrations. As molecules of interest have become more complex, theoretical spectra have been used in tandem with laboratory spectroscopic analysis or as a replacement when experimental data is unavailable. However, it is difficult to determine which theoretical methodologies can best simulate experiment. This study examined the performance of EOM-CCSD and 10 TD-DFT functionals (B3LYP, BH&HLYP, BMK, CAM-B3LYP, HSE, M06-2X, M11, PBE0, ωB97X-D, and X3LYP) to produce reliable vacuum UV absorption spectra for 19 small oxygenates and hydrocarbons using vertical excitation energies. The simulated spectra were analyzed against experiment using both a qualitative analysis and quantitative metrics, including cosine similarity, relative integral change, mean signed error, and mean absolute error. Based on our ranking system, it was determined that M06-2X was consistently the top performing TD-DFT method with BMK, CAM-B3LYP, and ωB97X-D also producing reliable spectra for these small combustion species.

Tensor Hypercontraction Form of the Perturbative Triples Energy in Coupled-Cluster Theory.

We present the working equations for a reduced-scaling method of evaluating the perturbative triples (T) energy in coupled-cluster theory, through the tensor hypercontraction (THC) of the triples amplitudes (tijkabc). Through our method, we can reduce the scaling of the (T) energy from the traditional O(N7) to a more modest O(N5). We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields submillihartree (mEh) differences from CCSD(T) when evaluating absolute energies and sub-0.1 kcal/mol energy differences when evaluating relative energies. Finally, we demonstrate that this method converges to the true CCSD(T) energy through the systematic increasing of the rank or eigenvalue tolerance of the orthogonal projector, as well as exhibiting sublinear to linear error growth with respect to system size.

The highly exothermic hydrogen abstraction reaction H2Te + OH → H2O + TeH: comparison with analogous reactions for H2Se and H2S.

The "gold standard" CCSD(T) method is adopted along with the correlation consistent basis sets up to aug-cc-pV5Z-PP to study the mechanism of the hydrogen abstraction reaction H2Te + OH. The predicted geometries and vibrational frequencies for reactants and products are in good agreement with the available experimental results. With the ZPVE corrections, the transition state in the favorable pathway of this reaction energetically lies 1.2 kcal mol-1 below the reactants, which is lower than the analogous relative energies for the H2Se + OH reaction (-0.7 kcal mol-1), the H2S + OH reaction (+0.8 kcal mol-1) and the H2O + OH reaction (+9.0 kcal mol-1). Accordingly, the exothermic reaction energies for these related reactions are predicted to be 47.8 (H2Te), 37.7 (H2Se), 27.1 (H2S), and 0.0 (H2O) kcal mol-1, respectively. Geometrically, the low-lying reactant complexes for H2Te + OH and H2Se + OH are two-center three-electron hemibonded structures, whereas those for H2S + OH and H2O + OH are hydrogen-bonded. With ZPVE and spin-orbit coupling corrections, the relative energies for the reactant complex, transition state, product complex, and the products for the H2Te + OH reaction are estimated to be -13.1, -1.0, -52.0, and -52.6 kcal mol-1, respectively. Finally, twenty-eight DFT functionals have been tested systematically to assess their ability in describing the potential energy surface of the H2Te + OH reaction. The best of these functionals for the corresponding energtics are -9.9, -1.4, -46.4, and -45.4 kcal mol-1 (MPWB1K), or -13.1, -2.4, -57.1, and -54.6 kcal mol-1 (M06-2X), respectively.

Probing the Potential Energy Profile of the I + (H2O)3 → HI + (H2O)2OH Forward and Reverse Reactions: High Level CCSD(T) Studies with Spin-Orbit Coupling Included.

Three different pathways for the atomic iodine plus water trimer reaction I + (H2O)3 → HI + (H2O)2OH were preliminarily examined by the DFT-MPW1K method. Related to previous predictions for the F/Cl/Br + (H2O)3 reactions, three pathways for the I + (H2O)3 reaction are linked in terms of geometry and energetics. To legitimize the results, the "gold standard" CCSD(T) method was employed to investigate the lowest-lying pathway with the correlation-consistent polarized valence basis set up to cc-pVQZ(-PP). According to the CCSD(T)/cc-pVQZ(-PP)//CCSD(T)/cc-pVTZ(-PP) results, the I + (H2O)3 → HI + (H2O)2OH reaction is predicted to be endothermic by 47.0 kcal mol-1. The submerged transition state is predicted to lie 43.7 kcal mol-1 above the separated reactants. The I···(H2O)3 entrance complex lies below the separated reactants by 4.1 kcal mol-1, and spin-orbit coupling has a significant impact on this dissociation energy. The HI···(H2O)2OH exit complex is bound by 4.3 kcal mol-1 in relation to the separated products. Compared with simpler I + (H2O)2 and I + H2O reactions, the I + (H2O)3 reaction is energetically between them in general. It is speculated that the reaction between the iodine atom and the larger water clusters may be energetically analogous to the I + (H2O)3 reaction. The iodine reaction I + (H2O)3 is connected with the analogous valence isoelectronic bromine/chlorine reactions Br/Cl + (H2O)3 but much different from the F + (H2O)3 reaction. Significant difference with other halogen systems, especially for barrier heights, are seen for the iodine systems.