Elimination Channel Research Articles

Theoretical study on the corrosion of thorium nuclear fuel by water: The effect of two-state reaction mechanism

The title reaction was investigated by DFT calculations. This process realizes in two steps. In the first step, singlet and triplet potential energy surfaces cross each other. We found that two-state reaction (TSR) mechanism is involved, enabling singlet product to be favored energetically. Then, ThO continues to react with H2O to form ThO2. Only the activation energy of singlet addition–elimination channel matches well with experimental reports. This work illustrates the occurrence of TSR mechanism in the corrosion of actinide nuclear fuel and further suggests a potential yet crucial impact on related fields. It deserves particular attention.

Dimethylcarbene versus Direct Propene Formation in Dimethylketene Photodissociation.

Highly reactive carbenes are usually produced by photolysis of ketenes, diazoalkanes, or diazirines. Sequential kinetic pathways for deactivation of nascent carbenes usually involve bimolecular reactions in competition with isomerization producing stable products such as alkenes. However, the direct photolytic production of stable products, effectively bypassing formation of free carbenes, has been postulated for over 50 years but remains very poorly understood. Often termed "rearrangement in the excited state" (RIES), examples include 1,2-hydrogen migration within photoexcited carbene precursors yielding alkenes and the Wolff rearrangement in photogenerated carbonyl-substituted carbenes producing ketenes. In this study, the two competing CO elimination channels from photoexcited gaseous dimethylketene, producing dimethylcarbene and propene, were studied as a function of electronic excitation energy, under collision-free conditions, by using photofragment translational energy spectroscopy with vacuum ultraviolet photoionization of the products. A significant fraction of the dimethylcarbene → propene isomerization exothermicity (∼300 kJ/mol) was released as propene + CO translational energy, indicating that propene is formed prior to or concurrent with CO elimination. An increase in the propene yield with increasing excitation energy suggests that the effective potential energy barrier for this channel lies ∼24 kJ/mol above the energetic threshold for dimethylcarbene formation via C═C bond fission. Possible mechanisms for direct propene elimination are discussed in light of the observed energy dependence for the competing pathways.

Theoretical Study of the Mechanism and Kinetics of the Oxidation of Cyclopenta[a]Naphthalenyl Radical C13H9 with Molecular Oxygen.

Electronic structure/Rice-Ramsperger-Kassel-Marcus Master equation calculations were applied to unravel the oxidation mechanism and kinetics of the cyclopenta[a]naphthalenyl radical with molecular oxygen. The reaction has been shown to proceed through the addition of O2 in the ortho-position in the five-membered ring of C13H9. At low temperatures, the reaction yields a collisionally stabilized C13H9O2 complex, which rapidly decomposes back to the reactants. In the high-temperature regime, above 800, 900, 1125, and 1375 K at pressures of 0.03, 1, 10, and 100 atm, respectively, the reaction forms bimolecular products including 3H-/1H-cyclopenta[a]naphthalen-3-one + OH as the prevailing product together with 1-ethanol-substituted 2-naphthyl radical + CO and 3H-benzo[f]chromen-3-one + H as minor ones, with the branching ratio of the OH elimination channel growing with temperature and the rate constants for the individual bimolecular channels being independent of pressure. The calculated rate constants and product branching for cyclopenta[a]naphthalenyl + O2 closely agree with those reported earlier for the indenyl + O2 reaction and are recommended for the combustion kinetic models for the oxidation reactions of five-membered rings on free edges of larger polycyclic aromatic hydrocarbon molecules. The results also confirm that the oxidation of a π radical located on a five-membered ring with molecular oxygen is very slow.

Dynamical investigations of the O(3P) + H2O reaction at high collision energies on an accurate full-dimensional potential energy surface

The reaction between O(3P) and H2O is of significance in combustion, atmospheric and interstellar chemistry. Using an accurate full-dimensional potential energy surface (PES) for the lowest triplet state of the H2O2 system, the quasi-classical trajectory method is employed to run dynamical simulations between O(3P) and H2O at hyperthermal collision energies of 50–100 kcal mol−1, which may access the hydrogen abstraction channel OH + OH, the hydrogen elimination channel H + HO2 and the oxygen exchange channel O + H2O. The integral cross sections (ICSs), differential cross sections, product energy/state distributions and reaction mechanisms are studied for the channels leading to products OH + OH and H + HO2.

