Isomer-resolved unimolecular dynamics of the hydroperoxyalkyl intermediate (•QOOH) in cyclohexane oxidation.

The oxidation of cycloalkanes is important in the combustion of transportation fuels and in atmospheric secondary organic aerosol formation. A transient carbon-centered radical intermediate (•QOOH) in the oxidation of cyclohexane is identified through its infrared fingerprint and time- and energy-resolved unimolecular dissociation dynamics to hydroxyl (OH) radical and bicyclic ether products. Although the cyclohexyl ring structure leads to three nearly degenerate •QOOH isomers (ß-, γ-, and δ-QOOH), their transition state (TS) barriers to OH products are predicted to differ considerably. Selective characterization of the ß-QOOH isomer is achieved at excitation energies associated with the lowest TS barrier, resulting in rapid unimolecular decay to OH products that are detected. A benchmarking approach is employed for the calculation of high-accuracy stationary point energies, in particular TS barriers, for cyclohexane oxidation (C6H11O2), building on higher-level reference calculations for the smaller ethane oxidation (C2H5O2) system. The isomer-specific characterization of ß-QOOH is validated by comparison of experimental OH product appearance rates with computed statistical microcanonical rates, including significant heavy-atom tunneling, at energies in the vicinity of the TS barrier. Master-equation modeling is utilized to extend the results to thermal unimolecular decay rate constants at temperatures and pressures relevant to cyclohexane combustion.

Vibrational spectroscopy and dissociation dynamics of cyclohexyl hydroperoxide.

Organic hydroperoxides (ROOH) are ubiquitous in the atmospheric oxidation of volatile organic compounds (VOCs) as well as in low-temperature oxidation of hydrocarbon fuels. The present work focuses on a prototypical cyclic hydroperoxide, cyclohexyl hydroperoxide (CHHP). The overtone OH stretch (2νOH) spectrum of jet-cooled CHHP is recorded by IR multiphoton excitation with UV laser-induced fluorescence detection of the resulting OH products. A distinctive IR feature is observed at 7012.5 cm-1. Two conformers of CHHP are predicted to have similar stabilities (within 0.2 kcal mol-1) and overtone OH stretch transitions (2νOH), yet are separated by a significant interconversion barrier. The IR power dependence indicates that absorption of three or more IR photons is required for dissociation of CHHP to cyclohexoxy (RO) and OH radical products. Accompanying high-level single- and multi-reference electronic structure calculations quantitatively support the experimental results. Calculations are extended to a range of organic hydroperoxides to examine trends in bond dissociation energies associated with RO + OH formation and compared with prior theoretical results.

Roaming in the Unimolecular Decay of syn-Methyl-Substituted Criegee Intermediates.

Alkene ozonolysis generates transient carbonyl oxide species, known as Criegee intermediates, which are a significant nonphotolytic source of OH radicals in the troposphere. This study demonstrates that unimolecular decay of syn-methyl-substituted Criegee intermediates proceeds via 1,4 H atom transfer to vinyl hydroperoxides, resulting in OH fission to O-O products or, alternatively, OH roaming to hydroxycarbonyl products. Newly generated Criegee intermediates are shown to yield hydroxycarbonyls with sufficient internal excitation to dissociate via C-C fission to acyl and hydroxymethyl (CH2OH) radicals. The stabilized Criegee intermediates and unimolecular products are rapidly cooled in a pulsed supersonic expansion for photoionization detection with time-of-flight mass spectrometry. CH2OH products are identified by 2 + 1 resonance-enhanced multiphoton ionization via the 3pz Rydberg state upon unimolecular decay of CH3CHOO, (CH3)2COO, (CH3)(CH3CH2)COO, and (CH3)(CH2═CH)COO (methyl vinyl ketone oxide). The stabilized Criegee intermediates are separately detected using 10.5 eV photoionization. This study provides the first experimental evidence of roaming in the unimolecular decay of isoprene-derived methyl vinyl ketone oxide and extends earlier studies that reported stabilized hydroxycarbonyl products.

Bimolecular Reaction of Methyl-Ethyl-Substituted Criegee Intermediate with SO2.

