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Both glycolaldehyde and glyoxal were pyrolyzed in a set of flash-pyrolysis microreactors. The pyrolysis products resulting from CHO-CH2OH and HCO-CHO were detected and identified by vacuum ultraviolet (VUV) photoionization mass spectrometry. Complementary product identification was provided by argon matrix infrared absorption spectroscopy. Pyrolysis pressures in the microreactor were about 100 Torr, and contact times with the microreactors were roughly 100 μs. At 1200 K, the products of glycolaldehyde pyrolysis are H atoms, CO, CH2═O, CH2═C═O, and HCO-CHO. Thermal decomposition of HCO-CHO was studied with pulsed 118.2 nm photoionization mass spectrometry and matrix infrared absorption. Under these conditions, glyoxal undergoes pyrolysis to H atoms and CO. Tunable VUV photoionization mass spectrometry provides a lower bound for the ionization energy (IE)(CHO-CH2OH) ≥ 9.95 ± 0.05 eV. The gas-phase heat of formation of glycolaldehyde was established by a sequence of calorimetric experiments. The experimental result is ΔfH298(CHO-CH2OH) = -75.8 ± 1.3 kcal mol(-1). Fully ab initio, coupled cluster calculations predict ΔfH0(CHO-CH2OH) of -73.1 ± 0.5 kcal mol(-1) and ΔfH298(CHO-CH2OH) of -76.1 ± 0.5 kcal mol(-1). The coupled-cluster singles doubles and noniterative triples correction calculations also lead to a revision of the geometry of CHO-CH2OH. We find that the O-H bond length differs substantially from earlier experimental estimates, due to unusual zero-point contributions to the moments of inertia.

HOCO is an important intermediate in combustion and atmospheric processes because the OH + CO → H + CO2 reaction represents the final step for the production of CO2 in hydrocarbon oxidation, and theoretical studies predict that this reaction proceeds via various intermediates, the most important being this radical. Isotopic investigations of trans- and cis-HOCO have been undertaken using Fourier transform microwave spectroscopy and millimeter-wave double resonance techniques in combination with a supersonic molecular beam discharge source to better understand the formation, chemical bonding, and molecular structures of this radical pair. We find that trans-HOCO can be produced almost equally well from either OH + CO or H + CO2 in our discharge source, but cis-HOCO appears to be roughly two times more abundant when starting from H + CO2. Using isotopically labelled precursors, the OH + C(18)O reaction predominately yields HOC(18)O for both isomers, but H(18)OCO is observed as well, typically at the level of 10%-20% that of HOC(18)O; the opposite propensity is found for the (18)OH + CO reaction. DO + C(18)O yields similar ratios between DOC(18)O and D(18)OCO as those found for OH + C(18)O, suggesting that some fraction of HOCO (or DOCO) may be formed from the back-reaction H + CO2, which, at the high pressure of our gas expansion, can readily occur. The large (13)C Fermi-contact term (aF) for trans- and cis-HO(13)CO implicates significant unpaired electronic density in a σ-type orbital at the carbon atom, in good agreement with theoretical predictions. By correcting the experimental rotational constants for zero-point vibration motion calculated theoretically using second-order vibrational perturbation theory, precise geometrical structures have been derived for both isomers.

A high level ab initio calculation of the cis-trans isomerization barrier height in the first excited singlet electronic state of acetylene is found to agree very well with a recent experimental determination.

In this paper, a new algorithm for computing Franck-Condon overlaps using the Doktorov recurrence equations is proposed. One of the major computational stresses of using the recurrence equations arises from searching data structures for overlaps that are stored in memory. The proposed algorithm alleviates this problem by tracking, throughout the algorithm, the locations in memory of overlaps that are required to use the recurrence relations. The tracking procedure helps to significantly reduce the run time of the algorithm compared to existing implementations.

We present a simple quasi-diabatization scheme applicable to spectroscopic studies that can be applied using any wavefunction for which one-electron properties and transition properties can be calculated. The method is based on rotation of a pair (or set) of adiabatic states to minimize the difference between the given transition property at a reference geometry of high symmetry (where the quasi-diabatic states and adiabatic states coincide) and points of lower symmetry where quasi-diabatic quantities are desired. Compared to other quasi-diabatization techniques, the method requires no special coding, facilitates direct comparison between quasi-diabatic quantities calculated using different types of wavefunctions, and is free of any selection of configurations in the definition of the quasi-diabatic states. On the other hand, the method appears to be sensitive to multi-state issues, unlike recent methods we have developed that use a configurational definition of quasi-diabatic states. Results are presented and compared with two other recently developed quasi-diabatization techniques.

The peroxyiodomethyl radical, CH2IOO, was generated in cryogenic matrices using tandem supersonic nozzles. One hyperthermal nozzle decomposes diiodomethane (CH2I2) to generate intense beams of CH2I radicals, while the second nozzle continuously deposits O2/argon (Ar) on the matrix at 10 K. The CH2I and O2 in the Ar matrix react to produce the target peroxy radical (CH2IOO). The absorption spectra of the products are monitored with a Fourier transform infrared spectrometer. Eight of the 12 fundamental infrared bands for CH2IOO were observed in an argon matrix at 5 K. The experimental frequencies (cm(-1)) are ν3 = 1407.3, ν4 = 1230.4, ν5 = 1223.2, ν6 = 1085.3, ν7 = 919.9, ν8 = 839.9, ν9 = 567.5, and ν10 = 496.2. Additional confirmation for the vibrational assignment comes from a study of the CH2I(18)O(18)O isotopic species. The six observed frequencies (cm(-1)) for CH2I(18)O(18)O are ν3 = 1407.8, ν4 = 1228.0, ν6 = 1030.8, ν7 = 899.6, ν8 = 836.0, and ν10 = 494.6. Unlike CH2I(16)O(16)O, the ν5 and ν9 bands were not observed for CH2I(18)O(18)O. To guide the experimental analysis, ab initio calculations of the infrared spectrum based on second-order vibrational perturbation theory were performed using force fields computed with relativistic coupled-cluster methods. The experimental frequencies are shown to be in good agreement with the computed fundamental frequencies except for ν9 (for CH2IOO) and ν10 (for CH2I(18)O(18)O). Our findings were compared with the study by Lee and Lee conducted in a para-H2 matrix. The fundamental frequencies are in good agreement (within 6 cm(-1)) except for the two low-frequency modes, ν9 (for CH2IOO) and ν10 (for CH2I(18)O(18)O) likely due to different matrix shifts for para-H2 and Ar matrices. In addition, our calculations are in somewhat better agreement with the experiment values than the calculations by Lee and Lee. Our study also shows that reaction CH2I + O2 produces the peroxy radical CH2IOO in cold matrices (10 K) instead of Criegee intermediate CH2OO, which is generated in gas phase (300 K and low pressure); the same finding was also reported by Lee and Lee.