Thermal Decomposition of 2-Methyltetrahydrofuran behind Reflected Shock Waves over the Temperature Range of 1179–1361 K

The thermal unimolecular decomposition of 2-methyltetrahydrofuran (2-MTHF) was studied behind reflected shock waves in a single-pulse shock tube over the temperature range of 1179-1361 K and pressure range of 9-17 atm. Methane, ethylene, ethane, 1,3-butadiene, propylene, acetaldehyde, and acetylene were identified as products in the decomposition of 2-MTHF. A reaction scheme was proposed to explain the mechanism for the observed products. The experimentally determined rate coefficients were best fit to an Arrhenius expression for the overall decomposition and is represented as ktotalexp(1179-1361 K) = (3.23 ± 0.59) × 1011 s-1 exp(-51.3 ± 1.4 kcal mol-1/RT). Quantum chemistry methods were used to calculate the energetics and kinetics of various possible unimolecular dissociation pathways involved in the thermal decomposition of 2-MTHF. The initial decomposition of 2-MTHF occurs predominantly via ring-methyl (C-CH3) single bond fission, leading to the formation of tetrahydrofuran (C4H7O) radical, and methyl radical was found to be the major reaction compared to all the possible initial bond fission, ring opening, and molecular elimination channels. The temperature-dependent rate coefficients for the unimolecular dissociation of 2-MTHF were calculated using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory in combination with the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of electronic structure calculations over the temperature range of 800-1500 K. The computed high-pressure limiting rate coefficients for the initial decomposition of 2-MTHF through C-CH3 single bond fission channel were found to be ∼2 times higher in the temperatures between 800 and 900 K, and above this temperature, they agree well with the values reported in the literature.

Dissociative Ionization of Molecular CF2Br2 under 800 and 400 nm Intense Femtosecond Laser Fields

The interaction between the CF2Br2 molecule and 800/400 nm intense femtosecond laser fields is investigated by direct current (dc) sliced velocity mapping imaging implementation. By analyzing the kinetic energy release distribution and angular distribution of fragment ions, the dissociation channels along C-Br bond cleavage have been determined. The isotropic structure of the angular distribution for CF2Br+ ions is attributed to the coupling between the excited states. Additionally, a unique elimination channel of CF2Br2+ → CF2 + Br2+ has been observed and identified in the case of 400 nm laser field, in which the two C-Br bonds break asynchronously.

Photodissociation of CH2BrCHBrC(O)Cl at 248 nm: probing Br2 as the primary fragment using cavity ring-down spectroscopy.

The photodissociation of 2,3-dibromopropionyl chloride (CH2BrCHBrC(O)Cl, 2,3-DBPC) at 248 nm was carried out to study Br2 as the primary molecular product in the B3Π+0u ← X1Σ+g transition using cavity ring-down absorption spectroscopy. The rotational spectra (v'' = 0-2) were acquired and assigned with the aid of spectral simulation. It is verified that the obtained Br2 fragment is attributed to the one-photon dissociation of 2,3-DBPC and is free from contributions of secondary reactions. The vibrational ratio of the Br2 population of v(0):v(1):v(2) is equal to 1:(0.58 ± 0.12):(0.23 ± 0.09), corresponding to the Boltzmann vibrational temperature of 623 ± 38 K. The quantum yield of Br2 eliminated from 2,3-DBPC is estimated to be 0.09 ± 0.04. The dissociation pathways of 2,3-DBPC and its potential energy surfaces were calculated using density functional theory. By employing the CCSD(T)//M062X/6-31+g(d,p) level of theory, transition state barriers and corresponding reaction energies were calculated for the Br, Cl, Br2, BrCl, HBr and HCl elimination channels. The unimolecular rate constant for Br2 elimination was determined to be 2.09 × 105 s-1 using Rice-Ramsperger-Kassel-Marcus (RRKM) theory, thus explaining the small quantum yield of the Br2 channel.