Methyl-ethyl-substituted Criegee intermediate (MECI) is a four-carbon carbonyl oxide that is formed in the ozonolysis of some asymmetric alkenes. MECI is structurally similar to the isoprene-derived methyl vinyl ketone oxide (MVK-oxide) but lacks resonance stabilization, making it a promising candidate to help us unravel the effects of size, structure, and resonance stabilization that influence the reactivity of atmospherically important, highly functionalized Criegee intermediates. We present experimental and theoretical results from the first bimolecular study of MECI in its reaction with SO2, a reaction that shows significant sensitivity to the Criegee intermediate structure. Using multiplexed photoionization mass spectrometry, we obtain a rate coefficient of (1.3 ± 0.3) × 10-10 cm3 s-1 (95% confidence limits, 298 K, 10 Torr) and demonstrate the formation of SO3 under our experimental conditions. Through high-level theory, we explore the effect of Criegee intermediate structure on the minimum energy pathways for their reactions with SO2 and obtain modified Arrhenius fits to our predictions for the reaction of both syn and anti conformers of MECI with SO2 (ksyn = 4.42 × 1011 T-7.80exp(-1401/T) cm3 s-1 and kanti = 1.26 × 1011 T-7.55exp(-1397/T) cm3 s-1). Our experimental and theoretical rate coefficients (which are in reasonable agreement at 298 K) show that the reaction of MECI with SO2 is significantly faster than MVK-oxide + SO2, demonstrating the substantial effect of resonance stabilization on Criegee intermediate reactivity.

A five-carbon unsaturated Criegee intermediate: synthesis, spectroscopic identification, and theoretical study of 3-penten-2-one oxide.

Biogenic alkenes, such as isoprene and α-pinene, are the predominant source of volatile organic compounds (VOCs) emitted into the atmosphere. Atmospheric processing of alkenes via reaction with ozone leads to formation of zwitterionic reactive intermediates with a carbonyl oxide functional group, known as Criegee intermediates (CIs). CIs are known to exhibit a strong absorption (π* ← π) in the near ultraviolet and visible (UV-vis) region due to the carbonyl oxide moiety. This study focuses on the laboratory identification of a five-carbon CI with an unsaturated substituent, 3-penten-2-one oxide, which can be produced upon atmospheric ozonolysis of substituted isoprenes. 3-Penten-2-one oxide is generated in the laboratory by photolysis of a newly synthesized precursor, (Z)-2,4-diiodopent-2-ene, in the presence of oxygen. The electronic spectrum of 3-penten-2-one oxide was recorded by UV-vis induced depletion of the VUV photoionization signal on the parent m/z 100 mass channel using a time-of-flight mass spectrometer. The resultant electronic spectrum is broad and unstructured with peak absorption at ca. 375 nm. To complement the experimental findings, electronic structure calculations are performed at the CASPT2(12,10)/aug-cc-pVDZ level of theory. The experimental spectrum shows good agreement with the calculated electronic spectrum and vertical excitation energy obtained for the lowest energy conformer of 3-penten-2-one oxide. In addition, OH radical products resulting from unimolecular decay of energized 3-penten-2-oxide CIs are detected by UV laser-induced fluorescence. Finally, the experimental electronic spectrum is compared with that of a four-carbon, isoprene-derived CI, methyl vinyl ketone oxide, to understand the effects of an additional methyl group on the associated electronic properties.

OH Roaming and Beyond in the Unimolecular Decay of the Methyl-Ethyl-Substituted Criegee Intermediate: Observations and Predictions.

Alkene ozonolysis generates short-lived Criegee intermediates that are a significant source of hydroxyl (OH) radicals. This study demonstrates that roaming of the separating OH radicals can yield alternate hydroxycarbonyl products, thereby reducing the OH yield. Specifically, hydroxybutanone has been detected as a stable product arising from roaming in the unimolecular decay of the methyl-ethyl-substituted Criegee intermediate (MECI) under thermal flow cell conditions. The dynamical features of this novel multistage dissociation plus a roaming unimolecular decay process have also been examined with ab initio kinetics calculations. Experimentally, hydroxybutanone isomers are distinguished from the isomeric MECI by their higher ionization threshold and distinctive photoionization spectra. Moreover, the exponential rise of the hydroxybutanone kinetic time profile matches that for the unimolecular decay of MECI. A weaker methyl vinyl ketone (MVK) photoionization signal is also attributed to OH roaming. Complementary multireference electronic structure calculations have been utilized to map the unimolecular decay pathways for MECI, starting with 1,4 H atom transfer from a methyl or methylene group to the terminal oxygen, followed by roaming of the separating OH and butanonyl radicals in the long-range region of the potential. Roaming via reorientation and the addition of OH to the vinyl group of butanonyl is shown to yield hydroxybutanone, and subsequent C-O elongation and H-transfer can lead to MVK. A comprehensive theoretical kinetic analysis has been conducted to evaluate rate constants and branching yields (ca. 10-11%) for thermal unimolecular decay of MECI to conventional and roaming products under laboratory and atmospheric conditions, consistent with the estimated experimental yield (ca. 7%).