The thermal decomposition of cyclohexanone (C6H10═O) has been studied in a set of flash-pyrolysis microreactors. Decomposition of the ketone was observed when dilute samples of C6H10═O were heated to 1200 K in a continuous flow microreactor. Pyrolysis products were detected and identified by tunable VUV photoionization mass spectroscopy and by photoionization appearance thresholds. Complementary product identification was provided by matrix infrared absorption spectroscopy. Pyrolysis pressures were roughly 100 Torr, and contact times with the microreactors were roughly 100 μs. Thermal cracking of cyclohexanone appeared to result from a variety of competing pathways, all of which open roughly simultaneously. Isomerization of cyclohexanone to the enol, cyclohexen-1-ol (C6H9OH), is followed by retro-Diels-Alder cleavage to CH2═CH2 and CH2═C(OH)-CH═CH2. Further isomerization of CH2═C(OH)-CH═CH2 to methyl vinyl ketone (CH3CO-CH═CH2, MVK) was also observed. Photoionization spectra identified both enols, C6H9OH and CH2═C(OH)-CH═CH2, and the ionization threshold of C6H9OH was measured to be 8.2 ± 0.1 eV. Coupled cluster electronic structure calculations were used to establish the energetics of MVK. The heats of formation of MVK and its enol were calculated to be ΔfH298(cis-CH3CO-CH═CH2) = -26.1 ± 0.5 kcal mol(-1) and ΔfH298(s-cis-1-CH2═C(OH)-CH═CH2) = -13.7 ± 0.5 kcal mol(-1). The reaction enthalpy ΔrxnH298(C6H10═O → CH2═CH2 + s-cis-1-CH2═C(OH)-CH═CH2) is 53 ± 1 kcal mol(-1) and ΔrxnH298(C6H10═O → CH2═CH2 + cis-CH3CO-CH═CH2) is 41 ± 1 kcal mol(-1). At 1200 K, the products of cyclohexanone pyrolysis were found to be C6H9OH, CH2═C(OH)-CH═CH2, MVK, CH2CHCH2, CO, CH2═C═O, CH3, CH2═C═CH2, CH2═CH-CH═CH2, CH2═CHCH2CH3, CH2═CH2, and HC≡CH.

Transition state theory is central to our understanding of chemical reaction dynamics. We demonstrate a method for extracting transition state energies and properties from a characteristic pattern found in frequency-domain spectra of isomerizing systems. This pattern-a dip in the spacings of certain barrier-proximal vibrational levels-can be understood using the concept of effective frequency, ω(eff). The method is applied to the cis-trans conformational change in the S1 state of C2H2 and the bond-breaking HCN-HNC isomerization. In both cases, the barrier heights derived from spectroscopic data agree extremely well with previous ab initio calculations. We also show that it is possible to distinguish between vibrational modes that are actively involved in the isomerization process and those that are passive bystanders., (Copyright © 2015, American Association for the Advancement of Science.)

The problem of the generally inferior convergence behavior of higher-order coupled cluster methods, such as CCSDT and CCSDTQ, compared to CCSD is analyzed in terms of Møller-Plesset perturbation theory. A new structure for the CCSDT and CCSDTQ equations (and various approximations of these) is proposed which reorders contributions between the various cluster amplitudes and emphasizes lower-order corrections to the energy at each iteration. Numerical testing of the proposed method compared to the widely used direct inversion in the iterative subspace convergence acceleration technique shows significant improvement in the rate of convergence and total time-to-solution, especially for methods including quadruple excitations.

The calculation of absolute total cross sections requires accurate wave functions of the photoelectron and of the initial and final states of the system. The essential information contained in the latter two can be condensed into a Dyson orbital. We employ correlated Dyson orbitals and test approximate treatments of the photoelectron wave function, that is, plane and Coulomb waves, by comparing computed and experimental photoionization and photodetachment spectra. We find that in anions, a plane wave treatment of the photoelectron provides a good description of photodetachment spectra. For photoionization of neutral atoms or molecules with one heavy atom, the photoelectron wave function must be treated as a Coulomb wave to account for the interaction of the photoelectron with the +1 charge of the ionized core. For larger molecules, the best agreement with experiment is often achieved by using a Coulomb wave with a partial (effective) charge smaller than unity. This likely derives from the fact that the effective charge at the centroid of the Dyson orbital, which serves as the origin of the spherical wave expansion, is smaller than the total charge of a polyatomic cation. The results suggest that accurate molecular photoionization cross sections can be computed with a modified central potential model that accounts for the nonspherical charge distribution of the core by adjusting the charge in the center of the expansion.

The value for the HCN → HNC 0 K isomerization energy has been investigated by combining state-of-the-art electronic structure methods with the Active Thermochemical Tables (ATcT) approach. The directly computed energy difference between HCN and HNC at the HEAT-456QP level of theory is 5236 ± 50 cm(-1). This is substantially lower (by ∼470 cm(-1) or ∼1.3 kcal/mol) than the recently proposed high-level multireference configuration interaction value of 5705 ± 20 cm(-1) of Barber et al. ( Mon. Not. R. Astron. Soc. 2014, 437, 1828-1835 ). The discrepancy was analyzed by the ATcT approach, using several distinct steps, which (a) independently corroborated the current single-reference HEAT-456QP result, (b) independently found that the recent multireference-based value is highly unlikely to be correct within its originally stated uncertainty, and (c) produced a recommended value of 5212 ± 30 cm(-1) for the HCN → HNC isomerization energy at 0 K, based on all currently available knowledge. The ATcT standard enthalpies of formation at 0 and 298 K for HCN, HNC, and their cations and anions are also presented.

