Product Translational Energy Distributions Research Articles

Predissociation dynamics of the A2Σ+ state of SH radical: Fine-structure state distributions of the S(3PJ) products.

Photo-predissociation of rovibrational levels of SH (A2Σ+, v' = 0-6) is studied using the high-n Rydberg atom time-of-flight technique. Spin-orbit branching fractions of the S(3PJ=2,1,0) products are measured in the product translational energy distributions. The SH A2Σ+v' = 0 state predissociates predominantly via coupling to the 4Σ- repulsive state. As the vibrational level v' increases, predissociation dynamics change drastically, with all three repulsive states (4Σ-, 2Σ-, and 4Π) involved in the dissociation. Nonadiabatic interactions and quantum interferences among these dissociation pathways affect the fine-structure state distributions of the S(3PJ=2,1,0) products.

Vibrational Mode-Specific Dynamics of the OH + C2H6 Reaction.

We investigate the effects of the initial vibrational excitations on the dynamics of the OH + C2H6 → H2O + C2H5 reaction using the quasi-classical trajectory method and a full-dimensional analytical ab initio potential energy surface. Excitation of the initial CH, CC, and OH stretching modes enhances, slightly inhibits, and does not affect the reactivity, respectively. Translational energy activates the early-barrier title reaction more efficiently than OH and CC stretching excitations, in accord with the Polanyi rules whereas CH stretching modes have similar or higher efficacy than translation, showing that these rules are not always valid in polyatomic processes. Scattering angle, initial attack angle, and product translational energy distributions show the dominance of direct stripping with increasing collision energy, side-on OH and isotropic C2H6 attack preferences, and substantial reactant-product translational energy transfer without any significant mode specificity. The reactant vibrational excitation energy of OH and C2H6 flows into the H2O and C2H5 product vibrations, respectively, whereas product rotations are not affected. The computed mode-specific H2O vibrational distributions show that initial OH excitation appears in the asymmetric stretching vibration of the H2O product and allow comparison with experiments.

Ethylcarbene versus Direct Propene Formation in the Near-UV Photodissociation of Ethylketene

The competing pathways in the photodissociation of gaseous ethylketene at excitation wavelengths of 320.0, 340.0, and 355.1 nm were studied using photofragment translational energy spectroscopy. The primary dissociation channel was C═C bond fission producing ethylcarbene (CH3CH2CH; also known as propylidene) and CO. Product translational energy distributions are consistent with theoretical predictions that ground state ethylcarbene lies ∼34 kJ/mol higher in energy than its isomer dimethylcarbene (CH3CCH3). A second dissociation channel involved direct formation of propene prior to or concurrent with CO elimination. The measured product branching ratios indicate that the effective potential energy barrier for the direct propene channel lies below the energetic threshold for ethylcarbene formation. A minor C-C bond fission channel was also observed, leading to CH3 + CH2CHCO products. Comparisons are made to the results of our recent studies of methylketene and dimethylketene photodissociation.

Combining Machine Learning and Spectroscopy to Model Reactive Atom + Diatom Collisions.

The prediction of product translational, vibrational, and rotational energy distributions for arbitrary initial conditions for reactive atom + diatom collisions is of considerable practical interest in atmospheric re-entry. Because of the large number of accessible states, determination of the necessary information from explicit (quasi-classical or quantum) dynamics studies is impractical. Here, a machine-learned (ML) model based on translational energy and product vibrational states assigned from a spectroscopic, ro-vibrational coupled energy expression based on the Dunham expansion is developed and tested quantitatively. All models considered in this work reproduce final state distributions determined from quasi-classical trajectory (QCT) simulations with R2 ∼ 0.98. As a further validation, thermal rates determined from the machine-learned models agree with those from explicit QCT simulations and demonstrate that the atomistic details are retained by the machine learning which makes them suitable for applications in more coarse-grained simulations. More generally, it is found that ML is suitable for designing robust and accurate models from mixed computational/experimental data which may also be of interest in other areas of the physical sciences.

Ultraviolet Photodissociation Dynamics of the Cyclohexyl Radical: The H-Atom Product Channel.

