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.

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.

Concordant Mode Approach for Molecular Vibrations.

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(2df,p). Remarkably, the frequency residuals given by the diagonal CMA-0A(nc) scheme exhibit mean absolute deviations (MADs) of only 0.2 cm-1 and standard deviations less than 0.5 cm-1; the corresponding zero-point vibrational energies (ZPVEs) have negligible errors in the vicinity of 0.3 cm-1.

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

Hierarchical, convergent ab initio benchmark computations were performed followed by a systematic analysis of DFT performance for five pericyclic reactions comprising Diels-Alder, 1,3-dipolar cycloaddition, electrocyclic rearrangement, sigmatropic rearrangement, and double group transfer prototypes. Focal point analyses (FPA) extrapolating to the ab initio limit were executed via explicit quantum chemical computations with electron correlation treatments through CCSDT(Q) and correlation-consistent Gaussian basis sets up to aug'-cc-pV5Z. Optimized geometric structures and vibrational frequencies of all stationary points were obtained at the CCSD(T)/cc-pVTZ level of theory. The FPA reaction barriers and energies exhibit convergence to within a few tenths of a kcal mol-1. The FPA benchmarks were used to evaluate the performance of 60 density functionals (eight dispersion-corrected), covering the local-density approximation (LDA), generalized gradient approximations (GGAs), meta-GGAs, hybrids, meta-hybrids, double-hybrids, and range-separated hybrids. The meta-hybrid M06-2X functional provided the best overall performance [mean absolute error (MAE) of 1.1 kcal mol-1] followed closely by the double-hybrids B2K-PLYP, mPW2K-PLYP, and revDSD-PBEP86 [MAE of 1.4-1.5 kcal mol-1]. The regularly used GGA functional BP86 gave a higher MAE of 5.8 kcal mol-1, but it qualitatively described the trends in reaction barriers and energies. Importantly, we established that accurate yet efficient meta-hybrid or double-hybrid DFT potential energy surfaces can be acquired based on geometries from the computationally efficient and robust BP86/DZP level.

Identification and Reactivity of s-cis,s-cis-Dihydroxycarbene, a New [CH2O2] Intermediate.

We report the first preparation of the s-cis,s-cis conformer of dihydroxycarbene (1cc) by means of pyrolysis of oxalic acid, isolation of the lower-energy s-trans,s-trans (1tt) and s-cis,s-trans (1ct) product conformers at cryogenic temperatures in a N2 matrix, and subsequent narrow-band near-infrared (NIR) laser excitation to give 1cc. Carbene 1cc converts quickly to 1ct via quantum-mechanical tunneling with an effective half-life of 22 min at 3 K. The potential energy surface features around 1 were pinpointed by convergent focal point analysis targeting the AE-CCSDT(Q)/CBS level of electronic structure theory. Computations of the tunneling kinetics confirm the time scale of the 1cc → 1ct rotamerization and suggest that direct 1cc → H2 + CO2 decomposition may also be a minor pathway. The intriguing latter possibility cannot be confirmed spectroscopically, but hints of it may be present in the measured kinetic profiles.

Reaction Profiles and Kinetics for Radical-Radical Hydrogen Abstraction via Multireference Coupled Cluster Theory.