UV photodissociation dynamics of the acetone oxide Criegee intermediate: experiment and theory.

The photodissociation dynamics of the dimethyl-substituted acetone oxide Criegee intermediate [(CH3)2COO] is characterized following electronic excitation to the bright 1ππ* state, which leads to O (1D) + acetone [(CH3)2CO, S0] products. The UV action spectrum of (CH3)2COO recorded with O (1D) detection under jet-cooled conditions is broad, unstructured, and essentially unchanged from the corresponding electronic absorption spectrum obtained using a UV-induced depletion method. This indicates that UV excitation of (CH3)2COO leads predominantly to the O (1D) product channel. A higher energy O (3P) + (CH3)2CO (T1) product channel is not observed, although it is energetically accessible. In addition, complementary MS-CASPT2 trajectory surface-hopping (TSH) simulations indicate minimal population leading to the O (3P) channel and non-unity overall probability for dissociation (within 100 fs). Velocity map imaging of the O (1D) products is utilized to reveal the total kinetic energy release (TKER) distribution upon photodissociation of (CH3)2COO at various UV excitation energies. Simulation of the TKER distributions is performed using a hybrid model that combines an impulsive model with a statistical component, the latter reflecting the longer-lived (>100 fs) trajectories identified in the TSH calculations. The impulsive model accounts for vibrational activation of (CH3)2CO arising from geometrical changes between the Criegee intermediate and the carbonyl product, indicating the importance of CO stretch, CCO bend, and CC stretch along with activation of hindered rotation and rock of the methyl groups in the (CH3)2CO product. Detailed comparison is also made with the TKER distribution arising from photodissociation dynamics of CH2OO upon UV excitation.

Electronic Spectroscopy and Dissociation Dynamics of Vinyl-Substituted Criegee Intermediates: 2-Butenal Oxide and Comparison with Methyl Vinyl Ketone Oxide and Methacrolein Oxide Isomers.

The 2-butenal oxide Criegee intermediate [(CH3CH═CH)CHOO], an isomer of the four-carbon unsaturated Criegee intermediates derived from isoprene ozonolysis, is characterized on its first π* ← π electronic transition and by the resultant dissociation dynamics to O (1D) + 2-butenal [(CH3CH═CH)CHO] products. The electronic spectrum of 2-butenal oxide under jet-cooled conditions is observed to be broad and unstructured with peak absorption at 373 nm, spanning to half maxima at 320 and 420 nm, and in good accord with the computed vertical excitation energies and absorption spectra obtained for its lowest energy conformers. The distribution of total kinetic energy released to products is ascertained through velocity map imaging of the O (1D) products. About half of the available energy, deduced from the theoretically computed asymptotic energy, is accommodated as internal excitation of the 2-butenal fragment. A reduced impulsive model is introduced to interpret the photodissociation dynamics, which accounts for the geometric changes between 2-butenal oxide and the 2-butenal fragment, and vibrational activation of associated modes in the 2-butenal product. Application of the reduced impulsive model to the photodissociation of isomeric methyl vinyl ketone oxide reveals greater internal activation of the methyl vinyl ketone product arising from methyl internal rotation and rock, which is distinctly different from the dissociation dynamics of 2-butenal oxide or methacrolein oxide.

Electronic Absorption Spectroscopy and Photochemistry of Criegee Intermediates.