The ultraviolet (UV) photodissociation dynamics of the jet-cooled cyclohexyl (c-C6H11) radical is studied using the high-n Rydberg atom time-of-flight (HRTOF) technique. The cyclohexyl radical is produced by the 193 nm photodissociation of chlorocyclohexane and bromocyclohexane and is examined in the photolysis wavelength region of 232-262 nm. The H-atom photofragment yield (PFY) spectrum contains a broad peak centered at 250 nm, which is in good agreement with the UV absorption spectrum of the cyclohexyl radical and assigned to the 3p Rydberg states. The translational energy distributions of the H-atom loss product channel, P(ET)'s, are bimodal, with a slow (low ET) component peaking at ∼6 to 7 kcal/mol and a fast (high ET) component peaking at ∼44-48 kcal/mol. The fraction of the average translational energy in the total excess energy, ⟨fT⟩, is in the range of 0.16-0.25 in the photolysis wavelength region of 232-262 nm. The H-atom product angular distribution of the slow component is isotropic, while that of the fast component is anisotropic with an anisotropy parameter of β ≈ 0.5-0.7. The bimodal product translational energy and angular distributions indicate two dissociation pathways to the H + C6H10 products in cyclohexyl. The high-ET anisotropic component is from a repulsive, prompt dissociation on a repulsive potential energy surface coupling with the Rydberg excited states to produce H + cyclohexene. The low-ET isotropic component is consistent with the unimolecular dissociation of hot radical on the ground electronic state after internal conversion from the Rydberg states. The similarity of the photodissociation dynamics of the cyclohexyl radical to the previously studied small linear and branched alkyls expands on the understanding of the dissociation dynamics of alkyl radicals to include larger cyclic alkyl radicals.

Direct Observation of Ethylidene (CH3CH), the Elusive High-Energy Isomer of Ethylene.

Despite experimental efforts spanning more than 80 years, there has been no direct observation of free ethylidene (CH3CH), the simplest alkyl-substituted carbene. Here, we report that ethylidene is indefinitely stable in the absence of collisions if produced in the triplet ground state at energies below the threshold for intersystem crossing. Near-UV photolysis of gaseous methylketene, or propenal (followed by isomerization to methylketene), leads to CO loss producing triplet ethylidene, which is detected by photoionization mass spectrometry. Electronically excited singlet ethylidene is also produced, rapidly undergoing isomerization by a 1,2-hydrogen atom shift, producing highly vibrationally excited ethylene. The measured product translational energy distributions verify the theoretically calculated enthalpy of formation of triplet ethylidene and are consistent with a singlet-triplet energy gap of approximately 12.5 kJ/mol.

State-to-state predissociation dynamics of hydroxyl radical via the A2Σ+ state

ABSTRACT Photo-predissociation dynamics of jet-cooled hydroxyl radical (OH) via several rovibrational levels (v′ = 2–4, N′ = 0–2, J′ = 0.5–2.5, F 1) in the A2Σ+ state are studied using the high–n Rydberg-atom time-of-flight (HRTOF) technique. Spin–orbit branching fractions and angular distributions of the H(2S) + O(3PJ = 2,1,0) product channels are measured in the product translational energy distributions. The A2Σ+ v′ = 2 and 3 states of OH predissociate predominantly via the single 14Σ− repulsive state, while the A2Σ+ v′ = 4 state predissociates via the 14Σ−, 12Σ−, and 14Π repulsive states and quantum interferences among these dissociation pathways play an important role in the O(3PJ = 2,1,0) product fine-structure state distribution. The experimental O(3PJ) product spin–orbit branching ratios are in excellent agreement with the full quantum multichannel scattering calculations that include all the interactions in the crossing region, recoupling zone, and asymptotic zone [Parlant and Yarkony, J. Chem. Phys. 110, 363 (1999)]. The product angular distributions strongly depend on the rotational transitions and rotational levels in the A2Σ+ state. The measured anisotropy parameters are in reasonable agreement with predictions from the simulation programme (Betaofnu) [Kim et al., J. Chem. Phys. 125, 133316 (2006)], using dissociation lifetime, excitation frequency, rotational level, and rotational constant. The predissociation time scales of OH A2Σ+ are determined to be 130 ± 30 ns and ≥ 14 ± 3 ps for the v′ = 2, N′ = 2, J′ = 2.5 and v′ = 4, N′ = 0, J′ = 0.5 levels, respectively.