We report high-resolution photoelectron spectra of the simplest carbanions, CH₃⁻ and CD₃⁻. The vibrationally resolved spectra are dominated by a long progression in the umbrella mode (ν₂) of ˙CH₃ and ˙CD₃, indicating a transition from a pyramidal C(3v) anion to the planar D(3h) methyl radical. Analysis of the spectra provides electron affinities of ˙CH₃ (0.093(3) eV) and ˙CD₃ (0.082(4) eV). These results enable improved determination of the corresponding gas-phase acidities: Δ(acid)H(0K)°(CH₄) = 414.79(6) kcal/mol and Δ(acid)H(0K)°(CD₄) = 417.58(8) kcal/mol. On the basis of the photoelectron anisotropy distribution, the electron is photodetached from an orbital with predominant p-character, consistent with the sp³-hybridized orbital picture of the pyramidal anion. The double-well potential energy surface along the umbrella inversion coordinate leads to a splitting of the vibrational energy levels of the umbrella mode. The inversion splittings of CH₃⁻ and CD₃⁻ are 21(5) and 6(4) cm⁻¹, respectively, and the corresponding anion umbrella vibrational frequencies are 444(13) and 373(12) cm⁻¹, respectively. Quantum mechanical calculations reported herein show good agreement with the experimental data and provide insight regarding the electronic potential energy surface of CH₃⁻.

The millimeter-wave spectrum of hydrazoic acid (HN3) was analyzed in the frequency region of 235-450 GHz. Transitions from a total of 14 isotopologues were observed and fit using the A-reduced or S-reduced Hamiltonian. Coupled-cluster calculations were performed to obtain a theoretical geometry, as well as rotation-vibration interaction corrections. These calculated vibration-rotation correction terms were applied to the experimental rotational constants to obtain mixed theoretical/experimental equilibrium rotational constants (Ae, Be, and Ce). These equilibrium rotational constants were then used to obtain an equilibrium (Re) structure using a least-squares fitting routine. The Re structural parameters are consistent with a previously published Rs structure, largely falling within the uncertainty limits of that Rs structure. The present Re geometric parameters of HN3 are determined with exceptionally high accuracy, as a consequence of the large number of isotopologues measured experimentally and the sophisticated (coupled-cluster theoretical treatment (CCSD(T))/ANO2) of the vibration-rotation interactions. The Re structure exhibits remarkable agreement with the CCSD(T)/cc-pCV5Z predicted structure, validating both the accuracy of the ab initio method and the claimed uncertainties of the theoretical/experimental structure determination.

High -accuracy coupled cluster methods in combination with microcanonical semiclassical transition state theory are used to investigate a plausible formation mechanism of the simplest Criegee intermediate in a CH4/O2 discharge experiment. Our results suggest that the Criegee intermediate is produced in a three-step process: (i) production of methyl radical by cleavage of a C-H bond of CH4; (ii) association of methyl radical with molecular oxygen to form a vibrationally excited methyl peroxy, which is in a rapid microequilibrium with the reactants; and finally, (iii) H-abstraction of CH3OO by O2, which results in the formation of cool CH2OO, which has insufficient internal energy to rearrange to dioxirane.

In the field of chemical kinetics, the solution of a two-dimensional master equation that depends explicitly on both total internal energy (E) and total angular momentum (J) is a challenging problem. In this work, a weak-E/fixed-J collisional model (i.e., weak-collisional internal energy relaxation/free-collisional angular momentum relaxation) is used along with the steady-state approach to solve the resulting (simplified) two-dimensional (E,J)-grained master equation. The corresponding solutions give thermal rate constants and product branching ratios as functions of both temperature and pressure. We also have developed a program that can be used to predict and analyze experimental chemical kinetics results. This expedient technique, when combined with highly accurate potential energy surfaces, is cable of providing results that may be meaningfully compared to experiments. The reaction of singlet oxygen with methane proceeding through vibrationally excited methanol is used as an illustrative example.

The thermal decomposition of cyclopentadienone (C5H4═O) has been studied in a flash pyrolysis continuous flow microreactor. Passing dilute samples of o-phenylene sulfite (C6H4O2SO) in He through the microreactor at elevated temperatures yields a relatively clean source of C5H4═O. The pyrolysis of C5H4═O was investigated over the temperature range 1000-2000 K. Below 1600 K, we have identified two decomposition channels: (1) C5H4═O (+ M) → CO + HC≡C-CH═CH2 and (2) C5H4═O (+ M) → CO + HC≡CH + HC≡CH. There is no evidence of radical or H atom chain reactions. To establish the thermochemistry for the pyrolysis of cyclopentadienone, ab initio electronic structure calculations (AE-CCSD(T)/aug-cc-pCVQZ//AE-CCSD(T)/cc-pVQZ and anharmonic FC-CCSD(T)/ANO1 ZPEs) were used to find ΔfH0(C5H4═O) to be 16 ± 1 kcal mol(-1) and ΔfH0(CH2═CH-C≡CH) to be 71 ± 1 kcal mol(-1). The calculations predict the reaction enthalpies ΔrxnH0(1) to be 28 ± 1 kcal mol(-1) (ΔrxnH298(1) is 30 ± 1 kcal mol(-1)) and ΔrxnH0(2) to be 66 ± 1 kcal mol(-1) (ΔrxnH298(2) is 69 ± 1 kcal mol(-1)). Following pyrolysis of C5H4═O, photoionization mass spectrometry was used to measure the relative concentrations of HCC-CHCH2 and HCCH. Reaction 1 dominates at low pyrolysis temperatures (1000-1400 K). At temperatures above 1400 K, reaction 2 becomes the dominant channel. We have used the product branching ratios over the temperature range 1000-1600 K to extract the ratios of unimolecular rate coefficients for reactions 1 and 2 . If Arrhenius expressions are used, the difference of activation energies for reactions 1 and 2 , E2 - E1, is found to be 16 ± 1 kcal mol(-1) and the ratio of the pre-exponential factors, A2/A1, is 7.0 ± 0.3.

We report the gas-phase optical detection of Si2C near 390 nm and the first experimental investigation of the rovibrational structure of its (1)A1 ground electronic state using mass-resolved and fluorescence spectroscopy and variational calculations performed on a high-level ab initio potential. From this joint study, it is possible to assign all observed Ka = 1 vibrational levels up to 3800 cm(-1) with confidence, as well as a number of levels in the Ka = 0, 2,  and 3 manifolds. Dixon-dip plots for the bending coordinate (ν2) allow an experimental determination of a barrier to linearity of 783(48) cm(-1) (2σ), in good agreement with theory (802(9) cm(-1)). The calculated (Ka, ν2) eigenvalue lattice shows an archetypal example of quantum monodromy (absence of a globally valid set of quantum numbers) that is reflected by the experimentally observed rovibrational levels. The present study provides a solid foundation for infrared and optical surveys of Si2C in astronomical objects, particularly in the photosphere of N- and J-type carbon stars where the isovalent SiC2 molecule is known to be abundant.