Decomposition of 2,6‐diamino‐3,5‐dinitropyrazine‐1‐oxide (LLM‐105): From thermodynamics to kinetics

AbstractThe mechanism of initial decomposition of energetic compound is crucial to understand the heat release efficiency, impact sensitivity, toxic emission, and so on. In the present study, we progressively explored the thermodynamic and kinetic features of the decomposition of LLM‐105, or 2,6‐diamino‐3,5‐dinitropyrazine‐1‐oxide, a kind of nitro compound in energetic materials using theoretical calculations. The bond dissociation energies (BDEs), bond orders, and the decomposition pathways were investigated by high‐level quantum chemical calculations, and the temperature‐ and pressure‐dependent rate coefficients were computed by Rice‐Ramsperger‐Kassel‐Marcus (RRKM)/master equation simulations. Although thermodynamic properties, for example, BDEs and bond orders, provide preliminary estimates on a possible decomposition mechanism including trigger bonds with relatively low computational costs, kinetic studies are necessary to determine all reaction pathways and competition relationships among various pathways. The potential energy surface at the theoretical level of DLPNO‐CCSD(T)/CBS//M06‐2X‐D3/6‐311++G(d,p) reveals the complicated decomposition mechanism including the bottlenecks of all channels. The computed rate coefficients showthat the reaction channels yielding NO2 will dominate the initial decomposition at high temperature (>1000 K), while the NO elimination channels play a controlling role at low temperature (<800 K).

A theoretical kinetics study on low-temperature oxidation of n-C4H9 radicals

The low-temperature oxidation mechanism of n‑butyl radicals (n-C4H9) has been investigated by high level quantum chemical calculations coupled with the Rice–Ramsperger–Kassel–Marcus/Master Equation (RRKM/ME) theory. The potential energy surfaces (PES) were explored at the QCISD(T)/CBS//B3LYP/6-311++G(d,p) level. The temperature- and pressure-dependent rate constants were computed and fitted in modified Arrhenius parameters. The major reaction channels were discussed to more deeply understand the competing relationships between chain branching, chain propagation and termination reactions. The results show that the 1,5 H-shift reaction is more competitive than the 1,6 H-shift and 1,4 H-shift for isomerization reactions of n‑butyl peroxy radicals, and the concerted HO2 elimination channel to form butene becomes more important at high temperatures. Furthermore, based on our calculations, a revised kinetic model was developed to describe n-butane oxidation. Good consistency between model predictions and experimental data was shown. This study enhances our understanding of the combustion mechanism of n-butane and can be used as a reliable reference for mechanistic understanding of larger alkanes.

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.

Theoretical and experimental studies on concerted elimination of 1, 2‐bromochloroethane monocation to C2H4+ and BrCl

AbstractAb initio calculations for the concerted elimination of 1, 2‐bromochloroethane monocation (1,2‐C2H4BrCl+) to C2H4+ and BrCl are performed using the Minnesota density functional M06‐2X and the def2‐TZVP basis set. Ab initio calculations are also carried out for the concerted elimination of 1,2‐C2H4BrCl+ to C2H4 and BrCl+ because the positive charge can be assigned to either moiety in the dissociative ionization process of 1,2‐C2H4BrCl+. Our results demonstrate that the concerted elimination channel of 1,2‐C2H4BrCl+ to C2H4+ and BrCl is preferred and that 1,2‐C2H4BrCl+ surpasses two energy barriers and then separates into C2H4+ + BrCl through an asynchronous concerted process. Experimentally, we confirm that this elimination channel is from the dissociative ionization process of 1,2‐C2H4BrCl+ by using dc‐slice imaging technique. The time‐of‐flight mass spectra of 1,2‐bromochloroethane induced by femtosecond laser pulses show that C2H4+ occurs at a laser intensity of 6.0 × 1013 W/cm2, and BrCl+ occurs at a higher laser intensity than C2H4+. This finding is consistent with the theoretical result that the appearance energy of C2H4+ is lower than that of BrCl+. As such, the low‐velocity component of BrCl+ is absent from our sliced images.