VUV photodissociation of DNCO: dynamics of the D atom elimination channel

The D atom Rydberg tagging time-of-flight technique was applied to investigate the photodissociation dynamics of DNCO in the vacuum ultraviolet 133–137 nm region. The D atom product was detected and the corresponding product translational energy distributions and angular distributions were obtained. Three product channels, D + NCO(X2Π), D + NCO(A2Σ+) and D + NCO(B2Π), which arise from different dissociation pathways have been observed. It is found that the D + NCO(X2Π) channel involves two different dissociation pathways; one is via internal conversion from the excited state to the S0 state, and the other is via internal conversion from the excited state to the S1 state. The D + NCO(A2Σ+) channel was ascribed to be from dissociation on S2 surface, and the D + NCO(B2Π) channel possibly come from a relatively slow dissociation process. Vibrational structures observed in the D + NCO(A2Σ+) channel shows that there is dominant bending with a little stretching vibrational excitation of NCO(A2Σ+). This is consistent with what has been found in the previous study following VUV photodissociation of HNCO in a similar wavelength region.

Photodissociation dynamics of the tert-butyl perthiyl radical.

The photodissociation dynamics of the tert-butyl perthiyl (t-BuSS) radical are investigated by fast-beam coincidence translational spectroscopy. A fast (6 keV-8 keV) beam of neutral t-BuSS radicals is produced via photodetachment of the corresponding anion, followed by photodissociation at 248 nm (5.00 eV) or 193 nm (6.42 eV) and coincident detection of the neutral products. Photofragment mass and translational energy distributions are obtained at both wavelengths. At 248 nm, the dominant product channel (90%) is found to be S loss, with a product translational energy distribution that peaks close to the maximum available energy and an anisotropic photofragment angular distribution, indicating dissociation along a repulsive excited state. A minor channel (10%) leading to the formation of S2 + t-Bu is also observed. At 193 nm, both two- and three-body dissociation are observed. The formation of S2 + t-Bu is the dominant two-body product channel, with multiple electronic states of the S2 molecule produced via excited-state dissociation processes. The formation of S + t-BuS is a minor two-body channel at this dissociation energy. The three-body channels are S2 + H + isobutene, S2 + CH3 + propene, and S + SH + isobutene. The first two of these channels result from a sequential dissociation process in which the loss of S2 from t-BuSS results in ground-state t-Bu with sufficient internal energy to undergo secondary fragmentation. The third three-body channel, S + SH + isobutene, is attributed to the loss of internally excited HS2 from t-BuSS, which then rapidly dissociates to form S + SH in an asynchronous concerted dissociation process.

Ultraviolet photodissociation dynamics of the n-butyl, s-butyl, and t-butyl radicals.

Photodissociation dynamics of the jet-cooled n-butyl radical via the 3s Rydberg state and the s-butyl radical via the 3p Rydberg states in the ultraviolet region of 233 nm-258 nm, as well as the t-butyl radical via the 3d Rydberg states at 226 nm-244 nm, are studied using the high-n Rydberg atom time-of-flight technique. The H-atom photofragment yield spectra of the n-butyl, s-butyl, and t-butyl radicals show a broad feature centered around 247 nm, 244 nm, and 234 nm, respectively. The translational energy distributions of the H + C4H8 products, P(ET)'s, of the three radicals are bimodal, with a slow (low ET) component peaking at ∼6 kcal/mol and a fast (high ET) component peaking at ∼52 kcal/mol-57 kcal/mol, ∼43 kcal/mol, and ∼37 kcal/mol for n-butyl, s-butyl, and t-butyl, respectively. The fraction of the products' translational energy in the available energy, ⟨ fT⟩, is 0.31, 0.30, and 0.27 for n-butyl, s-butyl, and t-butyl, respectively. The H-atom product angular distributions of the slow component are isotropic for all three radicals, while those of the fast component are anisotropic for n-butyl and s-butyl with an anisotropy parameter β ∼ 0.7 and ∼ 0.3 and that of the fast component of t-butyl is nearly isotropic. The bimodal product translational energy and angular distributions indicate two dissociation pathways to the H + C4H8 products in these three radicals, a direct, prompt dissociation on the repulsive potential energy surface coupling with the Rydberg excited states, and a unimolecular dissociation of the hot radical on the ground electronic state after internal conversion from the Rydberg states.