We report infrared spectra of nitromethane anion, CH3NO2 (-), in the region 700-2150 cm(-1), obtained by Ar predissociation spectroscopy and electron detachment spectroscopy. The data are interpreted in the framework of second-order vibrational perturbation theory based on coupled-cluster electronic structure calculations. The modes in the spectroscopic region studied here are mainly based on vibrations involving the heavier atoms; this work complements earlier studies on nitromethane anion that focused on the CH stretching region of the spectrum. Electron detachment begins at photon energies far below the adiabatic electron affinity due to thermal population of excited vibrational states.

A systematic relativistic coupled-cluster study is reported on the harmonic vibrational frequencies of the O(h), C(3v), and C(2v) conformers of XeF6, with scalar-relativistic effects efficiently treated using the spin-free exact two-component theory in its one-electron variant (SFX2C-1e). Atomic natural orbital type basis sets recontracted for the SFX2C-1e scheme have been shown to provide rapid basis-set convergence for the vibrational frequencies. SFX2C-1e as well as complementary pseudopotential based computations consistently predicts that both O(h) and C(3v) structures are local minima on the potential energy surface, while the C(2v) structure is a transition state. Qualitative disagreement between the present results for the O(h) structure and those from CCSD(T)-F12b calculations [Peterson et al., J. Phys. Chem. A 116, 9777 (2012)], which yielded a triply degenerate imaginary frequency for the O(h) structure, is attributed here to the high sensitivity of the computed harmonic frequencies of the t(1u) bending modes to the basis-set effects of triples contributions.

Photoionization cross sections and partial ion yields of Xe and XeF2 from Xe 3d(5/2), Xe 3d(3/2), and F 1s subshells in the 660-740 eV range are compared to explore effects of the F ligands. The Xe 3d-ϵf continuum shape resonances dominate the photoionization cross sections of both the atom and molecule, but prominent resonances appear in the XeF2 cross section due to nominal excitation of Xe 3d and F 1s electrons to the lowest unoccupied molecular orbital (LUMO), a delocalized anti-bonding MO. Comparisons of the ion products from the atom and molecule following Xe 3d photoionization show that the charge-state distribution of Xe ions is shifted to lower charge states in the molecule along with production of energetic F(+) and F(2+) ions. This suggests that, in decay of a Xe 3d core hole, charge is redistributed to the F ligands and the system dissociates due to Coulomb repulsion. The ion products from excitation of the F 1s-LUMO resonance are different and show strong increases in the yields of Xe(+) and F(+) ions. The subshell ionization thresholds, the LUMO resonance energies, and their oscillator strengths are calculated by relativistic coupled-cluster methods and agree well with measurements.

We report the discovery in space of a disilicon species, SiCSi, from observations between 80 and 350 GHz with the IRAM 30m radio telescope. Owing to the close coordination between laboratory experiments and astrophysics, 112 lines have now been detected in the carbon-rich star CW Leo. The derived frequencies yield improved rotational and centrifugal distortion constants up to sixth order. From the line profiles and interferometric maps with the Submillimeter Array, the bulk of the SiCSi emission arises from a region of 6″ in radius. The derived abundance is comparable to that of SiC 2 . As expected from chemical equilibrium calculations, SiCSi and SiC 2 are the most abundant species harboring a Si-C bond in the dust formation zone and certainly both play a key role in the formation of SiC dust grains.

The rotational spectrum of the elusive but fundamentally important silicon carbide SiCSi has been detected using sensitive microwave techniques aided by high-level ab initio methods. Its equilibrium structure has been determined to very high precision using isotopic substitution and vibrational corrections calculated quantum-chemically: it is an isosceles triangle with a Si-C bond length of 1.693(1) Å, and an apex angle of 114.87(5)°. Now that all four Si(m)C(n) clusters with m + n = 3 have been observed experimentally, their structure and chemical bonding can be rigorously compared. Because Si2C is so closely linked to other Si-bearing molecules that have been detected in the evolved carbon star IRC+10216, it is an extremely promising candidate for detection with radio telescopes.

The fraction of the collisionally stabilized Criegee species CH2OO produced from the ozonolysis of ethylene is calculated using a two-dimensional (E, J)-grained master equation technique and semiclassical transition-state theory based on the potential energy surface obtained from high-accuracy quantum chemical calculations. Our calculated yield of 42 ± 6% for the stabilized CH2OO agrees well, within experimental error, with available (indirect) experimental results. Inclusion of angular momentum in the master equation is found to play an essential role in bringing the theoretical results into agreement with the experiment. Additionally, yields of HO and HO2 radical products are predicted to be 13 ± 6% and 17 ± 6%, respectively. In the kinetic simulation, the HO radical product is produced mostly from the stepwise decomposition mechanism of primary ozonide rather than from dissociation of hot CH2OO.

The A˜(2)E(″)←X˜(2)A2 (') spectrum of NO3 radical from 7550 cm(-1) to 9750 cm(-1) has been recorded and analyzed. Our spectrum differs from previously recorded spectra of this transition due to jet-cooling, which narrows the rotational contours and eliminates spectral interference from hot bands. Assignments of numerous vibronic features can be made based on both band contour and position including the previously unassigned 30 (1) band and several associated combination bands. We have analyzed our spectrum first with an independent anharmonic oscillator model and then by a quadratic Jahn-Teller vibronic coupling model. The fit achieved with the quadratic Jahn-Teller model is excellent, but the potential energy surface obtained with the fitted parameters is in only qualitative agreement with one obtained from ab initio calculations.

Singlet dihydroxycarbene (HOC̈OH) is produced via pyrolytic decomposition of oxalic acid, captured by helium nanodroplets, and probed with infrared laser Stark spectroscopy. Rovibrational bands in the OH stretch region are assigned to either trans,trans- or trans,cis-rotamers on the basis of symmetry type, nuclear spin statistical weights, and comparisons to electronic structure theory calculations. Stark spectroscopy provides the inertial components of the permanent electric dipole moments for these rotamers. The dipole components for trans, trans- and trans, cis-rotamers are (μa, μb) = (0.00, 0.68(6)) and (1.63(3), 1.50(5)), respectively. The infrared spectra lack evidence for the higher energy cis,cis-rotamer, which is consistent with a previously proposed pyrolytic decomposition mechanism of oxalic acid and computations of HOC̈OH torsional interconversion and tautomerization barriers.

The theory of non-orthogonal spin-adaptation for closed-shell molecular systems is applied to coupled cluster methods with quadruple excitations (CCSDTQ). Calculations at this level of detail are of critical importance in describing the properties of molecular systems to an accuracy which can meet or exceed modern experimental techniques. Such calculations are of significant (and growing) importance in such fields as thermodynamics, kinetics, and atomic and molecular spectroscopies. With respect to the implementation of CCSDTQ and related methods, we show that there are significant advantages to non-orthogonal spin-adaption with respect to simplification and factorization of the working equations and to creating an efficient implementation. The resulting algorithm is implemented in the CFOUR program suite for CCSDT, CCSDTQ, and various approximate methods (CCSD(T), CC3, CCSDT-n, and CCSDT(Q)).

