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.

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.

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.

Fulminic acid: a quasibent spectacle.

Fulminic acid (HCNO) played a critical role in the early development of organic chemistry, and chemists have sought to discern the structure and characteristics of this molecule and its isomers for over 200 years. The mercurial nature of the extremely flat H-C-N bending potential of fulminic acid, with a nearly vanishing harmonic vibrational frequency at linearity, remains enigmatic and refractory to electronic structure theory, as dramatic variation with both orbital basis set and electron correlation method is witnessed. To solve this problem using rigorous electronic wavefunction methods, we have employed focal point analyses (FPA) to ascertain the ab initio limit of optimized linear and bent geometries, corresponding vibrational frequencies, and the HCN + O(3P) → HCNO reaction energy. Electron correlation treatments as extensive as CCSDT(Q), CCSDTQ(P), and even CCSDTQP(H) were employed, and complete basis set (CBS) extrapolations were performed using the cc-pCVXZ (X = 4-6) basis sets. Core electron correlation, scalar relativistic effects (MVD1), and diagonal Born-Oppenheimer corrections (DBOC) were all included and found to contribute significantly in determining whether vibrationless HCNO is linear or bent. At the all-electron (AE) CCSD(T)/CBS level, HCNO is a linear molecule with ω5(H-C-N bend) = 120 cm-1. However, composite AE-CCSDT(Q)/CBS computations give an imaginary frequency (51i cm-1) at the linear optimized geometry, leading to an equilibrium structure with an H-C-N angle of 173.9°. Finally, at the AE-CCSDTQ(P)/CBS level, HCNO is once again linear with ω5 = 45 cm-1, and inclusion of both MVD1 and DBOC effects yields ω5 = 32 cm-1. A host of other topics has also been investigated for fulminic acid, including the dependence of re and ωi predictions on a variety of CBS extrapolation formulas, the question of multireference character, the N-O bond energy and enthalpy of formation, and issues that give rise to the quasibent appellation.

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.

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.

Comparative Study of Neutral and Cationic Sn2H2: Toward Laboratory Detection of the Cation.

Group 14 M2H2 isomers (M = Si, Ge, Sn, and Pb) have attracted interest due to their radically differing electronic structures from acetylene. To better understand the Sn-H interactions of the neutral and cationic Sn2H2 structures, we present the most rigorous study of these systems to date. CCSD(T)/cc-pwCVTZ harmonic frequencies are presented as the first predictions for the neutral and cationic species to date. CCSDT(Q)/CBS relative energies are reported using the focal point approach, confirming the butterfly isomer as the global minimum on the potential energy surface for both the neutral and cationic species. In all, there exist 7 minima and 15 transition states. NBO analysis is also performed to elucidate the changes in bond order going from neutral to cation across all isomers of Sn2H2. Our results provide insights into the important Sn-H interaction and provide guidance for future work that may detect Sn2H2+ in the laboratory for the first time.

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.

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.

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.

Accurate and efficient open-source implementation of domain-based local pair natural orbital (DLPNO) coupled-cluster theory using a t1-transformed Hamiltonian.

We present an efficient, open-source formulation for coupled-cluster theory through perturbative triples with domain-based local pair natural orbitals [DLPNO-CCSD(T)]. Similar to the implementation of the DLPNO-CCSD(T) method found in the ORCA package, the most expensive integral generation and contraction steps associated with the CCSD(T) method are linear-scaling. In this work, we show that the t1-transformed Hamiltonian allows for a less complex algorithm when evaluating the local CCSD(T) energy without compromising efficiency or accuracy. Our algorithm yields sub-kJ mol-1 deviations for relative energies when compared with canonical CCSD(T), with typical errors being on the order of 0.1 kcal mol-1, using our TightPNO parameters. We extensively tested and optimized our algorithm and parameters for non-covalent interactions, which have been the most difficult interaction to model for orbital (PNO)-based methods historically. To highlight the capabilities of our code, we tested it on large water clusters, as well as insulin (787 atoms).

Trinuclear and Tetranuclear Ruthenium Carbonyl Nitrosyls: Oxidation of a Carbonyl Ligand by an Adjacent Nitrosyl Ligand.