Ultraviolet photodissociation dynamics of DNCO + hν → D + NCO: Two competitive pathways

Photodissociation dynamics of DNCO + hν → D + NCO at photolysis wavelengths between 200 and 235 nm have been studied using the D-atom Rydberg tagging time-of-flight technique. Product translational energy distributions and angular distributions have been determined. Nearly statistical distribution of the product translational energy with nearly isotropic angular distribution was observed at 210–235 nm, which may come from the predissociation pathway of internal conversion from S1 to S0 state followed by decomposition on S0 surface. At shorter photolysis wavelengths, in addition to the statistical distribution, another feature with anisotropic angular distribution appears at high translational energy region, which can be attributed to direct dissociation on S1 surface. Compared with HNCO, the direct dissociation pathway for DNCO photodissociation opens at higher excitation energy. According to our assignment of the NCO internal energy distribution, dominantly bending and a little stretching excited NCO was produced via both dissociation pathways.

Ab Initio and Quasiclassical Trajectory Study of the O(3P) + 2-Propanol Hydrogen Abstraction Reaction.

We present a theoretical study of the hydrogen abstraction reaction from 2-propanol by ground-state oxygen atoms. First, ab initio calculations are used to characterize the stationary points of the potential energy surface. Rotation around the C-C-O-H dihedral affords two conformers in 2-propanol, which gives rise to 13 hydrogen abstraction reaction pathways grouped into three channels, Cα, Cβ, and O, depending on the abstraction site. Reaction at Cα exhibits the lowest barrier and largest exothermicity, followed by reaction at Cβ, and at 2-propanol's oxygen atom. Additional ab initio calculations beyond the stationary points are employed to obtain a grid of energies with which a specific-reaction-parameters (SRP) PM6 semiemipirical Hamiltonian is derived for the title reaction. The SRP-PM6 model captures the energetics of the reaction with higher accuracy than some conventional first-principles methods but is efficient enough to allow for extensive reaction dynamics calculations. Quasiclassical trajectories are subsequently propagated with the SRP-PM6 Hamiltonian to obtain reaction dynamics properties that are compared to experiments. Product translational energy and angular distributions for reaction at Cα with the two conformers of 2-propanol are in good agreement with recent molecular-beam measurements, and they exhibit largely backward scattering with modest energy release to relative translation. Most of the energy is deposited into the organic product, substantiating a reaction mechanism dominated by rebound dynamics.

Multidimensional H Atom Tunneling Dynamics of Phenol: Interplay between Vibrations and Tunneling.

Multidimensional facets of the hydrogen tunneling dynamics of phenol excited in S1 (ππ*) have been unraveled to give particular S1 vibronic states strongly coupled or actively decoupled to the O-H tunneling coordinate. Strong mode-dependent variation of the tunneling rate measured with picosecond lasers indicates that tunneling probability is extremely sensitive to low-frequency vibrational modes seemingly orthogonal to the O-H elongation coordinate unless the rate of energy randomization exceeds that of tunneling. The multidimensional nature of tunneling has also been manifested in efficient internal-to-translational energy transfers observed at S1 vibronic modes strongly coupled to the tunneling coordinate, giving insights into otherwise the formidable multidimensional map of tunneling process. The nonadiabatic bifurcation dynamics in the later stage of the chemical reaction has been disentangled by analyzing picosecond time-resolved product state distributions, resolving a long controversial issue regarding the origin of high or low kinetic energy component of the product translational energy distributions.

Correlation between the velocity scattering angle and product relative translational energy for SN2 reactions. Comparison of experiments and direct dynamics simulations

In previous research, direct dynamics simulations have been used to provide atomistic information for the Cl− + CH3I, F− + CH3I, and OH− + CH3I SN2 and proton transfer (PT) reactions. An important component of these simulations is comparison with molecular beam, ion imaging experiments. From the simulations, comparisons may be made with the product translational energy distributions determined from the experiments and the simulations give quite good agreement with these distributions. Though the experiments provide the in-plane angular distribution for a reaction’s product translational energy distribution, the number of direct dynamics trajectories for a simulation is not sufficient to compare with this angular distribution. In the work presented here, the average percentage product translational energy partitioning for forward scattered events with scattering angle θ = 0–90° and for backward scattered events with θ = 90–180° are compared for the experiments and simulations. Overall good agreement is found, with a maximum difference as high as 5–10%. Additional atomistic details, regarding the dynamics of these reactions, are provided by scatter plots of their product relative translational energy versus the scattering angle θ.