Radical-radical abstractions in hydrocarbon oxidation chemistry are disproportionation reactions that are generally exothermic with little or no barrier yet are underappreciated and poorly studied. Such challenging multireference electronic structure problems are tackled here using the recently developed state-specific multireference coupled cluster methods Mk-MRCCSD and Mk-MRCCSD(T), as well as the companion perturbation theory Mk-MRPT2 and the established MRCISD, MRCISD+Q, and CASPT2 approaches. Reaction paths are investigated for five prototypes involving radical-radical hydrogen abstraction: H + BeH → H2+ Be, H + NH2 → H2 + NH, CH3 + C2H5 → CH4 + C2H4, H + C2H5 → H2 + C2H4, and H + HCO → H2 + CO. Full configuration interaction (FCI) benchmark computations for the H + BeH, H + NH2, and H + HCO reactions prove that Mk-MRCCSD(T) provides superior accuracy for the interaction energies in the entrance channel, with mean absolute errors less than 0.3 kcal mol-1 and percentage deviations less than 10% over the fragment separations of relevance to kinetics. To facilitate combustion studies, energetics for the CH3 + C2H5, H + C2H5, and H + HCO reactions were computed at each level of theory with correlation-consistent basis sets (cc-pVXZ, X = T, Q, 5) and extrapolated to the complete basis set (CBS) limit. These CBS energies were coupled with CASPT2 projected vibrational frequencies along a minimum energy path to obtain rate constants for these three reactions. The rigorous Mk-MRCCSD(T)/CBS results demonstrate unequivocally that these three reactions proceed with no barrier in the entrance channel, contrary to some earlier predictions. Mk-MRCCSD(T) also reveals that the economical CASPT2 method performs well for large interfragment separations but may deteriorate substantially at shorter distances.

Riddles of the structure and vibrational dynamics of HO3 resolved near the ab initio limit.

The hydridotrioxygen (HO3) radical has been investigated in many previous theoretical and experimental studies over several decades, originally because of its possible relevance to the tropospheric HOx cycle but more recently because of its fascinating chemical bonding, geometric structure, and vibrational dynamics. We have executed new, comprehensive research on this vexing molecule via focal point analyses (FPA) to approach the ab initio limit of optimized geometric structures, relative energies, complete quartic force fields, and the entire reaction path for cis-trans isomerization. High-order coupled cluster theory was applied through the CCSDT(Q) and even CCSDTQ(P) levels, and CBS extrapolations were performed using cc-pVXZ (X = 2-6) basis sets. The cis isomer proves to be higher than trans by 0.52 kcal mol-1, but this energetic ordering is achieved only after the CCSDT(Q) milestone is reached; the barrier for cis → trans isomerization is a minute 0.27 kcal mol-1. The FPA central re(O-O) bond length of trans-HO3 is astonishingly long (1.670 Å), consistent with the semiexperimental re distance we extracted from microwave rotational constants of 10 isotopologues using FPA vibration-rotation interaction constants (αi). The D0(HO-O2) dissociation energy converges to a mere 2.80 ± 0.25 kcal mol-1. Contrary to expectation for such a weakly bound system, vibrational perturbation theory performs remarkably well with the FPA anharmonic force fields, even for the torsional fundamental near 130 cm-1. Exact numerical procedures are applied to the potential energy function for the torsional reaction path to obtain energy levels, tunneling rates, and radiative lifetimes. The cis → trans isomerization occurs via tunneling with an inherent half-life of 1.4 × 10-11 s and 8.6 × 10-10 s for HO3 and DO3, respectively, thus resolving the mystery of why the cis species has not been observed in previous experiments executed in dissipative environments that allow collisional cooling of the trans-HO3 product. In contrast, the pure ground eigenstate of the cis species in a vacuum is predicted to have a spontaneous radiative lifetime of about 1 h and 5 days for HO3 and DO3, respectively.

Wigner numbers.

All reduced Wigner rotation matrix elements dM'M J(θ) can be evaluated very efficiently as a linear combination of either cos(Nθ) or sin(Nθ) terms as N runs in unit steps from either 0 or 12 to J. Exact, infinite-precision formulas are derived here for the Fourier coefficients in these dM'M J(θ) expressions by finding remarkable analytic solutions for the normalized eigenvectors of arbitrarily large matrices that represent the JY angular momentum operator in the basis of JZ eigenstates. The solutions involve collections of numbers Wm,n J for (m, n) = (J-M, J-N) ∈ [0, 2J] that satisfy the recursion relation (m+1)Wm+1,n J-2(J-n)Wm,n J+(2J-m+1)Wm-1,n J=0. These quantities, designated here as Wigner numbers, are proved to be integers that exhibit myriad intriguing mathematical properties, including various closed combinatorial formulas, (M, N) sum rules, three separate M-, N-, and J-recursion relations, and a large-J limiting differential equation whose applicable solutions are products of a polynomial and a Gaussian function in the variable z = -21/2(J + 1)-1/2M. Accordingly, the Wigner numbers constitute a new thread of mathematics extending outside the context of their immediate discovery. In the midst of the Wm,n J proofs, a class of previously unknown combinatorial summation identities is also found from Wigner number orthonormalization conditions.