Interest in Criegee intermediates (CIs), often termed carbonyl oxides, and their role in tropospheric chemistry has grown massively since the demonstration of laboratory-based routes to their formation and characterization in the gas phase. This article reviews current knowledge regarding the electronic spectroscopy of atmospherically relevant CIs like CH2 OO, CH3 CHOO, (CH3 )2 COO and larger CIs like methyl vinyl ketone oxide and methacrolein oxide that are formed in the ozonolysis of isoprene, and of selected conjugated carbene-derived CIs of interest in the synthetic chemistry community. Of the aforementioned atmospherically relevant CIs, all except CH2 OO and (CH3 )2 COO exist in different conformers which, under tropospheric conditions, can display strikingly different thermal loss rates via unimolecular and bimolecular processes. Calculated photolysis rates based on their absorption properties suggest that solar photolysis will rarely be a significant contributor to the total loss rate for any CI under tropospheric conditions. Nonetheless, there is ever-growing interest in the absorption cross sections and primary photochemistry of CIs following excitation to the strongly absorbing 1 ππ* state, and how this varies with CI, with conformer and with excitation wavelength. The later part of this review surveys the photochemical data reported to date, including a range of studies that demonstrate prompt photo-induced fission of the terminal O-O bond, and speculates about possible alternate decay processes that could occur following non-adiabatic coupling to, and dissociation from, highly internally excited levels of the electronic ground state of a CI.

Substituent Effects on the Electronic Spectroscopy of Four-Carbon Criegee Intermediates.

Atmospheric ozonolysis of biogenic and anthropogenic alkenes generates zwitterionic carbonyl oxide intermediates (R1R2C═O+O-), known as Criegee intermediates, with different structural motifs and conformations. This study reports a systematic laboratory study of substituent effects on the electronic spectroscopy of four-carbon Criegee intermediates (CIs) with methyl-ethyl (MECI) and isopropyl (IPCI) groups, which are isomers produced in ozonolysis of asymmetric branched alkenes. The four-carbon CIs are separately generated by an alternative synthetic route, and spectroscopically characterized on the strong π* ← π transition associated with the carbonyl oxide group in a pulsed supersonic expansion with VUV photoionization at 118 nm and UV-induced depletion of the m/z 88 signal. The resultant broad and unstructured UV spectral features for MECI and IPCI are peaked at ca. 320 and 330 nm, respectively, with large absorption cross-sections of ca. 10-17 cm2. Comparisons are made with the four-carbon CIs formed in isoprene ozonolysis, methyl vinyl ketone oxide (MVK-oxide) and methacrolein oxide (MACR-oxide), which have the same backbone connectivity as MECI and IPCI but have extended conjugation across the vinyl and carbonyl groups. A remarkable 50 nm shift of the peak absorption to longer wavelength is observed for MVK-oxide and MACR-oxide compared to MECI and IPCI, respectively. Vertical excitation energies computed theoretically agree well with the experimental findings, confirming that the spectral shifts are caused by the extended π conjugation in the isoprene-derived Criegee intermediates.

Energy-resolved and time-dependent unimolecular dissociation of hydroperoxyalkyl radicals (˙QOOH).

Hydroperoxyalkyl radicals (˙QOOH) are transient intermediates in the atmospheric oxidation of volatile organic compounds and combustion of hydrocarbon fuels in low temperature (<1000 K) environments. The carbon-centered ˙QOOH radicals are a critical juncture in the oxidation mechanism, but have generally eluded direct experimental observation of their structure, stability, and dissociation dynamics. Recently, this laboratory demonstrated that a prototypical ˙QOOH radical [˙CH2(CH3)2COOH] can be synthesized by an alternative route, stabilized in a pulsed supersonic expansion, and characterized by its infrared (IR) spectroscopic signature and unimolecular dissociation rate to OH radical and cyclic ether products. The present study focuses on a partially deuterated ˙QOOD analog ˙CH2(CH3)2COOD, generated in the laboratory by H-atom abstraction from partially deuterated tert-butyl hydroperoxide, (CH3)3COOD. IR spectral features associated with jet-cooled and isolated ˙QOOD radicals are observed in the vicinity of the transition state (TS) barrier leading to OD radical and cyclic ether products. The overtone OD stretch (2νOD) of ˙QOOD is identified by IR action spectroscopy with UV laser-induced fluorescence detection of OD products. Direct time-domain measurement of the unimolecular dissociation rate for ˙QOOD (2νOD) extends prior rate measurements for ˙QOOH. Partial deuteration results in a small increase in the TS barrier predicted by high level electronic structure calculations due to changes in zero-point energies; the imaginary frequency is unchanged. Comparison of the unimolecular decay rates obtained experimentally with those predicted theoretically for both ˙QOOH and ˙QOOD confirm that unimolecular decay is enhanced by heavy-atom tunneling involving simultaneous O-O bond elongation and C-C-O angle contraction along the reaction pathway.

