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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 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

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.

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.

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.

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...

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.

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.

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.

Lithiation of an imidazole-based monothiolate, 2, by excess n-butyllithium gives a white powder containing both a lithiated product and an nBuLi contaminant (in a ca. 1:1 molar ratio). This white p...

Dimerizations of fulvene metal tricarbonyl complexes of the type (C

Approximating molecular wave functions involves heavy numerical effort; therefore, codes for such tasks are written completely or partially in efficient languages such as C, C++, and Fortran. While these tools are dominant throughout quantum chemistry packages, the efficient development of new methods is often hindered by the complexity associated with code development. In order to ameliorate this scenario, some software packages take a dual approach where a simpler, higher-level language, such as Python, substitutes the traditional ones wherever performance is not critical. Julia is a novel, dynamically typed, programming language that aims to solve this two-language problem. It gained attention because of its modern and intuitive design, while still being highly optimized to compete with "low-level" languages. Recently, some chemistry-related projects have emerged exploring the capabilities of Julia. Herein, we introduce the quantum chemistry package Fermi.jl, which contains the first implementations of post-Hartree-Fock methods written in Julia. Its design makes use of many Julia core features, including multiple dispatch, metaprogramming, and interactive usage. Fermi.jl is a modular package, where new methods and implementations can be easily added to the existing code. Furthermore, it is designed to maximize code reusability by relying on general functions with specialized methods for particular cases. The feasibility of the project is explored through evaluating the performance of popular

Four different reaction pathways are initially located for the reaction of Cl atom plus water trimer Cl + (H

All important stationary points on the potential energy surface (PES) for the reaction OH + (H2O)3 → (H2O)2OH + H2O have been fully optimized using the “gold standard” CCSD(T) method with the large Dunning correlation-consistent cc-pVQZ basis sets. Three types of pathways were found. For the pathway without hydrogen abstraction, the barrier height of the transition state (TS1) is predicted to lie 5.9 kcal mol−1 below the reactants. The two major complexes (H2O)3⋯OH (CP1 and CP2a) are found to lie 6.3 and 11.0 kcal mol−1, respectively, below the reactants [OH + (H2O)3]. For one of the H-abstraction pathways the lowest classical barrier height is predicted to be much higher, 6.1 kcal mol−1 (TS2a) above the reactants. For the other H-abstraction pathway the barrier height is even higher, 15.0 (TS3) kcal mol−1. Vibrational frequencies and the zero-point vibrational energies connected to the PES are also reported. The energy barriers for the H-abstraction pathways are compared with those for the OH + (H2O)2 and OH + H2O reactions, and the effects of the third water on the energetics are usually minor (0.2 kcal mol−1).

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.

The 1-norbornyl (nor) ligand is known experimentally to form stable transition metal alkyl derivatives through direct metal–carbon bond formation. This appears to be related to its steric bulk and inaccessibility towards β-hydrogen elimination, as exemplified by the tetraalkyls (nor)4M, some of which are very stable. In this connection we have used density functional theory and the DLPNO-CCSD(T) method to investigate the 1-norbornylcobalt carbonyl derivatives (nor)Co(CO)n (n = 4, 3, 2, 1) and (nor)2Co2(CO)n (n = 7, 6, 5). Low-energy structures of the unsaturated systems (nor)Co(CO)n (n = 3, 2) and (nor)2Co2(CO)n (n = 6, 5) are found to have agostic hydrogen atoms from a CH2 group adjacent to the Co–C bond. Such agostic hydrogen atoms form a C–H–Co bridge with a bonding Co–H distance less than ∼2 A. In such structures unsaturation is relieved by donation of an additional two electrons from the C–H bond of this norbornyl CH2 group. In addition, structures in which carbonyl migration from cobalt to carbon has occurred to form acyl norCO ligands are among the lowest energy structures. The resulting acyl carbonyl groups of the norCO ligands serve as spacers between the bulky 1-norbornyl ligand and the cobalt carbonyl moiety. Furthermore, such neutral norCO acyl ligands can either be one-electron donors to a cobalt atom, bonding solely through the carbonyl carbon, or three-electron donor η2-μ-norCO groups bridging a central Co2 unit through both the acyl carbon and oxygen atoms. The strengths of the agostic C–H–Co interactions have been characterized by their reduced density gradient (RDG) values.