Probing the Delicate Balance between Pauli Repulsion and London Dispersion with Triphenylmethyl Derivatives.

The long-known, ubiquitously present, and always attractive London dispersion (LD) interaction was probed with hexaphenylethane (HPE) derivatives. A series of all- meta hydrocarbyl [Me, iPr, tBu, Cy, Ph, 1-adamantyl (Ad)]-substituted triphenylmethyl (TPM) derivatives [TPM-H, TPM-OH, (TPM-O)2, TPM•] was synthesized en route, and several derivatives were characterized by single-crystal X-ray diffraction (SC-XRD). Multiple dimeric head-to-head SC-XRD structures feature an excellent geometric fit between the meta-substituents; this is particularly true for the sterically most demanding tBu and Ad substituents. NMR spectra of the iPr-, tBu-, and Cy-derived trityl radicals were obtained and reveal, together with EPR and UV-Vis spectroscopic data, that the effects of all- meta alkyl substitution on the electronic properties of the trityl scaffold are marginal. Therefore, we concluded that the most important factor for HPE stability arises from LD interactions. Beyond all- meta tBu-HPE we also identified the hitherto unreported all- meta Ad-HPE. An intricate mathematical analysis of the temperature-dependent dissociation constants allowed us to extract Δ Gd298(exptl) = 0.3(5) kcal mol-1 from NMR experiments for all- meta tBu-HPE, in good agreement with previous experimental values and B3LYP-D3(BJ)/def2-TZVPP(C-PCM) computations. These computations show a stabilizing trend with substituent size in line with all- meta Ad-HPE (Δ Gd298(exptl) = 2.1(6) kcal mol-1) being more stable than its tBu congener. That is, large, rigid, and symmetric hydrocarbon moieties act as excellent dispersion energy donors. Provided a good geometric fit, they are able to stabilize labile molecules such as HPE via strong intramolecular LD interactions, even in solution.

Nucleophilic Influences and Origin of the SN 2 Allylic Effect.

The potential energy surfaces for the SN 2 reactions of allyl and propyl chlorides with 21 anionic and neutral nucleophiles was studied by using ωB97X-D/6-311++G(3df,2pd) computations. The "allylic effect" on SN 2 barriers was observed for all reactions, and compared with propyl substrates, the energy barriers differed by -0.2 to -4.5 kcal mol-1 in the gas phase. Strong correlations of the SN 2 net activation barriers with cation affinities, proton affinities, and electrostatic potentials at nuclei demonstrated the powerful influence of electrostatic interactions on these reactions. For the reactions of anionic (but not neutral) nucleophiles with allyl chloride, some of the incoming negative charge (0.2-18 %) migrated into the carbon chains, which would provide secondary stabilization of the SN 2 transition states. Activation strain analysis provided additional insight into the allylic effect by showing that the energy of geometric distortion for the reactants to reach the SN 2 transition state was smaller for each allylic reaction than for its propyl analogue. In many cases, the interaction energies between the substrate and nucleophile in this analysis were more favorable for propyl chloride reactions, but this compensation did not overcome the predominant strain energy effect.

Most favorable cumulenic structures in iron-capped linear carbon chains are short singlet odd-carbon dications: a theoretical view.