The phenyl radical (C6H5(·)) is the prototypical σ-type aryl radical and one of the most common aromatic building blocks for larger ring molecules. Using a combination of rotational spectroscopy of singly substituted isotopic species and vibrational corrections calculated theoretically, an extremely accurate molecular structure has been determined. Relative to benzene, the phenyl radical has a substantially larger C-Cipso-C bond angle [125.8(3)° vs. 120°], and a shorter distance [2.713(3) Å vs. 2.783(2) Å] between the ipso and para carbon atoms., (© 2015 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

The vibronic coupling model of Köppel, Domcke, and Cederbaum is a powerful means to understand, predict, and analyze electronic spectra of molecules, especially those that exhibit phenomena that involve breakdown of the Born-Oppenheimer approximation. In this work, we describe a new parallel algorithm for carrying out such calculations. The algorithm is conceptually founded upon a "stencil" representation of the required computational steps, which motivates an efficient strategy for coarse-grained parallelization. The equations involved in the direct-CI type diagonalization of the model Hamiltonian are presented, the parallelization strategy is discussed in detail, and the method is illustrated by calculations involving direct-product basis sets with as many as 17 vibrational modes and 130 billion basis functions.

We report a combined experimental and theoretical study of the low-lying electronic states of cyclopentadienone (C5H4O). The cyclopentadienone anion (C5H4O(-)) was generated in the gas phase via reaction of atomic oxygen radical anions (O(-)) with cyclopentanone (C5H8O). Photoelectron imaging was used to gain access to the first three electronic states of C5H4O, including the X (1)A1 ground state and the (3)B2 and (3)A2 excited states. The first two state assignments are supported by the Franck-Condon simulations of the vibrational progressions observed in the X (1)A1 and (3)B2 bands in the photoelectron spectra. The adiabatic electron affinity of cyclopentadienone in the ground state is determined to be EA(X (1)A1) = 1.06 ± 0.01 eV, and the corresponding values for the first two excited states are EA((3)B2) = 2.56 ± 0.02 eV and EA((3)A2) = 3.45 ± 0.01 eV. These experimental determinations are in excellent agreement with the CCSD(T) theory predictions, lending further confidence to the above state assignments. On the basis of these results, the lowest singlet-triplet splitting (between the X (1)A1 and (3)B2 states) in cyclopentadienone is ΔES-T = 1.50 ± 0.02 eV.

A Chirped-Pulse millimeter-Wave (CPmmW) spectrometer is applied to the study of chemical reaction products that result from pyrolysis in a Chen nozzle heated to 1000-1800 K. Millimeter-wave rotational spectroscopy unambiguously determines, for each polar reaction product, the species, the conformers, relative concentrations, conversion percentage from precursor to each product, and, in some cases, vibrational state population distributions. A chirped-pulse spectrometer can, within the frequency range of a single chirp, sample spectral regions of up to ∼10 GHz and simultaneously detect many reaction products. Here we introduce a modification to the CPmmW technique in which multiple chirps of different spectral content are applied to a molecular beam pulse that contains the pyrolysis reaction products. This technique allows for controlled allocation of its sensitivity to specific molecular transitions and effectively doubles the bandwidth of the spectrometer. As an example, the pyrolysis reaction of ethyl nitrite, CH3CH2ONO, is studied, and CH3CHO, H2CO, and HNO products are simultaneously observed and quantified, exploiting the multi-chirp CPmmW technique. Rotational and vibrational temperatures of some product molecules are determined. Subsequent to supersonic expansion from the heated nozzle, acetaldehyde molecules display a rotational temperature of 4 ± 1 K. Vibrational temperatures are found to be controlled by the collisional cooling in the expansion, and to be both species- and vibrational mode-dependent. Rotational transitions of vibrationally excited formaldehyde in levels ν4, 2ν4, 3ν4, ν2, ν3, and ν6 are observed and effective vibrational temperatures for modes 2, 3, 4, and 6 are determined and discussed.

We use gas-phase negative ion photoelectron spectroscopy to study the quasilinear carbene propargylene, HCCCH, and its isotopologue DCCCD. Photodetachment from HCCCH– affords the X̃(3B) ground state of HCCCH and its ã(1A), b̃ (1B), d̃(1A2), and B̃(3A2) excited states. Extended, negatively anharmonic vibrational progressions in the X̃(3B) ground state and the open-shell singlet b̃ (1B) state arise from the change in geometry between the anion and the neutral states and complicate the assignment of the origin peak. The geometry change arising from electron photodetachment results in excitation of the ν4 symmetric CCH bending mode, with a measured fundamental frequency of 363 ± 57 cm(–1) in the X̃(3B) state. Our calculated harmonic frequency for this mode is 359 cm(–1). The Franck–Condon envelope of this progression cannot be reproduced within the harmonic approximation. The spectra of the ã(1A), d̃(1A2), and B̃(3A2) states are each characterized by a short vibrational progression and a prominent origin peak, establishing that the geometries of the anion and these neutral states are similar. Through comparison of the HCCCH– and DCCCD– photoelectron spectra, we measure the electron affinity of HCCCH to be 1.156 ± (0.095)(0.010) eV, with a singlet–triplet splitting between the X̃(3B) and the ã(1A) states of ΔEST = 0.500 ± (0.01)(0.10) eV (11.5 ± (0.2)(2.3) kcal/mol). Experimental term energies of the higher excited states are T0 [b̃(1B)] = 0.94 ± (0.20)(0.22) eV, T0 [d̃(1A2)] = 3.30 ± (0.02)(0.10) eV, T0 [B̃(3A2)] = 3.58 ± (0.02)(0.10) eV. The photoelectron angular distributions show significant π character in all the frontier molecular orbitals, with additional σ character in orbitals that create the X̃(3B) and b̃(1B) states upon electron detachment. These results are consistent with a quasilinear, nonplanar, doubly allylic structure of X̃(3B) HCCCH with both diradical and carbene character.