Scattering Dynamics of Nitromethane and Methyl Formate on Highly Oriented Pyrolytic Graphite (HOPG)

The gas–surface scattering dynamics of nitromethane (CH3NO2) and methyl formate (HCOOCH3) on a highly oriented pyrolytic graphite (HOPG) surface have been investigated as part of a broader effort to evaluate the efficacy of a funnel-like neutral gas concentrator that has been proposed as a mass spectrometer inlet for the characterization of tenuous planetary atmospheres or plumes. Molecular beams of CH3NO2 and HCOOCH3 with incidence energies, Ei, of 106.5 and 98.8 kJ mol–1, respectively, were directed at the surface with incidence angles, θi, of 70, 45, and 30°. A rotatable mass spectrometer, employing electron-impact ionization, was used to collect angle-resolved time-of-flight (TOF) distributions of the molecules that scattered inelastically from the surface, allowing angular distributions of the scattered product flux and translational energy distributions at a given final angle, θf, to be obtained. The TOF distributions of the scattered products detected the parent ion mass-to-charge ratios and their respective dominant ion fragments were identical, indicating that CH3NO2 and HCOOCH3 fragmented in the ionizer of the detector and not while colliding with the surface. The scattering dynamics suggested that the parallel momentum of the molecules was conserved during impact with the surface. The translational energy and angular distributions of CH3NO2 and HCOOCH3 were identical when θi = 70°. For θi = 45 and 30°, the HCOOCH3 angular distributions were shifted to a slightly larger θf than the CH3NO2 distributions. The molecules scattered from the surface through impulsive scattering (IS) and quasitrapping (QT) pathways. The IS molecules retained a large fraction of their incidence translational energy when colliding with the surface. The QT molecules transferred more energy, but they did not come completely into thermal equilibrium with the surface before scattering into the vacuum. The QT molecules had a lobular angular distribution with a maximum flux far from the surface normal, indicating that they retained some memory of their incident conditions despite losing a significant amount of energy at the surface. The results presented in this article demonstrate that for Ei near 100 kJ mol–1, these molecules would not dissociate upon impact with the surfaces of a gas concentrator constructed of HOPG. Although the observed scattering dynamics suggest that such a concentrator could perform well for a variety of molecular species, accurate concentration factors are ultimately molecule-specific and determined by the details of the molecule–surface interaction potential.

Photodissociation dynamics of H2O at 111.5 nm by a vacuum ultraviolet free electron laser.

Photodissociation dynamics of H2O via the F̃ state at 111.5 nm were investigated using the high resolution H-atom Rydberg "tagging" time-of-flight (TOF) technique, in combination with the tunable vacuum ultraviolet free electron laser at the Dalian Coherent Light Source. The product translational energy distributions and angular distributions in both parallel and perpendicular directions were derived from the recorded TOF spectra. Based on these distributions, the quantum state distributions and angular anisotropy parameters of OH (X) and OH (A) products have been determined. For the OH (A) + H channel, highly rotationally excited OH (A) products have been observed. These products are ascribed to a fast direct dissociation on the B̃1A1 state surface after multi-step internal conversions from the initial excited F̃ state to the B̃ state. While for the OH (X) + H channel, very highly rotationally excited OH (X) products with moderate vibrational excitation are revealed and attributed to the dissociation via a nonadiabatic pathway through the well-known two conical intersections between the B̃-state and the X̃-state surfaces.

Combined Experimental-Theoretical Study of the OH + CO → H + CO2 Reaction Dynamics.

A combined experimental-theoretical study is performed to advance our understanding of the dynamics of the prototypical tetra-atom, complex-forming reaction OH + CO → H + CO2, which is also of great practical relevance in combustion, Earth's atmosphere, and, potentially, Mars's atmosphere and interstellar chemistry. New crossed molecular beam experiments with mass spectrometric detection are analyzed together with the results from previous experiments and compared with quasi-classical trajectory (QCT) calculations on a new, full-dimensional potential energy surface (PES). Comparisons between experiment and theory are carried out both in the center-of-mass and laboratory frames. Good agreement is found between experiment and theory, both for product angular and translational energy distributions, leading to the conclusion that the new PES is the most accurate at present in elucidating the dynamics of this fundamental reaction. Yet, small deviations between experiment and theory remain and are presumably attributable to the QCT treatment of the scattering dynamics.

