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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 ($t_{ijk}^{abc}$). Through our method we can reduce the scaling of the (T) energy from the traditional O($N^{7}$) to a more modest O($N^{5}$). We also discuss implementation details to aid future research, development, and software realization of this method. Additionally, we show that this method yields sub-millihartree (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 sub-linear to linear error growth with respect to system size.

Comparison of the potential energy surface including the ZPVE corrections of the highly exothermic hydrogen abstraction reaction H2Te + OH with the H2Se + OH, H2S + OH, and H2O + OH reactions at the CCSD(T)/5Z level.

The DFT study suggests that the polarization of CC bonds is not the controlling factor of outer-sphere bifunctional CC bond hydrogenations. Instead, the “push–pull” type π-conjugative effect can contribute to these reactions.

The Concordant Mode Approach (CMA) is advanced as a novel hierarchy for increasing the system size and level of theory feasible for quantum chemical computations of harmonic vibrational frequencies. The key concept behind CMA is that transferrable, internal-coordinate normal modes computed at an appropriate lower level of theory (B) comprise a superb basis for converging to vibrational frequencies given by a higher level of theory (A). Accordingly, high-level harmonic frequencies can be evaluated via CMA from a collection of single-point energies that essentially scales linearly in the number of atoms, providing nearly order-of-magnitude CPU time speedups. The accuracy of CMA methods was established by comprehensive tests on over 120 molecules for target Level A = CCSD(T)/cc-pVTZ with auxiliary Level B choices of both CCSD(T)/cc-pVDZ and B3LYP/6-31G(2

Heavy aldehyde and ketone analogues, R

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

A series of reactions between Lewis bases and an imidazole-based dithione dimer (1) has been investigated. Both cyclic(alkyl)(amino)carbene (CAAC) (2) and N-heterocyclic carbene (NHC) (4), in addition to N-heterocyclic silylene (NHSi) (6), demonstrate the capability to cleave the sulphur-sulphur bonds in 1, giving carbene-stabilized dithiolene (L0 ) zwitterions (3 and 5) and a spirocyclic silicon-dithiolene compound (7), respectively. The bonding nature of 3, 5, and 7 are probed by both experimental and theoretical methods.

The Br + (H2O)3→ HBr + (H2O)2OH reaction has been investigated using the CCSD(T) method with the basis sets as large as cc-pVQZ(-PP). The Br + (H2O)3reaction is also compared with related Br + H2O/(H2O)2and F/Cl + (H2O)3reactions.

Vanadium forms binuclear complexes with a variety of ligands often containing V≡V triple bonds. Many tetragonal divanadium paddlewheel complexes with bridging bidentate ligands have been experimentally characterized. This research exhaustively treats model tetragonal, trigonal, and digonal paddlewheel-type divanadium complexes V2 Lx (L=formamidinate, guanidinate, and carboxylate; x=2, 3, 4), each in the three lowest-energy spin states. The V-V formal bond orders are obtained from metal-metal MO diagrams for representative structures. A number of short V-V multiple bonds of order 3, 3.5, and 4 are found in these model complexes. The short V≡V triple bonds and singlet ground state predicted here for the model tetragonal complexes correspond well with the limited experimental results for the series of known tetragonal paddlewheels. Digonal divanadium lanterns with very short V-V quadruple bonds are predicted as interesting synthetic targets. The V-V bond distances are categorized into distinct ranges according to the formal bond order values from 0.5 to 4. These bond length ranges are compared with the ranges compiled for other divanadium complexes including carbonyl complexes.

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.

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 (EVIE) and relative energies. The EVIE 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.

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.

Recent experimental research by Cummins and co-workers has established the existence of a tetrahedrane molecule with one CH moiety replaced by phosphorus. We present here the first theoretical studies of the entire Pn(CH)3 (Pn = N, P, As, Sb, Bi) class of molecules. Geometries are obtained at the highly reliable CCSD(T)/aug-cc-pwCVTZ(-PP) level of theory. Harmonic vibrational frequencies are determined and analyzed to confirm the nature of each stationary point and provide helpful findings that may aid in the detection of each species. Most notable is the result that the geometric parameters associated with the (CH)3 moiety in the tetrahedranes exhibit little change under pnictogen substitution, while the Pn-C bonds and C-Pn-C bond angles greatly increase and decrease, respectively. Strain energies are predicted and range from 122.3 kcal mol-1 (N(CH)3) to 99.4 kcal mol-1 (Bi(CH)3) at the DF-CCSD(T)//B3LYP-D3/aug-cc-pV(T+d)Z(-PP) level of theory. The obtained geometries are further analyzed with Natural Bond Orbital (NBO) methods to understand the bonding and electronic structure of each species. We also provide insight into how different substituents can help make the tetrahedrane structure more energetically favorable due to electron delocalization into substituent antibonding orbitals. The effect of additional delocalization also weakens the Pn-C bonds, especially for the heavier pnictogens. This work concludes with a list of considerations that summarize our key findings and motivate future work aimed at producing novel pnictogen-substituted tetrahedrane molecules.

A carbene-stabilized dithiolene zwitterion (

The geometries and energies of mononuclear and binuclear octafluorocyclohexadiene iron carbonyl derivatives have been studied using density functional theory. The lowest energy C6F8Fe(CO)3 tricarbo...

Four different reaction pathways are initially located for the reaction of Cl atom plus water trimer Cl + (H2O)3 → HCl + (H2O)2OH using a standard DFT method. As found for the analogous fluorine reaction, the geometrical and energetic results for the four chlorine pathways are closely related. However, the energetics for the Cl reaction are very different from those for fluorine. In the present paper, we investigate the lowest-energy chlorine pathway using the “gold standard” CCSD(T) method in conjunction with correlation-consistent basis sets up to cc-pVQZ. Structurally, the stationary points for the water trimer reaction Cl + (H2O)3 may be compared to those for the water monomer reaction Cl + H2O and water dimer reaction Cl + (H2O)2. Based on the CCSD(T) energies, the title reaction is endothermic by 19.3 kcal mol−1, with a classical barrier height of 16.7 kcal mol−1 between the reactants and the exit complex. There is no barrier for the reverse reaction. The Cl⋯(H2O)3 entrance complex lies 5.3 kcal mol−1 below the separated reactants. The HCl⋯(H2O)2OH exit complex is bound by 8.6 kcal mol−1 relative to the separated products. The Cl + (H2O)3 reaction is somewhat similar to the analogous Cl + (H2O)2 reaction, but qualitatively different from the Cl + H2O reaction. It is reasonable to expect that the reactions between the chlorine atom and larger water clusters may be similar to the Cl + (H2O)3 reaction. The potential energy profile for the Cl + (H2O)3 reaction is radically different from that for the valence isoelectronic F + (H2O)3 system, which may be related to the different bond energies between HCl and HF.

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.

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.

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···SO 2 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···SO 2 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···SO 2 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 SO 2 which may guide further research of related systems.

Reaction of the lithium dithiolene radical 2(•) with the imidazolium salt [{(Me)CN(i-Pr)}(2)CH](+)[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)}(2)CH](+)(2)[S(6)](2−) (4), and N-heterocyclic silylene 5, unexpectedly results in synergic THF ring-opening via a radical mechanism.

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.