Synthesis of Methanesulfonic Acid Directly from Methane: The Cation Mechanism or the Radical Mechanism?

In 2019, Diaz-Urrutia and Ott developed a high-yield method for direct conversion of methane to methanesulfonic acid and proposed a cationic chain reaction mechanism. However, Roytman and Singleton questioned this mechanism, and they favored a free-radical mechanism. In the present paper, we studied both the cationic chain and radical mechanisms and found the radical mechanism is more favorable, since it has a much lower energy barrier. However, the radical mechanism has not considered the effect of ions for the reaction taking place in oleum. Thus, we studied a simple model of a protonated radical mechanism, which further lowers the energy barrier. Although the true mechanism for the CH₄ + SO₃ reaction could be more complicated in electrolyte solutions, this model should be helpful for the further study of the mechanism of this reaction.

Heteroatom (N, P, As, Sb, Bi) Effects on the Resonance-Stabilized 2-, 3-, and 4-Picolyl Radicals

Important recent experimental studies have allowed the isomer-selective identification of the 2-, 3-, and 4-picolyl radicals. The picolyl radicals and their valence isoelectronic P, As, Sb, and Bi congeners are investigated here. For the three observed parent radicals, the theoretical ionization potentials agree with experiment to within 0.02 eV. Two rules are proposed for predicting vertical ionization potentials (E_VIE) and relative energies. The E_VIE values for these radicals will be higher when large percentages of the SOMO orbitals are distributed on the atoms with greater electronegativities. The cations of these systems were also studied along with the closed-shell methylpyridines and their P, As, Sb, and Bi analogs. The energies for the cationic species will lie lower when high percentages of π natural localized molecular orbitals occur on the more electronegative atoms. The structures of the 2- and 4-isomers strongly depend upon the heteroatoms, with the C-C linkages adopting a single-double alternating bond manner when the heteroatoms become heavier. The 3-isomers adopt roughly equal C-C bond distances with small changes from N to Bi.

Tris(Butadiene) Compounds versus Butadiene Oligomerization in Second-Row Transition Metal Chemistry: Effects of Increased Ligand Fields

The geometries, energetics, and preferred spin states of the second-row transition metal tris(butadiene) complexes (C₄H₆)₃M (M = Zr–Pd) and their isomers, including the experimentally known very stable molybdenum derivative (C₄H₆)₃Mo, have been examined by density functional theory. Such low-energy structures are found to have low-spin singlet and doublet spin states in contrast to the corresponding derivatives of the first-row transition metals. The three butadiene ligands in the lowest-energy (C₄H₆)₃M structures of the late second-row transition metals couple to form a C₁₂H₁₈ ligand that binds to the central metal atom as a hexahapto ligand for M = Pd but as an octahapto ligand for M = Rh and Ru. However, the lowest-energy (C₄H₆)₃M structures of the early transition metals have three separate tetrahapto butadiene ligands for M = Zr, Nb, and Mo or two tetrahapto butadiene ligands and one dihapto butadiene ligand for M = Tc. The low energy of the experimentally known singlet (C₄H₆)₃Mo structure contrasts with the very high energy of its experimentally unknown singlet chromium (C₄H₆)₃Cr analog relative to quintet (C₁₂H₁₈)Cr isomers with an open-chain C₁₂H₁₈ ligand.

Arbitrary-Order Derivatives of Quantum Chemical Methods via Automatic Differentiation

Herein, we present for the first time a general methodology for obtaining arbitrary-order nuclear coordinate derivatives of electronic energies derived from quantum chemistry methods. By leveraging modern advances in automatic differentiation software, we demonstrate that exact derivatives can be obtained for any method. This innovation completely bypasses the issues associated with the computational stability of applying numerical differentiation methods and dispenses the need to derive challenging formulae for analytic energy derivatives. We describe a freely available and open-source software implementation of our scheme and demonstrate its use in obtaining exact nuclear derivatives of energies from Hartree-Fock theory, second-order Møller-Plesset perturbation theory (MP2), and coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. Our sample computations include up to sextic derivatives and span a variety of test systems with up to 100 basis functions, confirming the viability of this scheme for a wide range of applications. Many of the results obtained have hitherto been unobtainable by exact means due to a lack of higher-order derivative formulae. The details of our implementation and possible further developments are discussed.

Carbene-mediated synthesis of a germanium tris(dithiolene)dianion

While the 1 : 1 reaction of 3 with an N-heterocyclic carbene ({(Me)CN(i-Pr)}2C:) in THF resulted in ligand-substituted product 4, the corresponding 1 : 2 reaction (in the presence of H2O) gives the first structurally characterized germanium tris(dithiolene)dianion 5 as the major product and the "naked" dithiolene radical 6˙ as a minor by-product. The structure and bonding of 4 and 5 were probed by experimental and theoretical methods. Our study suggests that carbene-mediated partial hydrolysis may represent a new method to access tris(dithiolene) complexes of main-group elements.