This mechanistic study demonstrates that an unusual η1 -coordinated alkyne complex is critical for the 1-pentyne 1,1-diboration reaction. The comparative studies suggest the "pull-push" antagonistic effect arising from Lewis acidity and steric congestion as the reason for the existence of η1 -coordinated alkyne complexes. Analogous η1 -coordinated alkene complexes are also predicted and seem to be promising for their application to the important olefin polymerization reaction.

Lithium-containing molecules, such as C2H2Li2, C6Li6, and several lithium halides, have been studied in the present paper, and the nature of lithium bonds in these structures is investigated. In co...

A series of imidazolium-based synthetic routes to imidazolium cyclopentadienides are reported. The 2:1 reaction of imidazolium (1) with [Cp2TiIIICl]2 gives [NHCDippH]+[Cp2TiIIICl2]− (NHCDipp = 2,6-diisopropylphenyl-substituted N-heterocyclic carbene) (2). The “inverse sandwich” imidazolium cyclopentadienide (3) is obtained as a crystalline solid via reaction of 1 with both [Cp2TiIIICl]2 and cyclopentadienyllithium (CpLi) (in a molar ratio of 2:1:1) in THF/toluene at elevated temperature. Notably, the 1:1 reaction of 1 with CpLi leads to the isolation of “multidecker” 4 in the solid state, while the corresponding 1:2 reaction of 1 with CpLi gives the crystals of CpLi-bound cyclopentadienyl-imidazolium complex 5. While compounds 3, 4, and 5 have been structurally characterized using single-crystal X-ray diffraction, in solution these complexes dissociate due to the conversion of [NHCDippH]+[Cp]− to both cyclopentadiene and NHCDipp through intramolecular proton transfer. The equilibrium of the acid–base conv...

We introduce a free and open-source software package (PES-Learn) which largely automates the process of producing high-quality machine learning models of molecular potential energy surfaces (PESs). PES-Learn incorporates a generalized framework for producing grid points across a PES that is compatible with most electronic structure theory software. The newly generated or externally supplied PES data can then be used to train and optimize neural network or Gaussian process models in a completely automated fashion. Robust hyperparameter optimization schemes designed specifically for molecular PES applications are implemented to ensure that the best possible model for the data set is fit with high quality. The performance of PES-Learn toward fitting a few semiglobal PESs from the literature is evaluated. We also demonstrate the use of PES-Learn machine learning models in carrying out high-level vibrational configuration interaction computations on water and formaldehyde.

A cornucopia of very high-level theoretical methods has been used to study cyclobutyne, a molecule that has been the center of much speculation. We conclude that cyclobutyne is a transition state in its singlet ground state, based on new coupled cluster and multireference computations presented in this research. This is substantially different from other theoretical studies proposing the existence of singlet cyclobutyne as a minimum. The singlet cyclobutyne transition state ( C

Criegee intermediates are important targets for study in atmospheric chemistry because of their capacity to oxidize airborne species. Among these species, ammonia has received critical attention for its presence in polluted agricultural or industrial areas and its role in forming particulate matter and condensation nuclei. Although methylamine has been given less attention than ammonia, both theoretical and experimental studies have demonstrated that the additional methyl substitution on the ammonia derivatives increases the rate constants for some systems. This suggests that the methylamine addition to Criegee intermediates could be more significant to atmospheric processes. In this work, geometries are optimized at the DF-CCSD(T)/ANO1 level for the methylamine addition reactions to the simplest Criegee intermediate and the anti- and syn-methylated Criegee intermediates. Energies for each stationary point were computed at the CCSD(T)/CBS level with corrections from the CCSDT(Q) method. Rate constants are obtained for each reaction using canonical transition state theory. Although methylamine addition proved to be a more favorable reaction relative to ammonia addition, the significantly lower concentration of atmospheric methylamine limits the prevalence of these reactions, even in the most optimal conditions. It is unlikely that the methylamine addition to Criegee intermediates will contribute significantly to the consumption of Criegee intermediates in the atmosphere.