Rapid Allylic 1,6 H-Atom Transfer in an Unsaturated Criegee Intermediate.

A novel allylic 1,6 hydrogen-atom-transfer mechanism is established through infrared activation of the 2-butenal oxide Criegee intermediate, resulting in very rapid unimolecular decay to hydroxyl (OH) radical products. A new precursor, Z/E-1,3-diiodobut-1-ene, is synthesized and photolyzed in the presence of oxygen to generate a new four-carbon Criegee intermediate with extended conjugation across the vinyl and carbonyl oxide groups that facilitates rapid allylic 1,6 H-atom transfer. A low-energy reaction pathway involving isomerization of 2-butenal oxide from a lower-energy (tZZ) conformer to a higher-energy (cZZ) conformer followed by 1,6 hydrogen transfer via a seven-membered ring transition state is predicted theoretically and shown experimentally to yield OH products. The low-lying (tZZ) conformer of 2-butenal oxide is identified based on computed anharmonic frequencies and intensities of its conformers. Experimental IR action spectra recorded in the fundamental CH stretch region with OH product detection by UV laser-induced fluorescence reveal a distinctive IR transition of the low-lying (tZZ) conformer at 2996 cm-1 that results in rapid unimolecular decay to OH products. Statistical RRKM calculations involving a combination of conformational isomerization and unimolecular decay via 1,6 H-transfer yield an effective decay rate keff(E) on the order of 108 s-1 at ca. 3000 cm-1 in good accord with the experiment. Unimolecular decay proceeds with significant enhancement due to quantum mechanical tunneling. A rapid thermal decay rate of ca. 106 s-1 is predicted by master-equation modeling of 2-butenal oxide at 298 K, 1 bar. This novel unimolecular decay pathway is expected to increase the nonphotolytic production of OH radicals upon alkene ozonolysis in the troposphere.

Infrared spectroscopic signature of a hydroperoxyalkyl radical (•QOOH).

Infrared (IR) action spectroscopy is utilized to characterize a prototypical carbon-centered hydroperoxyalkyl radical (•QOOH) transiently formed in the oxidation of volatile organic compounds. The •QOOH radical formed in isobutane oxidation, 2-hydroperoxy-2-methylprop-1-yl, •CH2(CH3)2COOH, is generated in the laboratory by H-atom abstraction from tert-butyl hydroperoxide (TBHP). IR spectral features of jet-cooled and stabilized •QOOH radicals are observed from 2950 to 7050 cm-1 at energies that lie below and above the transition state barrier leading to OH radical and cyclic ether products. The observed •QOOH features include overtone OH and CH stretch transitions, combination bands involving OH or CH stretch and a lower frequency mode, and fundamental OH and CH stretch transitions. Most features arise from a single vibrational transition with band contours well simulated at a rotational temperature of 10 K. In each case, the OH products resulting from unimolecular decay of vibrationally activated •QOOH are detected by UV laser-induced fluorescence. Assignments of observed •QOOH IR transitions are guided by anharmonic frequencies computed using second order vibrational perturbation theory, a 2 + 1 model that focuses on the coupling of the OH stretch with two low-frequency torsions, as well as recently predicted statistical •QOOH unimolecular decay rates that include heavy-atom tunneling. Most of the observed vibrational transitions of •QOOH are readily distinguished from those of the TBHP precursor. The distinctive IR transitions of •QOOH, including the strong fundamental OH stretch, provide a general means for detection of •QOOH under controlled laboratory and real-world conditions.

Dramatic Conformer-Dependent Reactivity of the Acetaldehyde Oxide Criegee Intermediate with Dimethylamine Via a 1,2-Insertion Mechanism.