Energetics and kinetics of various cyano radical hydrogen abstractions

The cyano radical (CN) is an abundant, open-shell molecule found in a variety of environments, including the atmosphere, the interstellar medium and combustion processes. In these environments, it often reacts with small, closed-shell molecules via hydrogen abstraction. Both carbon and nitrogen atoms of the cyano radical are reactive sites, however the carbon is more reactive with reaction barrier heights generally between 2-15 kcal mol^-1 lower than those of the analogous nitrogen. The CN + HX → HCN/HNC + X, with X = H, CH₃, NH₂, OH, F, SiH₃, PH₂, SH, Cl, C₂H, CN reactions have been studied at a high-level of theory, including CCSD(T)-F12a. Furthermore, kinetics were obtained over the 100-1000 K temperature range, showing excellent agreement with those rate constants that have been determined experimentally.

Binuclear Cobalt Paddlewheel-Type Complexes: Relating Metal-Metal Bond Lengths to Formal Bond Orders

Paddlewheel-type complexes are prominent among experimentally known binuclear cobalt complexes and incorporate substituted formamidinate, guanidinate, and carboxylate ligands in digonal, trigonal, and tetragonal arrays around the bimetallic core. Such complexes are modeled here by density functional theory using unsubstituted ligands, extending the whole set to incorporate a variety of metal oxidation states and spin multiplicities. The DFT results for ground state cobalt-cobalt bond lengths and ground state spin multiplicity of the model complexes are often quite close to the experimental results for the corresponding substituted complexes. The three series of complexes often exhibit parallel trends with regard to effects of change in the metal oxidation state and spin multiplicity. The formamidinate and guanidinate series show marked resemblances. The lowered symmetry in many model trigonal complexes implies that such deviations in the experimentally known congeners arise from the inherent electronic structure. For ground state species, the DFT results provide Co-Co bond orders (BOs) from MO occupancy considerations. Further, using a revised electron bookkeeping method, Co-Co formal bond order (fBO) values from 0.0 to 2.0 are assigned to all of the 85 complexes studied. The computed Co-Co bond lengths fall into distinct ranges according to the formal bond order values (from 0.5 to 2).

Coupled Cluster Externally Corrected by Adaptive Configuration Interaction

An externally corrected coupled cluster (CC) method, where an adaptive configuration interaction (ACI) wave function provides the external cluster amplitudes, named ACI-CC, is presented. By exploiting the connection between configuration interaction and CC through cluster analysis, the higher-order T₃ and T₄ terms obtained from ACI are used to augment the T₁ and T₂ amplitude equations from traditional CC. These higher-order contributions are kept frozen during the CC iterations and do not contribute to an increased cost with respect to coupled cluster including the single and double excitations (CCSD). We have benchmarked this method on three closed-shell systems: beryllium dimer, carbonyl oxide, and cyclobutadiene, with good results compared to other corrected CC methods. In all cases, the inclusion of these external corrections improved upon the "gold standard" CCSD(T) results, indicating that ACI-CCSD(T) can be used to assess strong correlation effects in a system and as an inexpensive starting point for more complex external corrections.

Assessing the orbital-optimized unitary Ansatz for density cumulant theory

The previously proposed Ansatz for density cumulant theory that combines orbital-optimization and a parameterization of the 2-electron reduced density matrix cumulant in terms of unitary coupled cluster amplitudes (OUDCT) is carefully examined. Formally, we elucidate the relationship between OUDCT and orbital-optimized unitary coupled cluster theory and show the existence of near-zero denominators in the stationarity conditions for both the exact and some approximate OUDCT methods. We implement methods of the OUDCT Ansatz restricted to double excitations for numerical study, up to the fifth commutator in the Baker-Campbell-Hausdorff expansion. We find that methods derived from the Ansatz beyond the previously known ODC-12 method tend to be less accurate for equilibrium properties and less reliable when attempting to describe H₂ dissociation. New developments are needed to formulate more accurate density cumulant theory variants.