Iron-capped, linear-carbon-chain dications have been investigated at the M06L/DZP level of quantum chemistry in order to determine their structural and electronic properties, focusing on differences between chains containing odd and even numbers of carbon atoms. Such differences result from changes in the electronic states and the acetylenic or cumulenic nature of the carbon chain. Interestingly, the short even-carbon chains exhibit distinct properties, but upon chain lengthening undergo a transition to structures similar to those of odd-carbon chains, with a turning point around [FeC10Fe]2+. On the other hand, the less extensively investigated short odd-carbon chains, such as [FeC5Fe]2+, [FeC7Fe]2+ and [FeC9Fe]2+, due to synthetic difficulty, are predicted to exhibit more exceptional properties than the short even-carbon chains in every aspect, such as excellent back bonding as well as more cumulenic and more nearly linear structures. This theoretical study suggests that more experimental work should be considered on metal-capped, short linear odd-carbon chains as potential building blocks for novel electronic and optical materials.

A Universal Integrated Rate Equation for Chemical Kinetics.

The overarching analytic integrated rate equation for the chemical kinetics of any reversible or irreversible reaction involving an arbitrary number of species and any integral orders is shown to be Π i=1r[1 - f i-1ξ( t)]γ i = e(-1) r  F0 t, where ξ( t) is the extent of reaction variable, the f i are roots of a polynomial of order r, the exponents are determined by γ i = Π k(≠ i)r( f i - f k)-1, and F0 is a factor involving the stoichiometric coefficients and rate constants ( k±). All integrated rate equations of elementary reactions appearing in chemical kinetics are special cases of this universal solution. Not only does the solution provide insight into the analytical form of the exponents γ i and F0 that govern the time evolution of the system, but it also provides an elegant framework for the pedagogy and application of kinetics in physical chemistry.

Intricate Conformational Tunneling in Carbonic Acid Monomethyl Ester.

Disentangling internal and external effects is a key requirement for understanding conformational tunneling processes. Here we report the s- trans/ s- cis tunneling rotamerization of carbonic acid monomethyl ester (1) under matrix isolation conditions and make comparisons to its parent carbonic acid (3). The observed tunneling rate of 1 is temperature-independent in the 3-20 K range and accelerates when using argon instead of neon as the matrix material. The methyl group increases the effective half life (τeff) of the energetically disfavored s- trans-conformer from 3-5 h for 3 to 11-13 h for 1. Methyl group deuteration slows the rotamerization further (τeff ≈ 35 h). CCSD(T)/cc-pVQZ//MP2/aug-cc-pVTZ computations of the tunneling probability suggest that the rate should be almost unaffected by methyl substitution or its deuteration. Thus the observed relative rates are puzzling, and they disagree with previous explanations involving fast vibrational relaxation after the tunneling event facilitated by the alkyl rotor.

Geometric Energy Derivatives at the Complete Basis Set Limit: Application to the Equilibrium Structure and Molecular Force Field of Formaldehyde.

Geometric energy derivatives which rely on core-corrected focal-point energies extrapolated to the complete basis set (CBS) limit of coupled cluster theory with iterative and noniterative quadruple excitations, CCSDTQ and CCSDT(Q), are used as elements of molecular gradients and, in the case of CCSDT(Q), expansion coefficients of an anharmonic force field. These gradients are used to determine the CCSDTQ/CBS and CCSDT(Q)/CBS equilibrium structure of the S0 ground state of H2CO where excellent agreement is observed with previous work and experimentally derived results. A fourth-order expansion about this CCSDT(Q)/CBS reference geometry using the same level of theory produces an exceptional level of agreement to spectroscopically observed vibrational band origins with a MAE of 0.57 cm-1. Second-order vibrational perturbation theory (VPT2) and variational discrete variable representation (DVR) results are contrasted and discussed. Vibration-rotation, anharmonicity, and centrifugal distortion constants from the VPT2 analysis are reported and compared to previous work. Additionally, an initial application of a sum-over-states fourth-order vibrational perturbation theory (VPT4) formalism is employed herein, utilizing quintic and sextic derivatives obtained with a recursive algorithmic approach for response theory.

Ring-Walking of Zerovalent Nickel on Aryl Halides.