Observation of the Carbon Elimination Channel in Vacuum Ultraviolet Photodissociation of OCS.

The textbook mechanism for OCS photodissociation mainly involves the CO + S or CS + O product channel via a single bond fission. However, a third dissociation channel concerning the cleavage of both C-S and C-O bonds yielding SO + C products, though thermodynamically allowed, has never been verified experimentally to date. By using a tunable vacuum ultraviolet laser light and time-sliced velocity map ion imaging technique, we have clearly observed the SO(X3Σ-) + C(3PJ=0) products as the vacuum ultraviolet laser photon energy gradually exceeds its thermodynamic threshold. The corresponding SO(X3Σ-) coproducts are highly vibrationally excited and show varying angular distributions from isotropic to anisotropic as the excitation photon energy increases. Theoretical analysis suggests that a fast nonadiabatic pathway plays a dominant role in the formation of the anisotropic SO products. That isotropic products arise as the excitation photon energies approach the thermodynamic threshold can be reasonably explained by the "roaming mechanism".

High-Temperature Unimolecular Decomposition of Diethyl Ether: Shock-Tube and Theory Studies

The unimolecular decomposition of diethyl ether (DEE; C2H5OC2H5) is considered to be initiated via a molecular elimination and a C-O and a C-C bond fission step: C2H5OC2H5 → C2H4 + C2H5OH (1), C2H5OC2H5 → C2H5 + C2H5O (2), and C2H5OC2H5 → CH3 + C2H5OCH2 (3). In this work, two shock-tube facilities were used to investigate these reactions via (a) time-resolved H-atom concentration measurements by H-ARAS (atomic resonance absorption spectrometry), (b) time-resolved DEE-concentration measurements by high repetition-rate time-of-flight mass spectrometry (HRR-TOF-MS), and (c) product-composition measurements via gas chromatography/MS (GC/MS) after quenching the test gas. The experiments were conducted at temperatures ranging from 1054 to 1505 K and at pressures between 1.2 and 2.5 bar. Initial DEE mole fractions between 0.4 and 9300 ppm were used to perform the kinetics experiments by H-ARAS (0.4 ppm), GC/MS (200-500 ppm), and HRR-TOF-MS (7850-9300 ppm). The rate constants, ktotal (ktotal = k1 + k2 + k3) derived from the GC/MS and HRR-TOF-MS experiments agree well with each other and can be described by the Arrhenius expression, ktotal(1054-1467 K; 1.3-2.5 bar) = 1012.81±0.22 exp(-240.27 ± 5.11 kJ mol-1/RT) s-1. From the H-ARAS experiments, overall rate constants for the bond fission channels, k2+3 = k2 + k3 have been extracted. The k2+3 data can be well described by the Arrhenius equation, k2+3(1299-1505 K; 1.3-2.5 bar) = 1014.43±0.33 exp(-283.27 ± 8.78 kJ mol-1/RT) s-1. A master-equation analysis was performed using CCSD(T)/aug-cc-pvtz//B3LYP/aug-cc-pvtz and CASPT2/aug-cc-pvtz//B3LYP/aug-cc-pvtz molecular properties and energies for the three primary thermal decomposition processes in DEE. The derived experimental data is very well reproduced by the simulations with the mechanism of this work. With regard to the branching ratios between bond fissions and elimination channels, uncertainties remain.

An Experimental and Theoretical Investigation of 1-Butanol Pyrolysis.

Bioalcohols are a promising family of biofuels. Among them, 1-butanol has a strong potential as a substitute for petrol. In this manuscript, we report on a theoretical and experimental characterization of 1-butanol thermal decomposition, a very important process in the 1-butanol combustion at high temperatures. Advantage has been taken of a flash pyrolysis experimental set-up with mass spectrometric detection, in which the brief residence time of the pyrolyzing mixture inside a short, resistively heated SiC tube allows the identification of the primary products of the decomposing species, limiting secondary processes. Dedicated electronic structure calculations of the relevant potential energy surface have also been performed and RRKM estimates of the rate coefficients and product branching ratios up to 2,000 K are provided. Both electronic structure and RRKM calculations are in line with previous determinations. According to the present study, the H2O elimination channel leading to 1-butene is more important than previously believed. In addition to that, we provide experimental evidence that butanal formation by H2 elimination is not a primary decomposition route. Finally, we have experimental evidence of a small yield of the CH3 elimination channel.