Semiclassical transition state theory, in combination with high accuracy quantum chemistry, is used to compute thermal rate constants from first principles for the O((3)P) + H2 reaction and its isotopic counterparts. In the temperature regime of 298-3500 K (which spans 8 orders of magnitude for rate constants), our theoretical results are in excellent agreement (within 5-15%) with all available experimental data from 298 to 2500 K but are somewhat too low (from 15 to 35%) at higher temperatures. Several possible reasons that might cause the degradation at high temperatures are discussed. Vibrational state-selected rate constants and their correlations with normal thermal rate constant are derived and are given in the Supporting Information.

Chirped-pulse Fourier transform microwave spectroscopy (CP-FTMW) is combined with a flash pyrolysis (hyperthermal) microreactor as a novel method to investigate the molecular structure of cyclopentadienone (C5H4═O), a key reactive intermediate in biomass decomposition and aromatic oxidation. Samples of C5H4═O were generated cleanly from the pyrolysis of o-phenylene sulfite and cooled in a supersonic expansion. The (13)C isotopic species were observed in natural abundance in both C5H4═O and in C5D4═O samples, allowing precise measurement of the heavy atom positions in C5H4═O. The eight isotopomers include: C5H4═O, C5D4═O, and the singly (13)C isotopomers with (13)C substitution at the C1, C2, and C3 positions. Microwave spectra were interpreted by CCSD(T) ab initio electronic structure calculations and an re molecular structure for C5H4═O was found. Comparisons of the structure of this "anti-aromatic" molecule are made with those of comparable organic molecules, and it is concluded that the disfavoring of the "anti-aromatic" zwitterionic resonance structure is consistent with a more pronounced C═C/C-C bond alternation.

We present a diabatization method applicable to spectroscopic studies based on Equation-of-Motion Coupled Cluster (EOM-CC) energies and biorthogonal wavefunctions that uses the Block Diagonalization (BD) approaches of Cederbaum et al. [L. S. Cederbaum, J. Schirmer, and H. D. Meyer, J. Phys. A: Math. Gen. 22, 2427 (1989)] and Domcke et al. [W. Domcke and C. Woywod, Chem. Phys. Lett. 216, 362 (1993); W. Domcke, C. Woywod, and M. Stengle, Chem. Phys. Lett. 226, 257 (1994)]. The method gives excellent agreement with coupling constants calculated using the analytic gradient approach of Ichino et al. [T. Ichino, J. Gauss, and J. F. Stanton, J. Chem. Phys. 130, 174105 (2009)]. While the BD method is a finite difference approach, it can be applied at any geometry, can generate (pointwise) diabatic potential energy surfaces, and can be used with EOM wavefunctions that include triple (or higher) excitations. The method is applied to several model systems and its sensitivity to orbital choice, excitation space, and projection space is explored.

Hydroxymethylene (HCOH) and its d1-isotopologue (HCOD) are isolated in low temperature helium nanodroplets following pyrolysis of glyoxylic acid. Transitions identified in the infrared spectrum are assigned exclusively to the trans-conformation based on previously reported anharmonic frequency computations [P. R. Schreiner, H. P. Reisenauer, F. C. Pickard, A. C. Simmonett, W. D. Allen, E. Mátyus, and A. G. Császár, Nature 453, 906 (2008); L. Koziol, Y. M. Wang, B. J. Braams, J. M. Bowman, and A. I. Krylov, J. Chem. Phys. 128, 204310 (2008)]. For the OH(D) and CH stretches, a- and b-type transitions are observed, and when taken in conjunction with CCSD(T)/cc-pVTZ computations, lower limits to the vibrational band origins are determined. The relative intensities of the a- and b-type transitions provide the orientation of the transition dipole moment in the inertial frame. The He nanodroplet data are in excellent agreement with anharmonic frequency computations reported here and elsewhere, confirming an appreciable Ar-matrix shift of the OH and OD stretches and strong anharmonic resonance interactions in the high-frequency stretch regions of the mid-infrared.

Carbenes are reactive molecules of the form R(1)-:C-R(2) that play a role in topics ranging from organic synthesis to gas-phase oxidation chemistry. We report the first experimental structure determination of dihydroxycarbene (HO-:C-OH), one of the smallest stable singlet carbenes, using a combination of microwave rotational spectroscopy and high-level coupled-cluster calculations. The semi-experimental equilibrium structure derived from five isotopic variants of HO-:C-OH contains two very short CO single bonds (ca. 1.32 Å). Detection of HO-:C-OH in the gas phase firmly establishes that it is stable to isomerization, yet it has been underrepresented in discussions of the CH2O2 chemical system and its atmospherically relevant isomers: formic acid and the Criegee intermediate CH2OO., (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim.)

A theoretical calculation of the laser-induced fluorescence excitation spectrum from X̃(2)E→Ã(2)A1 is carried out for CH3O and CD3O using a transition dipole moment surface expanded up to second order. The vibronic form of these operators is obtained using symmetry arguments. The Ã(2)A1 vibrational levels are calculated using Van Vleck perturbation theory, and the latter is used to adjust harmonic constants of the potential to match experimental fundamentals. The CH3O fit force field is tested on CD3O. For both molecules the transition energies are well reproduced, but there are systematic differences between experimental and theoretical intensities. The origins of these differences are discussed., (Copyright © 2013 Elsevier B.V. All rights reserved.)

A detailed vibrational analysis of the infrared spectra of cyclopentadienone (C5H4═O) in rare gas matrices has been carried out. Ab initio coupled-cluster anharmonic force field calculations were used to guide the assignments. Flash pyrolysis of o-phenylene sulfite (C6H4O2SO) was used to provide a molecular beam of C5H4═O entrained in a rare gas carrier. The beam was interrogated with time-of-flight photoionization mass spectrometry (PIMS), confirming the clean, intense production of C5H4═O. Matrix isolation infrared spectroscopy coupled with 355 nm polarized UV for photoorientation and linear dichroism experiments was used to determine the symmetries of the vibrations. Cyclopentadienone has 24 fundamental vibrational modes, Γvib = 9a1 ⊕ 3a2 ⊕ 4b1 ⊕ 8b2. Using vibrational perturbation theory and a deperturbation-diagonalization method, we report assignments of the following fundamental modes (cm(-1)) in a 4 K neon matrix: the a1 modes of X̃ (1)A1 C5H4═O are found to be ν1 = 3107, ν2 = (3100, 3099), ν3 = 1735, ν5 = 1333, ν7 = 952, ν8 = 843, and ν9 = 651; the inferred a2 modes are ν10 = 933, and ν11 = 722; the b1 modes are ν13 = 932, ν14 = 822, and ν15 = 629; the b2 fundamentals are ν17 = 3143, ν18 = (3078, 3076) ν19 = (1601 or 1595), ν20 = 1283, ν21 = 1138, ν22 = 1066, ν23 = 738, and ν24 = 458. The modes ν4 and ν6 were too weak to be detected, ν12 is dipole-forbidden and its position cannot be inferred from combination and overtone bands, and ν16 is below our detection range (<400 cm(-1)). Additional features were observed and compared to anharmonic calculations, assigned as two quantum transitions, and used to assign some of the weak and infrared inactive fundamental vibrations.