While ring-walking is a critical step in transition metal catalyzed cross-coupling reactions, the associated metastable intermediates are often difficult to isolate and characterize. In this work, theoretical structures and energetics for ring-walking and oxidative addition of zerovalent nickel with 1-bromo-2-methylbenzene, 2-bromopyridine, 2-bromo-3-methyl-thiophene, and 2-bromopyrrole were computed at the B3LYP-D3/TZ2P-LANL2TZ(f)-LANL08d level. The mechanisms vary qualitatively with substrate ring size and type-the catalyst weaves along the edges of the benzene and pyridine rings, cuts through the interior of the thiophene ring, and arcs along the bond opposite the nitrogen atom in the pyrrole ring. Analogous computations on the ring-walking and oxidative addition of zerovalent palladium with 1-bromo-2-methylbenzene reveal an energetic profile similar to that of Ni but with much weaker overall binding to the arene. In all cases, dispersion corrections are found to be very important for computing accurate metal-substrate binding energies.

Tunnelling in carbonic acid.

The cis,trans-conformer of carbonic acid (H2CO3), generated by near-infrared radiation, undergoes an unreported quantum mechanical tunnelling rotamerization with half-lives in cryogenic matrices of 4-20 h, depending on temperature and host material. First-principles quantum chemistry at high levels of theory gives a tunnelling half-life of about 1 h, quite near those measured for the fastest rotamerizations.

Conformers of Gaseous Serine.

The myriad conformers of the neutral form of natural amino acid serine (Ser) have been investigated by systematic computations with reliable electronic wave function methods. A total of 85 unique conformers were located using the MP2/cc-pVTZ level of theory. The 12 lowest-energy conformers of serine fall within a 8 kJ mol(-1) window, and for these species, geometric structures, precise relative energies, equilibrium and vibrationally averaged rotational constants, anharmonic vibrational frequencies, infrared intensities, quartic and sextic centrifugal distortion constants, dipole moments, and (14)N nuclear quadrupole coupling constants were computed. The relative energies were refined through composite focal-point analyses employing basis sets as large as aug-cc-pV5Z and correlation treatments through CCSD(T). The rotational constants for seven conformers measured by Fourier-transform microwave spectroscopy are in good agreement with the vibrationally averaged rotational constants computed in this study. Our anharmonic vibrational frequencies are compared to the large number of experimental vibrational absorptions attributable to at least six conformers.

Sub-Doppler infrared spectroscopy and formation dynamics of triacetylene in a slit supersonic expansion.

Infrared spectroscopy and formation dynamics of triacetylene are investigated in a slit jet supersonic discharge and probed with sub-Doppler resolution (≈60 MHz) on the fundamental antisymmetric CH stretch mode (ν5). The triacetylene is generated in the throat of the discharge by sequential attack of ethynyl radical with acetyelene and diacetylene: (i) HCCH → HCC + H, (ii) HCC + HCCH → HCCCCH + H, (iii) HCC + HCCCCH → HCCCCCCH + H, cooled rapidly in the slit expansion to 15 K, and probed by near shot-noise-limited absorption sensitivity with a tunable difference-frequency infrared laser. The combination of jet cooled temperatures (Trot = 15 K) and low spectral congestion permits (i) analysis of rotationally avoided crossings in the ν5 band ascribed to Coriolis interactions, as well as (ii) first detection of ν5 Π-Π hot band progressions built on the ν12 sym CC bend and definitively assigned via state-of-the-art ab initio vibration-rotation interaction parameters (αi), which make for interesting comparison with recent spectroscopic studies of Doney et al. [J. Mol. Spectrosc. 316, 54 (2015)]. The combined data provide direct evidence for significantly non-equilibrium populations in the CC bending manifold, dynamically consistent with a strongly bent radical intermediate and transition states for forming triacetylene product. The presence of intense triacetylene signals under cold, low density slit jet conditions provides support for (i) barrierless addition of HCC with HCCCCH and (ii) a high quantum yield for HCCCCCCH formation. Complete basis set calculations for energetics [CCSD(T)-f12/VnZ-f12, n = 2,3] and frequencies [CCSD(T)-f12/VdZ-f12] are presented for both radical intermediate and transition state species, predicting collision stabilization in the slit jet expansion to be competitive with unimolecular decomposition with increasing polyyne chain length.