The HOX⋯SO2 (X=F, Cl, Br, I) Binary Complexes: Implications for Atmospheric Chemistry

Sulfur dioxide and hypohalous acids (HOX, X=F, Cl, Br, I) are ubiquitous molecules in the atmosphere that are central to important processes like seasonal ozone depletion, acid rain, and cloud nucleation. We present the first theoretical examination of the HOX⋯SO₂ binary complexes and the associated trends due to halogen substitution. Reliable geometries were optimized at the CCSD(T)/aug-cc-pV(T+d)Z level of theory for HOF and HOCl complexes. The HOBr and HOI complexes were optimized at the CCSD(T)/aug-cc-pV(D+d)Z level of theory with the exception of the Br and I atoms which were modeled with an aug-cc-pwCVDZ-PP pseudopotential. 27 HOX⋯SO₂ complexes were characterized and the focal point method was employed to produce CCSDT(Q)/CBS interaction energies. Natural Bond Orbital analysis and Symmetry Adapted Perturbation Theory were used to classify the nature of each principle interaction. The interaction energies of all HOX⋯SO₂ complexes in this study ranged from 1.35 to 3.81 kcal mol^-1 . The single-interaction hydrogen bonded complexes spanned a range of 2.62 to 3.07 kcal mol^-1 , while the single-interaction halogen bonded complexes were far more sensitive to halogen substitution ranging from 1.35 to 3.06 kcal mol^-1 , indicating that the two types of interactions are extremely competitive for heavier halogens. Our results provide insight into the interactions between HOX and SO₂ which may guide further research of related systems.

High level ab initio investigation of the catalytic effect of water on formic acid decomposition and isomerization

Formic acid (FA) is a ubiquitous molecule found in the atmosphere, and is relevant to many important processes. The FA molecule generally exists as the trans isomer, which can decompose into H2O and CO (dehydration). It can also exist in the less favorable cis isomer which can decompose into H2 and CO2 (decarboxylation). Our work examines the complexes formed between each isomer of FA with water. We present geometries and vibrational frequencies obtained at the reliable CCSD(T)/aug-cc-pVTZ level of theory for seven FAwater complexes. We utilize the focal point method to determine CCSDT(Q)/CBS plus corrections binding energies of 7.37, 3.36, and 2.02 kcal mol-1 plus 6.07, 3.79, 2.60, and 2.55 kcal mol-1 for the trans-FAwater and cis-FAwater complexes, respectively. Natural bond orbital analysis is used to further decompose the interactions in each complex and gain insight into their relative strengths. Furthermore, we examine the effect that a single water molecule has on the barrier heights to each decomposition pathway by optimizing the transition states and verifying their connectivity with intrinsic reaction coordinate computations as well as utilizing a kinetic model. Water lowers the barrier to dehydration by at most 15.78 kcal mol-1 and the barrier to decarboxylation by up to 15.90 kcal mol-1. Our research also examines for the first time the effect of one water molecule on the interconversion barrier and we find that the barrier from trans to cis is not catalyzed by water due to the strong FA and water interactions. Our results highlight some instances where different binary complexes result in different decomposition pathways and even a case where one binary complex can form the same decomposition products via two distinct mechanisms. Our results provide a reliable benchmark of the FAH2O system as well as provide insight into future studies of similar atmospheric systems.

Unusual Structures of the Parent Molecules Diarsene, Distibene, and Dibismuthene: Toward Their Observation

There is considerable interest, from both experimental and theoretical perspectives, in molecules incorporating multiple bonds between main group elements. Herein, we not only consider the parent molecules HE=EH (E=As, Sb, Bi), but also a number of their isomers. For each E₂ H₂ molecule, a number of different structures were optimized with four different DFT methods. Final structures were determined with the coupled cluster method CCSD(T) using large basis sets, namely cc-pVQZ-PP, incorporating relativistic psuedopotentials. All feasible dissociation pathways are examined. For all three E₂ H₂ molecules the trans isomer lies lowest in energy, with the cis isomer higher by 2.7 (As), 2.1 (Sb), and 1.8 (Bi) kcal mol^-1 , respectively. However, both cis and trans structures should be observable, as large barriers (27.7, 20.5, and 17.7 kcal mol^-1 ) separate them. For both the cis and trans structures, in the infrared the strong E-H stretching frequencies should also be observable. Only the cis structures have dipole moments (0.62, 0.01, and 0.83 debye, respectively), and their observation by microwave spectroscopy would be stunning. Also considered were the higher energy vinylidene-like, pyramidal, monobridged, and linear structures. We conclude that molecules such as HSb=SbH-Fe(CO)₄ , HBi=BiH-Fe(CO)₄ , and related systems, should be feasible synthetic targets.

A Stable Naked Dithiolene Radical Anion and Synergic THF Ring-Opening

Reaction of the lithium dithiolene radical 2^• with the imidazolium salt [{(Me)CN(i-Pr)}₂CH]⁺[Cl]^- (in a 1:1 molar ratio) gives the first stable naked anionic dithiolene radical 3^•, which, when coupled with hexasulfide, [{(Me)CN(i-Pr)}₂CH]⁺₂[S₆]^2- (4), and N-heterocyclic silylene 5, unexpectedly results in synergic THF ring-opening via a radical mechanism.