Identification of Critical Source Areas (CSAs) and Evaluation of Best Management Practices (BMPs) in Controlling Eutrophication in the Dez River Basin

Best Management Practices (BMPs) are commonly used to control pollution in the river basins. Prioritization of BMPs helps improve the efficiency and effectiveness of pollution reduction, especially in Critical Source Areas (CSAs) that produce the highest pollution loads. Recently, the Dez River in Khuzestan, Iran, has become highly eutrophic from the overuse of fertilizers and pesticides. In this basin, dry and irrigated farming produce 77.34% and 6.3% of the Total Nitrogen (TN) load, and 83.56% and 4.3% of the Total Phosphorus (TP) load, respectively. In addition, residential, pasture, and forest land uses together account for 16.36% of the TN and 12.14% of the TP load in this area. The Soil and Water Assessment Tool (SWAT) was implemented to model the Dez River basin and evaluate the applicability of several BMPs, including point source elimination, filter strips, livestock grazing, and river channel management, in reducing the entry of pollution loads to the river. Sensitivity analysis and calibration/validation of the model was performed using the SUFI-2 algorithm in the SWAT Calibration Uncertainties Program (SWAT-CUP). The CSAs were identified using individual (sediment, TN, TP) and combined indices, based on the amount of pollution produced. Among the BMPs implemented, the 10 m filter strip was most effective in reducing TN load (42.61%), and TP load (39.57%).

Photodissociation of CH2BrI using cavity ring-down spectroscopy: in search of a BrI elimination channel.

Photodissociation of CH2BrI was investigated in search of unimolecular elimination of BrI via a primary channel using cavity ring-down absorption spectroscopy (CRDS) at 248 nm. The BrI spectra were acquired involving the first three ground vibrational levels corresponding to A3Π1 ← X1Σ+ transition. With the aid of spectral simulation, the BrI rotational lines were assigned. The nascent vibrational populations for v'' = 0, 1, and 2 levels are obtained with a population ratio of 1 : (0.58 ± 0.10) : (0.34 ± 0.05), corresponding to a Boltzmann-like vibrational temperature of 713 ± 49 K. The quantum yield of the ground state BrI elimination reaction is determined to be 0.044 ± 0.014. The CCSD(T)//B3LYP/MIDI! method was employed to explore the potential energy surface for the unimolecular elimination of BrI from CH2BrI.

Resonance enhanced multiphoton ionisation (REMPI) detection of Cl(2Pj) atom in the photodissociation of halogenated pyrimidines at 235 nm: role of triplet states

ABSTRACTThe dynamics of chlorine atom (2Pj) formation in the photodissociation process of halogen substituted pyrimidines, namely, 2,4,6-trichloropyrimidine and 5-chloro-2,4,6-trifluoropyrimidine have been studied around 235 nm using Resonance Enhanced Multiphoton Ionisation Time-of-Flight Mass Spectrometry technique. For the chlorine atom dissociation channel, we have determined the translational energy distribution, the recoil anisotropy parameter, β, and the spin–orbit branching ratio. In both the molecules, the TOF profiles for Cl (2P3/2) and Cl* (2P1/2) are found to be independent of laser polarisation suggesting a zero value for β, within the experimental uncertainties. For 2,4,6-trichloropyrimidine, the average translational energies for Cl and Cl* elimination channels are determined to be 6.0 ± 1.2 and 7.0 ± 1.5 kcal/mol, respectively. Similarly, for 5-chloro-2,4,6-trifluoropyrimidine, the average translational energies for Cl and Cl* elimination channels are determined to be 6.5 ± 1.2 and 7.9 ± 1.6 kcal/mol, respectively. Computational calculations are performed to generate the potential energy curves along the dissociating C-Cl bond using equation of motion coupled cluster with single and double excitations (EOM-CCSD) method. Computational studies suggest the role of triplet states in the photodissociation process forming the Cl atom.