Reduced dimension variational calculations have been performed for the rovibrational level structure of the S1 state of acetylene. The state exhibits an unusually complicated level structure, for various reasons. First, the potential energy surface has two accessible conformers, trans and cis. The cis conformer lies about 2700 cm(-1) above the trans, and the barrier to cis-trans isomerization lies about 5000 cm(-1) above the trans minimum. The trans vibrations ν4 (torsion) and ν6 (asym. bend) interact very strongly by Darling-Dennison and Coriolis resonances, such that their combination levels and overtones form polyads with unexpected structures. Both conformers exhibit very large x36 cross-anharmonicity since the pathway to isomerization is a combination of ν6 and ν3 (sym. bend). Near the isomerization barrier, the vibrational levels show an even-odd K-staggering of their rotational levels as a result of quantum mechanical tunneling through the barrier. The present calculations address all of these complications, and reproduce the observed K-structures of the bending and C-C stretching levels with good qualitative accuracy. It is expected that they will assist with the assignment of the irregular patterns near the isomerization barrier.

Three open-chain isomers of C6H4(+) and two cyclic ones were detected following mass-selective trapping in 6 K neon matrixes. The open-chain cations 5-hexene-1,3-diyne (CH2═CH-CC-CC-H)(+) and cis- (cis-HCC-CH═CH-CCH)(+) and trans-3-hexene-1,5-diyne (trans-HCC-CH═CH-CCH)(+), possess two absorption systems commencing at 609 and 373, 622 and 385, and 585 and 373 nm, respectively. They are assigned to the 1 (2)A" and 2 (2)A" ← X (2)A", 1(2)A2 and 2 (2)A2 ← X (2)B1, and 1 (2)Bg and 2 (2)B(g) ← X (2)A(u) electronic transitions of these cations. Two overlapping systems are detected at around 420 nm and tentatively assigned to the 1 (2)A" ← X (2)A" electronic transitions of propargyl cyclopropene and 2 (2)B1 ← X (2)A2 of o-benzyne cation structures. The assignment of the electronic transitions is based on theoretical vertical excitation energies calculated with CASPT2 and EOMEE-CCSDT methods for 12 isomers of C6H4(+). These have been carried out at the geometries optimized using several ab initio methods. Adiabatic excitation energies were calculated for the five identified isomers of C6H4(+).

The (6,0)[16.0]1.5-X(2)Δ(5/2) and (7,0)[16.0]3.5-X(2)Δ(5/2) bands of IrSi have been recorded using high-resolution laser-induced fluorescence spectroscopy. The field-free spectra of the (191)IrSi and (193)IrSi isotopologues were modeled to generate a set of fine, magnetic hyperfine, and nuclear quadrupole hyperfine parameters for the X(2)Δ(5/2)(v = 0), [16.0]1.5(v = 6), and [16.0]3.5 (v = 7) states. The observed optical Stark shifts for the (193)IrSi and (191)IrSi isotopologues were analyzed to produce the permanent electric dipole moments, μ(el), of -0.414(6) D and 0.782(6) D for the X(2)Δ(5/2) and [16.0]1.5 (v = 6) states, respectively. Properties of the X(2)Δ(5/2) state computed using relativistic coupled-cluster methods clearly indicate that electron correlation plays an essential role. Specifically, inclusion of correlation changes the sign of the dipole moment and is essential for achieving good accuracy for the nuclear quadrupole coupling parameter eQq0.

The rotational spectrum of pyridazine (o-C4H4N2), the ortho disubstituted nitrogen analog of benzene, has been measured and analyzed in the gas phase. For the ground vibrational state of the normal isotopolog, over 2000 individual rotational transitions have been identified between 238 and 360 GHz and have been fit to 13 parameters of a 6th-order centrifugal distortion Hamiltonian. All transitions in this frequency region can now be predicted from this model to near experimental accuracy, i.e., well enough for the purpose of any future radio-astronomical search for this species. Three isotopologs, [3-(13)C]-C4H4N2, [4-(13)C]-C4H4N2, and [1-(15)N]-C4H4N2, have been detected in natural abundance, and several hundred lines have been measured for each of these species and fit to 6th-order Hamiltonians. Ten additional isotopologs were synthesized with enhanced deuterium substitution and analyzed to allow for a complete structure determination. The equilibrium structure (Re) of pyridazine was obtained by correcting the experimental rotational constants for the effects of vibration-rotation coupling using interaction constants predicted from CCSD(T) calculations with an ANO0 basis set and further correcting for the effect of electron mass. The final Re structural parameters are determined with excellent accuracy, as evidenced by their ability to predict 28 independent moments of inertia (Ia and Ib for 14 isotopologs) very well from 9 structural parameters. The rotational spectra of the six lowest-energy fundamental vibrational satellites of the main isotopolog have been detected. The rotational spectra of the five lowest-energy vibrational satellites have been assigned and fit to yield accurate rotational and distortion constants, while the fit and assignment for the sixth is less complete. The resultant vibration-rotation interaction (α) constants are found to be in excellent agreement with ones predicted from coupled-cluster calculations, which proved to be the key to unambiguous assignment of the satellite spectra to specific vibration modes.

Highly accurate calculations are reported for properties of vinylidene (H2C═C:), specifically the position of its zero-point vibrational level relative to that of acetylene and its equilibrium structure and ground state rotational constants. The isomerization energy of vinylidene calculated at the HEAT-456QP level of theory is 43.53 ± 0.15 kcal mol(-1), in agreement with the previous best estimate, but associated with a much smaller uncertainty. In addition, the thermochemical calculations presented here also allow a determination of the H2CC-H bond energy of the vinyl radical at the HEAT-345(Q) level of theory, which is 77.7 ± 0.3 kcal mol(-1). The equilibrium structure of vinylidene, estimated with an additivity scheme that includes treatment of correlation effects beyond CCSD(T) as well as relativistic and adiabatic (diagonal Born-Oppenheimer correction) contributions, is rCC = 1.2982 ± 0.0003 Å, rCH = 1.0844 ± 0.0003 Å, and θCCH = 120.05 ± 0.05°, with zero-point rotational constants (including vibrational contributions and electronic contributions to the moment of inertia) estimated to be A0 = 9.4925 ± 0.0150 cm(-1), B0 = 1.3217 ± 0.0017 cm(-1), and C0 = 1.1602 ± 0.0016 cm(-1).