The reactivity of carbonyl oxides has previously been shown to exhibit strong conformer and substituent dependencies. Through a combination of synchrotron-multiplexed photoionization mass spectrometry experiments (298 K and 4 Torr) and high-level theory [CCSD(T)-F12/cc-pVTZ-F12//B2PLYP-D3/cc-pVTZ with an added CCSDT(Q) correction], we explore the conformer dependence of the reaction of acetaldehyde oxide (CH3CHOO) with dimethylamine (DMA). The experimental data support the theoretically predicted 1,2-insertion mechanism and the formation of an amine-functionalized hydroperoxide reaction product. Tunable-vacuum ultraviolet photoionization probing of anti- or anti- + syn-CH3CHOO reveals a strong conformer dependence of the title reaction. The rate coefficient of DMA with anti-CH3CHOO is predicted to exceed that for the reaction with syn-CH3CHOO by a factor of ∼34,000, which is attributed to submerged barrier (syn) versus barrierless (anti) mechanisms for energetically downhill reactions.

Photodissociation dynamics of methyl vinyl ketone oxide: A four-carbon unsaturated Criegee intermediate from isoprene ozonolysis.

The electronic spectrum of methyl vinyl ketone oxide (MVK-oxide), a four-carbon Criegee intermediate derived from isoprene ozonolysis, is examined on its second π* ← π transition, involving primarily the vinyl group, at UV wavelengths (λ) below 300 nm. A broad and unstructured spectrum is obtained by a UV-induced ground state depletion method with photoionization detection on the parent mass (m/z 86). Electronic excitation of MVK-oxide results in dissociation to O (1D) products that are characterized using velocity map imaging. Electronic excitation of MVK-oxide on the first π* ← π transition associated primarily with the carbonyl oxide group at λ > 300 nm results in a prompt dissociation and yields broad total kinetic energy release (TKER) and anisotropic angular distributions for the O (1D) + methyl vinyl ketone products. By contrast, electronic excitation at λ ≤ 300 nm results in bimodal TKER and angular distributions, indicating two distinct dissociation pathways to O (1D) products. One pathway is analogous to that at λ > 300 nm, while the second pathway results in very low TKER and isotropic angular distributions indicative of internal conversion to the ground electronic state and statistical unimolecular dissociation.

Watching a hydroperoxyalkyl radical (•QOOH) dissociate.

A prototypical hydroperoxyalkyl radical (•QOOH) intermediate, transiently formed in the oxidation of volatile organic compounds, was directly observed through its infrared fingerprint and energy-dependent unimolecular decay to hydroxyl radical and cyclic ether products. Direct time-domain measurements of •QOOH unimolecular dissociation rates over a wide range of energies were found to be in accord with those predicted theoretically using state-of-the-art electronic structure characterizations of the transition state barrier region. Unimolecular decay was enhanced by substantial heavy-atom tunneling involving O-O elongation and C-C-O angle contraction along the reaction pathway. Master equation modeling yielded a fully a priori prediction of the pressure-dependent thermal unimolecular dissociation rates for the •QOOH intermediate-again increased by heavy-atom tunneling-which are required for global models of atmospheric and combustion chemistry.

Photodissociation Dynamics of CH2OO on Multiple Potential Energy Surfaces: Experiment and Theory.

UV excitation of the CH2OO Criegee intermediate across most of the broad span of the (B 1A')-(X 1A') spectrum results in prompt dissociation to two energetically accessible asymptotes: O (1D) + H2CO (X 1A1) and O (3P) + H2CO (a 3A''). Dissociation proceeds on multiple singlet potential energy surfaces that are coupled by two regions of conical intersection (CoIn). Velocity map imaging (VMI) studies reveal a bimodal total kinetic energy release (TKER) distribution for the O (1D) + H2CO (X 1A1) products with the major and minor components accounting for ca. 40% and ca. 20% on average of the available energy (Eavl), respectively. The unexpected low TKER component corresponds to highly internally excited H2CO (X 1A1) products accommodating ca. 80% of Eavl. Full dimensional trajectory calculations suggest that the bimodal TKER distribution of the O (1D) + H2CO (X 1A1) products originates from two different dynamical pathways: a primary pathway (69%) evolving through one CoIn region to products and a smaller component (20%) sampling both CoIn regions enroute to products. Those that access both CoIn regions likely give rise to the more highly internally excited H2CO (X 1A1) products. The remaining trajectories (11%) dissociate to O (3P) + H2CO (a 3A'') products after traversing through both CoIn regions. The complementary experimental and theoretical investigation provides insight on the photodissociation of CH2OO via multiple dissociation pathways through two regions of CoIn that control the branching and energy distributions of products.