Structural Properties of Gas Phase Molybdenum Sulfide Clusters [Mo3S13]2-, [HMo3S13]-, and [H3Mo3S13]+ as Model Systems of a Promising Hydrogen Evolution Catalyst.

Amorphous molybdenum sulfide (MoSx) is a potent catalyst for the hydrogen evolution reaction (HER). Since mechanistic investigations on amorphous solids are particularly difficult, we use a bottom-up approach and study the [Mo3S13]2– nanocluster and its protonated forms. The mass selected pure [Mo3S13]2– as well as singly and triply protonated [HMo3S13]− and [H3Mo3S13]+ ions, respectively, were investigated by a combination of collision induced dissociation (CID) experiments and quantum chemical calculations. A rich variety of HxSy elimination channels was observed, giving insight into the structural flexibility of the clusters. In particular, it was calculated that the observed clusters tend to keep the Mo3 ring structure found in the bulk and that protons adsorb primarily on terminal disulfide units of the cluster. Mo–H bonds are formed only for quasi-linear species with Mo centers featuring empty coordination sites. Protonation leads to increased cluster stability against CID. The rich variety of CID dissociation products for the triply protonated [H3Mo3S13]+ ion, however, suggests that it has a large degree of structural flexibility, with roaming H/SH moieties, which could be a key feature of MoSx to facilitate HER catalysis via a Volmer−Heyrovsky mechanism.

Excited states dissociation dynamics of indole-x-carboxaldehyde (x = 4, 5, 6, 7): Theoretical and experimental study

Excited state dissociation dynamics of indole-x-carboxaldehyde (x = 4, 5, 6, 7) has been investigated by ab initio calculations and photodissociation in a molecular beam at 193 nm using multimass ion imaging techniques. It was found that dissociation processes strongly depends on the position of HCO functional group. Fast component of H atom elimination in the photofragment translational energy distribution suggesting that dissociation occurs in a repulsive excited state, is quite intense for all isomers excluding indole-7-carboxaldehyde, which H atom elimination channel is almost quenched. However, this is the only isomer having intramolecular hydrogen bonding between NH and HCO groups. Ab initio calculations of the excited states potential energy surfaces (PES) demonstrate that the additional low lying conical intersection between S1 and S0 states is expected for the isomer with intramolecular hydrogen bond, which provides fast radiationless relaxation into the S0 state without loss of the H atom.

Vacuum ultraviolet photodissociation dynamics of N2O via the C1Π state: The N(2Dj=5/2, 3/2) + NO(X2Π) product channels.

We study the vacuum ultraviolet photodissociation dynamics of N2O via the C1Π state by using the time-sliced velocity map ion imaging technique. Images of N(2Dj=5/2, 3/2) products from the N atom elimination channels were acquired at a set of photolysis wavelengths from 142.55 to 148.19 nm. Vibrational states of the NO(X2Π) co-fragments were partially resolved in experimental images. From these images, the product total kinetic energy release distributions (TKERs), branching ratios of the vibrational states of NO(X2Π) co-fragments, and the vibrational state specific angular anisotropy parameters (β) have been determined. Notable features were found in the experimental results: the TKERs show that the NO(X2Π) co-fragments are highly vibrationally excited. For the highly vibrationally excited state of NO(X2Π), a bimodal rotational structure is found at all the studied photolysis wavelengths. Furthermore, the vibrational state specific β values of both spin-orbit channels (j = 3/2, 5/2) clearly show a monotonic decrease as the vibrational quantum number of NO(X2Π) increases. These observations suggest that multiple dissociation pathways play a role in the formation of the N(2Dj=5/2, 3/2) + NO(X2Π) products: one corresponds to a fast dissociation pathway through the linear state (the C1Π state) following the initial excitation to a slightly bent geometry in the vicinity of the linear C1Π configuration, leading to the low rotationally excited components with relatively large β values; the other corresponds to a relatively slow dissociation pathway through the bent C(31A') or C(31A″) state, leading to moderately rotationally excited NO(X2Π) products with smaller β values.