The J = 1 ← J = 0 and J = 2 ← J = 1 rotational transitions of ruthenium monocarbide, RuC, have been recorded using the separated field pump/probe microwave optical double resonance technique and analyzed to determine the fine and hyperfine parameters for the X(1)Σ(+) state. The (101)Ru(I = 5/2) electric quadrupole parameter, eq0Q, and nuclear spin-rotation interaction parameter, C(I)(eff), were determined to be 433.19(8) MHz and -0.049(6) MHz, respectively. The equilibrium bond distance, r(e), was determined to be 1.605485(2) Å. Hartree-Fock and coupled-cluster calculations were carried out for the properties of the X(1)Σ(+) state. Electron-correlation effects are pronounced for all properties studied. It is shown that (a) the moderate scalar-relativistic contribution to eq0Q is entirely due to the coupling between scalar-relativistic and electron-correlation effects, (b) the spin-free exact two-component theory in its one-electron variant offers a reliable and efficient treatment of scalar-relativistic effects, and (c) non-relativistic theory performs quite well for the prediction of C(I)(elec), provided that electron correlation is treated accurately.

Production of acetic acid via gas-phase hydration of ketene by water (uncatalyzed and in the presence of an additional water molecule) was theoretically characterized using high-level coupled-cluster methods, followed by a two-dimensional master equation analysis to compute thermal reaction rate constants. The results show that the formation of acetic acid quite likely occurs in high-temperature combustion of biomass, but that the rate of formation should be negligible under ambient atmospheric conditions.

A silicon carbide microtubular reactor has been used to measure branching ratios in the thermal decomposition of furan, C4H4O. The pyrolysis experiments are carried out by passing a dilute mixture of furan (approximately 0.01%) entrained in a stream of helium through the heated reactor. The SiC reactor (0.66 mm i.d., 2 mm o.d., 2.5 cm long) operates with continuous flow. Experiments were performed with a reactor inlet pressure of 100-300 Torr and a wall temperature between 1200 and 1600 K; characteristic residence times in the reactor are 60-150 μs. The unimolecular decomposition pathway of furan is confirmed to be: furan (+ M) ⇌ α-carbene or β-carbene. The α-carbene fragments to CH2=C=O + HC≡CH while the β-carbene isomerizes to CH2=C=CHCHO. The formyl allene can isomerize to CO + CH3C≡CH or it can fragment to H + CO + HCCCH2. Tunable synchrotron radiation photoionization mass spectrometry is used to monitor the products and to measure the branching ratio of the two carbenes as well as the ratio of [HCCCH2]/[CH3C≡CH]. The results of these pyrolysis experiments demonstrate a preference for 80%-90% of furan decomposition to occur via the β-carbene. For reactor temperatures of 1200-1400 K, no propargyl radicals are formed. As the temperature rises to 1500-1600 K, at most 10% of the decomposition of CH2=C=CHCHO produces H + CO + HCCCH2 radicals. Thermodynamic conditions in the reactor have been modeled by computational fluid dynamics and the experimental results are compared to the predictions of three furan pyrolysis mechanisms. Uncertainty in the pressure-dependency of the initiation reaction rates is a possible a source of discrepancy between experimental results and theoretical predictions.

The reaction energy and barrier height of the title reaction are investigated using two high-level ab initio protocols, namely Focal Point Analysis (FPA) and modified High Accuracy Extrapolated Ab Initio Thermochemistry (HEAT) methods. It is concluded from these calculations that despite some multireference character, dynamic electron correlation plays a dominant role near the reaction barrier. Thus, the coupled-cluster method with higher excitations than singles and doubles gives a better description than the multireference configuration interaction method for the barrier height. The FPA and HEAT classical barrier heights, including the spin-orbit and other corrections, are 1.919 and 2.007 kcal/mol, respectively. The rate constants and H/D kinetic isotope effect for the title reaction are determined by semiclassical transition-state theory based on the anharmonic potential energy surface near the saddle point, and the agreement with experiment is excellent. The rate constants are also computed using a quasi-classical trajectory method on a global potential energy surface scaled to the FPA barrier height and a similar level of agreement with experimental data is obtained.

The rates of chemical reactions (or any activated process) are by definition determined by the flux of reactants (or initial states) that end up as products (or final states). The forward flux through any surface that divides reactants from products is a constant as long as only those trajectories that were reactants in the infinite past and products in the infinite future are included in the flux once and only once. Transition state theory (TST) ignores this last clause, thereby overestimating the rate if any of the trajectories recross the dividing surface. However, its advantage is that it replaces a dynamical calculation with a statistical integral over the TST geometry. The recent identification of roaming trajectories-those that persist for a long time as neither reactant nor product without ever visiting near the col on the energy landscape-apparently challenges the dogma that TST's only error lies in the omission of recrossing trajectories. This question is investigated using the isomerization reaction of ketene in which the experimental values are verified to be in reasonable agreement with both the exact and TST values. We have found two trajectories for the ketene isomerization that carry the signature of roaming, but their effect on the calculation of the reaction rate constant using classical transition state theory is small. Indeed, the existence of roaming trajectories is seen to impose a limitation on which dividing surfaces are appropriate for the calculation of either exact or approximate TST rates, but in this case, they do not unseat the existence of dividing surfaces that can be used safely to calculate TST rates.

A cost-effective treatment of scalar-relativistic effects on nuclear magnetic shieldings based on the spin-free exact-two-component theory in its one-electron variant (SFX2C-1e) is presented. The SFX2C-1e scheme gains its computational efficiency, in comparison to the four-component approach, from a focus on spin-free contributions and from the elimination of the small component. For the calculation of nuclear magnetic shieldings, the separation of spin-free and spin-dependent terms in the parent four-component theory is carried out here for the matrix representation of the Dirac equation in terms of a restricted-magnetically balanced gauge-including atomic orbital basis. The resulting spin-free four-component matrix elements required to calculate nuclear magnetic shieldings are then used to construct the corresponding SFX2C-1e Hamiltonian and its perturbed counterpart in the context of SFX2C-1e analytic derivative theory. To demonstrate the applicability of the approach, we report coupled-cluster calculations for prototypical problems such as the (17)O shieldings of transition-metal oxo complexes (MO4(2-), M = Cr, Mo, and W) and the (129)Xe shieldings of xenon fluorides (XeF2, XeF4, and XeF6).