Reduced Density Matrix Cumulants: The Combinatorics of Size-Consistency and Generalized Normal Ordering

Reduced density matrix cumulants play key roles in the theory of both reduced density matrices and multiconfigurational normal ordering. We present a new, simpler generating function for reduced density matrix cumulants that is formally identical with equating the coupled cluster and configuration interaction ansätze. This is shown to be a general mechanism to convert between a multiplicatively separable quantity and an additively separable quantity, as defined by a set of axioms. It is shown that both the cumulants of probability theory and the reduced density matrices are entirely combinatorial constructions, where the differences can be associated with changes in the notion of "multiplicative separability" for expectation values of random variables compared to reduced density matrices. We compare our generating function to that of previous works and criticize previous claims of probabilistic significance of the reduced density matrix cumulants. Finally, we present a simple proof of the generalized normal ordering formalism to explore the role of reduced density matrix cumulants therein. While the formalism can be used without cumulants, the combinatorial structure of expressing RDMs in terms of cumulants is the same combinatorial structure on cumulants that allows for a simple extended generalized Wick's theorem.

Comparative Study of the Thermal Stabilities of the Experimentally Known High-Valent Fe(IV) Compounds Fe(1-norbornyl)4 and Fe(cyclohexyl)4

The high stability of the experimentally known homoleptic 1-norbornyl derivative (nor)₄Fe of iron in the unusual +4 oxidation state is a consequence of the high reaction barriers of the singlet or triplet potential surfaces constrained by the global dispersion attraction and the great steric demands of the norbornyl groups. The much more limited stability of the corresponding cyclohexyl derivative (cx)₄Fe may result from the conical intersection between the singlet potential surface and the quintet spin potential surface arising from the weaker dispersion attraction and the reduced steric effect of the cyclohexyl groups relative to the 1-norbornyl groups. In contrast, the high stability of the likewise experimentally known (cx)₄M (M = Ru or Os) structures results from the larger ligand field splitting (Δ) of the d-orbital energies for the second and third-row transition metals ruthenium and osmium relative to that of the first-row transition metal iron. The cyclohexyl derivative (cx)₄Fe is predicted to be reactive toward carbon monoxide to insert CO into up to two Fe-C bonds. However, the dispersion effect as well as the much larger size of the 1-norbornyl substituents prevents similar reactivity of (nor)₄Fe with carbon monoxide.

Substituted Ortho-Benzynes: Properties of the Triple Bond

Ortho-benzyne has been well studied by both experiment and theory. Its substituted variants, however, have been less carefully examined. Benchmark data are computed for unsubstituted ortho-benzyne using several density functional theory functionals and basis sets, up to cc-pVQZ. Optimized geometries for the substituted ortho-benzyne as well as harmonic vibrational frequencies and singlet-triplet splittings are computed using the benchmarked functionals. A proximal (syn)OH substitution causes a mean θ₁ distortion of +8.1 ± 1.4° from ortho-benzyne. Substituting in the proximal position with F shifts the singlet-triplet splitting by +4.5 ± 0.4 kcal mol^-1 from ortho-benzyne. Natural bond orbital analysis, including natural Coulomb electrostatics, elucidates the presence of three influences from the selected substituents: hyperconjugative, resonance, and electrostatic effects.

Dibridged, Monobridged, Vinylidene-Like, and Linear Structures for the Alkaline Earth Dihydrides Be2H2, Mg2H2, Ca2H2, Sr2H2, and Ba2H2. Proposals for Observations

This research reports a search for peculiar monobridged structures of the E₂H₂ molecules (E = Be, Mg, Ca, Sr, Ba). For Be₂H₂ and Mg₂H₂, the monobridged geometry is not an equilibrium but rather a transition state between the vinylidene-like structure and the global minimum HE-EH linear geometry. However, for Ca₂H₂, Sr₂H₂, and Ba₂H₂, this situation changes significantly; the linear structure is no longer the global minimum but lies higher in energy than two other equilibria, the dibridged and monobridged structures. The planar dibridged structures of both Sr₂H₂ and Ba₂H₂ should be observable via IR spectroscopy. Although the remarkable monobridged structures lie 8.3 (Sr) and 7.6 kcal/mol (Ba) higher, the large IR intensities of the terminal E-H stretching frequencies may make the monobridged structures observable. The monobridged structures have sizable permanent dipole moments (3.07 and 3.06 D for Sr and Ba, respectively) and also should be observable via microwave spectroscopy.

Carbene-Stabilized Disilicon as a Silicon-Transfer Agent: Synthesis of a Dianionic Silicon Tris(dithiolene) Complex

Reaction of carbene-stabilized disilicon (1) with the lithium-based dithiolene radical (2^. ) affords the first dianionic silicon tris(dithiolene) complex (3). Notably, the formation of 3 represents the unprecedented utilization of carbene-stabilized disilicon (1) as a silicon-transfer agent. The nature of 3 was probed by multinuclear NMR spectroscopy, single-crystal X-ray diffraction, and DFT computations.