Energetics and Predissociation Dynamics of Small Water, HCl, and Mixed HCl-Water Clusters.

This Review summarizes recent research on vibrational predissociation (VP) of hydrogen-bonded clusters. Specifically, the focus is on breaking of hydrogen bonds following excitation of an intramolecular vibration of the cluster. VP of the water dimer and trimer, HCl clusters, and mixed HCl-water clusters are the major topics, but related work on hydrogen halide dimers and trimers, ammonia clusters, and mixed dimers with polyatomic units are reviewed for completion and comparison. The theoretical focus is on generating accurate potential energy surfaces (PESs) that can be used in detailed dynamical calculations, mainly using the quasiclassical trajectory approach. These PESs have to extend from the region describing large amplitude motion around the minimum to regions where fragments are formed. The experimental methodology exploits velocity map imaging to generate pair-correlated product translational energy distributions from which accurate bond dissociation energies of dimers and trimers and energy disposal in fragments are obtained. The excellent agreement between theory and experiment on bond dissociation energies, energy disposal in fragments, and the contributions of cooperativity demonstrates that it is now possible, with state-of-the-art experimental and theoretical methods, to make accurate predictions about dynamical and energetic properties of dissociating clusters.

Ultraviolet photodissociation dynamics of the n-propyl and i-propyl radicals.

Ultraviolet (UV) photodissociation dynamics of jet-cooled n-propyl (n-C3H7) radical via the 3s Rydberg state and i-propyl (i-C3H7) radical via the 3p Rydberg states are studied in the photolysis wavelength region of 230-260 nm using high-n Rydberg atom time-of-flight and resonance enhanced multiphoton ionization techniques. The H-atom photofragment yield spectra of the n-propyl and i-propyl radicals are broad and in good agreement with the UV absorption spectra. The H + propene product translational energy distributions, P(E(T))'s, of both n-propyl and i-propyl are bimodal, with a slow component peaking around 5-6 kcal/mol and a fast one peaking at ∼50 kcal/mol (n-propyl) and ∼45 kcal/mol (i-propyl). The fraction of the average translational energy in the total excess energy, 〈f(T)〉, is 0.3 for n-propyl and 0.2 for i-propyl, respectively. The H-atom product angular distributions of the slow components of n-propyl and i-propyl are isotropic, while that of the fast component of n-propyl is anisotropic (with an anisotropy parameter ∼0.8) and that of i-propyl is nearly isotropic. Site-selective loss of the β hydrogen atom is confirmed using the partially deuterated CH3CH2CD2 and CH3CDCH3 radicals. The bimodal translational energy and angular distributions indicate two dissociation pathways to the H + propene products in the n-propyl and i-propyl radicals: (i) a unimolecular dissociation pathway from the hot ground-state propyl after internal conversion from the 3s and 3p Rydberg states and (ii) a direct, prompt dissociation pathway coupling the Rydberg excited states to a repulsive part of the ground-state surface, presumably via a conical intersection.

Photodissociation of Methyl Iodide via Selected Vibrational Levels of the B̃ ((2)E3/2)6s Rydberg State.

We have determined the I (2)P3/2 and (2)P1/2 branching fractions following the photodissociation of methyl iodide (CH3I) via a number of vibronic bands associated with the B̃ ((2)E3/2)6s Rydberg state at excitation wavelengths between 201.2 and 192.7 nm. Vacuum ultraviolet light at 118.2 nm was used to ionize both the product iodine atoms and the methyl radical cofragments, and velocity map ion imaging was used to determine the product translational energy distributions and angular distributions. The known relative photoionization cross sections for I (2)P3/2 and (2)P1/2 at 118.2 nm were used to determine the corresponding branching fractions. The results extend our earlier work at 193 nm by Xu et al. (J. Chem. Phys. 2013, 139, 214310), and complement the closely related work of González et al. (J. Chem. Phys. 2011, 135, 021102). We find that for most of the excited vibronic levels of the B̃ state studied, the I (2)P3/2 branching ratio is small, but nonzero, and that this channel is associated with internally excited CH3 radicals. The results are discussed in relation to the recent theoretical results of Alekseyev et al. (J. Chem. Phys. 2011, 134, 044303).