Trinuclear and tetranuclear ruthenium carbonyls of the types Ru3(CO)n(NO)2, Ru3(N)(CO)n(NO), Ru3(N)2(CO)n, Ru3(N)(CO)n(NCO), Ru3(CO)n(NCO)(NO), Ru4(N)(CO)n(NO), Ru4(N)(CO)n(NCO), and Ru4(N)2(CO)n related to species observed experimentally in the chemistry of Ru3(CO)10(µ-NO)2 have been investigated using density functional theory. In all cases, the experimentally observed structures have been found to be low-energy structures. The low-energy trinuclear structures typically have a central strongly bent Ru-Ru-Ru chain with terminal CO groups and bridging nitrosyl, isocyanate, and/or nitride ligands across the end of the chain. The low-energy tetranuclear structures typically have a central Ru4N unit with terminal CO groups and a non-bonded pair of ruthenium atoms bridged by a nitrosyl or isocyanate group.

Lantern-type dinickel complexes: An exploration of possibilities for nickel-nickel bonding with bridging bidentate ligands.

Many binuclear nickel complexes have NiNi distances suggesting NiNi covalent bonds, including lantern-type complexes with bridging bidentate ligands. This DFT study treats tetragonal, trigonal, and digonal lantern-type complexes with the formamidinate, guanidinate, and formate ligands, besides some others. Formal bond orders (ranging from zero to two) are assigned to all the NiNi bonds on the basis of MO occupancy considerations. A VB-based electron counting approach assigns plausible resonance structures to the dinickel cores. Model tetragonal complexes with the dimethylformamidinate and the dithioformate ligands have singlet ground states whose non-covalently bonded NiNi distances are close to those in their experimentally known counterparts. Trigonal dinickel complexes are unknown, but are predicted to have quartet ground states with NiNi bonds of order 0.5. The model digonal complexes are predicted to have triplet ground states, but the predicted NiNi bond lengths are longer than those found in their experimentally known counterparts. This could owe to inadequate treatment of electron correlation by DFT in these short NiNi bonds with their multiconfigurational character. All the NiNi bond distances here are categorized into ranges according to the NiNi bond orders of 0, 0.5, 1, 1.5, and 2, no NiNi bonds of order higher than two being identified. The NiNi bonds of given order in these lantern-type complexes are consistently shorter than the corresponding NiNi bonds in dinickel complexes having carbonyl ligands, attributable to the metalmetal bond lengthening effect of CO ligands.

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.

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.

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.

High-Level Coupled-Cluster Study on Substituent Effects in H2 Activation by Low-Valent Aluminyl Anions.

The synthesis of novel aluminyl anion complexes has been well exploited in recent years. Moreover, the elucidation of the structure and reactivity of these complexes opens the path toward a new understanding of low-valent aluminum complexes and their chemistry. This work computationally treats the substituent effect on aluminyl anions to discover suitable alternatives for H2 activation at a high level of theory utilizing coupled-cluster techniques extrapolated to the complete basis set. The results reveal that the simplest AlH2- system is the most reactive toward the activation of H2, but due to the low steric demand, severe difficulty in the stabilization of this system makes its use nonviable. However, the results indicate that, in principle, aluminyl systems with -C, -CN, -NC, and -N chelating centers would be the best choices of ligand toward the activation of molecular hydrogen by taking care of suitable steric demand to prevent dimerization of the catalysts. Furthermore, computations show that monosubstitution (besides -H) in aluminyl anions is preferred over disubstitution. So our predictions show that bidentate ligands may yield less reactive aluminyl anions to activate H2 than monodentate ones.

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.

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.

Enthalpies of formation for Criegee intermediates: A correlation energy convergence study.

Criegee intermediates, formed from the ozonolysis of alkenes, are known to have a role in atmospheric chemistry, including the modulation of the oxidizing capacity of the troposphere. Although studies have been conducted since their discovery, the synthesis of these species in the laboratory has ushered in a new wave of investigations of these structures, both theoretically and experimentally. In some of these theoretical studies, high-order corrections for correlation energy are included to account for the mid multi-reference character found in these systems. Many of these studies include a focus on kinetics; therefore, the calculated energies should be accurate (<1 kcal/mol in error). In this research, we compute the enthalpies of formation for a small set of Criegee intermediates, including higher-order coupled cluster corrections for correlation energy up to coupled cluster with perturbative quintuple excitations. The enthalpies of formation for formaldehyde oxide, anti-acetaldehyde oxide, syn-acetaldehyde oxide, and acetone oxide are presented at 0 K as 26.5, 15.6, 12.2, and 0.1 kcal mol-1, respectively. Additionally, we do not recommend the coupled cluster with perturbative quadruple excitations [CCSDT(Q)] energy correction, as it is approximately twice as large as that of the coupled cluster with full quadruple excitations (CCSDTQ). Half of the CCSDT(Q) energy correction may be included as a reliable, cost-effective estimation of CCSDTQ energies for Criegee intermediates.